Mathematical, Astronomical, and Geometric Lexicon, that is, a collection and explanation of all things in any way pertaining to both branches, indeed to almost all mathematics. With a brief explication of new theorems and clarification of exotic words, so that it may not unjustly be called the sum and storehouse of all mathematical disciplines.
Creator: Girolamo Vitali | Date: 1668 | Notes: Original title: Lexicon mathematicum astronomicum geometricum, hoc est rerum omnium ad utramque immò & ad omnem ferè mathesim quomodocumque spectantium, collectio, & explicatio. Adiecta brevi novorum Theorematum expensione, verborumque exoticorum dilucidatione, ut non iniuria disciplinarum omnium Mathematicarum summa, & Promptuarium dici possit. Auctore Hieronymo Vitali Capuano Clerico Regulari vulgo Theatino. An alphabetical Neo-Latin lexicon of the mathematical sciences, especially astronomy, geometry, chronology, and related technical vocabularies, designed to collect and explain terms from learned languages and to present mathematics as a demonstrative science of the highest certainty. The work also includes brief discussions of disputed natural-philosophical topics, including sympathetic healing and the weapon-salve, alongside its lexical entries. 👉 <a href="https://tryleo.ai/collections/exlatinis/the-weapon-salve-and-the-alphabet-how-a-working-cleric-filed-astrology-under-trifles-and-mathematics-under-certain-knowledge">Read our introductory primer, full report, and finding guide here</a> 📜 <a href="https://archive.org/details/bub_gb_Qs8dKhStZZcC">View the original file on Internet Archive</a> This text was transcribed and translated as part of the ExLatinis project—an effort by Leo to make English translations of every published text in Latin in early modern Europe (between 1450 and 1750) available to the public for free online.
- Title
- Mathematical, Astronomical, and Geometric Lexicon, that is, a collection and explanation of all things in any way pertaining to both branches, indeed to almost all mathematics. With a brief explication of new theorems and clarification of exotic words, so that it may not unjustly be called the sum and storehouse of all mathematical disciplines.
- Creator
- Girolamo Vitali
- Date
- 1668
- Notes
- Original title: Lexicon mathematicum astronomicum geometricum, hoc est rerum omnium ad utramque immò & ad omnem ferè mathesim quomodocumque spectantium, collectio, & explicatio. Adiecta brevi novorum Theorematum expensione, verborumque exoticorum dilucidatione, ut non iniuria disciplinarum omnium Mathematicarum summa, & Promptuarium dici possit. Auctore Hieronymo Vitali Capuano Clerico Regulari vulgo Theatino. An alphabetical Neo-Latin lexicon of the mathematical sciences, especially astronomy, geometry, chronology, and related technical vocabularies, designed to collect and explain terms from learned languages and to present mathematics as a demonstrative science of the highest certainty. The work also includes brief discussions of disputed natural-philosophical topics, including sympathetic healing and the weapon-salve, alongside its lexical entries. 👉 <a href="https://tryleo.ai/collections/exlatinis/the-weapon-salve-and-the-alphabet-how-a-working-cleric-filed-astrology-under-trifles-and-mathematics-under-certain-knowledge">Read our introductory primer, full report, and finding guide here</a> 📜 <a href="https://archive.org/details/bub_gb_Qs8dKhStZZcC">View the original file on Internet Archive</a> This text was transcribed and translated as part of the ExLatinis project—an effort by Leo to make English translations of every published text in Latin in early modern Europe (between 1450 and 1750) available to the public for free online.
Document notes
Original title: Lexicon mathematicum astronomicum geometricum, hoc est rerum omnium ad utramque immò & ad omnem ferè mathesim quomodocumque spectantium, collectio, & explicatio. Adiecta brevi novorum Theorematum expensione, verborumque exoticorum dilucidatione, ut non iniuria disciplinarum omnium Mathematicarum summa, & Promptuarium dici possit. Auctore Hieronymo Vitali Capuano Clerico Regulari vulgo Theatino. An alphabetical Neo-Latin lexicon of the mathematical sciences, especially astronomy, geometry, chronology, and related technical vocabularies, designed to collect and explain terms from learned languages and to present mathematics as a demonstrative science of the highest certainty. The work also includes brief discussions of disputed natural-philosophical topics, including sympathetic healing and the weapon-salve, alongside its lexical entries. 👉 Read our introductory primer, full report, and finding guide here 📜 View the original file on Internet Archive This text was transcribed and translated as part of the ExLatinis project—an effort by Leo to make English translations of every published text in Latin in early modern Europe (between 1450 and 1750) available to the public for free online.
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Y.2. 14-22-D-23
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VITALLS VORDO RERVM. Videt posse duquod formam MINVITVR, VT ELEMENTA REPEAT. TURBANT VAGANT. VIRIRES AVGLT OVASSATIO HIERONYMI VITALIS CLER REGVL. LEXICON MATHEMATICVM. CAM eo aram enim compendia BIBLIOTECA NAZ. ROMA VITTORIO EMANUELE
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VITALIS ORDER OF THINGS. It sees that the form can be diminished, so that it may return to the elements. DISTURB WANDER. FORCES AUGLT OVASSATIO HIERONYMI VITALIS CLER REGUL. MATHEMATICAL LEXICON. CAM eo aram enim compendia NATIONAL LIBRARY. ROME VITTORIO EMANUELE
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LEXICON MATHEMATICVM ASTRONOMICVM GEOMETRICVM, Hoc est Rerum omnium ad utramque immò & ad omnem ferè Mathesim quomodocumque spectantium, Collectio, & explicatio. Adjecta breui nouorum Theorematum expensione, verborumque exoticorum dilucidatione vt non injuriâ Disciplinarum omnium Mathematicarum summa, & Promptuarium dici possit. Auctore HIERONYMO VITALE Capuano Clerico Regulari vulgò Theatino. PARISIIS, Ex Officina LUDOVIC. BILLAINE, in Palatio Regio. DC. LXVIII. Cum Licentijs. BIBLIOTECA NAZ. VITTORIO EMANUELE
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LEXICON MATHEMATICAL ASTRONOMICAL, GEOMETRICAL, that is, A collection and explanation of all matters pertaining in one way or another, indeed almost to all Mathematics. To which is added a brief examination of new theorems, and an elucidation of exotic words, so that not without reason it may be called the sum and repository of all mathematical disciplines. By HIERONYMO VITALE of Capua, Regular Cleric, commonly called Theatine. PARIS, From the workshop of LUDOVIC. BILLAINE, in the Royal Palace. 1668. With permissions. NATIONAL LIBRARY VICTOR EMANUEL
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EMINENTISSIMO AC REVERENDISSIMO PRINCIPI D. GVIDOBALDO S.R.E. CARDINALI DE THVN ARCHIEPISCOPO ET PRINCIPI SALISBURGENSI, AC RATISSONENSE GERMANIÆ PRIMATI. AC S. R. SEDIS LEGATO PERPETVO S. R. Imperij Principi, &c. Hieronymus Vitalis æternam felicitatem. RVBESCEREM ad in- fularum purpuram, Cardinalis amplissime, nisi animorum con- ciliatrix humanitas promican- tem ab ea fulgorem blandissimè temperaret. Auersaris enim pessimam optima- rum indolem, qui quoad sublimius gloriæ apo- gaum euehuntur, hoc magis eripiunt se popu- lorum aspectui, id vnum commune cum sideri- bus habentes, quod subiecta sibi capita despiciant mortalium oculis imperuj (quasi verò in gloria fiat, & abieEtta, qua sub oculos cadit celsitudo.) 2 ij
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MOST EMINENT AND MOST REVEREND PRINCE D. GVIDOBALD CARDINAL OF THE HOLY ROMAN CHURCH ARCHBISHOP AND PRINCE OF SALISBURY, AND PRIMATE OF GERMANY, AND PERPETUAL LEGATE OF THE HOLY APOSTOLIC SEE Prince of the Holy Roman Empire, &c. Hieronymus Vitalis wishes eternal happiness. I should blush for the purple of the infula, most illustrious Cardinal, were it not that humanity, the reconciler of hearts, most gently tempered the splendor that was advancing from it. For you turn away from the worst of the dispositions of the best, who, so far as they are borne up to the loftier summit of glory, so much the more withdraw themselves from the sight of the people, having only this in common with the stars, that they look down on the heads subject to them from the eyes of mortals, ruling as if, indeed, there were glory in a height that is made low and cast down, which falls under the eyes. 2 ij
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Quin potius regiam æmularis Iouis alitem, quæ ita se Cælo permittit, vt terris interdu[m] illabi non dedignetur; Imò sic te præstas omnibus æqualem, nulla vt re supra hominum vulgus eminere videaris, quam meritis. Accedit quod libertatem non relinquis spectatoribus tuis, quos in te semel intenderint, torquere oculos alio possint, adò sunt intui vnius admiratione defixi: ea propter vitio dare non potes, si te importanus adeam, cum totus cuilibet te intuenti pateas, teque adeunti, facias sine fastidio copiam tui. Atque hîc ego non committam, velatiùs excurratoratio indagatura quænam ex tot quibus præfulges virtutibus, te ad tantum honoris fastigium promouerit; an probitas morum singularis? an rerum Ciuilium, & Ecclesiasticarum peritia? an maximarum rerum ponderi, non impar animus? an denique studium pietatis, & in tuendâ bellantis Ecclesiæ gloria inuictâ strennitas? constat enim omnes unà conspirasse virtutes, vt te ad tantam dignitatem certatim proucherent, cum quid quid in hierophantis, & præsidibus Religionis effusum est, in te vno ad inuidiam expressum miretur orbis, adeò vt tibi vni plausisse vates videatur cum cecinit. Sparguntur in omnes In te mixta fluunt, & quæ diuisa, beatos Efficiunt, collecta tenes. CLAYD. Qua propter si virtus est vera animarum
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Why rather do you emulate Jupiter’s royal bird, which so entrusts itself to the sky that it does not disdain at times to alight on the earth? Indeed, so do you show yourself equal to all, that in no thing beyond the common crowd of men do you seem to excel, save in merit. Added to this is the fact that you do not leave your spectators freedom: once they have fixed their gaze on you, they cannot turn their eyes elsewhere, so much are they held fast, captivated by the admiration of a single object. For that reason you cannot take it amiss if I approach you with importunity, since you stand open to whoever looks upon you, and to whoever comes near you you grant access to yourself without displeasure. And here I shall not undertake, by a more extended discourse, to inquire which among your many virtues that shine forth has advanced you to so great a height of honor: whether singular integrity of character? whether expertise in civil and ecclesiastical affairs? whether a mind not unequal to the weight of the greatest matters? or, finally, devotion to piety and unconquerable zeal in defending the glory of the militant Church? For it is clear that all the virtues have conspired together, so as to raise you competitively to such dignity, since whatever has been bestowed upon the hierophants and leaders of religion, the world marvels to see magnificently reproduced in you alone, to envy; so much so that the poet seems to have applauded you alone when he sang: “Scattered among all, in you they flow together; and what, when divided, makes men blessed, when collected you possess.” CLAYD. Wherefore, if virtue is the true health of souls...
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consecrauerunt; Antonini gratiam aucupetur suâ Oppianus Icthyologiâ, Vitruuius Augustum Architecturâ sibi conciliet, Commodi fauores ex- petat Pollucis Onomatologia, dignitates à Vespa- fiano suâ Plinius Physicâ emendicet: ego sane post habitis quibuscumque emolumentis peritu- ro operi, Mecanatis immortalitate consulo. Fu- turum enim speraui vt quâ olim industriâ, Phydias dum elegantem illam Mineruam effin- geret, proprium in agide cælauit, celauitque vul- tum, vt æternum sibi nomen compararet, sic me tibi dicatitiâ hacce epistolâ insinuarem, vibran- tisque illius gloriæ, qua circunfusus coruscas, quosdam operi meo radios inspirares. Hac ergo ratione abundè mihi satisfactum putabo, si tuis sub auspicijs prodeat Lexicon hoc Mathematicum, neque enim timebit Stoica censorum super- cilia, nec temporis omnia deprædantis reformi- dabit ingluuiem. Quapropter tuos affusus ad pedes illud depono, vt sin minus purpuræ tuæ innoluatur ambitu, extremam saltem laciniam delibans, tutissimum nanciscatur inter tot de- bachantis inuidiæ morsus præsidium. Vale.
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Let Oppian, by his Ichthyology, seek the favor of Antoninus; let Vitruvius win Augustus over by his Architecture; let Pollux, with his Onomasticon, seek the goodwill of Commodus; let Pliny, with his Natural History, beg dignities from Vespasian: for my part, setting aside whatever profit there may be, I look to the immortality of Maecenas for this work, though it is doomed to perish. For I had hoped that, just as Phidias once, with that same industry, when he was fashioning that elegant Minerva, concealed his own name and his own face in the shield in order to win himself an eternal reputation, so I might introduce myself to you by this dedicatory letter, and might inspire some rays of that dazzling glory with which you shine all around into my work. For this reason I shall think myself abundantly satisfied, if this Mathematical Lexicon goes forth under your auspices; for then it will fear neither the haughtiness of Stoic critics nor the greed of time, which devours all things. Wherefore I lay it at your feet, and if it cannot be enfolded within the ambit of your purple, then at least, by touching the outermost hem, may it obtain the safest refuge amid so many bites of raging envy. Farewell.
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PRÆFATIO AD LECTOREM In qua operis Idea, Auctoris mens, ac di- cendorum ratio explicatur. Athematicas disciplinas, quò cæteris præstantiores, eò hominibus huius sæculi despectiores, atque odiosiores, inter nouissimas curas à paucis admodum cæli à plurimis eleuati, ab omnibus vniuersim, ceu studiorum retrimenta, & quisquilias cæteris artibus post haberi, Amice Lector, amarissimè semper indolui. Quippe cum eæ sint, quæ animum nostrum virtutibus imbuunt, ad nobilissimâ erigunt, ad Dei formam efformant, ac divinæ illius sapientiæ vniuersa bellissimè ordinantis semitas calcare edocent, mirum est, quàm malè apud quosdam audiant; vt inter euanidas scientias, otiosas inutiles, ac poenè dixerim perniciosas connumerentur. Diogenes ille â
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PREFACE TO THE READER In which the idea of the work, the author’s intention, and the manner of what is to be said are explained. The mathematical disciplines, the more excellent they are than the rest, the more by the people of this age they are despised, and even hated, among the very latest concerns, by very few indeed who are lifted up toward heaven, by most and by all in general, as the refuse of studies and as trash, are placed after the other arts, O friendly reader, I have always most bitterly grieved. For these are the studies which imbue our mind with virtues, raise it to the most noble things, fashion it after the form of God, and teach it to tread the paths of that divine wisdom which orders all things most beautifully. It is astonishing how badly they are regarded by some, so that they are counted among vain sciences, idle, useless, and I might almost say pernicious ones. Diogenes that
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consecrauerunt; Antonini gratiam aucupetur suâ Oppianus Icthyologiâ, Vitruuius Augustum Architecturâ sibi conciliet, Commodi fauores ex- petat Pollucis Onomatologia, dignitates à Vespasiano suâ Plinius Physicâ emendicet: ego sane post habitis quibuscumque emolumentis perituro operi, Mecanatis immortalitate consulo. Futurum enim speraui vt quâ olim industriâ, Phydiæ dum elegantem illam Mineruam effingeret, proprium in agide cælauit, celauitque vultum, vt æternum sibi nomen compararet, sic me tibi dicatitiâ hæcce epistolâ insinuarem, vibrantisque illius gloriæ, qua circufusus coruscas, quosdam operi meo radios inspirares. Hac ergo ratione abundè mihi satisfactum putabo, si tuis sub auspicijs prodeat Lexicon hoc Mathematicum, neque enim timebit Stoïcæ censorum supercilia, nec temporis omnia deprædantis reformidabit ingluuiem. Quapropter tuos affusus ad pedes illud depono, vt sin minus purpuræ tuæ innoluatur ambitu, extremam saltem laciniam delibans, tutissimum nanciscatur inter tot debachantis inuidiamorsus præsidium. Vale.
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they have consecrated it; let Oppianus court the favor of Antoninus through his Ichthyology, let Vitruvius win Augustus over to himself through Architecture, let Pollux seek the favor of Commodus through his Onomasticon, let Plinius beg dignities from Vespasian through his Physic; for my part, having set aside whatever advantages there might be in a work destined to perish, I look instead to the immortality of Mecaenas. For I have hoped that, just as once, by his industry, Phidias, while fashioning that elegant Minerva, secretly carved his own likeness and concealed his face in the shield, so as to win himself an enduring name, thus I too might insinuate myself to you by this little letter of dedication, and inspire certain rays of that sparkling glory with which you shine around me into my work. Therefore I shall think myself abundantly satisfied if this Mathematical Lexicon goes forth under your auspices; for it will fear neither the censorious brows of the Stoics, nor dread the devouring greed that preys on all things in time. Wherefore, casting it at your feet, I lay it before you, that, if it cannot be wrapped in the embrace of your purple, at least by touching the outer fringe of it, it may gain the safest protection amid the many bites of ravaging envy. Farewell.
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PRÆFATIO AD LECTOREM In qua operis Idea, Auctoris mens, ac di- cendorum ratio explicatur. M Athematicas discipli- nas, quò cæteris præ- stantiores, eò homi- nibus huius sæculi de- spectiores, atque odio- liores, inter nouissimas curas à paucis admo- dum coeli à plurimis eleuati, ab omnibus vniuersim, ceu stu- diorum retrimenta, & quisquilias cæteris artibus post haberi, Amice Lector, ama- rissimè semper indolui. Quippe cum eæ sint, quæ animum nostrum virtutibus im- buunt, ad nobilissimâ erigunt, ad Dei for- mam efformant, ac divinæ illius sapientiæ vniuersa bellissimè ordinantis semitas cal- care edocent, mirum est, quàm malè apud quosdam audiant; vt inter euanidas scien- tias, otiosas inutiles, ac poenè dixerim perniciosas connumerentur. Diogenes ille â
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PREFACE TO THE READER In which the idea of the work, the author’s intention, and the method of what is to be said are explained. I have always felt most bitterly, dear Reader, that mathematical disciplines, the more they excel the others, the more they are despised and hated by the men of this age; and that, among the latest concerns of very few, though above the earth to a very great number, they are universally by all put after the other arts, as if the refuse and dregs of studies. For indeed they are the studies which imbue our mind with virtues, raise it to the noblest things, shape it after the form of God, and teach it to tread the paths of that divine wisdom which orders all things most beautifully. It is astonishing how ill they are spoken of by some, so that they are numbered among fleeting, idle, useless, and, I would almost say, harmful sciences. That Diogenes â
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PRAEFATIO. Cynicus, homo, inquam, ad hominum irrisionem factus, qui sua Philosophia tu- midus cæteros aspernabatur, cuidam Ho- roscopon ostendenti Bellum, inquit, hercle instrumentum! Verum tamen ne frustremur cæ- na: invidè carpens ac sugillans geometri- cas artes, quasiearum ope coenam quidem sibi quisque parare queat. At enim si Allæ sunt facultates ad humanæ vitæ rationem ineundam conducentes, si vllæ Rei- publicæ necessariæ, cuiibus opportunæ, eæ sunt Mathematicæ, & quæ in Mathe- matica fundantur artes, hoc est mechani- cæ. Quandoquidem ipsa olim scientiarum rudimenta, ipsa naturalis Philosophia, vt auct ot est Gellius à Mathesis ruderibus in- cipiebant. Etenim refert Philosophiæ no- men vti ex Pythagora effluxisse ita & Ma- thematicæ appellationem â [mercur]ij [satur]i [venus] [mercur]ia. hoc est disciplina, seu à [mercur]io [venus], quod est dis- co, & doceo deriuatam. Mathemata enim dicuntur artes, quæ firmis demonstrationibus constant: quæ quidem idcircò ad disciplinam animo inserendam aptissimæ inveniuntur. Namque ita Natura facti su- mus, vt nihil tenere mente possimus, ni aliquo modo sub sensu cadat, ac speciem aliquam præse ferant entis extensi. Cum igitur Mathematicæ disciplinæ totæ sint in rebus quantis, vt quantis exhibendis, ac
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PREFACE. The Cynic, I say, a man made for the derision of men, who, puffed up with his own philosophy, despised the rest, when someone showed him a horoscope, said, “A warlike instrument, by Hercules!” Yet let us not be cheated of our dinner: he spitefully carps at and vilifies the geometric arts, as though by their aid each man could not indeed prepare his dinner for himself. But if there are any faculties conducing to the conduct of human life, if there are any necessary to a commonwealth, any fitting for it, they are the Mathematical sciences, and those arts founded in Mathematics, that is, the mechanical arts. For once, the very rudiments of the sciences, the very natural philosophy, as Gellius observes, began from the rudiments of Mathematics. Indeed, as the name of Philosophy is said to have flowed from Pythagoras, so also the appellation of Mathematics is derived from [mercur]ij [satur]i [venus] [mercur]ia; that is, discipline, or from [mercur]io [venus], which is “I learn” and “I teach.” For the studies are called mathematical arts which consist in firm demonstrations; and for that very reason they are found most suitable for implanting instruction in the mind. For we are so made by nature that we can hold nothing in mind unless it somehow falls under the senses and presents some likeness of an extended being. Since therefore the mathematical disciplines are wholly concerned with quantitative things, in exhibiting quantities as quantities, and
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PRAEFATIO. proponendis, in eisque mensurandis, & eô- parandis inter se, iure ipsarum notitia an tonomasticè disciplinæ nomen promeruit, quandoquidem ipsæ solæ sunt, quæ mentis nostræ duritiam superare, ignorantiæ te- nebras discutere, ac scientiis omnibus adi- tum aperire valent, atque ad id factæ sunt. Hinc testatur idem Gellius, triplicem fuis- se ordinem eorum, qui sub Pythagora pro- ficiebant. Quidam enim dicebantur Anusinot, hoc est, auditors, qui ab ingressu silere, atque audire tantum iubebantur ad certum tempus, quo durante nihil eis percontari licebat, quamvis non rectè quæ ab aliis docebantur perciperent, neque etiam commentari, quæ audierant, concessum erat: Veruntamen, vbi tacere & audire didicerant, jamque coepissent esse silentio eruditi, mox verba facere, & quæritare de iisque, quæ audierant scribere, ac diffi- cultates expromere, dabatur illis aditus, atque hi Mathemati appellabantur ab iis ar- tibus quas iam dicere, & meditari eæpe- rant. Posteà his scientiarum suppetiis in- structi, ad percipienda mundi opera, Na- turæque principia procedebant, quo tem- pore ouerit audiebant, quod iam exinde ob Mathematicas disciplinas, superiores scientias sublimioraque studia capessenda apti inveniebantur. Proindeque pueris á ij
Transcription: Translated (English)
PREFACE. In proposing them, and in measuring them, and comparing them with one another, the knowledge of them itself deservedly earned the name of a discipline, for it is they alone which are able to overcome the hardness of our mind, dispel the darkness of ignorance, and open a path to all the sciences; and they were made for this very purpose. Hence the same Gellius testifies that there were three orders among those who made progress under Pythagoras. For some were called Anusinot, that is, auditors, who from the moment of entering were ordered to keep silence and to listen only for a certain time; during which they were allowed to ask nothing, even if they did not rightly understand what was taught by others, nor was it permitted them to make notes of what they had heard. Nevertheless, when they had learned to keep silence and to listen, and had already begun to be disciplined by silence, then at length permission was given them to speak, to inquire, and to write down what they had heard, and to bring forward difficulties; and these were called Mathematici by reason of the arts which they had now begun to speak of and contemplate. Afterwards, furnished with these aids to knowledge, they advanced to understand the workings of the world and the first principles of Nature, at which time they heard ouerit that they were found fit to undertake the higher sciences and more exalted studies by reason of the mathematical disciplines. Therefore for boys
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PRÆFATIO. Geometriæ, Musices, & Arithmetica rudimenta tanquam certa, fundataque scientiarum principia primò in scholis exhibebantur, vt iis demum exerciti ad majora Philosophiæ studia inienda redderentur idonei. Vnde est quod id perperam assumens Picus lib. 12. aduersus Astrologos cap. 2. exinde mathematicas facultates elevare nititur, & graphicè contra eas inuehitur, inquiens: Mathematica sapientes non facit, quare veteribus puerorum studium fuit imò qui ei soli totum se tradit, occasiones errorum in Philosophia maximas parit. At enim verò tantum abest quod Mathesis Philosophiam destruat atque in errores abducat, ut eam solam Philosophiæ studiis adeò necessariam censuerit Plato, teste Io. Grammatjco in p. Phys. c. 45. vt in Gymnasiij limine inscriptum vellet id eis à hoc est Geometriæ ignarus huc non adueniat: & Xenocrates Platonis auditor cuidam Mathesis ignaro scholam suam frequentare expostulanti dixisse fertur. Abi, cares enim ansis, & adminiculis Philosophiæ. Quod autem pueris olim addiscenda traderetur, id potiùs eius necessitatem, atque vtilitatem arguit, quam, quod quicquam contra illam evincat. Porro Mathematicarum disciplinarum dignitatem, commoda, atque vtilitates quis
Transcription: Translated (English)
PREFACE. The rudiments of Geometry, Music, and Arithmetic were first presented in the schools as certain and well-founded principles of the sciences, so that those trained in them might afterward be made fit to enter upon the greater studies of Philosophy. Whence it is that Picus, wrongly assuming this, in book 12 against the Astrologers, chapter 2, attempts thereby to diminish the mathematical sciences, and inveighs against them vividly, saying: Mathematics does not make men wise; for which reason it was formerly the study of boys; indeed, he who gives himself wholly to it alone produces the greatest occasions of error in Philosophy. But in truth, so far is Mathematics from destroying Philosophy and leading men into error, that Plato judged it alone so necessary for the studies of Philosophy, as John Grammaticus testifies in Phys. p. c. 45, that he wished it inscribed at the threshold of the Academy, namely: Let no one enter here who is ignorant of Geometry; and Xenocrates, a hearer of Plato, is said to have replied to someone ignorant of Mathematics who complained of not being allowed to frequent his school: Go away; for you lack the handles and supports of Philosophy. And the fact that it was formerly handed down to be learned by boys argues rather for its necessity and usefulness than anything against it. Moreover, who would deny the dignity, advantages, and usefulness of the mathematical disciplines?
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PRAEFATIO: explicare poterit? e[ss]e in summo certitudinis gradu positæ sunt, vt Philosophus ipse testatur. eædem ad ciuium pacem, ad gentium communicationem, ad bellorum ordinem factæ sunt: per eas militarem disciplinam, vrbium stabilimenta, ædificiorum ordinem, locorum interualla, menium commoda, negotiantium fidem, totius orbis commercium, cælestium notitiam, & cum terrenis hisce communicationem habemus: Has Ægyptiorum Sacerdotes, cum liberos suos liberalibus artibus instruendos traderent, curabant inprimis eos ediscere, vt metari agros nolent, vbi Nili excursu confusi forent: sicque posset ciuium concordia custodiri, quod & Strabo, & Herodotus, ac de Persis etiam scribit Alexander ab Alexandro lib. 2. dier. genial. cap. 25. Has leges summe commendant & præcipiunt in C. Artem Geometriæ. ad has addiscendas cogi homines posse vult Penna in lib. 2. c. de excurs. art. lib. 10. Bartholus quoque in sua Tiberina figuris Geometricis vtens, has facultates Iurisperitis vtiles esse ostendit, & Arist. in rebus Philosophiæ difficillimis explicandis mathematicis demonstrationibus vsus est. Medicina nonne sine Astronomiæ directione ægris esset incommoda atque exitialis? quæ enim sub certo stellarum positu exhi- â iij
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PREFACE: Can it be explained? They have been placed at the highest degree of certainty, as the Philosopher himself testifies. They were made for the peace of citizens, for the communication of nations, for the order of wars: through them military discipline, the foundations of cities, the arrangement of buildings, the intervals between places, the convenience of walls, the trust of merchants, the commerce of the whole world, knowledge of celestial things, and our communication with these earthly matters. The priests of the Egyptians, when they entrusted their sons to be instructed in the liberal arts, took care above all that they should learn these things, namely not to measure fields where they had been confused by the overflow of the Nile: and thus the concord of citizens might be preserved, as Strabo and Herodotus also write, and Alexander ab Alexandro writes of the Persians as well, lib. 2, dier. genial., cap. 25. These laws are highly commended and expressly prescribed in C. Arte Geometriæ. Penna, in lib. 2, c. de excurs. art. lib. 10., holds that men can be compelled to learn these things. Bartholus too, in his Tiberina, using geometric figures, shows that these skills are useful to jurists, and Aristotle, in explaining the most difficult matters of philosophy, made use of mathematical demonstrations. Would Medicine not be troublesome and even deadly to the sick without the guidance of Astronomy? For what is exhibited under a fixed position of the stars... â iij
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PRAEFATIO. bita prodesse compertum est, hæc incongruo tempore data euocant mortem; quod & Ouidius obseruauit cum cecinit. Temporibus medicina valet: data tempore prosunt. Et data non apto tempore vina nocent. Theologia etiam & Sacrarum Scripturarum notitia, & explanatio multum à Mathesi adjuvatur vt probat D. Augustinus lib. 2. de doctrina Christiana cap. 16 & seqq. ac testatur etiam D, Hieromymus to. 1. 1 p. 5. Vnde & sacræ paginæ Deum ipsum sæpius introducunt omnia inpondere & mensura, & numero disponentem; & Ecclesia secundum Astronomiæ regulas ritus suos instituit, ac nouillunia, & temporum rationes ordinat, sidelibusque exhibet observandas. Tandem nulla est scientia quæ nos adeò in Deum erigit, ac supernæ Patriæ desiderium in nobis excitat, quàm exilestium rerum notitia. Siquidem, vt ait, Psaltes Cæli enarrant gloriam Dei. Per eam enim tenetur quodammodo in manibus coelum ac fit vt cæteris omnibus spretis, ad idem seriò possidendum animum applicemus. Felices animæ, quibus hæc cognoscere primis, Inque domos superas scandere cura fuit, Credibile est illos pariter vitiisque, iocisque Altius humanis exercuisse caput.
Transcription: Translated (English)
PREFACE. Things that are known to be beneficial, when given at an unsuitable time, summon death; as Ovid observed when he sang: Medicines are effective at the right time: given at the proper time they are useful. And wines given at the wrong time are harmful. Theology also, and the knowledge and exposition of Holy Scripture, are greatly aided by Mathematics, as St. Augustine proves in book 2 of De Doctrina Christiana , chapter 16 and following, and St. Jerome also testifies, vol. 1, p. 5. Hence the sacred pages themselves very often introduce God disposing all things by weight, measure, and number; and the Church, according to the rules of Astronomy, establishes its rites, and orders the new moons and the reckoning of times, and presents them to the faithful to be observed. Finally, there is no science which so raises us up to God, and awakens in us the desire of the heavenly Fatherland, as the knowledge of celestial things. Indeed, as he says, the Psalms of Heaven declare the glory of God. For through them heaven is, as it were, held in our hands, and it comes about that, despising all other things, we seriously apply our minds to possessing the same. Happy are the souls for whom it was a first care to know these things, and to climb to the homes above. It is credible that they likewise exercised their heads more highly than human vices and jests.
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PRAEFATIO. Nam Venus, & vinum sublimia pectora fregit, Officiumque fori, militiaue labor. Nec levis ambitio, perfusaque gloria fuco: Magna neque fames sollicitauit opum. Admouere oculis distantia sidera nostris, Ætheraque ingenio supposuisse suo. Sic petitur cælu[m], non vt ferat Ossam Olympus, Summaque Peliacus sidera tangat apex. Sic fatus verè Ovidius Pastorum 1. Cùm igitur tantæ sint Mathematicæ disciplinæ præstat hîc causam tantæ contrarietatis auertere, & invidiam, quam apud homines contraxerint aperire: quî factum sit, vt quæ ex se ipsis tam bonæ, tam vtiles, tam innocentes sunt, tam malè postea olere cæperint: vt ex iis quædam tanquam inutiles censeantur, quædam etiam vti perniciosæ ac Reipublicæ pestis abolitæ, atque in disciplinæ dedecus Imperatorum lege professores, ac Mathematici vniuersim Vrbe proscriberentur. Equidem nil est in rerum natura tam bonum, quod non Daemonis astu, suorumque fraudibus corrumpi queat: Et quia ea est bonitatis conditio, vt præteruersa monstrosa fiat, ac deformissima (corruptio namque optimi pessima) inde fit, vt quæ maximè bona sunt, ea si tricis & sordidis adulterentur, nil illis perniciosius sit,
Transcription: Translated (English)
PREFACE. For Venus and wine have broken lofty hearts, as have the duties of the forum and the labors of war. Nor did light ambition, nor glory steeped in false show, nor great hunger for riches entice me. They have brought distant stars before our eyes, and taught the mind to set beneath itself the ether. Thus one seeks heaven, not that Olympus may bear Ossa, and the Peliac summit touch the highest stars. So spoke the true Ovid in Pastorum 1. Since, then, the Mathematical disciplines are so great, it is best here to turn aside the cause of so great a contradiction, and to explain the hatred which they have incurred among men: how it came to pass that things which in themselves are so good, so useful, so innocent, should afterward begin to smell so badly: so that some of them are regarded as useless, and some even as harmful and as a plague to the commonwealth, abolished, and to the disgrace of learning, teachers and mathematicians in general were by the law of the emperors proscribed from the City. For indeed there is nothing in nature so good that it cannot be corrupted by the craft of the Devil and the frauds of his own. And because such is the condition of goodness, that when it is overturned it becomes monstrous and most misshapen (for corruption of the best is the worst), it comes about that those things which are especially good, if they are adulterated with trickery and foulness, nothing is more harmful to them,
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PRÆFATIO. nil euadat infensius. Videmus id passim in alimétis, quæ quo salubriora, si postea cor- rumpantur, aut venenis inficiantur, eò sunt humanæ vitæ exitialiora. Cùm igitur dia- bolus ab initio Dei similitudinem ex arro- gantia appetierit, postmodum superna pa- tria pullus, nil magis affectet, quam Dei simiam facere, & perfectissima quæque in Dei contemptum corrumpere, atque ho- minibus exhibere. Quod & D. Petrus Chry- sologus aliò respiciens adnotauit serm. 155. sic inquiens. Vbi Christus piè nostram natus est ad salutem mox diabolus diuinæ bonitati numerosa genuit, & perniciosa portenta, vt ridiculum de religione componeret in sacrile- gium verteret sanctitatem, de honore Dei Deo pararet injuriam. Nonne Theologia scien- tia est omnium nobilissima, & diuina, quæ nos in Dei cognitionem ducit, quæ mores instruit, quæque altissima rimatur myste- ria, atque illius beatificæ visionis, quæ æternæ gloriæ summa est, speculum esse, æmulam & primum gradum non inani glo- riatione se jactat? At quid ea corrupta execrabilius? Quid scelestius? Quid Ec- clesiæ perniciosius? Nonne ex ea tot hæ- reses pullularunt? Nonne tot infandæ do- gmatum aborsiones? Religio nonne virtu- tum omnium Princeps est, ac Regina? At enim hanc in superstitionem transformare
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PREFACE. nothing becomes more harmful. We see this everywhere in foods, which, the more wholesome they are, if afterward they are corrupted or infected with poisons, are the more deadly to human life. Since therefore the devil from the beginning, in his arrogance, sought the likeness of God, and afterward, as a brood sprung from the heavenly homeland, he aims at nothing more than to make himself God’s ape, and to corrupt whatever is most perfect in contempt of God, and to present it to men. This also St. Peter Chrysologus, looking elsewhere, noted in sermon 155, saying thus: “Where Christ was born piously for our salvation, there the devil immediately brought forth numerous and pernicious monsters against divine goodness, so that he might turn what is ridiculous in religion into sacrilege, sanctity into sin, and prepare an injury to God out of the honor of God.” Is not Theology the most noble and divine of all sciences, which leads us to the knowledge of God, instructs morals, and explores the highest mysteries, and, as a mirror of that beatific vision which is the summit of eternal glory, boasts not without good reason that it is both a rival and the first step? But what is more abominable than theology corrupted? What more wicked? What more destructive to the Church? Have not so many heresies sprung from it? Have not so many monstrous abortions of dogmas? Is not religion the prince and queen of all virtues? Yet to transform this into superstition
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PRAEFATIO. studet nequissimus hostis, vt de honore Dei, Deo parare possit iniuriam. Naturæ dona, & maxima adjumenta suis tricis sæpe maculat, & corrumpit inuidus, vt ijs vel religione adducti non vtamur in nostrum commodum tamquam suspectis, vel sanè tanquam ab eo exhibitis, ac deprauatis. Hoc ipsum plane efficit in sublimioribus Mathesis disciplinis: etenim nil ipsis ab initio innocentius, nil vtilius; nil humano generi conducentius fuit: At enim vel inde, quia nobis proficue, quia earum legitimus vsus homines ad vitæ optimè instituendi rationem conducit, ideò eas potissimu[m] superstitionibus satagit conspirare, & cum ex alia parte futura præsciendi à nostræ conditionis exordio naturalis nobis insit affectus, ex hoc genio ad naturæ limites transigendos nos studet impellere, ac non modò quæ à naturalibus causis necessario pendent, prænoscere, verum etiam, quæ vltrà captum sunt, quæ à libera voluntate pendent, tanquam ex astris ortum ducant, perscutari curiosos quosque minusque cautos extimulat, adigitque. Hinc Astronomiæ Astrologia successit, & quia hæc notitia experimentalis tantum erat, & curiosa nimis, quæ mire animos hominum titillabat, Chaldæi super omnes superstitiosiores in eam toti incubuerunt:
Transcription: Translated (English)
PREFACE. The most wicked enemy strives, in order that from the honor of God he may be able to prepare an injury for God. He often stains and corrupts with his wiles the gifts of nature and the greatest aids, so that, either led by religion, we do not use them for our own advantage as if they were suspect, or indeed as if they had been presented and corrupted by him. This he plainly accomplishes in the loftier disciplines of Mathematics; for in truth nothing was at the beginning more innocent, nothing more useful, nothing more conducive to the human race. But because they are profitable to us, because their legitimate use leads men to the proper ordering of life, therefore he chiefly labors to conspire against them with superstitions; and since on the other hand, from the very beginning of our condition, there has been implanted in us a natural desire to foresee the future, from this impulse he seeks to drive us beyond the limits of nature, and not only to know beforehand what necessarily depends on natural causes, but also to investigate, as though they derived their origin from the stars, those things which lie beyond our grasp and depend on free will, and thus he excites and impels the curious and the less cautious alike. Hence Astrology succeeded Astronomy; and because this knowledge was merely experimental, and excessively curious, and wonderfully tickled the minds of men, the Chaldeans, more superstitious than all others, devoted themselves wholly to it.
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PRAEFATIO. vnde omnes Philosophiæ limites prætergressi ad diuinatoriam simpliciter, siue ambitione ducti, siue spe quæstus illecti se conuerterunt. Vnde iam omnis Mathesis co[n]spurcata, omnis Mathematica disciplina iam malè audire cæpit, proindeque & Mathematici Vrbe pulli, & omnis eoru[m] scientia tanquam infamis, & Reipublicæ exitialis est habita. Eapropter operæ pretium me facturum existimaui, si laruam tandem nobilissimis his facultatibus tollerem, ac zizania à tritico segregarem: eas suo nitori suæ innocentiæ restituendo, quod vt assequerer, in hoc opere id mihi præfixi, vt non tam Mathesis principia veræ Philosophiæ innixa, quam etiam vanitates, quibus conspurcata fuit, ostenderem, vt ijs perspectis Mathesis studiosus eam tutò capesseret, bonam doctrinam teneret, falsam reijceret, atque à se toto animo ablegaret. Opus equidem magni laboris, & quod Atlanthæos humeros expostulasset, ni bonorum amicorum, ac præcipuè eruditissimi conciuis mei Angeli Duratij, (qui & opera, & libris iugiter mihi astitit) in eo exornando auxilium accessisset, ac plurima suppeditasset. Lexicon ergò Mathematicum, ex omnibus Mathesis scriptoribus compilaui, in id præcipuè incumbens
Transcription: Translated (English)
PREFACE. Whence all the boundaries of Philosophy being overstepped, they turned simply to divination, whether led by ambition or enticed by hope of gain. Whence now all Mathesis became defiled, and the whole discipline of Mathematics began to be spoken of ill; and thus Mathematici too, were shunned by the City, and all their science was regarded as infamous, and destructive to the Republic. For this reason I judged that I should be doing something worthwhile if I should at last remove the mask from these most noble faculties, and separate the tares from the wheat: restoring them to their own purity and innocence, which in order that I might achieve, I set this before me in the present work, namely that I should show not only the principles of Mathesis, resting on true Philosophy, but also the vain matters with which it was defiled, so that, these having been seen, the student of Mathesis might take it up safely, hold fast to sound doctrine, reject what is false, and banish it from himself with his whole soul. Indeed, it was a work of great labor, and one that would have required Atlantean shoulders, had not the help of good friends, and especially of my most learned fellow citizen Angelo Duratio, (who stood by me continually both with his work and with his books), assisted in its embellishment and supplied many things. Therefore I compiled this Mathematical Lexicon from all the writers on Mathesis, directing my chief effort to this end
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PRAEFATIO. vt & abstrusiora vocabula, vt plurimum Araba, Aegyptiaca, Barbara (quandoquidem apud has nationes Mathematicæ disciplinæ potissimum floruerunt) explicarem, & vniuersæ Mathesis Principia, Canones, Pronuntiata, Demonstrationes, Problemata, ordinatissima methodo dilucido scribendi genere, atque absoluta verborum descriptione traderem, ac penè ad viuum delineata oculis exhiberem. Vt proptereà facile sit cuiuis haud rudis ingenij, suo Marte plenam harum scientiarum notitiam comparare, aut saltem quemvis Authorem expedite percurrere. Quod adeò difficile Anatolius æstimauit, vt vel ob id Mathematicas scientias, disciplinas dixerit appellatas, quod cum cæteræ facultates libroru[m] lectione, ac solo discursu percipi possint; hæ nonnisi Magistro docente ac demonstrante: quandoquidem vt rectè monebat M. Tullius, Mathematici in magna rerum obscuritate, recondita arte multiplici ac subtili versantur: vt proptere à non ab re nec sine magno consilio censendum sit, veteres illos, ac prudentes viros constituisse, vt à teneris annis pueri in eiusmodi artibus erudirentur. Sed enim hac in re, ni fallor, palmam proripuisse me arbitror, clauumque nodo fixisse. Etenim cum rerum intelligentia magna ex parte ex terminorum
Transcription: Translated (English)
PREFACE. So that I might explain the more obscure vocabularies, such as for the most part the Arabic, Egyptian, and Barbarian ones (inasmuch as among these nations the mathematical disciplines flourished especially), and might present the Principles, Canons, Pronouncements, Demonstrations, and Problems of the whole of Mathematics in a very orderly method, in a lucid style of writing, and with an exact description of the words, and might exhibit them, as it were, drawn almost to life before the eyes. So that it may easily be possible for anyone not lacking in talent to acquire on his own a full knowledge of these sciences, or at least to read through any author with ease. This Anatolius judged so difficult that for this very reason he said the mathematical sciences were called disciplines, because while the other faculties may be learned by reading books and by reasoning alone, these can be understood only with a teacher instructing and demonstrating: since, as M. Tullius rightly warned, mathematicians deal with great obscurity of things, in a hidden art, manifold and subtle; so that for this reason it is not without cause nor without great consideration that the ancients and prudent men are thought to have ordained that boys should be instructed in such arts from tender years. But indeed in this matter, unless I am mistaken, I believe I have snatched the palm and fixed the nail in the knot. For since the understanding of things depends in large part upon the terms
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PRAEFATIO. examinantur, attexere, atque ipsi præfigere, quò quivis quidquid non ita vulgarè, non ita obuium quætitate præsto sit inuenire; sicque doctiores haberet, quæ non multo labore, atque vnico ictu oculi in multis possent ingenij auiditatem explere. Alia verò non vulgaria, quæ incidenter quidem non tamen minus obseruatione digna sparsim in opere dicta sunt, huius signi ad margine appinxionem indigitauimus. Cæterum quæ hic puriora, atque innocentiora præcepta ex Astrologicis allegauero, ea non nisi ex Ptolemæo, aut ab Ecclesia probatis scriptoribus sumpti, ve in operis excursione prudens lector videre poterit. Quod si quid adhuc ex Pontano, aut Firmionimis audenter, præsertim de stellis fixis, dictum inuenerit, id vel vbi opus fuerit explico moderor, castigo aut Philosophicis rationibus comprobo; aut sanè ad purum ornatum appono: cum aliàs hi auctores magni nominis sint non tam doctrinæ veritate quam stili elegantia, vnde & eorum opera ab Ecclesia permissa sunt in Pontano quidem ob poëtis excellentiam, quæ cum primoribus poësis pugnat; in Firmicò autem ob Sermonis amoenitatem: quod ideo ab Latinæ linguæ Professoribus præsertim Ambrosio
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PREFACE. to be examined, appended, and set before them, so that anyone might find whatever is not so common, not so obvious, ready at hand; and thus would have more learned matter, which with little labor and at a single glance of the eye could satisfy, in many ways, the avidity of ingenuity. Other things, however, not common, which incidentally indeed, though no less worthy of observation, have been scattered through the work in passing, we have indicated by the insertion of this sign in the margin. Moreover, the purer and more innocent precepts from Astrological writings which I have here adduced, are taken only from Ptolemy, or from writers approved by the Church, as the prudent reader will be able to see in the course of the work. But if he should still find anything from Pontanus, or Firmicus, boldly stated, especially about the fixed stars, I either explain, moderate, or correct it where needed, or confirm it with philosophical reasons; or indeed set it down merely for ornament: since otherwise these authors are men of great name, not so much for the truth of their doctrine as for the elegance of their style, and for that reason their works have also been permitted by the Church, in Pontanus’ case on account of the excellence of his poetry, which clashes with the foremost poets; in Firmicus’ case, however, on account of the charm of his diction: and therefore by the Professors of the Latin language, especially Ambrose
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PRÆFATIO. Calepino ex eo sæpissime testimonia desumuntur. Quæ verò à me minus cautè, minus fundatè in hoc opere dicta sunt non modò S. R. E. censuræ sed & tuæ humanissime lector castigationi lubens subiicio.
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Preface. From Calepino, testimonies are very often drawn. Whatever has been said by me less cautiously, less soundly in this work, I willingly submit not only to the censure of the Holy Roman Church, but also to your most kindly correction, reader.
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Censura Patrum Reuisorum. ADMODVM REVERENDE PATER. Exicon Mathematicum à Patre D. Hieronymo Vitali nostrę Congregationis Theologo elaboratum, demandato Admodum R.P vestrę perlegimus; nihilque ineodatum est offendere, quod Catholica Fidei, aut bonis moribus adversetur. Perutile profectò opus, & quod vel terminorum elucidando proprietates, vel idemtidem varias exoticasque dirimendo quæstiones, vberem Mathematicarum scientiarum studiosis offerat segetem. Typis proinde dignum existimavimus Neapoliprid. Kal. Augusti 1663. D. ANTONIVS CARAFA Cler. Reg. S. Theol. Prof. electus Episcopus Vgentinus. D. CAROLVS PIGNATELLVS Cler. Reg. Sac. Theol. Profess. Approbatio. D. Angelus Pistachius Prepositus Generalis Clericorum Regularium. Hoc opus inscriptum, Lexicon Mathematicum, à P. D. Hieronymo Vi-
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Censorship of the Reviser Fathers. MOST REVEREND FATHER. The Mathematical Lexicon, elaborated by Father D. Hieronymus Vitali, theologian of our Congregation, by your order we have read through; and nothing has been found therein that offends, or is contrary to the Catholic Faith or good morals. Indeed, a very useful work, and one which, whether by elucidating the properties of terms, or by resolving various and exotic questions from time to time, offers a rich harvest to students of mathematical sciences. We therefore judged it worthy of the press. At Neapoli, the Kalends of August, 1663. D. ANTONIVS CARAFA, Cler. Reg. Prof. of Sacred Theology, elected Bishop of Ugento. D. CAROLVS PIGNATELLVS, Cler. Reg. Prof. of Sacred Theology. Approval. D. Angelus Pistachius, Prepositor General of the Clerics Regular. This work, entitled Mathematical Lexicon, by P. D. Hieronymus Vi-
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tali nostræ Congregationis Theologo compositum, & iuxta præfixam assertionem P.P. Theologorum, quibus id commisimus, approbatum, vt Typis mandetur, quoad nos spectat, facultatem concedimus. In quorum fidem præsentes litteras manu propria subscripsimus, & solito nostro sigillo firmauimus. Romæ Kalendis Februarij 1664. D. ANGELVS PISTACHIVS Præpositus Generalis Cleric. Regul. Locus † sigilli. D. CAROLVS LOBELLS C. R. Secret. -------------------------------------------------------- Opus attitulatum de vulnerum, aliorumque morborum curatione magnetica quæstiones tres Auctore Admod. Reu. Patre Hieronimo Vitali Clerico Regulari à me reuisum, potest ad publicam vtilitatem typis mandari, cum nihil contineat contra Orthodoxam & Catholicam doctrinam & bonos mores. In quorum fidem has propriam manu subsignaui in Conuentu S. Augustini de Padua Ordinis Prædicatorum tertio nonas Februarij 1659. Ego F. CYPRIANVS PHILIPPINVS Ordin. Prædicatorum Sac. Theol. Magister & in vniuersitate Patauina eiusdem facultatis publicus Professor.
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Having been composed for the Theologian of our Congregation, and, according to the prefixed assertion of the Fathers Theologians to whom we entrusted this matter, approved, that it may be committed to print, so far as concerns us, we grant permission. In witness whereof we have subscribed these present letters with our own hand, and confirmed them with our customary seal. At Rome, on the Kalends of February 1664. D. ANGELVS PISTACHIVS, General Prepositor of the Clerics Regular. Place † of the seal. D. CAROLVS LOBELLS, C. R. Secretary. -------------------------------------------------------- The work entitled On the magnetic treatment of wounds and other diseases, three questions, by the Most Reverend Father Hieronimo Vitali, Cleric Regular, reviewed by me, may be committed to print for the public benefit, since it contains nothing against Orthodox and Catholic doctrine or good morals. In witness whereof I have signed these by my own hand in the Convent of St. Augustine of Padua, of the Order of Preachers, on the third day before the Nones of February 1659. I, F. CYPRIANVS PHILIPPINVS, of the Order of Preachers, Master of Sacred Theology, and public Professor of the same faculty in the University of Padua.
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HIERONYMI VITALIS CLERICI REGULARIS LEXICON MATHEMATICVM ALPHABETICO ORDINE digestum, & compilatum. A , FIGVRA celebtris est, ac familiaris omnibus Ma- <1.> thematicis: non quidem quà prima litteraru[m] nota, atque Alphabeti vtriusque tam Græci, quàm Larini < > maximum, primumque in ordine Elementum; sed quà Mathesis janua, præcipuumque Mechani- < > corum omnium, quæ à Mathesi prodeunt instrumetum: in quo velut in compendio, omnia ferè Geomettica Elementa, omnis Triangulorum proportio, omnis quanritatis mensura, omnis Sinuum, Secantium, & Tangentium praxis, & omnia denique instrumenta ad Mathesin quovis modo spectantia restricta < > sunt. Quadram vulgus Italorum vocat: Latini Normam, seu < > Amussim, constantem duabus regulis planis in tectum angu- < > lum coëuntibus, atque aliâ in media distantia vtrique transuer- < > sâ, quæ eas inuicem nectat, ac Triangulum æquilaretum cum < > illis constituat, efformetque. Hanc Suem humiliro deli- < > neasse non sine cælesti consilio scribit Cicero lib. 1. de Diui- < > natione: Hanc è Phoenice in Græciam à Cadmo allaram testa- < > tur Plinius lib. 7. c. p. 16. de rerum inuentoribus agens. Egre- < > gium sanè inuentum, ac propè dixerim; diuinum. Nec, quia < > vulgare, & vel ipsis Cæmentarijs obuium, à sublimiorum dis- < > ciplinarum Professoribus aspernandum; vt proptereà eius lau- < > des hic accensere, munia explicare, nostro instituto æstime- < > nus indignum. Etenim & in hoc instrumento, Circini non ob- < > curam speciem, & in eo Regulam spectare est. Duo, inquam, < > A
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HIERONYMUS VITALIS CLERIC OF THE REGULAR MATHEMATICAL LEXICON IN ALPHABETICAL ORDER compiled and arranged. A , a celebrated figure, and familiar to all mathematicians: not indeed as the first letter of the alphabet, and the greatest and first element in the order of both the Greek and the Latin alphabet, but as the gateway of Mathematics, and the chief instrument of all mechanical things which proceed from Mathematics: in which, as it were in brief, nearly all the elements of Geometry, all the proportion of triangles, all the measure of quantity, all the practice of sines, secants, and tangents, and finally all instruments in any way pertaining to Mathematics, are contained. The common people of Italy call it a square; the Latins, a rule, or a straightedge, consisting of two flat rules meeting in a roof-like angle, and of another transverse one midway between them, which joins them together, and forms with them, and makes, an equilateral triangle. Cicero writes that this was traced not without heavenly counsel by the sow in book 1 of On Divination: Pliny testifies that it was brought from Phoenicia into Greece by Cadmus, in book 7, ch. p. 16, while discussing inventors of things. Truly a splendid invention, and, I might almost say, a divine one. Nor because it is common, and even at hand to builders themselves, is it to be scorned by professors of the higher disciplines; so that for that reason we should think it unworthy of our purpose to add its praises here and explain its uses. For in this instrument there is to be seen both the not obscure shape of the compasses and the rule. Two, I say, A
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METHEMATICVM. ortum etediderim vulgare nomen, Abacum, quo nos Itali Arithmeticas notas promiscuè explicamus: eas inquam, quæ certo ordine ac methodo inter se dispositæ, quemuis nume- rum vel innumerabilem comprehendunt. Vt mirum sit totam Arithmeticam, hoc est amplissimam facultatem omnium Ma- thematicarum potissimam, sine qua nec vlla comparari po- est, nec ( poenè dixerim) diu Orbis confistere, in paruo, de- cem videlicet numeralium Elementorum ambitu contineri. Ea sunt 1.2.3.4.5.6.7.8.9.0. Quæ ab vnitate vsque ad nouem progrediendo, singulorum numerorum per ordinem notæ unt & characteres: numerus autem denarius per o. cifram, talis Zero dictam exprimitur, non quidem se sola, sed alte- ius notæ additione quam in decuplum auget, totque denarios indicat, quot vnitates, numerus; seu nota illi præposita si- gnificare habet: itaut si hæc fuerit 1. cum fulcimento illius ci- liæ o. (se sola nihil significantis) exprimar decem, hoc est num denarium: si 2. eidem præponatur, indicet viginti, hoc est duos denarios: si tres, triginta, hoc est tres denarios, & e deinceps vsque ad nonaginta. Hinc præpositâ, & superad- iâ aliâ figurâ, explicatur numerus centenarius, eodem ordine rogrediendo. Quòd si quarta nota addatur, ea erit numeri millenarij; si quinta, tot vnitates millenarij, hoc est tot mille- orum numerum, quot ea nota quæ cæteris anteponitur, se sola nitates significaret. Si sexta, tot centenoru[m] millium index est: demum seprima, per eam habetur numerus millenorum mil- um: itaut semper nota superaddita numerum posteriorem pro ii qualitate multiplicet ad caput semper reuertendo vsque in finitum. Itaque (vt id compendio repetam) vltima nota (si ioqui est significatiua) se sola, seu aliis comitata, indicat umerum simplicium vnitatum: penultima denarij: antepenul- na centenarij: quæ his omnibus anteponitur, tor indicat de- rios millenarij: quæ adhuc superadditur, centenos millena- dos, & sic deinceps prosequendo in infinitum, atque ad caput nper regrediendo. Ex hac numerorum connexione, propor- ne, collisione, ac respondentia tot miracula exantlantur, vt ritò Libellus non ità pridem in lucem editus, quo per varios merorum ordines arcana multa operari, perscrutarique ocemur, Thaumaturgus Mathematicus sit appellatus. Eum vi- ut curiosus lector, & non pigebit. BALANTICA siue Alantica, Arabicè Armillam sonat suspen- iam in summitate Astrolabij, Planisphærij, aut aliûs consi- lis instrumenti sitam ad illud perpendiculariter statuen- n; quo siderum distantias, positûs, altitudines, aliaque multa exquisitè contemplari possumus. A ij
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METHEMATICVM. I have set forth the common name, Abacus, by which we Italians indiscriminately explain the arithmetical signs: those, I say, which, arranged among themselves in a fixed order and method, comprehend any number, even an innumerable one. So it is a wonder that the whole of Arithmetic, that is, the most ample faculty and chief of all the Mathematical arts, without which nothing else can be compared, nor (I may almost say) can the world for long endure, should be contained within a small compass, namely the range of ten numeral elements. These are 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. Which, proceeding from unity up to nine, are the signs and characters of the individual numbers in order; but the number ten is expressed by the cipher 0, called Zero, not indeed by itself alone, but by the addition of another sign, which increases it tenfold, and indicates as many tens as the numeral, that is, the sign placed before it, is meant to signify units. Thus, if 1 be written with the support of that cipher 0 (which by itself signifies nothing), it expresses ten, that is, one denary; if 2 be placed before it, it indicates twenty, that is, two denaries; if 3, thirty, that is, three denaries; and so on up to ninety. Hence, with another figure added and placed before it, the centenary number is explained, proceeding in the same order. But if a fourth sign be added, it will be the sign of the thousand number; if a fifth, the number of units of a thousand, that is, as many thousands as that sign which, placed before the others, by itself would signify units. If a sixth, it is the indicator of hundreds of thousands; finally, if a seventh, by it is obtained the number of millions of thousands; so that always the added sign multiplies the number following it according to its quality, returning always to the head, and so on without end. Therefore, to repeat this briefly, the last sign (if it is significant) by itself, or accompanied by others, indicates the number of simple units; the penultimate, of tens; the antepenultimate, of hundreds; that which is placed before all these, indicates tens of thousands; that which is added still above, hundreds of thousands; and so on continuing infinitely, and always returning to the head. From this connection, proportion, collision, and correspondence of numbers, so many wonders are brought forth, that rightly the little book not long ago published, in which we are taught to perform and investigate many hidden things through various orders of numbers, has been called Thaumaturgus Mathematicus. The curious reader may see it, and will not regret it. BALANTICA, or Alantica, in Arabic signifies the armilla suspended at the summit of an astrolabe, planisphere, or other similar instrument, set there in order to position it perpendicularly; by means of which we can most accurately observe the distances, positions, altitudes of the stars, and many other things.
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4 LEXICON 6. ABEN RAS, vel Ras Eleanin, latinè Caput Draconis: dicitur apud Arabes stella fixa pellucida in Capite Draconis sideris ad polum Arcticum, quod ipsum polum Zodiaci ambit & circumplectitur. Ipsa autem stella distat nunc à polo Arctico 15. ferè gr. estque tertiæ magnitudinis de natura mixta ex Ioue, Saturno, & Marte, Vide fusius in Veibo Draco. 7. ABKACHALEVS Chaldaicè, seù, vt passim corrupto nomine circumfertur, Garacles: Caput Herculis, seù Pollucis alterius Geminorum, & subsequentis: stella videlicet rufa, & subflaua de natura Martis secundæ magnitudinis, inter Regias quidem computata, sed tamen est etiam vna ex violentis De qua proinde nugantur Astrologi, quod si cum Luminari Condi- tionario reperta fuerit, altero in signo violento existente, mor- tem portendat itidem violentam. Existit nunc in gradu ferè 19. Cancri cum gr. 6. latitudinis borealis. 8. ABSCISSIO LVMINIS, Arab. Almana, est deterioratio Planetæ, quæ contingit quoties tres Planetæ fuerint intia fines suo- rum Orbium, itaut medius sit ponderosus; alius leuior in pau- cioribus gradibus signi eidem ponderoso applicans, ac rettius, qui sit in pluribus gradibus, desluatque à ponderoso post par- tilem cum eo coniunctionem; vetum antequam primus dire- stè gradiens corpore jungatur ponderoso illi, tertius interim factus retrogradus eidem denuò retrocedens jungatur: tunc iste tertius diceretur lumen prioris abscindere. Potest id etiam accidere alio modo: is est, cum ex tribus medius applicat ad coniunctionem posterioris, sed alius leuior, qui est in paucio- ribus partibus, cursu illum anteuenit, eoque relictio, prius corpore jungatur tertio, quam secundus id prius affectans. Quod sæpissimè præstat Luna omnium velocissima. In eo igi- tur casu diceretur abscissum lumen eius, qui prior alteri applica- bat ab eo qui postremò eidem applicans, ociùs tamen ad illum pertingit. 9. ABSIS, seu Apsis, Græcè, Suida teste, propriè significat for- nicis curuaturam. Hinc apud Astronomos transferri solet ad si- gnificandam tum summam, & superiorem Circuli partem, in qua planeta existens maximè à terra elongatur; tum insimam, in qua sit terræ proximior, quam fieri possit. Et illud quidem punctum in quo maximè elongatur, dicitur Apogæum, ab Ara- bibus verò Aux: hoc autem Perigæum, & Oppositum Ausis in quo manens Planeta à Græcis appellatur Hypaugus, hoc est terra vicinus. Potiò huiusmodi puncta considerantur tàm in Eccentricis, quàm in Epicyclis? quæ quidem (licet lentissimo motu) cientur, & locum permutant in Zodiaco; ac singuli planetæ proprias Absides habent in certis Zodiaci gradibus, vt
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4 LEXICON 6. ABEN RAS, or Ras Eleanin, in Latin Caput Draconis: among the Arabs it is said to be a fixed, bright star in the Head of the Dragon, near the Arctic pole, which itself surrounds and embraces the pole of the Zodiac. This star is now about 15 degrees from the Arctic pole, and is of the third magnitude, of a mixed nature from Jupiter, Saturn, and Mars. See more fully under the word Draco. 7. ABKACHALEVS in Chaldaic, or, as it is commonly corrupted in name, Garacles: the Head of Hercules, or of the other Pollux of the Twins, and the one that follows; that is, a reddish and somewhat yellowish star, of the nature of Mars, of the second magnitude, counted among the Royal Stars, but nevertheless also one of the violent ones. Concerning this, astrologers nonsensically say that if it is found with a Conditionary Luminary, while the other is in a violent sign, it portends a violent death likewise. It now lies at about the 19th degree of Cancer, with 6 degrees of northern latitude. 8. ABSCISSION OF LIGHT, Arab. Almana, is the deterioration of a planet, which happens whenever three planets are within the limits of their own orbits, so that the middle one is ponderous; the other, lighter one, applying in fewer degrees of the sign to that same ponderous one and proceeding more directly, is in more degrees, and after a partial conjunction with the ponderous one slips away from it; yet before the first, moving directly, is joined bodily to that ponderous one, the third in the meantime, becoming retrograde and again moving backward, is joined to the same: then this third would be said to cut off the light of the first. This can also happen in another way: that is, when among the three the middle one applies to conjunction with the one behind it, but another, lighter one, which is in fewer degrees, overtakes it in its course and leaving it behind is joined bodily to the third before the second can first accomplish that. This the Moon, the swiftest of all, very often brings about. In that case the light of the one who had been applying to the other before he who last applies to the same, yet reaches him sooner, would be said to have been cut off. 9. ABSIS, or Apsis, in Greek, according to Suidas, properly signifies the curve of an arch. Hence among astronomers it is customarily transferred to signify both the highest, upper part of a circle, in which a planet being situated is at the greatest distance from the earth; and the lowest, in which it can be closest to the earth. That point in which it is most distant is called the Apogee, by the Arabs however Aux; but this one the Perigee, and the opposite of Aux, in which the planet remaining is called by the Greeks Hypaugus, that is, near the earth. Such points are more properly considered both in eccentric circles and in epicycles, which indeed, though with very slow motion, are moved and change position in the Zodiac; and each planet has its own apsides in certain degrees of the Zodiac, as
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LEXICON 6 que anni tempestas, quoadusque Apogæo Solis ad Libram perueniente, par sit earum regionum cum nostris conditio. Cæterum hæc obiter dicta sint, ex occasione incidentis de Absidum mutatione sermonis. De earum motus proportione, ac legibus vide apud citatum Ricciol. lib. 3 cap. 24. ß 25. 12. ABTERRANII dicuntur venti quidam impetuosi altè è terra spirantes (vnde & Altani audiunt) & in Mare progredientes illud subitis motibus quatiendo, ac terribiles tempestares cien- do. Vocantur autem græcè Apogæi quasi è terra spirantes. De his multa Plinius lib. 2. cap. 43. AC 13. ACARNAR, siue Acharnahar, aut Acharnaharim, Arab. dicitur extrema fluuij, fixa primæ magnitudinis de natura Iouis, & Ve- neris in extremitate Eridani posita atque in logitudine sub gr. 21. Arietis cum latir. australi gr. fere 60. Hæc in Horoscopo inuenta magnam fortunam pollicetur, vt author est Ptolemeus: idque præsertim si Iouis, aut Veneris benigno radio fulciatur. Badem in Tabulis Persicis vocatur Aulax, id est saluus. 14. ACENTACER in sphæra barbarica dicitur terrius Decanus Arietis, cuius dispositio spectat ad Venerem; proindeque habet iudicium solestiæ, mansuetudinis, ludorum, munditiarum, io- corum, &c. 15. ACTINOBOLIVM vocat sæpissimè Ptolemeus motum dire- ctionis rectum, quo scilicer dirigatur significator in co[n]sequen- tia signa: sicut econtra Horinaum appellat motum directionis conuersum, qui fiat in præcedentia loca: ea inquam, quæ suc- cessiuè acquirantur per motum diurnum, cuiusmodi est directio Aphætæ constituti inter decimam domum, & septimam, ad cardinem Occidentis. Qua de re plura vide in V. Directio. 16. ACHRONICVS, seu Achronichius, idem sonat Græcè ac La- tinè temporalis: coque nomine significatur certus ortus, & oc- casus siderum, ad differentiam ortus, & occasus Cosmici, nec- non Heliaci, de quibus in suis locis. Est autem propriè ortus & occasus Achronicus, cùm stella, aut quodlibet coeli punctum vespere, sole ad occasum vergente suprà horizontem ad orientem emergit; vel cum ipso sole infra horizontem descen- dit. Verùm adhuc licet impropriè, achronicè oriri dicitur quælibet stella, quæ noctis tempore, sole sub inferiori he- mispherio delitescente, ipsa interim quauis hora suprà hori- zontem ascendit, ac nostrum hemisphærium lustrat: sicut & occidere achronicè semper, cum de nocte vergit ad occasum, & infà horizontem deprimitur. Hinc sequitur, semper signum illud in quo sol reperitur, vespere occidere achronicè, cum ra- men manè non achronicè, sed cosmicè oriatur. Econtrà si-
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LEXICON 6 for the time during which the Sun is at its apogee in Libra, until the condition of those regions becomes equal to ours. But these things have been said in passing, from the occasion of the digression concerning the change of the Absides. See Ricciolus cited above, book 3, chapter 24, § 25, for the proportion and laws of their motion. 12. ABTERRANII are certain impetuous winds blowing high out of the earth (whence they are also called Altani) and advancing into the sea, shaking it with sudden movements and raising terrible storms. They are called in Greek Apogæi, as it were “blowing from the earth.” Pliny says much about these in book 2, chapter 43. AC 13. ACARNAR, or Acharnahar, or Acharnaharim, in Arabic, is said to be the extremity of the river, a fixed star of the first magnitude, of the nature of Jupiter and Venus, situated at the end of Eridanus and in longitude under 21 degrees of Aries, with southern latitude of almost 60 degrees. Found in the horoscope, it promises great fortune, as Ptolemy says; especially if supported by the favorable ray of Jupiter or Venus. The same in the Persian Tables is called Aulax, that is, “safe.” 14. ACENTACER in the barbaric sphere is called the third Decan of Aries, whose disposition pertains to Venus; and therefore it has the meaning of pleasantness, gentleness, games, cleanliness, jokes, and the like. 15. ACTINOBOLIVM Ptolemy very often calls the direct motion of direction, by which the significator is directed in the following signs; just as, on the contrary, he calls Horinum the reversed motion of direction, which is made toward the preceding places: namely, those which are successively acquired by the diurnal motion, such as the direction of the Aphæta placed between the tenth house and the seventh, to the western angle. On this matter see more under V. Direction. 16. ACHRONICVS, or Achronichius, sounds the same in Greek as temporalis in Latin; and by that name is signified a certain rising and setting of the stars, distinct from the cosmic, as well as the heliacal rising and setting, of which in their proper places. Properly speaking, an achronic rising and setting occurs when a star, or any point of the heavens, in the evening, the sun inclining toward setting, rises above the horizon in the east; or when it descends with the sun itself below the horizon. Yet even improperly, a star is said to rise achronically when, at night, the sun hiding beneath the lower hemisphere, it meanwhile ascends above the horizon at any hour and surveys our hemisphere: and likewise to set achronically always when it inclines toward setting by night and is depressed below the horizon. Hence it follows that that sign in which the sun is found always sets achronically in the evening, although in the morning it rises not achronically, but cosmically. Conversely si-
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MATHEMATICVM. gnum oppositum ei in quo sol reperitur, vespere otiri achronicè, & manè cosmicè occidere. Plura exempla huius orris, & occasus stellarum exhibent nobis Poërx: qui volet, videat apud Iunctinum in Commentarijs ad spharam 10. de Sacro-Bosco. ACTISAL, seu etiam Alictisal arab. idem sonat ac coniunctio, 17. seu potiùs applicatio ad coniunctionem: hoc est, cum planeta leuior existens intra fines orbis, quantum se extendit lux planetæ ponderosi, pergit ad eius coniunctionem partilem, hoc est in minuto. Huius dictionis frequentem vsum inuenies in Qua- dripartiro Ptolemxi, necnon in Centiloquio ex versione Ara- bica Hali Rodoan. ACONTIÆ gtecè cometes sunt, seù potiùs aërex impressiones 18. instar iaculi (vnde & nomen hauserunt) quia iaculi modo, in- quir Plinius lib. 2. cap. 25. vibrantur ocissimo significatu. Ex ijs quædam breuiores sunt, instar muctonis, omnium pallidissi- mæ, & quodam fulgore gladij retitentes, verum sine radijs quas Xyphias vocauere. Vide sub hac dictione. A cvt vs dicitur angulus apud Geometras, qui minor est recto, 19. magisque acuminatus, qua de re vide in V. Angulus. AD ADALOR Arabicè dicitur ventus ab occidente spirans, quem 20. nos Fauonium appellamus. Sumitur etiam à quibusdam generi- cè pro quolibet vento occidentali, qui lateraliter ipsi cardinali Fouonio aduiuat. ADIGEGE corrupto nomine, Arab. dicitur Cignus, Gallina, 21. Olor, sidus videlicet in octaua splæra ad borealem plagam constans stellis 17. inter quas præcipua est quæ Vulgò dicitur Cauda Caigni, Arabice Deneb. Adigege, secundæ magnitudinis. Notat autem Kircherus in Oedipo se in emendatis codicibus reperisse scriptum Eldigigi b. Schiscardus autem Addigagato. ADOR apud Prolemæum in textu arabico idem sonat, ac debi- 22. itas planetæ, cum videlicet fuerit in locis cadentibus, aut in iucasu, vel detrimento: siue etiam quacumque fuerit debili- ate affectus ex ijs quæ in proprijs locis connumerantur. ADORINGEN, seu vt habetur in textu Alxabirij, Adorogen, 23. dem sonat, ac dominus Decanorum: Diuidebant enim antiqui professores Astronomiæ tam Arabes quàm Iudæi vnumquod- ue signum in tres partes æquales, dando singulis planetis pat- em, hoc est decem gradus illius signi, qui proinde dicebarur ominus illius Decani. Cuius rei inquisitio sic traditur ab odem Alkabitio, & illustratur ab eius Commentatore 10. de axonia. Diuide, inquit Ascendens in tres partes æquales, aut quælibet pars constet ex decem gradibus, & si quidem scendat prima pars, seu facies signi, erit Adoringen, seu A iii
Transcription: Translated (English)
MATHEMATICVM. the sign opposite to that in which the sun is found; to rise in the evening achronically, and to set in the morning cosmically. More examples of this rising and setting of the stars are shown to us by the Poets: whoever wishes, let him look in Junctinus in the commentaries on the sphere of Sacro Bosco, 10. ACTISAL, or also Alictisal in Arabic, means the same as conjunction, 17. or rather application to conjunction: that is, when a lighter planet, being within the bounds of the orb, so far as the light of the weightier planet extends, proceeds to its partile conjunction, that is, in a minute. You will find frequent use of this word in Ptolemy’s Quadripartitum, as well as in the Centiloquium from the Arabic version of Hali Rodoan. ACONTIÆ are called in Greek comets, or rather aerial impressions, 18. in the form of a dart (whence they also took their name), because, in the manner of a dart, as Pliny says, book 2, chapter 25, they flash with very swift motion. Some of these are shorter, in the form of a shuttle, of all the palest, and retaining a certain brightness like that of a sword, but without rays; these they called Xyphias. See under that term. ACUTUS is called by geometers an angle that is less than a right angle, 19. and more pointed; for this see under V. Angulus. ADALOR, in Arabic, is called the wind blowing from the west, which we call Favonius. It is also taken by some generically for any western wind that helps it laterally to the cardinal Favonius. ADIGEGE, by a corrupted name, is called in Arabic Cygnus, Gallina, Olor, that is, the constellation in the eighth sphere standing toward the northern region, consisting of 17 stars, among which the principal is that commonly called Cauda Cygni, in Arabic Deneb. Adigege is of the second magnitude. Kircher notes in Oedipus that in corrected manuscripts he found it written Eldigigi; Schiscard, however, Addigagato. ADOR, in Ptolemy’s Arabic text, means the debilities of a planet, when it is in falling places, or in detriment; or also when it is affected by whatever weakness is counted among the proper places. ADORINGEN, or as it is found in the text of Alxabiri, Adorogen, means the same as lord of the decans: for the ancient professors of astronomy, both Arabs and Jews, divided each sign into three equal parts, giving to each planet a part, that is, ten degrees of that sign, which therefore was called the lord of that decan. The inquiry into this matter is thus given by the same Alkabitio, and explained by his commentator, 10. de Axonia: “Divide,” says he, “the Ascendant into three equal parts, or let each part consist of ten degrees, and if the first part, or face of the sign, should ascend, it will be Adoringen, or...” A iii
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8 LEXICON dominator Decani ipse dominus signi: si verò ascendat secunda facies signi, dominus Decani erit secundus dominus triplicitatis, hoc est dominus signi eiusdem triplicitatis cum Ascendente, quod per successionem signorum consequitur, eritque necessariò in quinta Domo, vel circà. Si demum ascendat tertia facies signi; tunc pro domino Decani accipiendus est terrius dominus triplicitatis, quod necessario cadere debet est in nonam Domum. Sic pro exemplo : Ascendant in alicuius Natiuitate, duo, tres, &c. vsque ad decem gradus Arietis. Eius Decanus est Mars, quia ipse etiam est dominus eiusdem signi: Si verò ascendant vndecim gradus, aut alia quæuis pars secundæ faciei Arietis; tunc eius Decanus est Sol, quia ipse est dominus signi Leonis, quod est secundum signum immediatè sequens in ea triplicitate. At si ascendat tertia facies Arietis; tunc dominus Decani erit Iupiter, qui est dominus tertij signi eiusdem triplicitatis, nempè Sagittarij: Similiter, si ascendat prima facies Tauri, dominus eius Decani erit Venus: si secunda, Mercurius dominus Virginis secundi signi, eiusdem cum Tauro triplicitatis: si tertia, Saturnus dominus Capricorni tertij signi eiusdem triplicitatis. Et hæc est doctrina Decanorum, quam solum ad ornatum, & operis complementum explicare volui, ne curioso Lectori quid desit; cum aliàs, res sit euanida, superstitiosa, & mera Arabum nugamenta. 24. ADONCADO idem est, ac separatus à natura gubernante corpus. Vide Ptolem. in cap. 14. lib. 3. ex versione Arabica, & eius Commentatorem Hali super eum. Æ 25. ÆGIPAN hoc est Hircus æquoris, dicitur Persis, Capricorni signum, seu sidus, eoquod habeat figuram hirci-marini, seù potiùs, quia sit æquori maximè infensus, & procellosus. Hinc etiam aliquibus dicitur pelagi procella, imbrifer, &c. Arabicè Egedi vel Alcanarus. 26. ÆQVOCEROS item Græcè dicitur Capricornus apud Hyginu[m]. Qua de re vide exposit. Hermann. Cælaris in Arab. Phænomenon. 27. ÆQVATOR græcè pimerinos est Circulus maximus Sphæram æqualiter diuidens in duas partes, quarum vna ad polum Arcticum, altera ad Antarcticum vergit, ipso interim in medio consistente, & partes omnes æquante, vnde & nomen sortitus est: à priscis Astronomis dictus etiam Cingulum Mundi. Dicitur ad huc 28. ÆQVINOCIALIS, eoquod diem nocti æqualem faciat. Qui enim ipsum verticalem habent, semper quouis anni tépore dies noctibus æquales experiuntur: & nos, Sole eundem circulum tenente, quod bis in anno sit, cu[m] primas Arietis, & Libræ parte[m]
Transcription: Translated (English)
8 LEXICON dominator of a Decan is the lord of the sign itself: but if the second face of the sign rises, the lord of the Decan will be the second lord of the triplicity, that is, the lord of the sign of the same triplicity as the Ascendant, which follows by succession of signs, and will necessarily be in the fifth House, or near it. If finally the third face of the sign rises, then the third lord of the triplicity is to be taken as lord of the Decan, which must necessarily fall in the ninth House. Thus, for example: if in someone’s nativity there rise two, three, &c. up to ten degrees of Aries, its Decan is Mars, because he is also the lord of the same sign. But if eleven degrees, or any other part of the second face of Aries, rise, then its Decan is the Sun, because he is lord of the sign Leo, which is the second sign immediately following in that triplicity. But if the third face of Aries rises, then the lord of the Decan will be Jupiter, who is lord of the third sign of the same triplicity, namely Sagittarius. Likewise, if the first face of Taurus rises, the lord of its Decan will be Venus; if the second, Mercury, lord of Virgo, the second sign of the same triplicity as Taurus; if the third, Saturn, lord of Capricorn, the third sign of the same triplicity. And this is the doctrine of the Decans, which I have wished to explain only for ornament and to complete the work, lest anything be lacking to the curious reader; since otherwise the matter is vain, superstitious, and mere Arab nonsense. 24. ADONCADO is the same as separated from the nature governing the body. See Ptolemy, in chapter 14 of book 3, from the Arabic version, and his commentator Hali on the same. Æ 25. ÆGIPAN, that is, sea-goat, is what the Persians call the sign or constellation of Capricorn, because it has the shape of a sea-goat, or rather because it is most hostile and stormy to the sea. Hence it is also called by some the storm of the sea, rainy one, etc. In Arabic, Egedi or Alcanarus. 26. ÆQVOCEROS is likewise said in Greek of Capricorn by Hyginus. On this matter see the exposition of Hermannus Cælaris in the Arabic Phenomena. 27. ÆQVATOR in Greek, pimerinos, is the great circle dividing the sphere equally into two parts, one of which inclines toward the Arctic pole, the other toward the Antarctic, while it remains in the middle and equalizes all parts, whence it has also received its name: by the ancient astronomers it was also called the Girdle of the World. It is also called 28. ÆQVINOCIALIS, because it makes day equal to night. For those who have it vertical always experience, at whatever time of year, days equal to nights: and we, when the Sun holds this same circle, which happens twice a year, when the first part of Aries and Libra
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Transcription: ATR-1
MATHEMATICVM. 5 ingreditur, in quauis mundi plaga vniuersale æquinoctium ex- perimur. Dicitur etiam Circulus rectus, non quia rectè semper ascendar, sed qvia rectè, & æqualiter ex eisdem punctis Hori- zontis ad differentiam Zodiaci, qui vbiuis inæqualiter & obli- què semper ascendit, vt proptereà circulus obliquus & iste inonomasticè sit appellatus. Potro plura sunt Æquatoris officia, quæ fusè nimis recenset 29. lunctinus in sphæram 10. de Sacro-Bosco. Nos breuiter ea hic epi- ogabimus. Primò igitur haber secare quemuis Meridianum, d angulos rectos, & insuper in Sphæra recta p[er]solum Horizon- em, qui incidit in ipsos mundi polos. Secundò est mensura notus diurni, seù primi Mobilis, qui est communis cunctis ideribus: atque adeò qualibet hora ascendunt quindecim gra- lus Æquatoris, & Parallelorum ipsius. Tertiò est causa diuersi- aris dierum ac noctium artificialium, & vnfomitatis inte- pæ dici naturalis ex die ac nocte artificiali conflatæ. Quartò lesignar duo puncta cardinalia ortus, & occasus in Horizon- e, vnde noscuntur qualitates ventorum. Quintò est mensura, mò & subiectum Ascensionum, & Descensionum. Sextò est mensura longitudinis Geographicæ, quæ tanta est, quanta ars, seu arcus Æquatoris interceptus inter Meridianum om- ium primum constitutum in insulis Canatijs, & Meridianum sci, cuius longitudinem quærimus. Septimò tandem concurrit um Ecliptica ad reliquos anni dies determinandos, qui tam ungi sunt, quam plures, & plures Æquatoris gradus ascendunt ipsa Horizontem eo rempore, quo sol ab ortu ad occasum ertur. Hæc & alia munia habet Æquaror; quæ qui exactius oler, adeat Lunctinum citatum. ÆQUICRVRIA figura apud Astronomos est constitutio lumi- 30. nium cum Maleficis in coelesti Themate tam dira, & infausta, : qui sub ea in lucem edi comperiantur, enutriri non possint, d mox extinguantur. Quippè cum in ea ambo luminaria, à nibus hominum vita pendet, vel sanè alterutrum, quod sit ditionarium, plurimum à Maleficis infestetur; inde fit, vt tæ vsuram diu naro communicare non possint, sed ob ni- tam siccitarem humidum radicale protinùs absumatur, ex- iguaturque calor naturalis; vnde editus natus tanam influ- s sæuitiem sustinere non possit, sicque demum vitam cum orre commutet. De hac re fusè agir Ptolemæus lib. 3. Qua- p. cap. 91 innumeraque affert experimenta Lunctinus. Est tur figura Æquicruia constitutio angulorum & luminarium in Maleficarum altera, vel vtraque, ità vt exactè effoiment uangulum æquilaterum, vt explicat ipsemet Ptolemæus. uodcumque igitur luminare, vel alterum, vel vtrumque,
Transcription: Translated (English)
MATHEMATICVM. 5 When it enters, in whatever part of the world we are, we experience a universal equinox. It is also called the Right Circle, not because it always ascends straight, but because it rises straight and equally from the same points of the Horizon, in contrast to the Zodiac, which everywhere always ascends unequally and obliquely, so that for that reason the oblique circle and this one are so named by a single distinctive term. Moreover, there are many offices of the Equator, which Lunctinus in his commentary on the sphere of Sacro-Bosco, ch. 10, recounts at great length. We shall briefly set them out here. First, then, it may cut any Meridian at right angles, and furthermore, in the right Sphere, the whole Horizon, which touches the very poles of the world. Second, it is the measure of the diurnal motion, or of the Primum Mobile, which is common to all the stars; and so every hour fifteen degrees of the Equator and of its Parallels rise. Third, it is the cause of the diversity of artificial days and nights, and of the unevenness of the natural time made up from artificial day and night. Fourth, it marks the two cardinal points of sunrise and sunset on the Horizon, from which the qualities of the winds are known. Fifth, it is the measure, indeed also the subject, of Ascensions and Descensions. Sixth, it is the measure of geographical longitude, which is as great as the part, or arc, of the Equator intercepted between the first established meridian in the Canary Islands and the meridian of the place whose longitude we seek. Seventh and finally, it comes together with the Ecliptic to determine the remaining days of the year, which are as long as more and more degrees of the Equator rise above the Horizon at the time when the sun is carried from east to west. The Equator has these and other duties; he who wishes to know them more exactly should consult the cited Lunctinus. ÆQUICRVRIA, among astronomers, is a configuration of the luminaries with the malefics in a celestial figure so dire and unlucky that those who are known to be born under it cannot be nurtured, but soon perish. For in it both luminaries, on which human life depends, or at least one of them, which is the dispositary one, is greatly afflicted by the malefics; hence it happens that they cannot long communicate the use of life, but through such dryness the radical moisture is at once consumed, and natural heat is extinguished; wherefore the newborn infant cannot endure such a violent influence, and thus at last exchanges life for death. On this matter Ptolemy speaks at length in Book 3, chap. 91 of the Quadripartitum, and Lunctinus adduces countless experiments. Æquicruia is also the configuration of the angles and luminaries in one or both of the malefics, so that they exactly form an equilateral triangle, as Ptolemy himself explains. Whichever luminary, therefore, whether one or the other or both,
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MATHEMATICVM. 11 Titus eos, Parallelos declinationis vocauir, qua notione melius explicatur hæc æquipotentia. Qui profectò eadem ratione par- allelos in mundo adinuenit, qui sunt æquidistantiæ duorum siderum à Meridiano, vt esset, si v.g. alterum eorum consi- steret in cuspide vndecimæ, alterum in octauæ: inde enim es- formaretur perfectum Triangulum ex punctis in quibus ipsa consistunt, & angulo medij coeli. Vnde etiam in hac consti- tutione luminaris cum Malesica natus fortè non superuiuer, ( vt ego sæpiùs obseruaui) quia Malesicus luminare affligir ab angulo, atque in figura æquicuria, ac perinde est, ac si foret illi partiliter iunctus, aut oppositus ex diametro, vt consideranti patet. Verum id benè intelliget Lector, cum probè nouerit naturam, atque efficaciam horum parallelorum, quam nos fusè in loco explicabimus. ÆQVIDIVM, & Æquidiale dicebatur ab antiquis id ipsum < 32.> quod nos dicimus Æquinoctium, & Æquinoctiale: forsan po- riori iure, eoquod nox diei potiùs substernitur, ac famulari debet, quam dies nocti ( vt obseruar etiam August. in Psal. 70.) eò quòd Gen. 1, dicatur: Factum est vespere & manè dies vnus. Sed enim cedat nunc Antiquitas posteritati; quæque olim omnium magistra singulis quibusque rebus conuenientia iudidit nomina, iam modo se recentioribus conformare, atque eorum placitis morem gerere necesse est. Igitur ÆQVINOCITIVM dicitur tempus illud, quo sol initio Veris, & < 33.> Autumnj prima puncta Arietis, & Libræ tangens toto terrarum orbe dies noctibus æquales facit: tunc enim exquisitè est in medio Sphæræ in ipso circulo Æquatoris, non magis ad Bo- ream, quam ad Austrum declinans: quî sit, vt motu suo diurno non magis suprà quam infra horizontem degat, moretur- que, cum Æquator æqualiter semper procedat, sitque pars eius media, hoc est gr. 180. semper supra Horizontem, altera infra consistat, opus est Hinc circulus ille, vt suprà notauimus ab æqualitare quam facit dierum ac noctium, Æquinoctialis etiam dictus fuit. Porrò Æquinoctium semper, & vbique fiesi < 34.> Sole in Æquatote existente, nulli dubium est: At verò sem- per id fieri sole attingente initia Arietis, & Libræ non satis constat, ob motum irregularem octauæ spheræ. Qua in re col- ligenda maximè insudarunt præclarissimi Astronomi Georgius Peurbachius, Ioannes Regiomontanus, Nicolaus Copernicus, ac Tycho Brahe, qui in cælestium motuum obseruatione quin- quaginta amplius annos consumpsit, ac tandem comperuit, non semper, cum Sol fuerit in principio Arietis, & Libræ acci- dere æquinoctia, sicut nec etiam cùm fuerit in inirijs Cancri, & Capricorni, solstitia; sed aliquando ante, aliquando post, ali-
Transcription: Translated (English)
MATHEMATICVM. 11 Titus called them Parallels of declination, by which notion this equivalence is better explained. He indeed devised parallels in the world in the same way, namely the equal distances of two stars from the Meridian, as would be the case if, for example, one of them stood in the cusp of the eleventh house and the other in the eighth; for from this a perfect triangle would be formed from the points in which they themselves are situated, and from the angle of the midheaven. Whence also, in this constitution of a luminary with a malefic, one may perhaps not survive birth (as I have often observed), because the malefic afflicts the luminary by the angle, and in an equal-square figure, and is accordingly as if it were joined to it by partile aspect, or opposed diametrically, as is clear to one who considers it. But the Reader will understand this well, once he has properly learned the nature and efficacy of these parallels, which we shall explain at length in the proper place. AEQVIDIVM, and Æquidiale was the term used by the ancients for the very thing that we call Æquinoctium, and Æquinoctiale: perhaps with better right, because night is rather laid beneath the day, and ought to serve it, than the day night, as Augustine also observes on Psalm 70; because in Genesis 1 it is said: “And the evening and the morning were the first day.” But now let Antiquity yield to posterity; and what once, as teacher of all things, it judged with fitting names for each particular matter, must now conform itself to the more recent and comply with their opinions. Therefore ÆQVINOCITIVM is called that time when the sun, at the beginning of Spring and Autumn, touching the first points of Aries and Libra, makes days equal to nights throughout the whole world: for then it is exactly in the middle of the Sphere, in the very circle of the Equator, declining neither more toward the North nor toward the South; so that by its daily motion it dwells and remains no more above the horizon than below it, since the Equator always advances equally and its middle part, that is, 180 degrees, always lies above the horizon, while the other part lies below. Hence that circle, as we noted above, was also called Equinoctial from the equality it makes of days and nights. Moreover, it is no doubt that the Equinox always and everywhere occurs when the Sun is in the Equator: but that it always happens when the Sun touches the beginnings of Aries and Libra is not sufficiently certain, because of the irregular motion of the eighth sphere. In this matter the most distinguished astronomers Georgius Peurbachius, Ioannes Regiomontanus, Nicolaus Copernicus, and Tycho Brahe—who spent more than fifty years in observing the motions of the heavens, and finally discovered that the equinoxes do not always occur when the Sun is at the beginning of Aries and Libra, nor likewise the solstices when it is at the beginnings of Cancer and Capricorn; but sometimes before, sometimes after, and...
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12 LEXICON quando etiam, sed rarissimè, in eisdem punctis, eoquod ob deniationem Eclipticæ octauæ sphæræ ab Ecliptica primi Mo- bilis, non semper Ecliptica octauæ sphæræ rangit Æquinoctia- lem primi Mobilis, in principijs Arietis & Libræ, sed aliquan- do ante, aliquando post. Si quis auteim viam obseruandi mo- mentum Æquinoctij scire desideret, videar apud Blancanum pag. 103. & erit voti compos. Cæterum in Æquinoctijs, pi- tuita in hominibus crescere solet vsque ad Virgularum exor- tum in Vere, aut earundem occasum in Autumno. Eoque po- tissimum tempore succosa, acriaque assumi debent, & corpus exerceri. 35. ÆQVILATERVM dicitur corpus, aut siguta geometrica Trian- gularis, Quadrangularis, &c. quæ æqualia habeas latera: Vnde & anguli quos efformant æquales quoque esse conuenit: vt ex quinta propositione lib. 1. Elementorum Euclidis manifestè colli- gitur. 36. AER proptè dicitur tota illa regio quæ est inter sphætâ ignis, & terram: Elementum quidem crassius igne, sed longè inferio- ribus leuius; cuius descriptionem pulchre tradit Seneca in qua- stionibus naturalibus lib. 2. cap. 4. Quicælum, inquit, terram- que connectit, ima, & summa sic separat, vt tamen iungat; sepa- rat, quia medius interuenit; iungit, quia vtrique per hoc consen- sus est. Suprà se dat quidquid accepit a terris; rursus v. m siderum in terrena transfundit. In tres diuiditur regiones ab Arist. 1. 37. Meteor. text. 4. & reliquis Philosophis, supremam, mediam, & infimam. Hæc est quam nos respiramus, & extenditur vsque ad eam partem, quæ ex reflexione solarium radiorum non am- plius incalescit, & in ea generantur ros, pruina, trabes, &c. Media, vbi Meteora omnia efformantur, vt imbres, nuces grandines, &c. & frigidissima est, vt sæpiùs testatur Aristo- teles præsertim 2. Meteor. textu 9. cuius rei ratio est antiperi- stasis, eo quod vndique calore obsideatur; tum quia cum illuc vapotes peruenerint reducunur ad pristinam frigiditatem, adeoque aërem circumfusum infrigidaur: tum denique quia ibi nec reflexio solarium radiotum, vt infetiora, nec feruor ignis elementaris pertingit. Dicitur hæc regio ab aliquibus obscura, 38. ac renebrosa, non quia fortè sit talis, sed quia à dæmonibus inhabitetur, qui sæpissimè inibi coruscationes, imbres, & to- nitrua faciunt, de quibus ait Apostolus. Non est nobis colluctatio aduersus carnem & sanguinem, sed aduersus principatus, & potes- states, contra spiritualia nequitæ in cælestibus, mundi rectores tene- brarum harum. Cur autem huic aëris regioni destinari fuerint huiusmodi Angeli reprobi, explicat Augustinus his verbis. Nunquam Deus quos præciebat futuros malos fecisset, nisi pariter
Transcription: Translated (English)
12 LEXICON when also, but very rarely, in the same points, because of the deviation of the Ecliptic of the eighth sphere from the Ecliptic of the first Mobile, the Ecliptic of the eighth sphere does not always touch the Equinoctial of the first Mobile, in the beginnings of Aries and Libra, but sometimes before, sometimes after. If anyone nevertheless desires to know the way of observing the moment of the Equinox, let him look to Blancanus, p. 103, and he will attain his wish. Moreover, at the Equinoxes, phlegm is wont to increase in men up to the rising of the Virgulae in Spring, or their setting in Autumn. And therefore at that time especially, nourishing and pungent things should be taken, and the body exercised. 35. A SQUARE is said of a body, or a geometric figure, Triangular, Quadrangular, etc., which has equal sides: whence the angles which they form are also rightly equal, as is manifestly gathered from the fifth proposition of book 1 of Euclid's Elements. 36. AIR is properly said of that whole region which is between the sphere of fire and the earth: indeed, a thicker element than fire, but far lighter than the lower elements; whose description Seneca elegantly gives in the Natural Questions, book 2, chap. 4. “The air,” he says, “joins heaven and earth; it separates the lowest and the highest, yet so as still to unite them; it separates, because it intervenes between them; it joins, because through it there is agreement for each. It gives upward whatever it has received from the earth; in turn it pours down the powers of the stars into earthly things.” It is divided into three regions by Aristotle, Met. 1, text 4, and the other philosophers: the highest, the middle, and the lowest. This is the air which we breathe, and it extends as far as that part which no longer grows warm from the reflection of the sun's rays, and in it are generated dew, frost, clouds, and the like. The middle region is where all meteors are formed, such as rains, hailstones, and so forth, and it is the coldest, as Aristotle often testifies, especially in Met. 2, text 9, the reason for which is antiparistasis, because it is everywhere besieged by heat; then because when vapors have come there they are brought back to their original coldness, and thus they chill the surrounding air; and finally because there neither the reflection of the sun's rays, as in the lower regions, nor the heat of the elementary fire reaches. This region is said by some to be dark, 38. and gloomy, not because it may perhaps be such in itself, but because it is inhabited by demons, who most often make there lightnings, rains, and thunder, concerning which the Apostle says: “Our struggle is not against flesh and blood, but against principalities and powers, against the spiritual forces of wickedness in the heavenly places, the rulers of the darkness of this world.” But why such fallen angels were assigned to this region of the air is explained by Augustine in these words: “God would never have made those whom He foresaw would be evil, unless likewise...”
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LEXICON 14 dum accessumque Solis ad nostrum verticem significandum translatum est. Vnde ijs qui sub Æquatore degunt, quia bis in anno Sol accedit ad eorum verticem, in æquinoctijs nempe atque initijs Arietis, & Libræ, ideo binas æstates experiri contingit, binas etiam hyemes, seù potius calores remissiores in eiusdem recessu ad puncta solstitialia. Quod & Plinius tra- didit lib. 6. cap. 17. & nos alibi obseruauimus. Cæterum Æstatis conditiones, ac vices, vide apud Plinium eumdem lib. 2. cap. 38. 45. ÆETHER propriè audit apud Græcos sphæra ignis. Aristoteles verò in libris de Mundo hoc nomine intellexit cæli siderum- que substantiam. Vnde hodie Philosophi Astronomique omnes, Ætherem pro omni eo quod supra aërem elementaremque regionem consistit, accipiunt: proindeque vniuersum mun- dum in elementarem & æthereum dispescunt; atque in ele- mentari collocant elementa ipsa, terram, aquam aërem, &c sphæram ignis (si ea detur) in ætherea verò corpora cæle- stia, siue ea vnum cælum sint siue plures, sidera, planetas, aliaque phænomena, quæ de nouo in cælo generantur. Qua de re vide Argolum in Astronomcis lib. 1. cap. 4. & cap. 17. A F 46. AFETA Heleg. Vitæ dator. Vide Apheta. 47. AFLALEN Græcè pes, alter Geminorum Latine dicitur Stella fixa secundæ magnitudinis de natura Martis, & Mercurij in ca- pite Geminorum præcedentis consistens: Arabicè Auellar. Vn- de nescio qua ratione pes latinè interpretetur ab Hali in Com- mentar. ad Quadrip. Ptolemæi, cum alias extremus pes de na- tura Mercurij, & quartæ magnitudinis proprio nomine Propus appelletur, vt videre est apud Iunctinum in Catalogo stellarum fixarum, qui est in fine Commentarij ejusdem in Sphæram Io. de Sacro-Bosco. 48. AFRICVS ventus occidentalis lateralis Fauonio spirans im- mediatè à brumali occasu, oppositus ditestè Cæciæ, sic dictus, ab Africa, vnde exsufflat. Dicitur etiam Lybicus à Lybia. Na- tura sua frigidus est, & humidus, pluuiosus, & tempestatis in- dex: de quo sic cecinit Manilius. Africus est nimbis creber, creberque procellis. Flatu suo foeminas concipere facit, vt author est Plinius lib. 18. cap. 34. Ex eo cognominati sunt Mesofricus, & Ypafricus collaterales venti de quibus suo loco. AG 49. AGATICHI Græcè, hoc est bona fortuna, appellatur quinta Domus ab Horoscopo succedens angulo imi cæli; eoquia ex ea sumatur significatio de voluptatibus, gaudijs, conuiuijs, libe- ris, &c. respicit de trino Ascendens. Consignificator eius est
Transcription: Translated (English)
LEXICON 14 used to signify the approach of the Sun to our zenith. Hence, for those who dwell under the Equator, because the Sun approaches their zenith twice in a year, namely at the equinoxes and at the beginnings of Aries and Libra, it happens that they experience two summers, and also two winters, or rather milder heats, in its recession toward the solstitial points. This Pliny also recorded, book 6, chapter 17, and we have observed the same elsewhere. Otherwise, see Pliny himself on the conditions and changes of summer, book 2, chapter 38. 45. ÆTHER is properly called among the Greeks the sphere of fire. But Aristotle in his books On the World understood by this name the substance of the heavens and the stars. Hence today all philosophers and astronomers take Æther for everything that exists above the elementary region of air; and accordingly they divide the whole world into the elementary and the aethereal. In the elementary they place the elements themselves, earth, water, air, etc., and the sphere of fire, if such there be; but in the aethereal they place the celestial bodies, whether there be one heaven or several, the stars, planets, and other phenomena newly generated in the sky. On this matter see Argolus in the Astronomica, book 1, chapter 4 and chapter 17. A F 46. AFETA Heleg. Giver of life. See Apheta. 47. AFLALEN, in Greek “foot,” is called in Latin the other of the Twins, a fixed star of the second magnitude, of the nature of Mars and Mercury, situated in the head of Gemini preceding. In Arabic, Auellar. I do not know on what grounds it is translated “foot” in Latin by Hali in the Commentary on Ptolemy’s Quadripartitum, since otherwise the extreme foot, of the nature of Mercury and of the fourth magnitude, is called by its proper name Propus, as may be seen in Junctinus’s Catalogue of the fixed stars, which is at the end of the same Commentary on the Sphere of Io. de Sacro-Bosco. 48. AFRICUS, a western lateral wind blowing immediately from the winter sunset, opposite directly to Cæcias, so called from Africa, whence it blows. It is also called Lybicus from Libya. By nature it is cold and moist, rainy, and an indicator of storms, concerning which Manilius sang thus: Africus is rich in clouds, and rich in storms. By its breath it causes women to conceive, as Pliny is author, book 18, chapter 34. From it are named Mesofricus and Ypafricus, collateral winds, of which in their proper place. AG 49. AGATICHI, in Greek, that is, good fortune, is the name given to the fifth House succeeding the Horoscope, at the angle of the lower heaven; because from it is taken the signification of pleasures, joys, banquets, children, etc.; it regards the Ascendant by trine. Its co-significator is
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MATHEMATICVM. 15 ercurius, qui etiam inibi gaudet similiter. AGOTHODÆMON id est Bonus genius, Græcè audit vndecima 50. nus proximè succedens culmini, ac modò memoratæ op- ita. Ex ea sumitur significatio amicorum, felicitatis, rerum- speratarum. Gaudet in ea Iupiter. AGGLUTINATIO, seù contactus, teste Valla, dicitur quando- 51. : apud Astronomos coniunctio, & conuenientia duarum vel rimum stellarum in eadem parte signiferi: sed præsertim ipitur agglutinatio pro agglomeratione plurium fixarum in im, cuiusmodi sunt Nubeculæ duæ ad polum Antarcticum; iades, nec non omnes stellæ obscuræ, ac nebulosæ, quæ aliud sunt, vt obseruauit nouissimè Galilæus in suo Nuntio reo quam congeries plurium stellarum in vnum conuen- tium, quæ ob nimiam distantiam discerni singillatim non sunt, sed perinde, ac si vna esset se nostris obtutibus ex- pent. AGITATOR idem quod Eriethonius, vel Auriga, fidus ad Bo- 52. dem plagam existens in longitudine sub signo Geminorum. intinet stellas quatuordecim secundum Proloærum, at Ke- rus in eo ponit stellas 27. & Baierus 31. omnes ferè de natu- Martis, ac Mercurij, inter quas vna est insignior primæ gnitudinis in sinistro humero fulgens nomine Hircus. Dux in obscuræ seù potiùs quartæ magnitudinis in vola manus istæ, quæ hædi vulgo audiunt, valdè procellosæ, quippe- r pluuias in ortu suo generant, ventos excitant, & tem- states faciunt, sicut & Hircus. De quo multa Plinius lib. 18. ap. 26. vsque ad 29. Ideoque inimicum Nautis canit Germa- cus. Alia eius significata, vide in V. Auriga. AH AHARPH Saturni dicitur in sphæta barbarica tertius Deca- 53. s Tauri còmpetens Saturno, vnde extrahuntur significatio- s seruitutis, miseriæ, feritatis, necessitatis. AI RICHARD. Arab. Latinè, redditus luminis, & est cum vnsus 54. : plures planetæ transmittunt suum lumen vni tertio, qui ta- :n existat valdè debilis, vt puta retrogradus, vel combustus: :ic enim ob imbecillitatem suam retinere non valens trans- :llum lumen, reddit ipsis planetis immittentibus, seu potiùs :illos recidit lumen, quod alteri transmittebant. AIz, seu vt alij scribunt Alaiz, est conformitas planetæ cum 55. no, in sexu, & conditione temporis vt quando masculinus & arnus, de die est in signo masculino, & suprà terram, &c ontrà foemininus, sit in signo foeminino, & si nocturnus, de iete sit suprà terram. Alij rectius scribunt Haze.
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MATHEMATICUM. 15 Mercurius, who there also rejoices in like manner. AGOTHODÆMON, that is, Good Genius, is called in Greek the eleventh 50. nearest succeeding to the summit, and to the office just men- tioned. From it is taken the signification of friends, felicity, things hoped for. Jupiter rejoices in it. AGGLUTINATIO, or contact, says Valla, is said when-51. ever: among astronomers, conjunction and agreement of two or more stars in the same part of the zodiac: but especially agglutination is taken for an agglomeration of several fixed stars in one place, such as the two little clouds near the Antarctic pole; the Pleiades, as well as all dim and nebulous stars, which are nothing else, as Galileo most recently observed in his Nuncio than a cluster of several stars gathered into one, which, because of excessive distance, cannot be distinguished individually, but appear to our sight as though one thing. AGITATOR, the same as Eriethonius, or Auriga, faithful to Bo-52. the north, standing in longitude under the sign of Gemini. It contains fourteen stars according to Ptolemy, but Ke- pler places 27 stars in it, and Bayer 31, almost all of the nature of Mars and Mercury, among which one is more notable, of first magnitude, shining on the left shoulder, by name Hircus. The Driver is also of the fourth, or rather dark, magnitude in the palm of the hand in those stars, which are commonly called the kids, very stormy, since they produce rains at their rising, stir up winds, and make storms, just as Hircus does. On which much is said by Pliny, book 18, chap. 26 to 29. Therefore Germanicus sings of it as an enemy to sailors. See in V. Auriga for its other meanings. AH AHARPH is said of Saturn in the barbarous sphere, the third Deca-53. of Taurus, belonging to Saturn, whence are drawn significations of servitude, misery, ferocity, necessity. AI RICHARD. In Arabic, in Latin, return of light; and it is when one 54. planet transmits its light to a third, which then exists very weakly, as, for example, retrograde or combust: thus it, being unable by its weakness to retain the transmitted light, returns it to the planets sending it, or rather casts back upon them the light which it was transmitting to another. AIz, or as others write Alaiz, is the conformity of a planet with the Sun, in sex and in the condition of the time, as when masculine and diurnal, it is in a masculine sign, and above the earth, etc.; contrarily, if feminine, it is in a feminine sign, and if nocturnal, by night it is above the earth. Others more rightly write Haze.
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18 LEXICON omnes, & incombustæ, in quibus viilis foret inceptio cuiuscunque operis: inde iterum sequebantur aliæ duodecim horæ infottunatæ, combustæ, & post has aliæ 72. incombustæ ac bonæ vsque ad coniunctionem sequentem. Ratio autem diuisionis est, quod omnes horæ duodecim, quæ dantur soli secundum ordinem planetarum sunt combustæ, & infortunatæ, quæ verò reliquis planetis ascendentes ad summam 72. horarum sunt bonæ, & incombustæ. Et hoc est arcanum inanitatis quod includitur sub hoc Verbo Albuzie, siue Albutem. Qui plura volet videat Alkabitium. 80. ALCANTARVS promiscuè ac Alsedi apud Arabes dicitur Capricorni sidus; de quo vide in V. Capricornus. 81. ALCALFE, vel Alatraph, & Almuredin apud Nubianos dicitur Spica Virginis. 82. ALCHATIS Arabicè, Græcè lencos apud Ptolem. in Quadring. lib. 3. c. 3. ex versione Arabica audit Genitura trium foeminarum in vno pattu, in quam conueniant Venus, Luna & Mercurius? 83. ALCHINIB dicitur dextrum latus planetæ. 84. ALCHETIB Arab. idem sonat, ac virtus, & fortitudo planetæ. 85. ALCHTA DAPHA. Vide in V. Alkia. 86. ALCHINIRA Arab. est idem quod Haye: hoc est, quod Planeta masculinus, & diurnus, de die sit supra terram, & in signo masculino, ac diurno: de nocte verò sub terra. Similiter, quod Planeta foemininus, & nocturnus de nocte sit supra terram, de die sub terra, atque in signo foemino, & nocturno. 87. ALCHITOT Arab. Latinè Clausus, seu vectis teres in medio Astrolabij nectens rete, ac tabulas intra matrem medio alio clauunculo omnia in vnum premente, qui ob formam equi, quam vt plurimum præ se ferr, Latinè Caballus dicitur, Arabicè verò Alpharatz Stoslerin. 88. ALCOBOL. Arab. Latinè idem sonat, ac receptio: sitque cùm Planeta ponderosus, ac tardi motus recipit intra suum orbem alium leuem ad se aduentantem, vt cum eo corpore iungatur. 89. ALCOCODEN siue Alcochoden Arab. dicitur planeta dispositior loci hylegi, ad quem spectat in genituris vitæ prorogatio: iravt qui plures prærogatiuas obtinuerit in dicto loco, is gaudeat Alchocodea virtute, quæ in eo consistit, vt pro sui constitutione valida aut debili in coelesti figura, definiri possit numerus annorum nati. Promdeque si fortis sit in Angulo, in suis dignitatibus, non retrogradus, non combustus. is addat ad vitam nati (quam in genere significat vitæ datur)
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all, and unburnt, in which there would be the beginning of any work: then again there followed another twelve unfortunate hours, burned, and after these others 72. unburnt and good up to the next conjunction. The reason for the division is that all the twelve hours which are given to the Sun according to the order of the planets are burned and unfortunate; but those belonging to the remaining planets, ascending to the total 72. hours, are good and unburnt. And this is the secret of emptiness which is contained under this word Albuzie, or Albutem. Whoever wishes for more, let him see Alkabitium. 80. ALCANTARVS is commonly called, and Alsedi among the Arabs, the sign of Capricorn; see under V. Capricornus. 81. ALCALFE, or Alatraph, and Almuredin among the Nubians is called the Spica of Virgo. 82. ALCHATIS in Arabic, in Greek lencos, according to Ptolemy in Quadring. book 3, ch. 3, from the Arabic translation, is called the Geniture of three women in one womb, in which Venus, the Moon, and Mercury agree? 83. ALCHINIB is called the right side of the planet. 84. ALCHETIB in Arabic means the same as the strength and fortitude of the planet. 85. ALCHTA DAPHA. See under V. Alkia. 86. ALCHINIRA Arab. is the same as Haye: that is, that a masculine and diurnal planet, by day, is above the earth and in a masculine and diurnal sign; by night however below the earth. Likewise, that a feminine and nocturnal planet by night is above the earth, by day below the earth, and in a feminine and nocturnal sign. 87. ALCHITOT Arab. in Latin Clausus, or a round bar in the middle of the Astrolabe fastening the rete and the plates within the mater, pressing everything together with another small pin in the middle, which on account of its form, resembling a horse, as it very often does, is called in Latin Caballus, but in Arabic Alpharatz Stoslerin. 88. ALCOBOL. Arab. in Latin means reception: and it is when a heavy planet, of slow motion, receives within its orb another light one approaching it, so that it may be joined with that body. 89. ALCOCODEN or Alcochoden Arab. is called the planet most fitted to the place of the hyleg, to which in nativities the prolongation of life pertains: thus the one who has obtained the greater prerogatives in the said place, enjoys the Alchocoden virtue, which consists in this, that according to its strong or weak constitution in the celestial figure, the number of the native's years may be determined. And especially if it be strong in an Angle, in its dignities, not retrograde, not burned, it adds to the life of the native (which in general signifies the life given)
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MATHEMATICVM. 19 suos annos maiores: si mediocriter fortis, medios: ac tandem, si debilis minores; aut sanè, si nimium debilis, & afflictus, p[er]t[er]o annis det menses, aut dies. Ad quamrem circumfertur quædam tabella, quam nos, quia gratis effictam existimamus, imò, si verum dicere liceat, totam hanc Alchocoden doctrinam, ideò missam facimus. Qui eius fuerit curiosus, alios consulat. ALCOR Arab. dicitur stellula quædam minima quæ est pro- < 90.> pe mediam è tribus quæ sunt in cauda Vrsæ maioris ab Agri- colis Equitator dicta: estque adeò exilis, vt non nisi ab acutissimis oculis discerni possit. Ex quo ortum vulgare illud Adagium apud Arabes de homine, qui maxima non videt ac negligit, & minutissima quæque perspicit, aut perspexisse se iactat. Vidisti Alcor, sed non Lunam plenam. ALCYONII dies vocantur septem, qui proximè præcedunt < 91.> brumam, aut subsequuntur, qui maximè sereni sunt ac mi- tiores; vnde vulgò Aestas sancti Martini indigitantur. Quod a- deò verum est, vt eo tempore Alcyones aues, vt inquit Pli- nus passeribus paulò grandiores in matis littore ob securita- rem nidificare soleant, quod sanè non auderent, nisi natura dictante pernoscerent maximam tunc temporis instare aëris tranquillitatem; vt profectò ex eorum nidificatione his die- bus sit nomen inditum. Oritur autem hæc serenitas, vt habet Nyphus, eò quia, nimia solis absentia vapores pluuiatiles sur- sum non eleuantur, atque adeò nec pluuiis nec ventis locum turbandi aërem dare queunt. ALDEBARAN Latinè Lampas, seu Oculus Tauri, stella fixa < 92.> primæ magnitudinis ad instar lampadis ardens in oculo austra- li Tauri octau[m] sphæræ, tunc temporis existens in grad. 4. Geminorum, cum latitudine meridiana gr. ferè 3. Vna est ex ijs quæ regiæ dicuntur: verum etiam est ex violentis, cum sic de natura Martis, adeoque volunt Astrologi eam cum Lumi- naribus aut Malescis præsertim in ascendente violentam mor- tem minari. Dicitur etiam Romanis hæc stella Palilitium eo- < 93.> quod olim Romæ eo tempore oriebatur, quo festa Palilia ce- lebrabantur. Qua de re vide Plinium, lib. 18. cap. 26. ALDERAIMIN Arab. Dexter humerus Caphes: stella fixa ter- < 94.> tix magnitudinis de natura Saturni, & Iouis, in gradu ferè 8. Arietus tunc temporis sita cum maxima latitudine boreali; ideoque in nostro hæmispherio nunquam occidens. ALDHAFERA Arab. Latinè Iuba Leonis, stella fixa tertix < 95.> magnitudinis de natura Saturni, & Mercurij; tunc temporis < 96.> existens in gradu fere 23. Leonis. ALFANTIA Vide Alphantia. ALFAZIN Arab. idem sonat, ac frustratio: estque cum pla- B ij
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MATHEMATICVM. 19 their greater years; if moderately strong, the middle ones; and at last, if weak, the smaller; or indeed, if very weak and afflicted, he gives in pertero years months, or days. For this purpose a certain table is circulated, which we, because we think it falsely invented, indeed, if it may be said with truth, dismiss this whole doctrine of the Alchocoden for that reason. Whoever is curious about it, let him consult others. ALCOR, in Arabic, is called a certain very small star which is near the middle one of the three that are in the tail of Ursa Major, called by the farmers the Rider; and it is so slender that it can be distinguished only by the keenest eyes. From this has arisen that common proverb among the Arabs about a man who does not see and neglects the greatest things, and perceives, or boasts that he has perceived, the tiniest things: “You saw Alcor, but not the full Moon.” ALCYONII days are called the seven which most nearly precede the winter solstice, or follow it, and which are especially serene and milder; whence they are commonly called Saint Martin’s Summer. This is so true that at that time the Alcyon birds, as Pliny says, being a little larger than sparrows, are accustomed to build their nests on the sea shore in safety, which certainly they would not dare to do unless, taught by nature, they knew that at that time the greatest calm of the air was at hand; so that indeed from their nesting on these days the name seems to have been given. This serenity arises, as Nyphus says, because, owing to the sun’s long absence, the rainy vapors are not lifted upward, and thus neither rains nor winds can find a place to disturb the air. ALDEBARAN, in Latin Lampas, or the Eye of Taurus, a fixed star of the first magnitude, burning like a lamp in the southern eye of Taurus, the eighth sphere, then being at the 4th degree of Gemini, with a southern latitude of almost 3 degrees. It is one of those called royal; but it is also one of the violent, since it is of the nature of Mars, and therefore astrologers say that, with the luminaries or malefics, especially in the ascendant, it threatens a violent death. This star is also called by the Romans Palilitium, because in ancient times at Rome it rose at the time when the festival of the Parilia was celebrated. On this matter see Pliny, book 18, chapter 26. ALDERAIMIN, in Arabic, the right shoulder of Cepheus: a fixed star of the third magnitude, of the nature of Saturn and Jupiter, then situated at about the 8th degree of Aries, with the greatest northern latitude; and therefore never setting in our hemisphere. ALDHAFERA, in Arabic, in Latin the Mane of Leo, a fixed star of the third magnitude, of the nature of Saturn and Mercury; then being at about the 23rd degree of Leo. ALFANTIA See Alphantia. ALFAZIN in Arabic means the same as frustration: and is with the pla- B ij
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LEXICON neta alteri applicans coniunctione, manensque intrà sphæram lucis illius, interim fit retrogradus, & sine suo frustratur: est genus quoddam debilitatis, quod in maleficis semper in bonum cedit. 97. ALFRECCA siue Alphabet dicitur Arabicè Lucida in Corona Gnossia hoc est aperitio, ea enim exoriente tellus aperitur, & flores germinat. In tabulis Persicis dicitur Piramis, vel Pinacis hoc est pupilla, & sertum pupillæ. Est Stella splendidissima secundi honoris de natura Veneris & Mercurij. De qua vide plura in V. Corona Gnossia. 98. ALFELTA item Stella fixa in Dracone ad polum arcticum de natura Veneris & Mercurij: alio nomine Foca. 99. ALFRIDARIE, seu Fridaria, vel Ferdaria apud Arabes est quædam temporaria potestas, quam sibi arrogant Planetæ super vitam Nati, quæ à decenniorum dispositione parum differre videtur. Quandoquidem quilibet Planeta habet quandam determinatam, ac definitam temporis periodum, super quam disponit; vtpote Sol in natiuitate diurna gubernat vitam nati cum aliorum planetarum participatione, spatio anno- rum decem, sed ipse primus sibi vendicat septimam partem suorum annotum, nempe annum vnum solarem, menses quinque & dies circiter quatuor: Deinde intrant in eius dominij participationem cæteri planetæ per ordinem sequentes, singuli per septimam pariem. Quod, quia vanum est, atque à bonis omnibus deridetur, lubens omitto. 100. ALGEBAR fixa in sinistro Orionis pede. Vide Rigel. 101. ALGEBRA Arab. est certa regula de occulta numerorum parte, tam absolutorum, quam respectiuorum cognoscenda; qua de re erudite scripserunt Claius, & Nicolaus Tartalea 102. ALGEBRAATAR Arab. Latinè Diuisor, seu Dominus terminorum, in quibus incidit Directio, aut Profectio annua; apud Persas Zamoctar dictus. Estque is cui competit dominium finium, intà quos comprehenduntur certi quidam gradus singulorum signorum Zodiaci siue ad mentem Ptolemæi siue Ægyptiorum, quorum diuisio magis probarur à Professoribus, atque à Titis in sua Cælesti Philosophia eorum ratio elacidatur. Eius inuestigatio ex Arabum schola talis est: Ascensionibus obliquis Horoscopi adjice annos fluentes, dando singulis annis gradam ferè vnum ( eo modo quo explicabimus sub V. Directio) & aggregatum, reiecto si opus fuerit integro circulo, reperiatur in tabulis primi mobilis sub eleuazione poli tuæ regionis; nam gradus Zodiaci illi respondens erit terminus, in quem incidit Directio; & Planeta Dominus illius termini
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LEXICON by applying to another through conjunction, and remaining within the sphere of that light, meanwhile it becomes retrograde, and is frustrated without its own force: it is a certain kind of debility, which in malefics always turns to good. 97. ALFRECCA, or Alphabet, is called in Arabic Lucida in Corona Gnossia, that is, an opening; for at its rising the earth opens, and sprouts flowers. In the Persian tables it is called Piramis, or Pinacis, that is, the pupil, and the garland of the pupil. It is a most splendid star of the second rank, of the nature of Venus and Mercury. Concerning which see more in V. Corona Gnossia. 98. ALFELTA likewise a fixed star in Draco near the arctic pole, of the nature of Venus and Mercury: by another name Foca. 99. ALFRIDARIE, or Fridaria, or Ferdaria among the Arabs is a certain temporary power, which the Planets arrogate to themselves over the life of the Native, and which seems to differ little from the disposition of decennials. For each Planet has a certain determined and defined period of time over which it governs; namely, in a daytime nativity the Sun governs the life of the native together with the participation of the other planets, in a space of ten years, but it first claims for itself the seventh part of its years, namely one solar year, five months and about four days: then the other planets enter into participation of its dominion in order following, each by a seventh part. Which, because it is vain, and is mocked by all good men, I willingly omit. 100. ALGEBAR fixed in the left foot of Orion. See Rigel. 101. ALGEBRA, Arab., is a certain rule for knowing the hidden part of numbers, both absolute and relative; concerning which Clavius and Nicholas Tartaglia wrote learnedly. 102. ALGEBRAATAR, Arab. In Latin, Divider, or Lord of terms, in which Annual Direction or Profection falls; among the Persians called Zamoctar. And it is he to whom belongs dominion over the bounds within which are comprehended certain degrees of the individual signs of the Zodiac, whether according to Ptolemy’s or the Egyptians’ method, whose division is more approved by the Professors, and in Titius in his Celestial Philosophy their reasoning is clarified. Its investigation from the Arab school is this: to the oblique ascensions of the Horoscopium add the flowing years, giving to each year about one degree (in the manner explained under V. Direction), and the aggregate, after rejecting an entire circle if necessary, shall be found in the tables of the first mobile under the elevation of the pole of your region; for the degree of the Zodiac corresponding to it will be the term, into which the Direction falls; and the Planet Lord of that term
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111. LEXICON Prætereà ipso cum Sole ex oriente, vt notat Plinius, tota Na- tura reparitur, canes aguntur in rabiem, fluctuant in dolijs vina, febres ardentes grassantur, & maximos calores experi- mur, vt proptereà solemne omnibus obseruare sit dies ab eo dictos Caniculares. Est nunc in gradu 9. Cancri cum latitudine australi gr. ferè 40. Otitur tamen Romæ cum gr. 8. Leonis circa Kalendas Augusti. 112. ALHABOR item vocatur teste Strofoetino, clauus Astrola- bij, timpana, & rete in vnum intra Matrem nectens. 113. ALHAISETH, teste Baiero vocatur ab Hermete spica Vir- ginis, stella fixa, primæ magnitudinis: Arabicè Alimech. 114. ALHANTICA sine Alphantia dicitur Arab. Armilla suspen- soria astrolabij. Sicut &c 115. ALHADIDA appellatur Ostensor seu, quam vulgo vocant linea fiducia, Græcis Dioptra in medio Astrolabij sita, & ad limbum vsque protracta ad venandas stellarum altitudines, & cuiuscunque loci ascensiones rectas, aut descensiones. 116. ALHIRTO Arab. dicitur rostrum Gallina, stella fixa tettiæ magnitudinis de natura Veneris, & Mercurij, existens in gr. 26. Capricotni cum maxima latitudine boteali. Non longè ab hac Stella, anno 1600. apparuit aliud nouum Phænomenon, quod durauit vsque ad annum 1621. quo euanuit linguens ta- men loco suo quendam hiatum, qui vt testatur Argolus, ad hæc vsque tempora cernitur. 117. ALIBD Arab. idem sonat, ac Latinè deterioratio, & est cùm Planeta in cælesti themate reperitur in domibus cadenti- bus, quales sunt tertia, sexta, nona, & duodecima, in quibus multum deteriotatur. Sicut econtrà 118. ALICHEL, hoc est, profectus Planeta, dicitur quando est in Angulo, vel succedentibus, vbi mirum in modum proficit, & eius vis duplicatur. Qua de re vide quæ diximus suo loco. 119. ALICORAB, seu Alichorad idem est, ac Latinè contrarietas. Quod euenit, cùm aliquis Planeta leuis fuerit multotum gra- duum in signo, & alter illo ponderosior in paucioribus: ter- tius quoque leuior vadens ad coniunctionem ponderosi: sed antequam corpore iungantur, ille, qui primus in pluribus gra- dibus existens potius à ponderoso videbatur patate discessum, sit retrogradus, ac per ponderosum transiens, post coniun- ctionem cum eo iungitur etiam tertio leuiori, & sic destruitur coniunctio, quam ille, vt ita dicam, moliebatur cum poderoso. 120. ALICTISAL, seu Ictisal Arab. idem sonat, ac Latinè appli- catio, & est cum planeta leuis existens in coniunctione platica alterius ponderosi, vadit ad eius coniunctionem partilem, Econtrà
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111. LEXICON Moreover, with the Sun itself rising from the east, as Pliny notes, all nature is renewed; dogs are driven to madness, wines ferment in the casks, burning fevers prevail, and we experience the greatest heats, so that for this reason it is customary for all to observe the days called Canicular. It is now at 9 degrees of Cancer, with southern latitude of about 40 degrees. However, at Rome it is at 8 degrees of Leo around the Kalends of August. 112. ALHABOR is also called, according to Strofoetin, the pin of the astrolabe, joining the tympana and the rete into one within the mater. 113. ALHAISETH, according to Baier, is called by Hermes the ear of Virgo, a fixed star of first magnitude; in Arabic, Alimech. 114. ALHANTICA, or Alphantia, is called in Arabic the suspensory armilla of the astrolabe. And so forth. 115. ALHADIDA is called the pointer, or what is commonly called the fiducial line, the Greek Dioptra, situated in the middle of the astrolabe and extended to the limb, for seeking the altitudes of stars and the right ascensions or descensions of any place. 116. ALHIRTO, in Arabic, is called the beak of the Hen, a fixed star of the fifth magnitude, of the nature of Venus and Mercury, located at 26 degrees of Capricorn with maximum boreal latitude. Not far from this star, in the year 1600, there appeared another new phenomenon, which lasted until the year 1621, when it vanished, leaving nevertheless in its place a certain gap, which, as Argolus testifies, can still be seen to this day. 117. ALIBD, in Arabic, has the same meaning as deterioration in Latin, and it is when a planet is found in a celestial figure in cadent houses, such as the third, sixth, ninth, and twelfth, in which it deteriorates greatly. Likewise, conversely 118. ALICHEL, that is, the progress of a planet, is said when it is in an angle or in succedent houses, where it advances in a marvelous way, and its force is doubled. On this matter, see what we have said in its proper place. 119. ALICORAB, or Alichorad, is the same as contrariety in Latin. This happens when one planet is lighter by many degrees in a sign, and another, heavier than it, by fewer degrees; likewise a third lighter planet going toward conjunction with the heavier one: but before they are joined in body, the one who first existed in more degrees, and who seemed to be moving away from the heavier one, becomes retrograde, and, passing through the heavier one, after the conjunction is also joined with the third lighter one, and thus the conjunction is destroyed, which, so to speak, it was trying to form with the heavier one. 120. ALICITSAL, or Ictisal, in Arabic, has the same meaning as application in Latin, and is when a lighter planet existing in platick conjunction with another heavier one goes toward its partile conjunction. Conversely
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MATHEMATICVM. 23 ALINCIRAF idem est, ac separatio: cum videlicet planeta 111. leuis separaturà conunctione partili alterius ponderosi; sed tamen adhuc est in platica, hoc est intrà quantitatem orbis illius. ALIOT, Latinè equus. Eo nomine appellant promiscuè 122. Arabes singulas trium stellarum quæ sunt in cauda Vrsæ Ma- ioris, eoquia præseferunt quasi tres equos ex ordine dispositos ad trahendum Plaustrum. ALKAIR, siue Alkis, Aquila, Vulcur volans, Stella fixa se- 123. cundæ magnitudinis de natura louis, & Martis existens in gr. ferè 27. Capricorni cum gr 30. latitudinis borealis. ALKIA DAIHA Latinè idem sonat, ac pulsatio virutis: & 124. est cùm Planeta existens in suis dignitatibus respicit tardio- rem, qui nullam dignitatem habeat in loco alterius: tunc enim iste velocior pulsat, & mirit propitiam virtutem ad tardio- rem. Vide in V. Pulsatio. ALKINDVS, seu Dominus Ascone, est Cometæ species ad 125. instar Cornu (vnde & nomen hausit) de natura Mercurij, cum cauda oblonga coloris cerulei. ALKINIRA, Vide Alchinira. 126. ALKIREM Arabicè dicitur locus præcedentis luminarium 127. conunctionis ad inuestigandum quis totius illius lunationis dominium sortiatur. Sicut etiam ALLVRE dicitur cardo ipse interluniorum. Eo potissimum 128. verbo vtitur Author Centiloquij secundum versionem Ara- bicam Hali Rodoan præsertim propos. 46. sicut & præceden- tis meminit in propositione 58. ALMAGSTVM. Sic intitulatur Liber magnæ constructio- 129. nis Ptolemæi ex Arab. Al quod significat ordo, & Græco Megiston, vel Ægyptio Megasice quod maximum, atque per- fectum sonat. Opus planè diuinum, ac singulare in quo tota sphæricorum doctrina traditur, & explicatur. ALMANACH apud Arabes idem sonat, ac Latinè numeratio, 130. vel distribuo: ab radice Hebræa Mach, quod distribuit, seu numerauit, significat. Hinc apud Astronomos annotationes, & computationes cælestium motuum in dies singulos, quas Græce Ephemerides dixere, Almanach trito iam vel apud ipsum vulgus vocabulo audiunt. Eoque potissimum titulo Astrolo- gorum libri, in quibus astrorum motus, eclipses, aspectus planetarum, & alia huiusmodi oculis exhibentur, gaudent. ALMANAR Arab. idem sonat, ac supereminent a, & præ- 131. ponderauo vnius Planetæ super alium: Nos eluationem, seù Altitudinem dicimus Arabes tunc dicunt alicui planetæ com- petereius Almanar super alium, quando is fuerit situ emi- B itij
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MATHEMATICVM. 23 ALINCIRAF is the same as separation: namely, when a light planet is separated from the partile conjunction of another, weightier one; yet it is still in the platic, that is, within the quantity of that orb. ALIOT, in Latin, horse. By that name the Arabs indiscriminately call the three individual stars which are in the tail of Ursa Major, because they appear, as it were, like three horses arranged in order to draw the Wain. ALKAIR, or Alkis, Aquila, flying Vulture, a fixed star of the second magnitude, of the nature of Jupiter and Mars, situated at about 27 degrees of Capricorn, with 30 degrees of northern latitude. ALKIA DAIHA in Latin sounds the same as pulsation of virtue: and it is when a planet existing in its dignities regards a slower one, which has no dignity in the place of the other: then this swifter one strikes, and imparts a friendly virtue to the slower one. See in V. Pulsation. ALKINDVS, or Dominus Ascone, is a kind of comet in the likeness of a horn (whence also it takes its name), of the nature of Mercury, with an oblong tail of blue color. ALKINIRA, see Alchinira. 126. ALKIREM is said in Arabic to be the place of the preceding luminaries' conjunction, in order to investigate who shall obtain the rulership of that whole lunation. Likewise ALLVRE is said to be the very hinge of the interluniums. The Author of the Centiloquium uses this word especially in the Arabic version of Hali Rodoan, particularly proposition 46, as he also mentions the preceding in proposition 58. ALMAGSTVM. So is entitled Ptolemy's Book of the Great Construction, from the Arabic Al, which signifies order, and the Greek Megiston, or the Egyptian Megasice, which sounds as maximum and perfect. A truly divine and singular work, in which the whole doctrine of the spherics is handed down and explained. ALMANACH among the Arabs has the same sense as, in Latin, numeration or distribution: from the Hebrew root Mach, which means to distribute or to number. Hence among astronomers the annotations and computations of the heavenly motions for each day, which the Greeks called Ephemerides, are commonly known even among the common people by the name Almanach. And for that reason the books of astrologers, in which the motions of the stars, eclipses, aspects of the planets, and other such things are displayed to the eye, bear especially that title. ALMANAR, in Arabic, has the same sense as supereminence, and the preponderance of one planet over another: we say elevation, or altitude; the Arabs then say that a planet has Almanar over another when it has been situated emi- B itij
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LEXICON expositionem Hali, cum Planeta leuis existens in coniunctione partili alterius qui sit eo ponderosior, per motum suum separatur ab eo; reperitur tamen adhuc platicè configuratus, hoc est intra quantitatem lucis illius orbis. 146. ALOSAH Arab. idem ac Vindemiaror, Stella secundæ magnitudinis in Ala septemtrionali Virginis, teste Argolo in Pandosio Sphærico. 147. ALPHANTIA Alhantica Latinè Armilla suspensoria in Astrolabio. 148. ALPHARD seu Alpharad, dicitur item Arab. Cor Hydræ, Stella fixa primæ magnitudinis Ptolemeo, at secundum alios secundæ, de natuta Saturni & Venetis in medio Hydræ existens in longitudine gr. ferè 23. Leonis. Hæc vna est ex illis stellis, quas D. Thomas opus 28. art. 4. funereas dixit, ac monstruosam in icare vita terminationem, quippequæ cum sit natutæ mixtæ ex contrarijs qualitatibus, saturninis tamen prædominantibus, affert secum humotum corruptionem, si in horoscopo reperiatur, præsettim cum malo radio Veneris, aut Saturni, & si fuerit cum Anæreta statim eius qualitatibus imbutur, & portendit sæpè venenum, vt volunt Astrologi. Propterea antiqui illi obseruatores, ad eius naturam posteris explicandam, Hydræ, venenosi scilicet monstri, nomen, ac figuram illi dederunt. 149. ALPHECCA, siue Alphelta. Vide Alfecca. 150. ALPHERATZ, siue Alpharatz Arab. Latinè dicitur Muscida equi. Stella fixa tertiæ magnitudinis de natura complicata Martis, Louis, & Veneris, existens in gr. 27 Aquatij cum latitudine maxima boreali. Item & Ens[us] Alpharatz, & Marchab Alpharatz aliæ duæ stellæ secundæ magnitudinis de natura Martis, & Mercurij in scapulis, ac dextro humero Pegasi existentes, & circa grad. 20. Piscium. De ea in alicuius ortu occidente cum malefica, aut malo eius radio, sic cecinit Pontanus in Vrania. Executis, aut currulacerum, aut è calce cruentum, Aut dorso eietum stigmas deturbat ad vndas. 151. ALPHETA Arab. dicitur lucida Coronæ Gnossiæ stella fixa splendid illima secundæ magnitudinis de natura Veneris, & Mercurij existens nunc in gr. 7. Scorpij cum grad. 44. latitudinis borealis. Hæc ob sui venustatem, ac pulchritudinem dicitur Cæli pupilla, settum, flos, neque in Genethliacis ab hac significatione aberrat, facit enim natum delicijs deditum, mollem, flores, & vnguenta tractantem, vt propterea de ea in alicuius horoscopo reperta sic venustè cecinerit Pontanus in Vrania.
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LEXICON exposition of Hali, when a light planet, existing in a partial conjunction with another that is the more ponderous, is separated from it by its own motion; yet it is still found platically configured, that is, within the quantity of the light of that orb. 146. ALOSAH, Arab. the same as Vindemiaror, a star of the second magnitude in the northern Wing of Virgo, as testified by Argolus in the Sphærical Pandosion. 147. ALPHANTIA, in Latin Alhantica, the suspensory ring in the Astrolabe. 148. ALPHARD, or Alpharad, is likewise called by the Arabs the Heart of Hydra, a fixed star of the first magnitude according to Ptolemy, but according to others of the second; of the nature of Saturn and Venus, existing in the middle of Hydra, in longitude about 23 degrees of Leo. This is one of those stars which St. Thomas, in work 28, art. 4, called funerary, and a monstrous termination in life’s course; for since it is of a mixed nature from contrary qualities, yet with Saturn predominating, it brings with it corruption of humors, if it be found in the horoscope, especially with an evil ray of Venus or Saturn; and if it be with the Anareta, it is at once imbued with its qualities, and often portends poison, as astrologers will have it. Therefore those ancient observers, to explain its nature to posterity, gave it the name and figure of Hydra, that is, of the poisonous monster. 149. ALPHECCA, or Alphelta. See Alfecca. 150. ALPHERATZ, or Alpharatz, Arab. in Latin it is called Muscida equi. A fixed star of the third magnitude, of the mixed nature of Mars, Jupiter, and Venus, existing in 27 degrees of Aquarius, with greatest northern latitude. Likewise En[s]us Alpharatz, and Marchab Alpharatz, two other stars of the second magnitude, of the nature of Mars and Mercury, existing in the shoulders and right shoulder of Pegasus, and about 20 degrees of Pisces. Concerning it, when in someone’s nativity it sets with a malefic, or with its evil ray, Pontanus sang thus in Urania. Executis, aut currulacerum, aut è calce cruentum, Aut dorso eietum stigmas deturbat ad vndas. 151. ALPHETA, Arab. the bright star of the Gnossian Crown is called, a fixed star most splendid of the second magnitude, of the nature of Venus and Mercury, existing now in 7 degrees of Scorpio, with 44 degrees of northern latitude. Because of its grace and beauty it is called the eye of heaven, the threshold, the flower, nor does it fail in Genethliacs in this signification; for it makes one given to pleasures, soft, handling flowers and unguents, so that therefore, if found in someone’s horoscope, Pontanus thus beautifully sang of it in Urania.
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MATHEMATICVM. Stella sub hac natis studium manet dulcium odorum: Conficiunt vnguenta, & florea sarta coronant. Mundicies indignæ viro, comptusque puella Persimilis: quaque & Veneris molle imperat Astrum. Inde etiam occulus sub pectore pasciur ignis, In vetitumque ruunt, & amor noua vincula nectit. Quocirca Nate ardentes compesc furores, Et leges meditare, & honesti concipe formam. De ea verò in occasu reperta cum Saturno, aut malo eius ra- dio, mox subdit. Exponit Natum feris damnante senatu, Pro tumulo sauces canum, aut rabida ora leonum Accipient, tumulo Saturnus condet vbi ipse Insedit loca, primo sub flore iuuenta. Prætereà sidus hoc, vt author est Plinius, est valde tem- <152:> pestuosum, quo cum Sole occidente Venti excitantur, pluuix ingruunt, & ronitrua; similiter oriens cum eodem Sole facit acrem frigidum, rurbidum ac ventosum, cum Saturno autem adducit adhuc nuius, pro temporis qualitate, aut ad minus tempus frigidum, ac nebulosum. Oritut autem Romæ cum gradu 16. Libræ, occiditque cum decimo nono gradu Ca- <153.> pricorni. ALRAMECH, siue Alkameluz Arab. Arcturus, hoc est gla- dius & pugio Bootis, Stella fixa informis primæ magnitudinis prope clunes Bootis existens, atque in longitudine in gr. 19. Libræ cum gr. 31. latitudinis borealis: naturam habet mix- tam Iouis, & Martis. Plinius vocat hoc sidus horridum, eo- quia cum Sole occidens tempestates facit, & ventos australes fascitat. At verò in Generhliacis, inquit Pontanus in Vrania, quod addicit natos infami supplicio, vel etiam parat infelici carcere mortem, si occidat cum prauo radio Saturni, vel Mar- tis. At verò in exortu facit sidelem, veri amatorem, cui cre- dentur opes, & pretiosa regum supellex, vel etiam erit custos forium, inrimusque cubicularius. Addit Sadius, quod cum Ioue dat diuitiarum affluentiam, at cum Saturno earundem profligationem minatur. ALRVKABA Arab. Latinè Stella polatis Cynosura in extremo <154.> caudæ Visæ minoris sita, secundæ magnirudinis de natura Ve- neris, & Saturni, existens nunc temporis in gr. 24. Geminorum cum latitudine boreali gr. 66. adeoque omnium vicinissima polo Arctico, cum ab eo non distet nisi tres gradus. Obidque & Phœnice quoque appellata est, eoquod à Phœnicibus nautis plurimum obseruabarut: eum enim non adhuc com- perta esset vittus acus magneticæ, ideo ipsi ex hac Stella nosce-
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MATHEMATICVM. Under this star there remains the study of sweet odors for those born: they make unguents, and with flowers they crown garlands. Unseemly cleanliness for a man, and adornment very like a girl; and in every way the gentle star of Venus rules. Hence also the fire beneath the breast is fed, and they rush into what is forbidden, and love weaves new bonds. Therefore, child, restrain your burning passions, and meditate on the laws, and conceive the form of what is honorable. Concerning it, however, found in the west together with Saturn, or with his evil ray, he immediately adds: He explains that the child, condemned by a savage senate, will receive for a tomb the jaws of dogs, or the rabid mouths of lions; then Saturn will place him in a tomb where he himself has settled, in places first under the flower of youth. Moreover, this star, as Pliny states, is very stormy; when it sets with the Sun, winds are stirred up, rain falls, and thunder; similarly when it rises with the same Sun it makes the air bitter, cold, muddy, and windy; with Saturn, however, it brings more snow, according to the quality of the season, or at least cold and cloudy weather. It rises at Rome with the 16th degree of Libra, and sets with the 19th degree of Capricorn. <152:> ALRAMECH, or Alkameluz in Arabic, Arcturus, that is, the sword and dagger of Bootes, an ill-formed fixed star of the first magnitude, situated near the buttocks of Bootes, and in longitude at 19 degrees of Libra with 31 degrees of northern latitude; it has a mixed nature of Jupiter and Mars. Pliny calls this star “horrid,” because when setting with the Sun it makes storms and stirs up southern winds. But in the Genethliacs, says Pontanus in Urania, it assigns those born an infamous punishment, or even prepares death in an unhappy prison, if it sets with the evil ray of Saturn or Mars. Yet at its rising it makes one trustworthy, a lover of truth, to whom riches and the precious household goods of kings are entrusted; or else he will be a guardian of doors and a faithful chamberlain. Sadius adds that with Jupiter it gives an abundance of wealth, but with Saturn it threatens the destruction of the same. ALRVKABA, in Arabic; in Latin, the Pole Star Cynosura, situated at the very end of the tail of Ursa Minor, of the second magnitude, of the nature of Venus and Saturn; it is now in 24 degrees of Gemini with 66 degrees of northern latitude, and thus the nearest of all to the Arctic pole, since it is not distant from it by more than three degrees. For this reason it was also called Phoenice, because it was greatly observed by Phoenician sailors; for before the use of the magnetic needle had yet been discovered, they used to know from this star
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28 LEXICON bant, vbi consisterent, quò iter instituere deberent, quantumve a loco re nori essent. Hius influxus ab Astronomis minimè obseruantur, quippe qui si quos habeat, semper ijsdem sunt, cum semper eodem ferè loco consistat, & nullius penè sit motus, vnde pro loci, & sirus qualitate in influendo varieratem 155 aliquam subire possit. Hæc stella, inquit Ioannes Christmannus in obseruationibus solaribus, aliquando in ipsum polum recider cum singulis annis accedat ad polum arcticum, & declinationem acquirat secundoru[m] viginti: vnde cum tempore Hipparchi, hoc est annis abhinc retrò 1700. absuetit à polo gr. 12. & min. 24. & nunc currente anno à partu Virginis 1660. non disser nisi gr. 2. & min. 31. manifestum sit ipsam tandem anno ab incarnatione Domini 2125. debere in ipsum polum incidere. Ricciolus tamen tomo primo almagesti noui lib. 6. cap. 19: probl 5. in ea est sententia, vt nunquam, neque ipsa stella polaris, neque vlla alia assequutura sit adamussim Mundi polum. Quia, inquit, vt hoc assequeretur, deberet habere tantum latitudinis, quantum est complementum distantiæ polorum ab initio Cancri, ratione obliquitatis Eclipticæ, quæ in sententia ipsius deberet esse gr. 66. min. 30 oporteret ergo stellam istam non habere latitudinem maiorem gr. 66 min. 31. nec minotem gr. 66. min. 8. Sed quandonam, subdit, hæ conditiones concurrent simul, vt stella hæc sit in principio Cancri, in ipso tempore, quo ob variationem obliquitatis Eclipticæ, latitudo stellæ sit æqualis præcisè complemento obliquitatis, seù distantiæ? Latitudo autem stellæ polaris nunc est gr. 66. min. 2. Numquam ergo fuit, vel erit in ipso Mundi polo, etiamsi maximè sit ad illum necessura, & peruentura ad Cancri initium iuxta Tychonicum calculum anno 2092. & tunc distabit à mundi polo secundis septem: postea ab illo recedere incipiet. Hæc Ricciolus, dicens se olim deceptum authoritate Regiomontani; putasse hanc stellam assecuturam ipsum Mundi polum, sed postea re melius considerata, sententiam in melius commutasse. 156. ALTALISIM Arab. stella fixa secundæ magnitudinis de natura Iouis & Saturni posita in ipsa effusione aquæ Aquarij proximè Fomahand stellæ insigniori priuæ magnitudinis, cui contermina est alia stellula eiusdem naturæ & qualitatis ab Arabibus dicta Calbez. 157. ALTANI dicuntur Venti subterranei altè à terra spirantes, qui si in mare (è cuius regione semper exsufflant) progrediantur, Apogæi; si verò è mari ad terram reuertantur, Tropæi appellantur; de quibus vide Plinium, lib. 2. cap. 43. 158. ALTITUDO apud Astronomos idem significat, ac Exaltatio
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28 LEXICON bant, at which they would stop, by what route they ought to travel, or how far they were from the place. This influx is hardly observed by Astronomers, since if they have any influence at all, it is always the same, because they remain almost always in the same place and have scarcely any motion, so that according to the quality of the place and the sign they may undergo some variation in influence. This star, says Ioannes Christmannus in solar observations, sometimes falls as far as the pole itself, since each year it approaches the Arctic Pole and acquires a declination of twenty seconds: whence, from the time of Hipparchus, that is, 1700 years ago, it has moved away from the pole by 12 degrees and 24 minutes, and now, in the current year of the Virgin’s birth 1660, it differs by only 2 degrees and 31 minutes; it is therefore manifest that at last, in the year of the incarnation of the Lord 2125, it must fall into the pole itself. Ricciolus, however, tom. primo almagesti noui lib. 6. cap. 19: probl 5, holds the opinion that neither the pole star itself nor any other star will ever reach exactly the pole of the World. For, he says, in order to attain this it would need to have so much latitude as is the complement of the distance of the poles from the beginning of Cancer, by reason of the obliquity of the Ecliptic, which in his opinion ought to be 66 degrees 30 minutes; therefore that star would need not to have a latitude greater than 66 degrees 31 minutes nor less than 66 degrees 8 minutes. But when, he adds, will these conditions occur together, so that this star be at the beginning of Cancer at the very time when, by reason of the variation of the obliquity of the Ecliptic, the latitude of the star is exactly equal to the complement of the obliquity, or of the distance? The latitude of the pole star is now 66 degrees 2 minutes. Therefore it was never, nor will it ever be, at the very pole of the World, even if it is most near and approaching to it, and coming to the beginning of Cancer according to the Tychonic calculation in the year 2092, and then it will be seven seconds distant from the pole of the world; afterward it will begin to recede from it. Thus Ricciolus, saying that he was once deceived by the authority of Regiomontanus; that he had thought this star would reach the pole of the World, but later, the matter having been better considered, he changed his opinion for the better. 156. ALTALISIM, Arab. a fixed star of the second magnitude, of the nature of Jupiter and Saturn, placed in the very effusion of the water of Aquarius, near Fomahand, a more notable star of the first magnitude, beside which lies another little star of the same nature and quality, called by the Arabs Calbez. 157. ALTANI are called subterranean winds, blowing high from the earth, which if they move into the sea, from whose region they always blow, are called Apogæi; but if they return from the sea to the land, they are called Tropæi; concerning which see Pliny, book 2, chapter 43. 158. ALTITUDE among Astronomers signifies the same as Exaltation
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MATHEMATICVM. 29 accipitur pro vna ex quinque dignitatibus essentialibus, quas obtinent planetæ in signis, estque secunda in ordine post Domicilij prærogatiuam. Etenim in Zodiaco sunt quædam loca, in quibus constituri planetæ peculiares effectus, eosque potentiores, atque efficaciores in inferioribus hisce pro- ducunt. Huiusmodi autem præcipuè sunt Domus, & Altiru- dines: Cuius rei rationem rationabilemque distributionem ingeniosè affert Ptolemæus in primo Quadrip. cap. 17. Sol, in- quit, quia in Ariete incipit ad verticem nostrum accedere, at- que altior fieri, calor eius augescit, dies noctibus incipiunt præualere; ideo in Ariete exaltari oportet, atque aliquam di- gnitatem, quam altitudinem dicimus, obtinere. Luna cum Sol est in Ariete ipsi coniuncta, incipit è radijs eius emerge- re, atque aliquatenus apparere cum est in Tauro; vnde in Tauro conuenit exaltari. Similiter discurrendum in alijs Pla- netis: Nisi quod Ptolemæus ponit Planetam exaltari in toto signo, Arabes verò in certo gradu signi, vt verbi gratia Sol in gradu 19. Arietis, Saturnus in gr. 21. Libræ, Iupiter in gr. 15. Cancri, & sic de singulis. Cuius quidem placiti, neque vllam afferunt rationem, neque experimentum. Nihilominùs id obseruare, superuacaneum forte non erit. Porrò in quo signo potissimum quisque Planeta exaltetur, & signatè in quo gra- du iuxta Arabum placita dicemus in V Exaltatio. ALVEHEZIT Arab. idem sonat, ac stella cadentes: sunt enim < 159.> species quædam accensionum metheorologicarum in aere factæ, quæ significant siccos vapores. Hali Rodoan in Com- ment. ad Quadrip. Ptolemai. ALYNTHIÆ signum, teste Hali in Commentar. ad propos. < 160.> 31. Centiloquij est signum revolusionis anni, in quod videli- cercadunt Ascendens, alijque significatores in puncto annuæ Revolutionis. ALZIMON, quod interpretatur fusus corrupto apud Nubia- < 161.> nos, & Feczanos, vocabulo, dicitur spica Virginis, stella, de quasæpè incidit sermo. AM AMBLYGONIVM apud Geometras est figura triangularis, < 162.> quæ habearangulum vnum obtusum; in quo differ ab Oxy- gonio, quod habere debet omnes tres angulos acutos. Differt etiam ab æqualatere, quia cum istud habere debeat omnes an- gulos æquales, necessario deberet esse omni ex parte obtu- sangulum; quod ex Euclide propos. 17. &c, 2. primo libro, fieri non potest. Benè tamen amblygonium potest esse vel Isosceles, vel scaleum; si aut duo æqualia habeat latera, modò terrium vtrouis æqualium maius sit; aut omnia latera iuxæqualia sint,
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MATHEMATICVM. 29 is taken as one of the five essential dignities, which planets hold in the signs, and it is second in order after the prerogative of the Domicile. For there are in the Zodiac certain places in which the planets, when established there, produce special effects, and those more powerful and more efficacious in these lower things. Such are especially the Houses and the Exaltations. The reason for this, and its rational distribution, Ptolemy ingeniously gives in the first Quadripartitum, chap. 17. The Sun, he says, because in Aries it begins to approach our zenith and to become higher, its heat increases, and the days begin to prevail over the nights; therefore it ought to be exalted in Aries, and to obtain some dignity, which we call altitude. The Moon, when the Sun is in Aries and conjoined to it, begins to emerge from its rays and to appear somewhat when it is in Taurus; hence it is fitting that it be exalted in Taurus. Likewise one must reason concerning the other planets: except that Ptolemy places a planet as exalted in the whole sign, whereas the Arabs place it in a certain degree of the sign, as for example the Sun in the 19th degree of Aries, Saturn in the 21st of Libra, Jupiter in the 15th of Cancer, and so of each. For this opinion they give neither any reason nor any experiment. Nevertheless, it may perhaps not be superfluous to observe it. Moreover, in which sign each planet is most especially exalted, and specifically in which degree according to the Arabs’ opinion, we shall say under V Exaltatio. ALVEHEZIT, in Arabic, means the same as “falling stars”: for they are certain kinds of meteorological ignition in the air, which signify dry vapors. Hali Rodoan in his Commentary on Ptolemy’s Quadripartitum. ALYNTHIÆ sign, as Hali testifies in his Commentary on proposition 31 of the Centiloquium, is the sign of the year’s revolution, into which evidently the Ascendant and the other significators fall at the point of the annual revolution. ALZIMON, which in corrupted usage among the Nubians and Fezzans is interpreted as “spike,” is called the star of Virgo, of which mention is often made. AM AMBLYGONIUM, among geometers, is a triangular figure which has one obtuse angle; and in this it differs from the Oxygonium, which must have all three angles acute. It also differs from the equilateral, because since that ought to have all angles equal, it would necessarily have to be obtuse-angled on every side; which, according to Euclid, proposition 17 and following, in the first book, cannot be done. Yet an amblygonium can be either isosceles or scalene; if it has two equal sides, provided only that the third is greater than either of the equal ones; or if all its sides are unequal,
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LEXICON 33 modò angulorum inæqualium, quos efformare necessariò debet, vns sit obtusus, & reliquis omnibus maior. Sed de hac re vide sub Verbis Angulus, & Triangulus. 163. AMFROCKACIATOR Græcè, siue Arfocarazjeutu Arabicè, apud Ptolem. lib. 3. Quadrip. cap. 8. ex versione Arab. Hali, significat hominem occulta penetrantem, hoc est, qui ex certa cælorum positione satidicum spiritum sortiatur, atque arcana patefaciat, & vera pronuntiet. 164. AMNIMODAR apud Astronomos est Planeta rectificator Genitutæ, seù potiùs est via quædam rectificandi natalitium Thema, & inueniendi artificiosè gradum, præcisè Horoscopantem tempore editi foetus, à Ptolemæo inuenta, per constitutionem Planetæ obtinentis dominium in proximè præcedenti Luminarium coniunctione, vel oppositione. Cùm enim principale fundamentum in Genethliaca facultate, (quod artis sustentaculum iure nominat Ptolemæus) sit indagare quisnam gradus Zodiaci adamussim incidat in lineam orientalem in puncto, quo editur infans; idque difficile admodum sit obtinere siue ab hotologijs ob eotum varietatem, siue ab alijs instrumentis ob multas, quas inuoluunt difficultates, itavt vel minima variatio notabilem temporis differentiam importet, hæcque etiam multum iudicium Natiuitatis, quod totum ab gradu horoscopante pendet variare possit; ob id necessarium erat viam quandam certam, stabilem, ac naturæ principijs, rationi, atque experimentis consentaneam inuenire; qua ex Ascenstonu[m] doctrina ad datam proximè horam auspicari possimus, quisnam gradus reuera ascendat in Horoscopo cum foetus in lucem editur. Quam viam approbat etiam D. Thomas opusc. 28. art. 4 in responsione ad secundum, dum de hora natiuitatis sermonem iniens sic loquitur. Quia hora talis difficulter cognoscitur, ideò inuentum est remedium, vt accipiatur gradus ascendens circulæ, hoc est hora coniunctionis Luminarium, cui adaquatur circulus; quia ille habet influentiam ad communem necessitatem quæ proximè sequitur, vel accipiatur ascendens ad natiuitatem ex vtero. Hæc autem Ptolemæo alijsque antiquis Astronomis melior non eluxit, quam considerando habitudinem Planetæ prædominantis ad ptæcipuos coeli cardines: siquidem iugi obseruatione compertum est, sidera quæ præsunt nouilunijs, ac plenilunijs, maximas semper vires obtinuisse in tota illa lunatione, ac potissimè in generationibus rerum, vt non complementum habeant nisi cum Planeta totius lunationis dispositor inuenitur in situ mundi fortis & efficax ad dandum tebus edendis impulsum. 165. Hic enimusèo definite cuinam Planetæ competat rectifi-
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LEXICON 33 in the manner of unequal angles, which he must necessarily form, one shall be obtuse, and greater than all the rest. But on this matter see under the words Angulus, and Triangulus. 163. AMFROCKACIATOR, in Greek, or Arfocarazjeutu in Arabic, according to Ptolemy, lib. 3. Quadrip. cap. 8, from the Arabic version of Hali, signifies a man who penetrates hidden things, that is, one who from a certain position of the heavens obtains a divining spirit, and reveals secrets, and pronounces true things. 164. AMNIMODAR among Astronomers is the rectifier of the Nativity, or rather it is a certain method of rectifying the natal Theme, and of artificially finding the degree exactly horoscopic at the time of the birth of the child, invented by Ptolemy, through the constitution of the Planet holding dominion in the nearest preceding conjunction or opposition of the Luminaries. For since the principal foundation in the Genethliacal art, which Ptolemy rightly calls the support of the art, is to investigate which degree of the Zodiac falls precisely upon the eastern line at the point where the infant is born; and since this is very difficult to obtain, whether from horologies because of their variety, or from other instruments because of the many difficulties they involve, so that even the smallest variation may bring about a notable difference of time, and this also may greatly vary the judgment of the Nativity, which depends wholly on the horoscopic degree; for this reason it was necessary to find a certain, stable way, consonant with the principles of nature, reason, and experiments; by which, from the doctrine of Ascensions, we may from the given nearest hour ascertain which degree truly ascends in the Horoscope when the child is brought into the light. This way is also approved by St. Thomas opusc. 28, art. 4, in the reply to the second, when, beginning to speak of the hour of nativity, he says thus: Since such an hour is difficult to know, therefore a remedy was devised, namely that the ascending degree of the circle be taken, that is, the hour of the conjunction of the Luminaries, to which the circle is adjusted; because that has an influence on the common necessity which follows next, or the ascendant at the birth from the womb may be taken. But this did not appear to Ptolemy or the other ancient Astronomers more clearly than by considering the relation of the predominant Planet to the principal angles of the heaven: for by continual observation it has been found that the stars which preside over new moons and full moons always obtained the greatest power in that whole lunation, and especially in the generation of things, so that they do not have completion unless the Planet dispositor of the whole lunation is found in a position of the world strong and effective for giving impetus to the things to be brought forth. 165. Here it remains for us to determine to which Planet the rectifi-
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51 LEXICON nis; Planeta autem rectificans sit Venus, quæ in Natiuitate reperiatur in gr. 10. Geminorum; tunc, quia 10. sunt propinquiores tribus, quam 28. corrigitur gradus medij Coeli, locando in eo 10. gr. Leonis, sicque ad rationem eius constructa sit more solito cælestis figura locando in Ascendente 29. gr. Libræ &c. Quodsi Venus habeat 24. Geminorum totidem gradus Libræ constituantur in Ascendente, & sic reliquæ domorum cuspides per signa & gradus his gradibus per ascensionum doctrinam respondentes. Addunt alij, quod quando Planeta rectificans in suis gradibus est nimium distans à gradibus medij Coeli, vel Ascendentis, tunc rectificatio instituenda est per gradum Antiscij sui intuentis, vel imperantis, aut obedientis, prodireque etiam exactam, atque accidentibus congruam rectificationem. 168. Verum hic rectificandi modus, nisi meliùs instituatur, nec rationi, neque experimentis accommodari potest. Nam primò sequeretur, vt quando Planeta rectificator est nimium ponderosus, (quales ferè semper sunt Saturnus, & Iupiter) aut fuerit stationarius, vel errogradus, in quo statu insensibiliter mouetur in Zodiaco, ij omnes, qui in vna eademque lunatione nascerentur, deberent eundum gradum ascendentem habere, aut cælum culminans, si non in signo, saltem in numero graduum, quod est ridiculum. Deinde quæ proportio, quæ habitudo Planetæ rectificantis ad cardines, per hoc quod in numero tantum concordent, si non adsit alia congruentia, aut respectus? Quodsi dicas adesse in Antiscio, vel in aspectu in debita distantia, qui à numero ad numerum est partilis: ergò vbi saltem non erit familiaritas, & aspectus, (vt in signis inconjunctis) inanis prorsus euader hæc sola numerorum proportio. Præterquamquod radij ad Cardines accepti in partibus Zodiaci inanes reperiuntur, vt eruditè probat Titus in Cælesti Philosophia. 169. Quapropter ex Ptolemæi mente (vt ipsemet Titus obseruat in Breuiarijs ad Quadrupart.) accipienda est proportio sideris rectificantis ad cardines per aspectus in mundo in partibus proportionalibus domorum; ita vt sidus rectificans constituatur in cælesti figura in tanta distantia à cardinibus mundi accepta in partibus proportionalibus sui arcus, vt eorum aliquem, præcipuè verò Ascendentem respiciat aliquo radio, aut etiam sit in eius centro. Tali enim modo consideratus forris inuenitur, & efficax ad dandum impulsum foetui, vt emergat ex vtero, sibique arroget partum. Quæ proinde rectificatio multis experimentis probata inuenitur exacta, atque accidentibus apprimè cougrua: Sic enim in exemplo dato, si Venus planeta
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51 LEXICON nis; but let the rectifying planet be Venus, which in the Nativity is found in 10° Gemini; then, because 10° are nearer to 3 than 28, the degree of the Midheaven is corrected, placing in it 10° Leo, and thus, to this ratio being constructed in the usual manner, let the celestial figure be made by placing in the Ascendant 29° Libra, etc. But if Venus has 24° Gemini, let the same degrees of Libra be placed in the Ascendant, and so the remaining cusps of the houses by signs and degrees corresponding to these degrees according to the doctrine of ascensions. Others add that when the rectifying planet in its degrees is too distant from the degrees of the Midheaven, or of the Ascendant, then the rectification is to be established by the degree of its Antiscion, of the looking-on, or commanding, or obeying, and that it will even produce an exact rectification, fitting the accidents. 168. Yet this mode of rectifying, unless it is established more properly, can be accommodated neither to reason nor to experience. For first it would follow that when the rectifying planet is too heavy, as are almost always Saturn and Jupiter, or if it were stationary, or retrograde, in which state it moves imperceptibly in the Zodiac, all those who were born in one and the same lunation ought to have the same degree ascending, or the culminating heaven, if not in the sign, at least in the number of degrees, which is ridiculous. Then what proportion, what relation does the rectifying planet have to the angles, by this that they agree only in number, if no other congruence or relation is present? And if you say that this is present in the Antiscion, or in aspect at the proper distance, which from number to number is partial: therefore where at least there will not be familiarity, and aspect, (as in unconjoined signs) this sole proportion of numbers will become utterly empty. Besides, the rays taken to the Angles in the parts of the Zodiac are found to be empty, as Titus proves learnedly in Celestial Philosophy. 169. Wherefore, according to Ptolemy’s mind, as Titus himself observes in Breviaries to Quadrupart., the proportion of the star rectifying to the angles is to be taken through aspects in the world in proportional parts of the houses; so that the rectifying star is placed in the celestial figure at such a distance from the angles of the world, taken in proportional parts of its arc, that it may regard some one of them, especially the Ascendant, by some ray, or even be in its center. For in this way, when considered outside, it is found, and effective for giving an impulse to the fetus, so that it emerges from the womb and lays claim to the birth. This rectification therefore, proved by many experiments, is found exact and most fitting to the accidents: thus indeed in the example given, if Venus the planet
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MATHEMATICVM. 17. aneta rectificans reperiatur in octaua domo cum 10. gradibus eminorum, debet ita constitui, vt vel sit in media distantia ter Octauam, & Nonam, vnde emittat radium sesqui quatu[m] tum ad Ascendens, vel in cuspide nonæ domus, vnde ittit trinum, vel sanè in cuspide Octauæ, vnde emittit se ta m ad Culmen; idque pro maiori vicinitate, aut congruencum accidentibus Nati, corrigendo videlicet gradum do- is, vnde emittitur radius per gradum & præsentiam parti- n ipsius Planetæ rectificantissicque ad rationem eius nouam uram erigendo. Quod si hac in re, vnde ars tota dependet meam quoque 17. rentiam proferte non sit inuerecundum, eam submissè pro- am aliorum judicio examinandam, corrigendamque. Ita- e in hoc negotio rectificationis formam, non per gradum ineræ rectificantis (nisi fortè is angulum possideat) sed per proportionalem eius distantiam à cardinibus Mundi vnde ittat radium ad eorum aliquem instituerem. Deinde à mu- re rectificandi nullum Planetam excluderem, nisi fortè com- stum, aut ita sub Solis radiis existentem, vt jure censeatur ptus. Siquidem eius tunc vires à Sole sua potentia absumunt, qui proinde in eius locum subintrat, vt omnes communi- asserunt, in Planetarum combustione: in quo tantum casu em ipsum eius loco sufficerem, secundariò tamen, & per idens, per hoc quod gerit vices Planetæ predominantis, eius- veluti substitutus consideraretur, Cæterùm Luminaria ipsa se primò, & principaliter ad hoc munus assumere non pro- em ex communi ratione superiùs tacta, quòd ea sint gene- res rerum significatores. At verò quod aliàs Planeta rectifi- is sit dejectus, aut retrogradus, non videtur officere, quo nus in hanc rectificandi Prouinciam assumi possit. Nam, n hæc rectificatio, vt dictum est, per aspectum ad cardines ituenda sit retrogradatio Planetæ, esse in suo detrimentos casu, impertinens est ad hoc negotium: siquidem ea est io proprij motus in Zodiaco; aspectus autem ad cardines sit à partibus Zodiaci, sed à domibus per proportionalem antiam ab ipsis cardinibus acquisitam motu primi mobiliss, er partes sui arcus diurni, aut nocturni. Siue igitur sit velox Zodiaco, siue tardus, retrogradus, aut directus parum re- , cùm ad cardines Mundi æquè se habeat, vt possit probè orum aliquem suos radios proijcere. 178. imiliter, quod sit in suo detrimento, vel casu, aut etiam nico radio ab aliis infestatus, facit solùm quòd is naturam m peruertat, ac malignetur; Minimè verò, quòd non dem efficientiam æquè benè habere possit ad cardines,
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MATHEMATICVM. 17. If the rectifying planet be found in the eighth house with 10 degrees of the signs, it ought to be so placed that it may either be in the middle distance between the Eighth and Ninth, whence it may emit a sextile ray to the Ascendant; or in the cusp of the ninth house, whence it casts a trine; or indeed in the cusp of the Eighth, whence it emits a square to the Midheaven; and this according to greater proximity, or in agreement with the accidents of the native, correcting, namely, the degree of the house whence the ray is emitted, by the degree and presence of the part of the very planet being rectified, and so raising it to the measure of its new position. But if in this matter, on which the whole art depends, it should not be improper to state my own opinion as well, I submit it modestly to the judgment of others to be examined and corrected. Thus, in this matter of rectification, I would establish the form not by the degree of the luminary rectifying it (unless perhaps it possess an angle), but by its proportional distance from the angles of the world, whence it emits a ray to one of them. Next, from the number of the planet to be rectified I would exclude none, unless perhaps it be com- bust, or so situated under the rays of the Sun that it may rightly be judged combust. For then its powers are consumed by the Sun’s own potency, who therefore enters into its place, as all commonly assert in the combustion of planets: in which case alone I would substitute the Sun himself in its place, yet secondarily and by consequence, because he bears the function of the predominating planet, and thus would be considered as it were a substitute. Moreover, the Luminaries themselves I would not first and principally assume for this office, for the common reason stated above, namely that they are general significators of things. But as for a planet rectified in another respect, that it be depressed or retrograde does not seem to hinder its being taken into this business of rectification. For, since this rectification, as was said, must be performed by aspect to the angles of the world, the planet’s retrogradation is to be in its detrimental state, and is irrelevant to this business; for that is a variation of proper motion in the Zodiac, whereas aspect to the angles is not from the parts of the Zodiac, but from the houses, through the proportional distance acquired from the very angles by the motion of the first mobile, through the parts of its diurnal or nocturnal arc. Whether therefore it be swift in the Zodiac, or slow, retrograde, or direct, it matters little, since in relation to the angles of the world it is equally fitted, so that it may properly cast its rays to one of them. 178. Similarly, that it be in its detriment, or fall, or even assailed by an adverse ray from others, only causes that it may pervert and malign its nature; but by no means that it cannot have efficient power equally well in relation to the angles,
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MATHEMATICVM. 35 ommorationem, ac longè suauiorem, quam in toto Ital[i]æ actu: tantum abest vt vera sint, quæ de ijs locis dixere Poëtæ is oras esse ex nimio æstu prorsus inhabitabiles. Huiusmodi nt Incolæ aureæ Chersonesi, Insula S. Thomæ medium In- læ S. Laurentij, Sumarra, Maldiuiæ, aliæque regiones, pro- videre est in mappis Mundi. Et hi cum Polos habeant hori- onti adjacentes, nec vnum altero elatiorem, inde est, vt nnes stellas conspiciant, atque istæ æqualiter semper orian- t, & occidant. AMPHORA dicitur vndecimum ab Ariete signum. Vide < 176.> quarum. AMPLITUDO Ortiua apud Astronomos (idem dic de occi- < 177.> na) est latitudo, seu differentia ortus, & occasus stellæ, aut iusslibet partis coeli à Græcis ortus, & occasus æquatoris in prizonte, & vnde Sol oritur, & occidit initio Veris, & utumni. Quæ quidem semper æqualis est cum occidua, & uò maior fuerit hæc differentia ortus, & occasus, eò maior scitur Amplitudo, maiotque aut minor arcus diurnus. AMPORIM Græcè vocat Ambrosius miram illam Maris < 178.> fundationem reciprocationemque motus, quam integro die :quatuor momenta variat, fluctuatque quod ideò hunc mo- m nos vulgò fluxum, & refluxum maris vocamus. Contin- t enim præsertim in Oceano Atlantico atque in Mari supe- r, seu Adriatico, vt per ferè sex horas aquæ intumescant, ad tus decurrant, & augeantur: mox vicissim per sex alias horas creescant, retrocedant, ac minuantur. Huius motus recipro- tio vt omnium oculis obuia est, ita intellectus omnis aciem æstringit adeò, vt eius causam nemo adhuc Philosophorum muerit: Quinimò constans de eorum Principe fama est, quod um diu in huius abditissimi arcani speculatione fatigatus ma- is ac magis intricaretur, in morbum inciderit; ac tandem esperatione adactus in Euripum se præcipitem dedetit altiùs oc inclamans O Mare cum te capere non possum, tu me exci- : Possidonius cum Trabone, Solino, Mela, & communiori philosophantium schola eam in Lunæ motum refundit. Quo- nim tempore (inquit Possidonius apud Sætabonem) Luna Hori- mentem ascenderit, Mare ad terram ascendere incipit, quousqua l Cælo medium ipsa conscenderit: ubi verò declinare fidus ipsum perit, sensim ruriùs à terra pelagus ad medium mare delabessur, nec ad Occidentis punctum Luna descenderit: poste à mane rursus scendit quousque sub tellurem in medio, & imò coeli sit Luna: unde Mare à litore ad medium maris regredessur, quoad iterum una ad Orientem procedas, & eleuetur rursusque mare terras fluas. Hucusque Possidonius. Quod vel inde confirmari po- C ij
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MATHEMATICVM. 35 abode, and far more pleasant than in all Italy; so far are those things from being true which the Poets have said of those places, namely that their shores are altogether uninhabitable because of excessive heat. Of this kind are the Inhabitants of the Golden Chersonesus, the Island of St. Thomas at the middle of the Island of St. Laurence, Sumatra, the Maldives, and other regions, as may be seen in the maps of the world. And since these have poles adjacent to the horizon, and neither one higher than the other, it follows that they see all the stars, and that those stars always rise and set equally. AMPHORA is called the eleventh sign from Aries. See <176.> of which. AMPLITUDE of rising among the Astronomers (the same can be said of setting) is the latitude, or difference of the rising and setting of a star, or of any part of the heaven from the Greeks; the rising and setting of the equator in the horizon, and whence the Sun rises and sets at the beginning of Spring and Autumn. This is always equal to the setting amplitude, and the greater this difference of rising and setting is, the greater the Amplitude is known to be, and the greater or smaller the diurnal arc. AMPHORIM, in Greek, Ambrosius calls that wonderful founding and reciprocal motion of the sea, which over the whole day varies through four moments, and ebbs and flows; for this reason we commonly call this motion the flux and reflux of the sea. It happens especially in the Atlantic Ocean and in the Upper Sea, or Adriatic, so that for nearly six hours the waters swell, flow in, and increase; then in turn for six other hours they decrease, recede, and diminish. Although the reciprocity of this motion lies before the eyes of all, it so strains every mind’s power of understanding that no one of the philosophers has yet discovered its cause. Indeed, there is a constant report about their leader that, when he had long wearied himself in the investigation of this most hidden secret and was becoming more and more entangled, he fell ill; and at length, driven to despair, he threw himself into the Euripus, crying out in a louder voice, O Sea, since I cannot grasp you, you catch me! Posidonius, with Strabo, Solinus, Mela, and the more common school of philosophers, refers it to the motion of the Moon. “At the time,” says Posidonius apud Sætabonem, “when the Moon has risen above the horizon, the sea begins to rise toward the land, until it itself has ascended to the middle of the sky; but when that star begins to decline, the sea gradually descends again from the land to the middle of the sea, nor has the Moon descended to the point of the West; then in the morning it rises again until the Moon is beneath the earth in the middle and at the very bottom of the sky: hence the sea recedes from the shore to the middle of the sea, until again the Moon advances to the East, and is elevated, and the sea once more floods the lands.” Thus far Posidonius. Which may even be confirmed from that C ij
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LEXICON test, quia tota ista reciprocario in quatuor, vt dixi momenti parres tribura, horarum quinque supra viginti spatio absolui- tur; vna videlicet hora supra integrum diem naturalem; quan- ta est Luna periodus, & circumuolurio, donec ad eam coeli positionem, in qua pridie erat, reuertatur: siquidem ipsa mo- tu proprio ex Occidente in Orientem quindecim circiter gra- dus contra motum primi mobilis nititur, & retrocedit in vno die: quæ retrocessio facit, vt ferè per horam circuitum suum retardet, donec idem punctum teneat, quod Sol sua revolutio- ne facit spatio 24. horarum. Plinius, alijque, præsertim recen- tiores non modo ad Lunam, sed & ad Solem hunc motum re- ferunt. Obseruatunt enim in eorum aspectibus quadratis, aquas penè immobiles permanere: at vetò in coniunctionibus, & oppositionibus maximos fieri, & citissimos fluxus refluxusque. Cuius rei causam affert Molerus lib. 2. Isag. 8. ad Ephemer. Quia, inquit, quando Luminaria fuerint coniuncta dum mouentur mo- tu primi mobilis per quartam fluxus, mare velocissimè fluit, dum mouentur per quartam refluxus mare citissimè refluit, dum Lumi- naria sunt opposita; eo quia dum unum mouetur per quartam flu- xus, alterum etiam per quar:am oppositam huc fertur, ideò velo- cissimè aqua fluit, vel restuit. Dum Luminaria quadrata radiatio- ne se conspicunt, quia dum alterum est in Oriente, reliquum in Meridie, vel sub, vel supra terram, & hac duo puncta sunt fluxus, & refluxus, quia ab aqualibus potentiis aqua ad contrarias partes fertur, ideò immobilis permanet, hac de causa in quadraturis Lu- minarium nullo ferè mouetur motu. Hæc ille, docens subinde quarras Orientalem diurnam, quæ est à puncto Orientis ad punctum Meridiei, & illi oppositam Occidentalem, quæ est à puncto occasus ad Lineam imi coeli esse quartas fluxus eò quia Luminaria elogantur à terra & properam ad Lineam Meridia- nam: sicur etiam reliquas duas esse refluxus, quia à Meridiano elonganrrur, & terræ approximantur ad circulum horizontis. Verum & hic motus pro locorum diuersirare ac Marium positu ad Lunam, adhuc varius est in ipsis Luminarium quadraturis, aut coniunctionibus, vel oppositionibus; cum Mediterraneum, quod Italiam alluit, aut nullum, aut tam exiguum habeat flu- xum, & refluxum, vt minimè obseruari queat. Similiter Ocea- nus Australis, qui est proximus Mexico, Cubæ Insulæ, & aliis partibus Americæ nullum patitur æstum. E contra ma- gnus deprehenditur in Mari Siculo: adhuc maior versus Sep- tentionem, vt in Anglia, Hollandia, & Noruegia, & ma- ximus in fræro Magellanico, aliisque regionibus Occidenta- lioribus: vt proinde difficile admodum sit huius diuersitatis ra- tionem reddere. Cæterum ex triplici capite euenire potest hæc
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LEXICON test, because this whole reciprocity in four, as I said, is completed in a span of twenty-five hours; namely, one hour beyond the full natural day; such is the period and revolution of the Moon, until it returns to that position of the heavens in which it was the day before. For by its own motion from West to East it advances and recedes about fifteen degrees in a day against the motion of the first mobile, and this recession causes it to delay its circuit by nearly an hour, until it holds the same point which the Sun makes by its revolution in the space of 24 hours. Pliny and others, especially more recent writers, refer this motion not only to the Moon, but also to the Sun. For they have observed that in their quadrate aspects the waters remain almost motionless; but in conjunctions and oppositions there are the greatest and swiftest flood and ebb tides. Molerus gives the cause of this matter in lib. 2, Isag. 8. ad Ephemer. Because, he says, when the luminaries are conjoined while they move by the motion of the first mobile through the quarter of flood tide, the sea flows most swiftly; when they move through the quarter of ebb tide, the sea ebbs most swiftly; when the luminaries are opposite, because while one is moving through the quarter of flood tide, the other is also carried through the opposite quarter, therefore the water flows or ebbs most swiftly. When the luminaries regard one another by square aspect, because while one is in the East the other is in the South, or beneath or above the earth, and these are two points of flood and ebb, since the water is drawn toward contrary parts by equal powers, therefore it remains motionless; for this reason in the quadratures of the luminaries there is scarcely any motion at all. Thus he teaches that the eastern daily quarter, which is from the point of East to the point of South, and the western quarter opposite to it, which is from the point of setting to the line of the lower heaven, are quarters of flood tide, because the luminaries are removed from the earth and approach the meridian line; likewise that the other two are of ebb tide, because they are removed from the meridian and brought nearer to the circle of the horizon. Yet even here this motion, because of the diversity of places and the position of seas in relation to the Moon, is still variable even in the quadratures, conjunctions, or oppositions of the luminaries; since the Mediterranean, which washes Italy, has either no tide at all, or so slight a one that it can scarcely be observed. Likewise the Southern Ocean, which is nearest to Mexico, the island of Cuba, and other parts of America, suffers no tide. On the other hand, a great one is found in the Sicilian Sea; greater still toward the north, as in England, Holland, and Norway; and greatest in the Strait of Magellan and other more westerly regions: so that it is extremely difficult to give an account of this diversity. Moreover, this may arise from three causes
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MATHEMATICVM. 57 aris vicissitudo, vt optimè obseruat Titus in Cælesti Philosop[hi] alib[us] 1. cap. 20. Primò per motum localem aquarum con- trentium a locis vbi minuuntur ad loca, in quibus augentur: hoc modo contingeret, vt Luminaria attaheerent aquas aris suis radiis tanquam bibulis; dum instar spongiiæ mira- li suetu eas secum attrahunt quousque ad lineam Meridianam rgunt: deficere verò cum ab ea elongantur, & ad horizontem properant. Secundò, quod fiat in Mari vera augmentatio uarum, vel diminutio per veram productionem, & consum- ionem, quod nequit intelligi quomodo tam breui temporis atio in tanta aquarum copia fieri possit. Tertiò, quod im- aratâ substantia aquæ fiat rarefactio in accessu, & condensa- ex recessu luminarium ad Meridiem, siue ex calore, siue alia occulta qualitate: quemadmodum videmus in Ther- oscopiis instrumentis non ita pridem inuentis ad venandum locus, vel dies sit altero calidior, vel frigidior: posita enim ua in ampulla vitrea collo valde oblongo, & in superiori par- orisicij bene obturato, si locus fuerit calidior, aqua magis cendit in collo vasis, eò quia calor ambiens illam rarefacit: si rò fuerit frigidior, aqua descendit, eò quia frigus ambiens am condensat. Et hoc modo existimauit ipse Titus accidere ne Maris fluxum, atque refluxum. Tandem Arabes quos < 180.> am sequuntur multi ex recentioribus Astronomis hunc flu- m, & refluxum Maris aliud non esse putant, quam simpli- n motum aquæ ad motum vniuersiratis, vt nos dicemus in Aqua, quo vniuersa supra ipsam motu primi mobilis rapiun- t ab ortu ad occasum: qui tamen morus in aqua vtpote mo- lium omnium etassiore atque à p[er]timo mobili remorissima dissimus est, quippe q[ui]a ratione distanriæ, & propriæ graui- is magis resistit dato impulsui, quàm aër; hic magis, quàm hæraignis; hæc insuper magis quàm orbis Lunæ, & sic de iquis: Vnde maior est, & velocior aquæ motus sub æqua- e, quàm extrà, quia eriam ipse æquator vtpote magis à lis distans plus itineris facit, quàm reliquæ pattes Cæli: sed hac re iterum recurret sermo. Interim hic præterite nolo od ex Arist[otele] tradit Plinius; nullum nempe Animal, nisi in ris refluxu expirare: idque obseruatum ait in Oceano Gal- o, & solùm in homine. Quod tamen falsum arbitratur Bo- us. Verum Leuinus Lemnius de miraculis Natura lib. 4. c. 1. nij dictum improbare non audet, aircque solùm se obseruasse quos in Oceani accessu obiisse: & præsertim notat in mari- o Belgij tractu obæsos æstu accedente periclitari: contrà les, & macilentos in maris recessu faciliùs emori. Cuius rei sam aliam esse non arbitror, nisi quia cum Luna per access- C iii
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The alternation of the sea, as Titus observes very well in his Cælestis Philosophia , book 1, chapter 20, is explained first by the local motion of waters that run together from places where they are diminished to places where they are increased: in this way it would happen that the luminaries would attract the waters by their rays, as if by thirsty mouths, while like a sponge they draw them miraculously with themselves until they reach the meridian line; and that they would fail when they are drawn away from it and hasten toward the horizon. Secondly, that there is in the sea a true increase or decrease of waters by real production and consumption, which cannot be understood, since so great a change in so short a time could not be made in such a vast quantity of water. Thirdly, that an alteration of the substance of the water takes place, namely rarefaction on the approach, and condensation on the recession of the luminaries toward the south, either from heat or from some other hidden quality; just as we see in thermoscopes, instruments not long ago invented to discover whether a place or a day is warmer or colder than another: for if water is placed in a glass vessel with a very long neck, and the upper part of the orifice well stopped, if the place is warmer the water rises more in the neck of the vessel, because the surrounding heat rarefies it; if it is colder, the water descends, because the surrounding cold condenses it. And in this manner Titus himself thought that the ebb and flow of the sea occur. Finally, the Arabs, whom many recent astronomers follow, think that this flux and reflux of the sea is nothing other than a simple motion of the water in accordance with the motion of the universe, as we shall say in the section on Water, by which all things above it are carried by the motion of the first mobile from east to west; yet this motion in water, since it is the slowest of all motions and furthest removed from the first mobile, is very sluggish, because by reason of distance and its own gravity it resists the given impulse more than air does; air more than fire; fire again more than the sphere of the Moon, and so on: hence the motion of water is greater and swifter under the equator than outside it, because even the equator itself, being farther from the pole, makes a longer journey than the remaining parts of the sky; but on this matter we shall return again later. Meanwhile, I must not pass over what Pliny reports from Aristotle: namely, that no animal expires except during the ebb of the sea; and he says that this was observed in the Gallic Ocean, and only in man. This, however, Bochart judges to be false. But Levinus Lemnius, in De miraculis Naturae , book 4, chapter 1, does not dare to reject Pliny’s statement, and says only that he has observed some die at the incoming of the ocean; and especially notes that in the sea region of Belgium the obese are endangered by the incoming tide, whereas the lean and thin more easily die during the recession of the sea. I do not think there is any other reason for this, except that when the Moon is with the incoming tide...
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MATHEMATICVM. 39 orum non sit vitam abscindere, sed potiùs prorogare: Vnde us ad summum erit qualitatem Mortis decernere. Positâ unâ viæ Moderatrice Solis corpus dicitur interimere: sed id on facile admitterem, nisi forte esset nimium natura & qualitibus malesicorum imbutus: sic nec Mercurium, cùm sit valde debilis ex eadem ratione qua Apheta esse non potest. Plura ud Argolum de diebus criticis. ANALEMMA apud Astronomos Instrumentum Gnomonim est ad Solis vmbras venandas accommodatum instar sphæræ, quod potissimùm inseruit ad horologia Solaria describendi. Bernard. Baldus. ANAPHORA Græcè audit secunda Domus, quasi Parta In- ni, quæ proximè succedit Primæ infra terram; eò quod pertis veluti folibus Solem, aliaque sidera ad lineam Orientam detrudat ac peruehat. Ex ea sumunt Astrologi iudicium de abstantia, ac bonis, quæ propria industria, non ex hæredtra proueniunt: adeoque judicatur felix; estque qualitatis fri- idæ, & humidæ. ANAPHORÆ item vocantur ab aliquibus promiscuè domus accedenies, videlicet secunda, Quinta, Octava, & Vndecia; sicut è contra Casaphora cadentes ab angulis, quales sunt ertia, Sexta, Nona, & Duodecima. ANAPHORÆ etiam appellantur Ascensiones obliquæ signo- m per analogiam ad prædicta: sicut è contrario. ANAPHYSEMATA ex Apuleio in lib. de Mundo vocant ræci eos spiritus, qui de fundo vel hissibus terræ expelli ad iperna Maris solent. Nos communiori vocabulo sed ex Græ- sis similiter derivato Apogæos vocitamus. ANATOLAS dicitur Cardo ipse Orientis, quasi superata nebrarum densitate, lucem tandem aperiat. De eo vide plura IV. Horoscopus. ANAVBARACH apud Arabes est inanis quædam ipsorum ob- ruatio super Nouenarias Planetarum, de qua multa habent Ichabitius, & eius Commentator Ioannes de Saxonia. Itaque spiciendum docent quantum inambulauerit Planeta ex gra- ibus, & minutis in signo, vel domo cuius inquisitur Noue- aria: deinde diuidendum præcipiunt totum signum in nouem artes, dando cuilibet parti tres gradus, & minuta viginti, & idendum in quamnam partem ex istis ceciderit gradus Plane- s, aut Domus, cuius ediscere voles Nouenariam. Quo pax- ito, volunt dandam esse primam diuisionis partem Domino gui mobilis eiusdem triplicitatis, & secundam partem Do- mino sequentis signi; & sic per ordinem procedendo, quous- ue peruemiatur ad illam partem, in qua est Planeta, cuius C iii
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MATHEMATICVM. 39 whose function is not to cut off life, but rather to prolong it: hence it will at most be to determine the quality of death. With one ruler of the way being placed, the body of the Sun is said to kill: but I would not readily admit this, unless perhaps it were too much imbued by nature and by evil qualities; so neither Mercury, since he is very weak, for the same reason can be an Apheta. More on this in Argolus on critical days. ANALEMMA, among astronomers, is an instrument of gnomons adapted for hunting the shadows of the Sun, in the form of a sphere, and it is chiefly used for drawing sundials. Bernard. Baldus. ANAPHORA is called in Greek the second House, as it were the Parta Inni, which next succeeds the first beneath the earth; because it drives forward and carries forth the Sun and other stars, as if by means of wings, toward the line of the East. From it astrologers draw judgment concerning substance and goods that come by one’s own industry, not by inheritance; and thus it is judged fortunate; and it is of a cold and humid quality. ANAPHORAE are also called by some, in a mixed way, the succedent houses, namely the second, fifth, eighth, and eleventh; just as, on the contrary, Casaphora are the cadent houses from the angles, such as the third, sixth, ninth, and twelfth. ANAPHORAE are also called the oblique ascensions of the signs by analogy to the foregoing; as, conversely, ANAPHYSEMATA, from Apuleius in his book On the World, the Greeks call those spirits which are accustomed to be driven out from the depths or caves of the earth to the upper sea. We, by a more common term but one likewise derived from the Greeks, call them Apogæi. ANATOLAS is called the very hinge of the East, as though, after the density of shadows has been overcome, it finally opens the light. On this see more in IV. Horoscopus. ANAVBARACH among the Arabs is a certain empty calculation of theirs over the novenaries of the planets, about which Abū Maʿshar and his commentator Johannes de Saxonia have much to say. Thus they teach that one should observe how many degrees and minutes the planet has traversed in the sign or house whose novenary is being inquired into: then they order the whole sign to be divided into nine parts, giving to each part three degrees and twenty minutes, and to see into which part among these the degree of the planet, or of the house, whose novenary you wish to learn, has fallen. Once this is done, they want the first part of the division to be given to the lord of the moving sign of the same triplicity, and the second part to the lord of the following sign; and so proceeding in order, until one comes to that part in which is the planet, whose
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MATHEMATICVM. 41 Perpetuis etiam vnciss, & carceretesto Damnabit: si forte minax hinc inde benignum Suetidus, dubio certam vtrinque fauore. Vtcumque sit, hoc vnum moneo hueusque dicta seu vera sint, u Poëtarum somnia à nostro hemisphetio ob sideris maxi- am altitudinem longè fieri neque enim vnquam aut oritur, t occidit nisi fortè quoad paucas admodum stellas infimæ : quare & effectus etiam si quos haber infaustos in nihim cedunt. 196. ANEPATROS apud Ptolem. lib. 3. cap. 7. iuxta versionem rab significat genituram trium Masculotum, in quam con- niant, Satutnus, Iupiter, & Mars. ANGETENAR Arab. dicitur fixa in corpore Ceri quartæ ma- 197. nitudinis de naruta Satutni: de qua in V. Cetus. ANGVLVS dicitur id quod constat ex duabus lineis in vnum 198. unctum desinentibus: definitur enim ab Euclide quod sit dua am linearum mutuus contactus . Vnde in ædificiis, vbi duo pa- teres in vnum coëunt, anguli appellantur. Hinc apud Astro- mos quatuor Coeli puncta, seu Cardines, vnde Ottus, & Occasus, Culmen & Imum incipiunt Anguli appellari solent. tangulus quidem Medij Cæli dicitur Meridianus superior, culmen, Cor coeli, & decima domus, in qua Sol constiturus fficit Metidiem. Angulus Imi coeli Meridianus inferior, seu quarta domus. Angulus Orientis pars supra terram emergens scendens, Horosc. & Prima domus, ad quam cùm Sol per- enerit incipit diem: Angulus denique Occidentis dicitur pars la quæ à superiori ad inferius hemisphætium deprimitur, & unctum Occasus in qua Sol incipit noctem. Portò Angulus geneticè sumprus apud Geomerras diuiditur 199. n rectum, acutum, & obtusum. Angulus rectus est cum inea recta perpendiculariter cadit super aliam rectam in plano onsistentem, ita ut vtrinque æquale spatium liuquæ: vbi enim Iteram lineam tangit duos angulos rectos efformat. Acurus nior est Recto, hoc est minus spatium inter vtrumque latus clinquit, estque magis acuminatus: obtusus verò est recto najor, minusque acuminatus. Irem omnes illi anguli subdi- idi possunt in rectilineos, curuilineos & mixros. Rectilinei unt qui sub rectis lineis continentur: curu:linei, quorum traque linea curua est, & circularis: mixti denique quotum na linea curua est, altera recta. Ex tribus verò lineis se mutuo angentibus efficitur triangulum, quod dividitur in Rectan- gulum, Æquilaterum, Iosceles, Scalenum, Amblygonium, Oxygonium. Similiter ex quatuor lineis coëuntibus effoima- tur quadrangulum constans ex quatuor angulis: quod etiam di-
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MATHEMATICVM. 41 By perpetual bounds , and by prison and witness he will condemn: if perhaps, threatening on this side and on that, kindly with doubtful favor, certain on both sides. However it may be, this one thing I warn: whether the things said thus far be true or not, the dreams of the Poets from our hemisphere, because of the great altitude of the star, can by no means occur far away; for it never rises or sets except perhaps with regard to a very few of the lowest stars. Therefore even the effects, if any there are unfavorable, come to nothing. 196. ANEPATROS, in Ptolemy, book 3, chap. 7, according to the version means a nativity of three males, in which are joined Saturn, Jupiter, and Mars. ANGETENAR, in Arabic, is said of a fixed star in the body of Taurus of the fourth magnitude by the nature of Saturn; concerning which see in V. Cetus. 197. ANGLE is said of that which consists of two lines ending in one point: for it is defined by Euclid as the mutual contact of two lines. Hence in buildings, where two walls meet in one, they are called angles. Therefore among Astronomers the four points of the Heaven, or cardinal points, from which the East, West, Zenith, and Nadir begin, are also accustomed to be called Angles. The angle of the Midheaven is called the superior meridian, the zenith, the heart of heaven, and the tenth house, in which the Sun, being established, makes midday. The angle of the Imum coeli is the inferior meridian, or the fourth house. The angle of the East is the part rising above the earth, the Ascendant, and the first house, at which, when the Sun has arrived, day begins. The angle of the West, finally, is called the part which from the upper hemisphere is pressed down to the lower, and the point of sunset in which the Sun begins night. Moreover, an angle taken geometrically among Geometers is divided 199. into right, acute, and obtuse. A right angle is when a straight line falls perpendicularly upon another straight line lying in a plane, so that equal space remains on either side; for where one line touches another it forms two right angles. An acute angle is smaller than a right angle, that is, it leaves less space between the two sides, and is more pointed; but an obtuse angle is greater than a right angle, and less pointed. Likewise all those angles can be divided into rectilinear, curvilinear, and mixed. Rectilinear angles are those contained by straight lines; curvilinear, those whose lines on both sides are curved and circular; mixed, finally, those of which one line is curved, the other straight. But from three lines mutually touching one another a triangle is formed, which is divided into right-angled, equilateral, isosceles, scalene, obtuse-angled, and acute-angled. Similarly, from four converging lines a quadrilateral is formed, consisting of four angles: which also is di-
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42 LEXICON uiditur in perfectum quadratum, Rhombum, Rhomboidem, & Parallelogramma: Quorum singula, sicut & trianguli species suo loco sub propriis nominibus explicantur. 200. ANNAEL Arab. teste Hali, idem sonat, ac translatio lumi- nis quod contingit quandocumque fuerint tres Planetæ platicè coniuncti, quorum Medius superet alios in motu, & leuitates qui profecto ab vno ad alium transiens, dicitur transferre lu- men anterioris ad posteriorem. 201. ANNVLVS Astronomicus Instrumentum est Mathematicum pluribus annulis, seu circulis constans, ad sidetum positus, altrudines, declinationes metiendas aptissimum: quippe quod totam Sphæram, descriptosque in ea circulos, & præcipuas fixas, non secus ac Planisphærium, proindeque totam coele- stem doctrinam velut in speculo coarctaram, exquisitissimè continet. De eo scripserunt abundè Gemma Frisius, Ioan. Tuisner, Bonerus, Io. Dryan. & alij. 202. ANNVS communirer dicitur circuitus quidam temporis, quo expleto reditur ad idem punctum. Vnde Seruius ab Annulo di- ctum putat, alij à Græco verbo E' nec alij aliunde derivarum contendunt. Antonomasticè & absque vlloadiuncto accipitur pro integra Solis revolutione in Zodiaco, incipiendo ab initio Arieris vsque ad finem Piscium quæ perficitur spario 365. die- rum, & fere sex horarum. Hinc Astronomi annum compu- tant ab æquinoctio verno, & eam ob rem Mundum eò potissi- mum tempore creatum tenent. 203. Datut etiam annus Lunatis constans duodecim Lunationi- bus, quarum singulæ continent dies 29. hor. 12. & min. 44. ita ut totus annus includat dies 314. hor. 8. min. 48. sitque 11. fere diebus minor anno solati. Vnde exorta ratio Epactæ, Pe- riodus Callipica & aliæ æquationes de quibus infra. 204. Porrò Annus solaris diuiditur in Tropicum, & Sidereum: Tropicus est sparium temporis, quo Sol recurrit ad punctum æquinoctium, vel solstirium, vnde initio anni discesserat, & eius magnitudo est semper æqualis dierum 365. hor. 5 min. 55. circiter, & solum variatio est in aliquibus secundis, & terriis. Dicitur autem Tropicus à Græco verbo ποιος, quod conuer- sio interpretatur. Sidereus ad sidera, hoc est fixas refertur, & est spatium illud temporis, quo Sol, integro Zodiaco peragra- to reuertitur ad stellam fixam in cornu Arietis, seu aliam quamlibet, in octavo orbe consistentem; vnde semper maior Tropico est annus sidereus, & continet secundùm Thebir (qui primus huius anni siderei inventor fuisse creditur) dies 365. hor. 6. min 9. De qua re vide Ptolemæum lib. 3. sua magna constructionis.
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42 LEXICON is reduced into a perfect square, a rhombus, a rhomboid, and a parallelogram: each of which, just like the species of the triangle, is explained in its proper place under its own names. 200. ANNAEL. In Arabic, according to Hali, it means the same as the transference of light, which happens whenever three planets are in a platical conjunction, the middle one surpassing the others in motion and lightness; and indeed, passing from one to another, it is said to transfer the light of the former to the latter. 201. ANNVLVS, an astronomical instrument, is a mathematical device consisting of many rings or circles, fitted for observing the stars, most suitable for measuring altitudes and declinations; for it contains most accurately the whole sphere, and the circles described in it, and the principal fixed stars, no less than a planisphere, and therefore the whole doctrine of the heavens, as it were enclosed in a mirror. On it have written abundantly Gemma Frisius, Ioan. Tuisner, Bonerus, Io. Dryan., and others. 202. ANNVS is commonly called a certain circuit of time, after the completion of which one returns to the same point. Hence Servius thinks it is derived from annulus; others contend that it comes from the Greek word E' nec , and others derive it from elsewhere. Antonomastically, and without any added word, it is taken for the complete revolution of the Sun in the Zodiac, beginning from the beginning of Aries up to the end of Pisces, which is completed in the span of 365 days and almost six hours. Hence astronomers reckon the year from the vernal equinox, and for that reason hold that the world was created chiefly at that time. 203. There is also a lunar year, consisting of twelve lunations, each of which contains 29 days, 12 hours, and 44 minutes, so that the whole year includes 354 days, 8 hours, 48 minutes, and is almost 11 days shorter than the solar year. Hence arose the reckoning of the epact, the Callippic period, and other equations, of which below. 204. Moreover, the solar year is divided into tropical and sidereal: the tropical year is the span of time in which the Sun returns to the equinoctial point or solstitial point from which it had departed at the beginning of the year, and its length is always equal to about 365 days, 5 hours, 55 minutes, with the variation only of a few seconds and thirds. It is called tropical from the Greek word ποια, which is interpreted as “conversion.” The sidereal year refers to the stars, that is, the fixed stars, and is that span of time in which the Sun, having traversed the entire Zodiac, returns to the fixed star in the horn of Aries, or to any other fixed star situated in the eighth sphere; hence the sidereal year is always greater than the tropical, and according to Thebir—who is believed to have been the first inventor of this sidereal year—it contains 365 days, 6 hours, 9 minutes. On this matter see Ptolemy, book 3 of his Great Construction.
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MATHEMATICVM. 43 ANNVS Magnus simpliciter ab aliquibus dicitur reditus om- ium Stellarum ad idem punctum vnde discesserant ab initio lundi, cum primùm moueri coeptunt: quod sit ex Cicerone ratio 12954. annotum solatium. Astronomi verò rectiùs ap- pellant integram reuolutionem octauæ Sphæræ seu Firmamen- , quam Ptolemæus, alijque antiquiores statuebant in annis 000. Recensiotes autem in annis 4900 quo etiam tempore seruatum est, omnes orbes cælestes redire ad idem punctum si erant initio Mundi, cum primum creati sunt. Vnde (vt id siter dicam) non omninò inanis est opinatio illorum, qui plunt, totidem annis Mundum ipsum duraturum: eò quia perfecta sum opera, & dum tantum temporis spatium sim- ilis orbibus ad suum cursum perficiendum Diuina constituit cuidentia, æquum non esse, nec credibile, vt nolit postea rum motus absolui, atque ad idem punctum, vnde moueri operant, non redite. Sed hæc impersecutabilia sunt, quæ Deus sua posuit potestate: vnde circa ea ludere quidem potest umana sapientia, collineare non potest. ANNVS Ægyptium, qui etiam Persicam dicebatur, constabat < 306.> uolutione dierum 360. quot videlicet sunt gradus in Zodia- , itaut singuli menses 30. dierum spatio constituerentur. uoniam autem hac reuolutione Sol non petueniebat ad lo- m suum, vnde discesserat; sed adhuc quinque dies desidera- ntur; hos quasi adiectitios, & supernumerarios extra men- s ipsos, antequam nouum exorditentur annum computa- nt; neglecta intercalatione horarum sex, quæ singulis qua- iennis vnum diem constituunt: ideò absolutè hic annus erat ntum dierum 365. vt passim tradit Ptolemæus in Almagesto. At quia, vt modò diximus singulis annis prætermittebantur < 307.> oræ sex, quæ requirebantur, ad hoc vt Sol ad idem punctum diret, vnde discesserat; inde fiebat, vt quarto quoque anno, nus Ægyptius integro die ante solstitij pristini diem absol- retur, & in annis 40. anteuetteret per decem dies, & in nis 1460. per dies 365. hoc est per vnum annum. Quare olutis annis cælestibus 1460. transierant iam anni Ægyptij 61 & initium anni Ægyptij, seu prima dies primi mensis, ii dicebatur Thoth redibat ad eandem diem, tempusque cælo ngruens. Hæc verò periodus annorum Iulianorum, ac ferè cælestium 1460. sed Ægyptiorum 1641. dicta est. ANNVS MAGNVS Canscularis, & Periodus Cynica, seu So- < 308.> iaca, à Canicula, quæ Græcè dicitur Cynos, & Sothis, eò iod hæc periodus inuenta fuerit à coniunctione, & ottu ma- tino Solis cum Canicula. ANNI MAGNI Luni-solares sunt quibus peractis Lunæ, Solis. < 309.>
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MATHEMATICS. 43 The Great Year is simply called by some the return of all the stars to the same point from which they departed at the beginning of the world, when they first began to move; according to Cicero, this is a period of 12,954 years. Astronomers, however, more correctly call it the full revolution of the eighth sphere, or Firmament, which Ptolemy and other older writers placed at 36,000 years. More recent writers, however, place it at 4,900 years, at which time also it is held that all the celestial spheres return to the same point, if they were at the beginning of the world, when they were first created. Hence, to say so, the opinion of those is not altogether vain who think that the world itself will last for as many years, because, since the work is finished and for so long a span of time Divine providence has established similar spheres for the completion of their course, it is not fitting, nor believable, that afterwards their motions should not be brought to completion and return to the same point from which they began to move. But these things are beyond inquiry, since God has placed them in his own power: around them human wisdom may indeed play, but it cannot strike the mark. The Egyptian year, which was also called the Persian, consisted of 360 days, namely the number of degrees in the Zodiac, so that each month was constituted with a span of 30 days. But because with this revolution the Sun did not return to the place from which it had departed, five days were still lacking; these, as it were additional and supernumerary, were counted outside the months themselves, before they began the new year; the intercalation of six hours being neglected, which every four years makes one day: therefore this year was absolutely of only 365 days, as Ptolemy everywhere relates in the Almagest. But because, as we just said, in each year six hours were omitted, which were required for the Sun to return to the same point from which it had departed, it followed that every fourth year the Egyptian year was completed a whole day before the former day of the solstice, and in 40 years it advanced by ten days, and in 1,460 years by 365 days, that is, by one year. Therefore, when 1,460 celestial years had passed, 1,561 Egyptian years had already passed, and the beginning of the Egyptian year, or the first day of the first month, which was called Thoth, returned to the same day, and to a time corresponding to the heavens. This period of 1,460 Julian years, and almost celestial years, but 1,641 Egyptian years, was called the Great Period. The Great Canicular Year, and the Cynic, or Sothiac, Period, from Canicula, which in Greek is called Cynos and Sothis, because this period was found from the conjunction and morning rising of the Sun with Canicula. The Great Lunisolar Years are those in which, when they have been completed, the Moon, the Sun,
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44 LEXICON < 109.> que syzigia ad idem dici momentum reuertebantur: inde ANNVS MAGNVS Metonicus dictus est à Metone Atheniensi eius inuentore. Cùm enim, vt supra dictum est, quilibet annus Solaris superer annum Lunarem (constantem duodecim perfectis Lunationibus, quarum singulæ complentur diebus 29. hor. 12. min. 44.) vndecim ferè diebus; hinc est, vt singulis annis, Nouilunia totidem diebus anticipent, donec in annis 19. numerus compleatur, & Nouilunia redeant vt erant prius. Sicque annus iste Metonicus constat diebus 6939. cum horis 16. & dimidia, quot ferè diebus, & horis constant omninò vndeuiginti anni Solares, comprehendunt enim isti ad amussim dies 6939. & horas 18. itaut hæc periodus vna hora & semisse Lunarem superet, quam communem, & congruentem Luminarium periodum primus omnium inuenit Meton, vt diximus, à quo ei nomen est inditum: Et hic decemnouennalis recursus, Aurens numerus appellatus est, de quo suo loco. Porò quoniam Luna, vt modò dicebamus, horâ vna, & semisse à Solis decemnouennali cursu, discrepat, ac præcedit, inde sit, vt in quatuor annis magnis Metonicis, hoc est in annis communibus 76. ipsa anticipet per horas 6. & in annis 312. & sex mensibus, integrum diem præcedat, & successiuè semper magis ac magis excrescat hæc deuiatio, quæ tandem tum ob Lunæ Embolismicam Lunationem quæ aliquando anno Lunari superadditur, (qui proinde Annus Embolismicus hoc est insiritius dicitur constant ex re, decim Lunationibus) tum ob Solis inæqualem morum, in Zodiaco potest in ordinem reduci, atque exquisitissimè compleri; ita ut Annus lunaris ad amussim cum Solari conueniat. Qua de re consule librum nouæ rationis Kalendarij Romani restituendi jussu & authoritate Gregorij XIII editum. Cæterum hæc periodus communiter appellatur Callippica ab eius repertore Callippo, vt in loco dicemus. < 110.> ANNVS Periodicus apud Chronologos significat durationes & fata Imperiorum. Testantur enim Historiæ omnium temporum, si à prima sua origine repetantur Regna, & Respublicas potentiores quingentis tantummodo annis flotuisse; Plurima verò hunc terminum non attigisse; nulla aut pauca superasse. Annus ergò quingentesimus Imperiorum Periodicus dicitur, eò quia circa eius finem Imperia, & Monarchiæ, aut in torum cedere, aut mutationem aliquam considerabilem subire soleant. Id passim obseruare est in Imperio Græcorum, Medorum, Assyriorum, ac denique in Romano. Et mirum est, quomodo hebdomades septuaginta Danielis ad hanc etiam periodum apprimi respondeant, cum de aduentu Christi, & in-
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44 LEXICON < 109.> which returned to the same point of syzygy, that is, the moment: from this the GREAT YEAR was called Metonic, from Meton the Athenian, its inventor. For since, as was said above, any Solar year exceeds the Lunar year (consisting of twelve complete Lunations, each of which is completed in 29 days 12 hours 44 minutes) by nearly eleven days; hence it is that each year the New Moons anticipate by the same number of days, until in 19 years the number is completed, and the New Moons return as they were before. And so this Metonic year consists of 6939 days with 16 and a half hours, about as many days and hours as exactly nineteen Solar years contain; for these comprise to a nicety 6939 days and 18 hours, so that this period exceeds the Lunar one by one hour and a half, which common and fitting period of the luminaries Meton first of all discovered, as we said, from whom the name was given to it: and this nineteen-year return was called the Golden Number, of which elsewhere in its place. Moreover, since the Moon, as we were just saying, differs from and precedes the Solar nineteen-year course by one hour and a half, it follows that in four great Metonic years, that is, in 76 common years, it anticipates by 6 hours; and in 312 years and six months it precedes by a full day, and successively this deviation always grows more and more, which at length both because of the Moon’s Embolismic Lunation, which is sometimes added to the lunar year, (and therefore the Embolismic Year, that is, the intercalary one, is so called, consisting in fact of ten Lunations) and because of the Sun’s unequal motion in the Zodiac, can be brought back into order, and be completed most exactly; so that the lunar year matches the solar year exactly. On this matter consult the book on the new method of restoring the Roman Calendar, published by command and authority of Gregory XIII. Moreover, this period is commonly called the Callippic, from its discoverer Callippus, as we shall say in its place. < 110.> PERIODIC YEAR among Chronologists signifies the durations and fates of empires. For the histories of all times bear witness, if one traces back from their very origin, that kingdoms and republics of greater power have flourished for only five hundred years; very many indeed have not reached this limit; none or few have surpassed it. Therefore the five-hundredth year of empires is called Periodic, because toward its end empires and monarchies are wont either to decline altogether or to undergo some considerable change. This is plainly observable in the empire of the Greeks, Medes, Assyrians, and finally in the Roman. And it is remarkable how the seventy weeks of Daniel also correspond closely to this period, when concerning the coming of Christ, and the-
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46 LEXICON 116. ANTARES Græcè dicitur Cor Scorpij, Stella fixa primæ magnitudinis de natura Marris, & Iouis vna ex stellis regiis, sed etiam ex violentis. Vnde cum Luminaribus reperta maximas dignitates pollicetur, sed non sine vitæ discrimine, ac violentia: Cum Venere inclinat ad Musicam, & Poësin: Cum Luna in bono aspectu beneficarum gratiam Principum comparat, facitque eorum intimum familiarem. Vide in V. Cor Scorpij. 117. ANTASCONES, quasi sub contrario axe vocantur populi habitantes in locis diametraliter oppositis, à quorum videlicet plaga ad alteram correspondentem Linea imaginariè porrecta, necessariò transire debet per centrum Mundi, vnde etiam appellanur. 118. ANTIGENÆ ab Alberto Magno, quasi contrarios omninò effectus experientes: & à Græcis. 119. ANTICHTONES. Siquidem locorum diametraliter oppositorum incolæ ijsdem anni temporibus contrarios aliis effectus habent. Sic dum Sol in vna parte Meridiem facit, in altera Medium noctis inducit: dum vni diem longissimum, ac noctem breuissimam, alteri è contra noctem breuissimam, diem longissimum procreat: dum vni æstum, alteri frigus, dum vni Ver, alteri Autumnum parat, iis dempris, qui sub æquatore versantur, nam istis solum in diei noctisque alternatione est cum prædictis communicatio, cæterùm ibi vt alibi dictum est, semper & vbique æqvinoclitum: tam hic quàm illic eodem tempore hyems aut æstas: eadem caloris intensio, idem hominum color. Hi à nostris communiter sumpto à Græcis vocabulo appellanur. 120. ANTIPODES quasi obuersis pedibus incedentes, ambo enim, vt ait Plinius aduersa suis oppositis premunt vestigia; itaut vulgus existimet, nostros Antipodas, capire deorsum verso incedere. Hos derider D. Augustinus lib. 16. de Ciuitate Dei cap. 9. Imò ex testimoniis sacræ Scripturæ contendit probare nulla rarione credendum esse Antipodas inueniri, proindeque esse hæreticum illos astruere: Quia, inquit, cùm diuina Scripturæ testetur homines ex vno Adam in hoc nostro hemisphario progenitos, nunis absurdum est dicere, aliquos homines ex hoc in absurd hemispharum, impertransibilis Oceani immensitate traiecta, nauigare potuisse, vt etiam illic humanum genus propagarent. Id ipsum sensere etiam Lactantius Firmianus lib. 3. D[omi]num Instit. c. 24. Bedæ de ratione temporum cap. 32. Procopius Gazæus, alijque Patres, adeò vt olim malè audirent qui eos ex congruentiis ac Mundi situ admittere compellebantur, suamque sententiam proferre minimè auderent. Cæterum nostris temporibus vsq[ue] 121. adeò certum est dati Antipodas atque in regionibus nostris ter-
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46 LEXICON 116. ANTARES is called in Greek the Heart of Scorpius, a fixed star of the first magnitude, of the nature of Mars and Jupiter, one of the royal stars, but also among the violent ones. Hence, when found with the Luminaries, it promises the greatest dignities, but not without danger to life and with violence: with Venus it inclines to music and poetry: with the Moon in a good aspect it gains the favor of princes and makes one their intimate friend. See under V. Heart of Scorpius. 117. ANTASCONES, as it were under the opposite axis, are called peoples dwelling in places diametrically opposite, from whose region, as it were, to the corresponding other side, an imaginary line drawn must necessarily pass through the center of the world, from which they are also named. 118. ANTIGENAE, by Albertus Magnus, as it were experiencing wholly contrary effects: and from the Greeks. 119. ANTICHTONES. For inhabitants of places diametrically opposite have opposite effects at the same seasons of the year. Thus while the Sun makes noon in one part, it brings midnight in the other: while to one it produces the longest day and the shortest night, to the other, on the contrary, the shortest night and the longest day: while to one it prepares heat, to the other cold, while to one spring, to the other autumn, except for those who dwell under the equator, for with these only in the alternation of day and night is there communication with the aforesaid things; otherwise there, as elsewhere it has been said, it is always and everywhere equinoctial: both here and there at the same time winter or summer: the same intensity of heat, the same color of men. These are commonly called by ours, using a Greek word. 120. ANTIPODES, as it were walking with their feet turned backward; for both, as Pliny says, press their steps opposite to their opposites, so that the common people think that our Antipodes walk with their heads turned downward. Saint Augustine mocks these in book 16 of The City of God, chapter 9. Indeed, from the testimonies of Sacred Scripture he contends that by no means should it be believed that Antipodes are found, and therefore that it is heretical to assert them: because, he says, since divine Scripture testifies that men were begotten from one Adam in this our hemisphere, is it not absurd to say that some men could have sailed from this hemisphere to the opposite one, having crossed the immensity of the impassable Ocean, so that even there they might propagate the human race. The same opinion was held also by Lactantius Firmianus, book 3 of the Divine Institutes, chapter 24, Bede, On the Reckoning of Time, chapter 32, Procopius of Gaza, and other Fathers, so much so that in former times those who were compelled to admit them on the basis of correspondences and the position of the world were ill spoken of, and scarcely dared to put forward their own opinion. But in our times it is so certain that there are Antipodes, and that in our regions ter-
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MATHEMATICVM. 49 m latitudine meridiana gr. 5. verum eius Antiscium non erit gr. 5. Geminorum qui correspondet gradui 25. Cancri, vt garia tradunt præcepta, eò quia de iis minimè verificatur olemxi dictum, quod aquali semperis spatio oriuntur & aqua- rasso distent ab eodem vel ab viroque punctorum aquincetialium: id indagandum siue in Ecliptica, siue extra in eodem paral- o declinationis Lunæ, quæ cum data latitudine erit gr. 16. 1. 18. Igitur eius verum Antiscium erit grad. 14. min. 40. uri in Ecliptica; quia hic gradus rali præditus est declina- ne, atque incidit in eundem parallelum cum Luna: ad quem teà gradum directus Sol, iure dicitur ad Lunæ Antiscium solutus. Accidit etiam, vt Planeta tanta sit præditus latitudine, vt < 229.> indoque eius Antiscium extra Eclipticam prorsus, imò im extra viam realem alicuius Planeræ significatoris cadat; proinde eius Antiscium planè vacuum effectu remaneat, ppe quod nunquam ab aliquo significatore per viam suam lem incedentem per directionem attingi potest: & ideò in casu eius ratio habenda non est. Sic ponamus Martem repe- in eodem gradu 25. Cancri, sed cum latitudine boreali, m sanè habere potest graduum nouem: tunc eius Antis- n extra Zodiacum cadit, cùm eius declinatio sit grad. 30. m neque Sol neque vllus significator vquam attingit, cùm ummum ea in Sole excedere non possit gr. 23. min. 31. & in ra quacumque latitudine prædita maior esse nequeat, quam 26. min. 7. Vnde cùm nunquam possint pertingere ince- do per viam suam realem, ad parallelum declinationis rtis; nunquam etiam directione possunt ad eius Antiscium uci, benè verò ad eius Conirantiscium, seu parallelum di- sæ declinationis, quod secat Eclipticam, aut orbitam Lunæ quam realiter incedit; ita vt motu suo pergens, ad illud dem perueniat. adem ratione qua in Zodiaco per æquidistantiam à punctis < 230.> dinalibus considerantur Antisciæ, quæ sunt eiusdem po- iæ, & eiusdem penè actiuntaris, ac corpora ipsa Planeta- ; eadem inquam ratione fulia plurimis experimentis in- iosè admodum adinuenit P. de Titis in Calisti Philosophia, iscia in mundo per æquidistantiam videlicet à Cardini- mundi: quos, sicur illos parallelos declinationis, ita & in senti parallelos cosmicos placuit appellare, qui planè dem virtutis & efficaciæ atque Antiscia in Zodiaco, esse periuntur: sed de his iterum redibit sermo in V Paralleli. NTISCII apud Geographos appellantur populi habitantes in < 231.> s Antiscijs, sic dicti eò quod obuersas inuicem vmbras D
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MATHEMATICUM. 49 in a meridian latitude of 5 degrees; yet its Antiscion will not be 5 degrees of Gemini, which corresponds to the 25th degree of Cancer, as the rules teach, because in regard to them it is by no means verified that they are born at an equal interval and are equidistant from the same or from both points of the equinoctial: this must be investigated, whether in the Ecliptic or outside it, in the same parallel of the Moon’s declination, which with the given latitude will be 16 degrees, 1. 18. Therefore its true Antiscion will be the 14th degree, 40 minutes, in the Ecliptic; because this degree is endowed with such declination, and falls in the same parallel with the Moon: toward which degree, when the Sun is directed, it is rightly said to be released to the Moon’s Antiscion. It also happens that a planet is endowed with such latitude that <229.> and thus its Antiscion falls altogether outside the Ecliptic, indeed even outside the real path of some significator planet; therefore its Antiscion remains plainly void of effect, since it can never be reached by any significator advancing along its real path by direction: and therefore in such a case no account is to be taken of it. Thus let us suppose Mars to be found in the same 25th degree of Cancer, but with northern latitude, which indeed it can have of nine degrees: then its Antiscion falls outside the Zodiac, since its declination is 30 degrees, which neither the Sun nor any significator ever reaches, since the Sun itself cannot exceed 23 degrees, 31 minutes, and in any other star endowed with whatever latitude it cannot be greater than 26 minutes, 7. Whence, since they can never attain by proceeding along their real path the parallel of certain declination; neither can they by direction ever be led to its Antiscion, but indeed to its Conantiscion, or the parallel of opposite declination, which cuts the Ecliptic, or the Moon’s orbit in which it truly proceeds; so that as it advances by its motion, it reaches that same point. In the same manner in which in the Zodiac, by equidistance from the <230.> cardinal points, Antiscions are considered, which are of the same po- sition and nearly of the same activity, as the heavenly bodies themselves; in the same way, I say, Julius, by many experiments, very diligently devised in the Celestial Philosophy by P. de Titis, found cosmical antiscions in the world, namely by equidistance from the cardines of the world: which, just like those parallels of declination, have been pleased to call cosmical parallels in the present work, which are plainly discovered to be of the same power and efficacy as Antiscions in the Zodiac; but concerning these the discourse will return again in the Fifth Parallel. ANTISCII among geographers are called peoples dwelling in <231.> the Antiscions, so called because their shadows turn toward one another D
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50 LEXICON habeant; sicut & Ampliscij, qui quadruplicet vmbra verberantur; & Periscij, qui eandem habent versatilem, & circularem. Similiter. 232. ANTIPATHIA Græcè dicitur naturalis ille rerum diffensus, & conttarietas, quam passim videmus, & admiramur, ad aliam causam id refundere non valentes, quam in dependemiam, & subordinationem quam habent inferiora ista ad suas causas superiores vniuocas, vel diuersas. Qua de re vide in V. Sympathia. 233. ANTOCCI dicuntur: quasi contrahabitabiles, populi in æqualibus, sed oppositis parallelis, hinc inde ad æquatorem constituti, ira vt habeant eandem latitudinem locorum, eandem numero Poli elevationem, sed non eiusdem, quantum enim attollitur his Polus boreus, tantum illis austrinus, vnde consequenter habent æquales, sed in oppositis signis ascensiones, æquales arcus diurnos, pariterque nocturnos; æquales demum temporum dispositiones, locorumque temperies, sed non æquè, hoc est non in eisdem mensibus, sed in oppositis: dum enim istis solstitium æstiuum accidit, & vndique æstu torrentur, illos è conttatio hyemis rigor corripit, & insolens frigus: quando istis floridum Ver arridet, illi Autumuale, tempus experiuntur, & magnam fructuum copiam colligunt. Tales sunt accolæ capitis bonæ spei, & habitatores Moreæ, Zacynthi, &c. Extremum insulæ sancti Laurentij dictæ vulgò Madagascar, & Mate rubrum: sicut è contra Perioeci vocantur qui habitant sub vno Meridiano, eodemque parallelo, sed in locis eiusdem paralleli oppositis, vt dicemus in suo loco. A P 234. APARCTIAS Græcè dicitur ventus Septentrionalis vnsus ex quatuor Cardinalibus, sic dictus ab Arcto, seu Polo Arctico, vnde exsufflat. Est generaliter frigidus, & siccus, niuosus, serenitatis auctor, corruptionis viindex, & omnium saluberrimus, licer ob nimiam frigiditarem sit floribus, & germinibus nouis infensus: ab Italis audit Tramontana. 235. APELIOTES, Græcè Eurus, Latinè dicitur, ac Subsolanus, Venus spirans ab oriuæquinoctiali: sic dictus ab orenre Sole. Est item vns ex quatuor Cardinalibus, calidus, & siccus, sed tamen cum insigni temperie; ideoque à Ptolemæo sanguineus dictus. Noctu plerumque silet, & incipit spirare oriente Sole. Hyeme producit gelu: æstate verò serenitatem adducit. Conseruat corpora, ac salubriatis est parens. In Italia vocatur Leuante. 236. APERITIO Portarum apud Astrologos audiunt maximæ quædam atque euidentissimæ aëris, ac temporum mutationes quæ
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50 LEXICON have them; like the Ampliscij, who are beaten with a fourfold shadow; and the Periscij, who have the same shadow, changeable and circular. Likewise. 232. ANTIPATHIA is said in Greek to be that natural dissension of things, and contrariety, which we commonly see and admire, being unable to refer it to any other cause than to the dependence and subordination which these lower things have to their superior, univocal or diverse causes. On this matter see under V. Sympathia. 233. ANTOCCI are so called, as if “contrahabitabiles,” peoples situated in equal, but opposite parallels, here and there with respect to the equator, so that they have the same latitude of places, the same number of elevation of the Pole, but not the same one; for as much as the northern Pole is raised for these, so much is the southern for those, whence consequently they have equal, but in opposite signs, ascensions, equal daily arcs, and likewise nightly ones; equal finally dispositions of the seasons and temper of places, but not equally, that is, not in the same months, but in opposite ones: for when summer solstice happens to these, and they are scorched on every side by heat, those, on the contrary, are seized by the severity of winter and unusual cold: when flourishing Spring smiles on these, they experience an autumnal time, and gather a great abundance of fruits. Such are the inhabitants near the Cape of Good Hope, and the dwellers of Morea, Zacynthus, etc. Also the farthest part of the island called Saint Lawrence, commonly Madagascar, and the Red Sea: just as, on the contrary, Perioeci are called those who live under one Meridian and the same parallel, but in places opposite on the same parallel, as we shall say in its proper place. A P 234. APARCTIAS is said in Greek to be the Northern wind, one of the four Cardinals, so called from Arctos, or the Arctic Pole, from which it blows. It is generally cold and dry, snowy, the author of serenity, the avenger of corruption, and the most healthful of all, although because of its excessive cold it is hostile to flowers and new sprouts: among the Italians it is called Tramontana. 235. APELIOTES, in Greek Eurus, in Latin is called, and Subsolanus, the wind blowing from the equinoctial sunrise: so named from the rising Sun. It is likewise one of the four Cardinals, hot and dry, but nevertheless with notable temperateness; and therefore by Ptolemy called sanguineous. At night it usually is silent, and begins to blow at sunrise. In winter it produces frost; in summer, however, it brings serenity. It preserves bodies, and is the parent of healthfulness. In Italy it is called Leuante. 236. APERTIO of the Gates is what astrologers call certain great and very evident changes of the air and of the seasons which
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MATHEMATICVM: 51 unquam ferè fallunt, experientia teste, sed certissimum sem- er sortiuntur effectum; idque sit in certis Planetarum con- gressibus, aut irradiationibus. Et potissimum hoc obsetuatur Planetis dominis oppositarum domotum, vt Saturni, & So- s (Aquarius enim Saturni domicilium opponitur Leoni, cu- is dominator est Sol, & sic de reliquis.) Saturni, & Lunæ, luis & Mercurij, Martis, & Venetis. Quandocumque igitur ti Planetæ, vel corpore iunguntur, vel de quadrato, aut de pposito se respiciunt, magni quidam effectus expectandi sunt rea aëris mutationem; præsertim si Luna sese immisceat, :que ab vno ad alterum defluat. Et Saturni quidem cum Sole ongressus adducit aëris turbulentiam, frigus maximum, si temporis tatio id petat, in signis tetters nebulas: in aqueis plu- ias, & congruenti tempore, niues; præsertim si Saturnus erit dispositio præcedentis luminarium conjunctionis, aut ppositionis. Iouis, & Mercurij congressus, quadratus, aut ppositio adducit ventos magnos, terræ motus, eradicationes ar- orum, ædificiorum, & similium. Tandem Martis & Venetis onuenientia gignit imbres, grandines, coruscationes, toni- rua cum fructuum pernicie. Hæc, inquam, tria genera aperi- onis portarum semper sortiuntur suum effectum, minorem uidem quando inuicem conjunguntur, maiorem, quando pponuntur, & maximum, quando intercedit Luna, Venus, ut Mercurius, ita vt eorum aliquis defluat à leui ad pondero- um; vt si Luna defluerer à Sole ad Saturnum (aut Mercurius, ui ex se significator est pluuiæ) tunc enim magna imbrium opia expectanda erit, præsertim si eorum aliquis sit rettogra- us, aut si planeta retrogradus alteri portas aperientium cor- ore jungeretur. APHÆNETÆ Græcè dicuntur stellæ absconditæ synodicè ob < 237.> olem vicinum, cuius radijs earum fulgor extinguitur. APHETA, hoc est dimissor dicitur apud Græcos Vitæ dator < 238.> rabibus Hileg, seu Hylech; estque apud Astrologos luminare, lanera, aut alius locus in Coelo, qui in genituris vitæ domi- gium sortiatur. Et benè quidem affectus, robustus, in bono- um aspectu, vitam robustam, diuturnam, validam, pau- isque ægritudinibus obnoxiam pollicetur: malè constitutus, ebilis, in malorum dignitatibus, seu eorum hostili radio in- testatus, mala affert in vita, & quandoque interitum, si dire- tione perueniat ad locum Anæreticum, hoc est abscissorem. Quæ autem sint loca Anæretica, dictum est in V. anæreta. Pot- ò quinque tantum significatores ponit Ptolemæus, qui sortiri possint virtutem Aphæticam: luminare conditionarium; So- em nempè de die, Lunam de nocte: Planetam, qui plures D ij
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MATHEMATICVM: 51 never, as experience testifies, are they mistaken, but they almost always produce a certain effect; and this in the certain conjunctions or irradiations of the planets. And this is especially observed in the planets ruling opposite domiciles, as Saturn and the Sun, (for Aquarius, the domicile of Saturn, is opposite Leo, whose ruler is the Sun, and so of the rest), Saturn and the Moon, Jupiter and Mercury, Mars and Venus. Whenever therefore these planets are either joined by body, or behold one another by square or opposition, great effects are to be expected, especially as regards a change of the air; particularly if the Moon also be mixed in, and pass from one to another. And indeed the conjunction of Saturn with the Sun brings turbulence of the air, very great cold, if the season of the time demands it; in earthy signs, mists; in watery signs, rains; and in due season, snow; especially if Saturn be disposed according to the preceding conjunction or opposition of the luminaires. The conjunction, square, or opposition of Jupiter and Mercury brings great winds, earthquakes, the uprooting of trees, buildings, and the like. Finally, the conjunction of Mars and Venus produces rains, hail, lightning, thunder, with destruction of the fruits. These, I say, three kinds of opening of the gates always obtain their effect, indeed a lesser one when they are joined together, a greater when they are opposed, and the greatest when the Moon, Venus, or Mercury intervenes, so that one of them passes from light to heavy; as if the Moon passed from the Sun to Saturn (or Mercury, who of himself is a significator of rain), then a great abundance of rain is to be expected, especially if one of them be retrograde, or if the retrograde planet be joined in body to another of the gate-openers. APHÆNETÆ are called in Greek the stars hidden synodically by reason of their nearness to the Sun, by whose rays their brightness is extinguished. < 237.> APHETA, that is, the releaser, is called by the Greeks the giver of life, among the Arabs Hileg, or Hylech; and it is, among astrologers, the luminary, planet, or some other place in the heavens which in genitures obtains the lordship of life. Well-placed and strong, in good aspect, it promises a robust, long, strong life, and one subject to few illnesses; badly placed, weak, in the dignities of malefics, or harassed by their hostile ray, it brings evils in life, and sometimes death, if by direction it reaches the Anaretic place, that is, the cutting-off place. What the Anaretic places are has been said in V. anæreta. Moreover, Ptolemy sets down only five significators that can obtain the Aphhetic virtue: the conditionary luminary; the Sun by day, the Moon by night: the planet which has the most ... < 238.> D ij
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32 LEXICON prærogatiuas obtinet in locis luminarium, Ascendentis, partis fortunæ, & præcedentis luminarium conjunctionis, aut oppositionis, & ipsam partem fortunæ, seu horoscopum luna-rem de nocte: si modò reperiatur in locis idoneis, hoc est in Ascendente, decima, vndecima, nona & septima domibus videlicet, quæ aut sint ipse horoscopus, aut cum eo aliquam habent familiaritem, & aspectum. Hinc duodecima, & octa-ua, quia nullam cum horoscopo connexionem habent, & adhuc vaporibus è tertia emergentibus sunt implicatæ, ideò ab hoc negotio excluduntur: vnde si in iis reperiatur aliquis significator, ad quem aliàs de iure vitæ prorogatio pertine-ret, is prætermittitur, & sumitur alius ex ordine succedens; modò is etiam in locis aphæticis reperiatur: alioquin, si nullus ex quatuor supradictis idoneus fuerit repertus, assumendus est ipse horoscopus, & Linea orientalis in vitæ prorogationem; qui nihilominus semper, & vtcumque sit generalem habet vi-tæ, & valetudinis significationem. Quoad planetam potiores dignitates obtinentein in locis principalibus Genituræ modo enumeratis, aduertunt aliqui ipsum, præter idoneum cæli si-tum, debere esse insignitum optimis prærogatiuis, adhoc vt vice luminarium aphætica dignitate gaudere possit, nimirum vt sit in Angulis, plenus lumine, cursu velox, atque in suis dignitatibus essentialibus. Alij ab hac prærogatiua excludunt malesicos ob suam malignitatem, & Mercurium ob natnram eius versatilem, ac luminis imbecillitatem, & solos beneficos admittunt, eosque non absolutè, sed Iouem in Genituris viro-rum, Venerem autem in foeminarum, nec quidem frequenter, sed raro admodum & cum sunt in genitura nimium potentes, luminaribus vice versa debilibus, & afflictis: Alioquin semper aut pars fortunæ de nocte, aut horoscopus de die sumendum præcipientes. 239. APhAlIvm Græcè dicitur punctum illud in quo tellus, aut sidus aliquod maximè distar à Sole: sicut Perihelium punctum, in quo à Sole quam minimè distat. 240. APhERÆTÆ appellantur à Græcis planetæ minuti numero, quando videlicet efficiuntur tardiores, & eorum motus diurnus est minor motu medio: de qua re vide Maginum, aliosque in Isagog. 241. APhETES, teste Valla, dicitur planeta retrogradus, cum mouetur suo motu, proprio ab ortu ad occasum, hoc est à con-sequentibus in antecedentia signa. Posthetes autem, cùm est di-rectus, & mouetur ab occasu in ortum semper ad consequen-tia signa. 242. APhRvIMIS Græcobarbar, dicitur in Sphæra barbarica pri-
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32 LEXICON has precedence in the places of the luminaries, the Ascendant, the part of fortune, and the preceding conjunction or opposition of the luminaries, and the part of fortune itself, or the lunar horoscope at night: provided only it be found in suitable places, that is, in the Ascendant, tenth, eleventh, ninth, and seventh houses, namely, which are either the horoscope itself, or have some familiarity and aspect with it. Hence the twelfth and eighth, because they have no connection with the horoscope, and are still entangled with vapors emerging from the third, are therefore excluded from this business: whence, if in them there be found any significator to which, by right, the prorogation of life would otherwise belong, he is passed over and another next in order is taken; provided that he too be found in the aphhetic places: otherwise, if none of the four above-mentioned be found suitable, the horoscope itself, and the eastern line, are to be assumed for the prorogation of life; which nevertheless always, and in whatever way it be, has a general signification of life and health. As for the planet holding the chief dignities in the principal places of the nativity now enumerated, some note that it, in addition to a suitable position in the heavens, ought to be adorned with the best prerogatives, in order that it may be able to enjoy an aphhetic dignity in place of the luminaries, namely that it be in the angles, full of light, swift in course, and in its essential dignities. Others exclude the malefics from this prerogative on account of their malignity, and Mercury because of its changeable nature and weakness of light, and admit only the benefics, and these not absolutely, but Jupiter in the nativities of men, Venus in those of women, and not even frequently, but very rarely and when they are in the nativity excessively powerful while the luminaries, on the contrary, are weak and afflicted: otherwise always directing that either the part of fortune by night, or the horoscope by day, be taken. 239. APHALIUM is called by the Greeks that point at which the earth, or some star, is farthest from the Sun: just as Perihelium is the point at which it is nearest to the Sun. 240. APHERETÆ are called by the Greeks the planets when their number is diminished, namely when they become slower, and their daily motion is less than the mean motion: on this matter see Maginus and others in the Isagog. 241. APHETES, according to Valla, is said of a retrograde planet, when it moves by its own proper motion from east to west, that is, from the following signs into the preceding. Posthetes, however, when it is direct, and moves from west to east always toward the following signs. 242. APHRVIMIS, Greco-barbarous, is said in the barbaric Sphere pri-
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MATHEMATICVM. 57 ium auxilium adipisci: Idipsum experiuntur Lusitani tendentes ad Indias Orientales etiamsi secundis alioqui ventis fruan- tr. Cuius tei plurima afferunt experimenta Trimarchus lib. Meteor. disp. 1. sect. 6. Adrianus, Metius, & Furnerius lib. Hydrographia cap. 23. Caulam autem huius motus ascribit lem Turnerius Solis ardori; humores, atque halitus ad se erpetuò trahentis: vt etiam quintum, quem diximus mo- im, à polis ad æquatorem; & eo maximè intra tropicos, ib via scilicet Solis, vbi violentior apparet vterque motus eplerus eum refundit in Lunam, aquas, & humores omnes d se magnetica vi protestantem. Sed Arabes, & cum illis vicomercatus longè verosimilius id tribuunt motui primi mo- ilis rapientis secum omnes inferiores sphæras: atque adeò non modò cælos inferiores, sed & Aërem, & Oceanum; li- et hic quia cæteris sphæris remorior, sua vi, & aquatum rassitie aliquantò magis resistat, quam aër: hic magis, quam cæli superiores, vt aliàs adnotauimus. Cui opinioni nec refra- gatur Resta de Meteoris lib. 3. tr. 1. cap. 16. nec Mastrius ibid. mast. 4. num. 148. Quoad quintum verò motum, qui dicitur latitudinis à polis < 268.> æquatorem, eum jamptidem agnouit Arist. 1. Meteor. cap. text. 6. & sequuti sunt Alexander Aphrodiasus D. Thomas, Vicomercarius, Nyphus, & alij. Cuius causa alia sanè non est, vt benè discurrat Turnerius, quàm Solis calor, qui dum sem- pet intrà tropicos mouetur, aquas ad se allicit, & quæ sub llis sunt, paularim absumit: qui fit, vt ad earum libtamentum exæquandum, aquæ hincinde à Septentrione, & Austro versus æquatorem ruant; præsertim, si verum est quod ait idem Turnerius, Sole in Capricorno existenre, aquas, quæ intrà tropicos sunt, transire æquatorem, & naturali impetu ver- sus tropicum fluere; quod ipsum experiri est Sole existente in Cancro, nam illuc aquæ omnes accurrunt. Aristoteles ta- men, loco citato, hunc motum tribuit Aluminum multitudi- ni, & magnitudini, in Mæotin, & in Euxium mare sese exonerantium. Sextus denique motus Oceani est qui dicitur fluxus & refluxus spatio vigintiqnique circiter hotarum omninò in Lunam refundendus: de quo vide in Verbo Ampotim. Ex aquæ continuo motu Plotinus Philosophus, alijque < 269.> tam animatam dixêre. Quod fortassè non omninò incredi- bile exultimauetim, si non de anima tationali, neque de sen- sibili, aut vegetabili, sed de alia quadam alterius speciei, setmosit, quam jute dixetis locomotticem, & ea forsan cor- pora cælestia informantur, quæ illis intrinsecam vim sese
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MATHEMATICVM. 57 ium to obtain aid: the same thing is experienced by the Lusitanians heading toward the East Indies, even though they otherwise enjoy favorable winds. Of this matter Trimarchus gives many experiments, lib. Meteor. disp. 1. sect. 6. Adrianus, Metius, & Furnerius, lib. Hydrographia, cap. 23. The cause of this motion, however, Turnerius ascribes to the Sun’s heat, drawing humors and vapors continually to itself: thus also the fifth motion, which we said was from the poles to the equator; and especially within the tropics, that is, along the Sun’s path, where both motions appear more violent. Kepler refers it to the Moon, the waters, and all humors as acting by magnetic force. But the Arabs, and with them Vicomercatus, attribute it far more plausibly to the motion of the first mover, carrying along with it all the lower spheres: and so not only the lower heavens, but also the air and the ocean; although here, because it is slower than the other spheres, and because of the thickness of the watery element, it resists somewhat more than the air; this more than the higher heavens, as we have noted elsewhere. This opinion is not contradicted by Resta, De Meteoris, lib. 3. tr. 1. cap. 16, nor by Mastrius, ibid. mast. 4. num. 148. As for the fifth motion, however, which is called the motion of latitude from the poles to the equator, Aristotle already recognized it in 1 Meteor. cap. text. 6, and Alexander Aphrodisias, St. Thomas, Vicomercatus, Nyphus, and others followed him. Its cause is indeed nothing other, as Turnerius argues well, than the Sun’s heat, which, while it is continually moving within the tropics, attracts the waters to itself and gradually consumes those beneath it: this results in waters from here and there, from the North and the South, rushing toward the equator in order to restore their level; especially if what the same Turnerius says is true, namely that when the Sun is in Capricorn the waters that are within the tropics cross the equator and flow by natural impulse toward the tropic; the same thing can be observed when the Sun is in Cancer, for then all the waters rush there. Aristotle, however, in the cited passage, attributes this motion to the multitude and magnitude of the Aluminums discharging themselves into the Maeotic and into the Euxine sea. The sixth and final motion of the Ocean is that which is called ebb and flow, over a space of about twenty-five hours, and must altogether be referred to the Moon: see under the word Ampotim. From the continual motion of water Plotinus the philosopher and others called it animated. Which perhaps would not be altogether incredible if one were speaking not of rational soul, nor of sensitive or vegetative soul, but of some other soul of a different kind, which you might rightly call locomotive, and perhaps the heavenly bodies are informed by it, in which there is an intrinsic power to move themselves.
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MATHEMATICVM. 59 hi tres planetæ in eis dignitates obtinent; & Mars quidem, & Luna de nocte, Venus autem interdiu; adeoque dicitur trigonus Occidentalis propter Martis, & Lunæ dominatum. Quæ aurem regiones, & oppida huic triplicitati subsunt: vide in Ptolemæo lib 3. cap 2. AQUILA, vultur volans sidus in cælo ad Borealem plagam < 273.> instra Galaxiam stellas habens iuxta Ptolemæum & antiquiores 3. At Keplero reste 11. licet Baierus ei tribuat stellas omninò 31. sed confundit cum eo Antinoum. Omnes autem hæ stellæ sunt de natura Martis, & Iouis, inter quas splendida in scapulis secundæ magnitudinis Arabicè Alkasr. Hæc in Horoscopo dicit Pontanus quod facit feros, magnanimos, raptores, belligeros, mortis contemptores, sic enim canit; quibus Bella placens, & prada subacto ex hoste petita, Et spolijs vitam, & violenta agitare rapina: Nec dubiens etiam armatos incurrere in hostes, Nudi armos, mortemque velint pro laude pacisci. Quod si adhuc accesserit benignus radius Iouis, subdit, quod erunt victores, & parriam decorabunt, ac defendent armis ac victorijs. At si Sarurnus, aur Mars quouis modo astiterint, tunc facient quidem bellicosos, sed sub aliorum imperio. Id- ipsum confirmat Stadius. Oiitur autem Romæ cum gradu ferè 24. Sagittarij. AQVILO Boreas ventus Septentrionalis lateralis Septenttioni < 274.> inclinans ad Ortum; sic dictus à vehementissimo, ac celerimo flatu, quasi aquilæ volarum imitati velis. Est de natura sua frigidus, & succus, salubris, aërem purgans, & pro ratione temporis grandinosus, ac niuosus. Accipirur sæpenumero pro ipso vento Septentrionali vno, ex quatuor Cardinalibus ob vicinitatem, atque effectuum similitudinem: de eo vide Plin. lib. 2. cap. 47. AR ARA Sacrarium, Thutibulum, Lar, sidus in cælo ad Au- < 275.> stralem plagam nobis inconspicuum: de quo Cicero de Na- tura deorum. Deinde Nepa cernes propter fulgemiis acumen Aram, quam flatu permulces spiritus Austri. Coniinet stellas seprem omnes de natura Veneris, & parum Mercurij, inter quas præcipua tertiæ magnitudinis in medio Ammæ sita; quæ si in Horoscopo reperiatur (inquit Stadius) inclinat ad pietalem, ad sacerdoria capessenda, atque ad stu- dia sacrarum literarum, præserrim si bonum testimonium accesserit beneficarum: Ac verò in occasu cum malo radio
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MATHEMATICUM. 59 These three planets hold dignities in them; Mars indeed, and the Moon by night, Venus however by day; and therefore it is called the Western trigon because of the dominion of Mars and the Moon. What regions and towns are subject to this triplicity: see in Ptolemy, book 3, chap. 2. AQUILA, the flying vulture, a star in the heavens in the northern quarter within the Galaxy, having stars according to Ptolemy and the ancients 3. But according to Kepler 11; though Bayer assigns to it altogether 31 stars, but he confuses Antinous with it. All these stars are of the nature of Mars and Jupiter, among which the bright one in the shoulders of the second magnitude, in Arabic Alkasr. Of this in a horoscope Pontanus says that it makes men fierce, magnanimous, plunderers, warlike, despisers of death; for thus he sings; who, Delighting in war, and in plunder sought from a conquered enemy, And to spend life in spoils and violent robbery: Nor even shrinking to charge armed enemies, With bare shoulders, and they would rather bargain for death than for praise. But if there should still be added the benign ray of Jupiter, he adds that they will be victors, and will adorn and defend their fatherland with arms and victories. But if Saturn, or Mars in any way stand by, then they will indeed make men warlike, but under the command of others. This same thing is confirmed by Stadius. It rises at Rome with a degree of about 24 Sagittarius. AQVILO, Boreas, the northern wind, leaning sideways toward the north and inclining toward the east; so called from the very vehement and swift blast, as if imitating the flight of an eagle with its sails. It is by its nature cold and moist, wholesome, purging the air, and according to the season hail-bearing and snowy. It is often taken for the single north wind itself, from the four cardinal winds, because of its neighborhood and similarity of effects: concerning it see Pliny, book 2, chap. 47. AR ARA, a sanctuary, a thurible, a household god, a star in the heavens toward the southern quarter, invisible to us: concerning which Cicero in On the Nature of the Gods. Then you will see the altar by the gleam's sharpness, which the spirits of the South Wind soothe with their breath. It contains seven stars, all of the nature of Venus, and a little Mercury, among which the principal one of third magnitude is situated in the middle of the Altar; which if found in the horoscope (says Stadius) inclines to piety, to taking up sacred offices, and to studies of sacred letters, especially if a good testimony of benefics has been added: but indeed in the west with an evil ray
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Martis, aut Saturni, affert periculum combustionis. 276. ARANEA Rete, Voluellum in Astrolabio representans in plano omnem rationem primi mobilis sese in orbem rotando spatio quatuor, & viginti hotarum. In ea videre est descriptos nedum polos, & omnes circulos, qui concipiuntur in primo mobili, sed etiam præcipuas stellas fixas suo loco secundùm longitudinem, & latitudinem, ascensionem rectam atque declinationem, quam habent, additis etiam ad earum plenam noritiam singularum nominibus. Eius inuentorem ferunt fuisse Eudoxum quemdam Samium, qui etiam nomen indidit sumptum à reticula Araneæ cui est valdè persimilis: Arabicè dicitur albacantabus. 277. ARATEA sphæra dicitur globus Astronomicus vulgò Cælestis, in quo omnes stellæ fixæ suis quæque Asterismis inclusæ atque interstinctæ conspiciuntur vna cum positu ad æquatorem atque habitudine ad Zodiacum tam in longum, quam in latum: ita vt facili iure, huius instrumenti ope, possit quis stellam quamuis addiscere, locum in Zodiaco inuestigare, ortum & occasum noscere, ascensiones eruere, atque ad eam significatorum quemlibet per motum directionis deducere. Dicitur Aratae ab Arato antiquissimo poëta Græco eius inuentore, qui etiam Græcè elegantissimo carmine descriptit & explicauit, appellauitque librum Phanomena hoc est Apparentia. Quem posteà Germanicus Cæsar Augusti filius, Sextus Auienus Ruffus, & Marcus Tull. Cicero adhuc adolescens in latinum sermonem transtulerunt. 278. ARCHATAPIAS ex Græcobarb. dicitur in sphæra barbarica primus Decanus Piscium existens sub dispositione, ac dominatu Saturni, qui proinde dat ei significatum anxietatis, cogitationum profundarum, migrationis de loco ad locum, quærendi, & cumulandi opes &c. 279. ARCHITECTVRA ars est ex præceptis Geometricis comparata, qua traditur ratio extruendorum ritè quorumcunque ædificiorum humanæ vitæ commodis congruentium, ac penè ad vniuersi istius dispositionis idæam: Eius genera tria sunt ædificatio, Gnonomica, & Machinatio: Vide Vitruuium l.2.c.3. 280. ARCITENENS dictus est Sagittarius ab arcu, quem manibus gestat, vnde Sagittam ciaculare velle videtur, alio nomine Chyron, Centaurus &c. 281. ARCTOPHILAX Græcè hoc est Vrsacustos appellatur fidus in Cælo propè Vrsam constitutum, quasi ad eam constituendam alio nomine Vociferator, Bubulcus, Bootes. Stellas habet iuxta Ptolemæum 23. at secundùm Keplerum 18. & Baierum 34. qui tamen inter eas annumerat etiam informes circa consi-
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On Tuesday, or Saturday, it brings the danger of burning. 276. ARANEA, a web representing the Volvelle in the Astrolabe, in which, on a plane, the whole arrangement of the first mobile is shown by rotating itself in a circle in the space of twenty-four hours. In it one may see not only the poles described, and all the circles that are conceived in the first mobile, but also the principal fixed stars, each in its place according to longitude and latitude, right ascension and declination, which they have, with the names of each one also added for their full knowledge. They say its inventor was a certain Eudoxus of Samos, who also gave it the name, taken from the spider’s little web to which it is very similar; in Arabic it is called albacantabus. 277. ARATEA is the sphere, that is, the astronomical globe, commonly called the celestial sphere, in which all the fixed stars, enclosed and separated by their respective asterisms, are seen together with their position relative to the equator and their relation to the Zodiac, both in length and breadth: so that, quite rightly, by means of this instrument, one may learn any star, investigate its place in the Zodiac, know its rising and setting, determine its ascensions, and by direction bring to it any of the significators. It is called Aratea from Aratus, the most ancient Greek poet, its inventor, who also described and explained it in very elegant Greek verse, and entitled the book Phainomena, that is, Appearances. This was later translated into Latin by Germanicus Caesar, son of Augustus, Sextus Avienus Rufus, and Marcus Tullius Cicero while still a young man. 278. ARCHATAPIAS, from Graeco-barbarian usage, is said in the barbaric sphere to be the first Decan of Pisces, existing under the disposition and rule of Saturn, who therefore gives it the meaning of anxiety, deep thoughts, moving from place to place, seeking, and amassing wealth, etc. 279. ARCHITECTURE is an art based on geometric precepts, by which is taught the proper method of constructing any kind of building suited to the conveniences of human life, and almost to the idea of the arrangement of the whole. Its kinds are three: building, gnomonics, and machinery: see Vitruvius, book 2, chapter 3. 280. ARCITENENS is the name given to Sagittarius, from the bow which he carries in his hands, as though he wishes to shoot an arrow; by another name, Chiron, Centaurus, etc. 281. ARCTOPHILAX is the Greek term, meaning Bear-keeper, for the faithful one placed near the Bear in the sky, as though set to guard it; by another name, Vociferator, Bubulcus, Bootes. According to Ptolemy he has 23 stars, but according to Kepler 18, and according to Bayer 34, who nevertheless counts among them also the unformed stars around the constel-
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LEXICON Sagittario constituit Trigonum igneum, cuius dominatores sunt Sol, & Iupiter. Tempore Ptolemæi sub hoc signo erat si- dus, & constellatio Arietis in octaua sphæra continens stellas tredecim (exceptis quinque informibus circa ipsam) omnes ferè de natura Saturni, aut Martis, quarum prima in cornu borealì consistens immediatè incidebat in æquatorem; at nunc ob morum proprium octauæ sphæræ præcessit gr. ferè 28 Pri- mæ eius partes ventos & imbres faciunt, mitiùs tamen quàm tempore Ptolemæi: mediæ sunt temperatæ: extremæ tandem calidæ; cumque Zodiacus præditus sit latitudine, pars eius borealis est calidior, & nocua ob plures stellas ibi consistentes de naruta Martis & Mercurij: Australis verò frigida ob stellas de natura Saturni. 199. ARIO, teste Kirchero, Chaldaicè dicitur Leo, quintum ab Ariete signum: apud Hebræos autem Arich. 300. ARISIA, & Spica promiscuè appellatur fixa insignis in manu Vitginis, quæ triticeam spicam in manu gestare imagine præ- sesert: De ea satis dictum in Verbo Azimech, & alibi sæpè. 301. ARITHMETICA vna est ex principalioribus Mathesis disci- plinis, quæ versatur circa quantitatem discretam, seu mavis dicam, numeros (per quod contradistinguitur à Geometria, quæ considerat quantitatem continuam) tradens methodum supputandi, multiplicandi, & partiendi: proindeque omnes numetorum passiones, proportiones, & habitudines, quas ad- inuicem habent, considerat, atque aliis applicat, vt ex his tandem ad ignota deueniat. Sic positis tribus numeris notis, quartum numerum ignotum per proportionum regulam, quæ aliàs dicitur Aurea, præcipit inuenire: si videlicet secundus, & tertius multiplicentur ad inuicem, ac numerus ex multipli- catione productus diuidatur per primum: Nam numerus quo- tiens erit quartus quæsitus, hoc est cui tertius numerus cotes- pondet, & ad quem eandem seruat proportionem, quam pri- mus ad secundum. Hinc considerat in numeris additionem vnius ad alterum, quæ est duorum vel plurium numerorum in vnum collectio: substractionem, quæ est numeri minoris ab altero maiore subductio: multiplicationem, quæ est ductio vnius numeri in alium; sicque cum alter ipsorum augetur toties, quoties in altero continetur vnitas: ac tandem diuisio- nem quæ est partitio propositi alicuius numeri in partes ab al- tero numero denominatas. Ex ipsis autem numeris aliquem appellat partitorem, seu diuidentem, & est is qui denominat partes, in quas numerus diuidendus tribuitur; qui ob eam etiam causam denominator audit, quarenus denominat, & in- dicat partes, in quas vnum torum intelligitur esse diuisum: numeratorem
Transcription: Translated (English)
LEXICON Sagittarius constitutes the fiery Trigon, whose rulers are the Sun and Jupiter. In Ptolemy’s time under this sign was the constellation of Aries in the eighth sphere, containing thirteen stars (except five shapeless ones around it), almost all of the nature of Saturn or Mars, the first of which, standing in the northern horn, immediately fell upon the equator; but now because of the proper motion of the eighth sphere it has advanced about 28 degrees. The first parts of it produce winds and rains, though more mildly than in Ptolemy’s time: the middle parts are temperate: the extremities, finally, are hot; and since the Zodiac is endowed with latitude, its northern part is hotter and harmful because of the many stars there consisting of the nature of Mars and Mercury: the southern part, however, is cold because of the stars of the nature of Saturn. 199. ARIO, according to Kircher, in Chaldaean means Leo, the fifth sign from Aries: among the Hebrews, however, Arich. 300. ARISIA, and Spica are used interchangeably as names for the notable fixed star in the hand of Virgo, who is represented as holding an ear of grain in her hand: enough has been said about it under the word Azimech, and elsewhere often. 301. ARITHMETIC is one of the principal disciplines of Mathematics, which deals with discrete quantity, or, if I may say so, numbers (whereby it is distinguished from Geometry, which considers continuous quantity), providing the method of calculating, multiplying, and dividing: and therefore it considers all the properties, proportions, and relations of numbers among themselves, and applies them to other things, so that from these one may at last arrive at the unknown. Thus, given three known numbers, it prescribes finding a fourth unknown number by the rule of proportions, which is otherwise called the Golden Rule: namely, if the second and third are multiplied together, and the number produced by the multiplication is divided by the first. For the number sought will be the fourth, that is, the one to which the third number corresponds, and to which it preserves the same proportion as the first to the second. Hence it considers in numbers addition of one to another, which is the collection of two or more numbers into one; subtraction, which is the taking away of a smaller number from a larger one; multiplication, which is the carrying of one number into another; and so one of them increases as many times as unity is contained in the other; and finally division, which is the partition of some proposed number into parts named from another number. But from the numbers themselves it calls one a divisor, or divider, and this is the one that names the parts into which the number to be divided is apportioned; for which reason it is also called the denominator, insofar as it names and indicates the parts into which one whole is understood to be divided: numerator
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MATHEMATICVM. Accem stellis (quot videlicet chordæ sunt in Psalterio decachordo, quod per id nominis significatur) constans; apud nos Lyra, seu Fidicula. Keplerus autem in eo siderè considerat stellas vndecim, & Barcrus in sua Vranometria tredecim. ASBIA Græcè, Latinè dicitur Hydra. Vide suo loco. ASCENDENS, horoscopus, horizon, finitor Orientalis est linea illa in Oriente, vnde emergunt sidera, quæque diuidit hemisphærium superius nobis conspicuum ab inferiori, quod latet sub terra. Dicitur etiam angulus Orientis, & prima domus in cælesti figura Estque apud Astrologos significator vitæ, & corporis affectionum, morum itinerum &c. Significar etiam initia rerum, eo quod est domus initatiua cælestis motus. ASCENDENS etiam appellarur illa pars cæli, quæ incipit à li- nea Meridiana Imi cæli, & per viam Orientis incedens, vsq[ue] ad Meridianum superius extenditur (sicque includit tertiam, secundam, primam, duodecimam, vndecimam, ac decimam domum) vel inde dicta, quod per eam incedentes planetæ & partes primi mobilis semper ascendunt: sicut è contra descendens vocatur pars opposita, à linea Meridiana supra terram ad lineam Imi cæli per Occidentem gradiens, quia per eam planetæ semper descendunt. Hinc. ASCENSIONES, & d. ascensiones signorum sunt partes æquatoris, quæ cum tali signo, aut Zodiaci parte coascendunt, & simul descendunt; adeoque etiam planearum, quos in eisdem partibus reperiri contingit. Porrò ascensiones ac descensiones, aliæ rectæ, aliæ obliquæ. Ascensiones rectæ sunt partes æquatoris, quæ ascendunt per lineam rectam, adeoque comprehendunt omnes illas cæli parres, quæ sub linea recta ducta per polos muudi, & parres æquatoris oppositas continentur, quod accidit in sphæra recta, atque in sphæra obliqua tantum in circulo recto, seu Meridiano. Ascensiones, & descensiones obliquæ sunt partes æquatoris, quæ obliquè ascendunt, aut descendunt in sphæra obliqua vbi alter polorum attollitur: quoque obliquior erit sphæra, eò obliquior erit ascensio æquatoris, sicque minor portio eius ascendit cum signis Zodiaci borealibus, maiorum Australibus. E contrà maior arcus descendit in borealibus, quàm in australibus. Arcus verò differentiæ ascensionum, aut descensionum, qui intercipitur inter ascensionem rectam, & obliquam, vocatur DIFFERENTIA Ascensionalis, cuius ope extrahuntur ascensiones, ac descensiones obliquæ ad omnem poli elevationem. Datam elevatione poli alicuius regionis, ac declinatione sideris, statim apparet differentia ascensionalis, quæ pro ratione declinationis borealis, aut australis, addenda, vel subtrahenda E ij
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MATHEMATICVM. Consisting of stars (namely, as many as there are strings in the ten-stringed Psaltery, which is signified by that name); among us, Lyra, or Fidicula. Kepler, however, considers eleven stars in it, and Barocius in his Uranometria thirteen. ASBIA in Greek; in Latin it is called Hydra. See in its proper place. ASCENDENS, horoscopus, horizon, the eastern boundary is that line in the East, from which the stars emerge, and which divides the upper hemisphere, visible to us, from the lower, which lies hidden beneath the earth. It is also called the angle of the East, and the first house in the celestial figure. Among astrologers it is the significator of life, and of the affections of the body, of habits, journeys, etc. It also signifies the beginnings of things, because it is the initiating house of celestial motion. ASCENDENS is also called that part of the sky which begins from the meridian line of the lowest heaven, and, proceeding by way of the East, extends up to the upper meridian (and thus includes the third, second, first, twelfth, eleventh, and tenth houses), or so called because the planets and parts of the first mobile moving through it always ascend; just as on the contrary the descending is called the opposite part, from the meridian line above the earth to the line of the lowest heaven, moving through the West, because through it the planets always descend. Hence. ASCENSIONS, and so-called ascensions of signs, are parts of the equator which, together with a particular sign, or part of the Zodiac, co-ascend, and at the same time descend; and likewise also those of the planets, which may happen to be found in those same parts. Moreover, ascensions and descensions are some right, others oblique. Right ascensions are parts of the equator which ascend by a straight line, and therefore comprehend all those parts of the sky which are contained beneath a straight line drawn through the poles of the world, and the opposite parts of the equator; which occurs in the right sphere, and in the oblique sphere only in the right circle, or Meridian. Oblique ascensions and descensions are parts of the equator which ascend or descend obliquely in an oblique sphere where one of the poles is elevated: the more oblique the sphere, the more oblique will be the ascent of the equator, and thus a smaller portion of it ascends with the northern signs of the Zodiac, a larger with the southern. On the contrary, a larger arc descends in the northern than in the southern. But the arc of difference of ascensions or descensions, which is intercepted between the ascent right and oblique, is called the ASCENSIONAL DIFFERENCE, by means of which oblique ascensions and descensions are derived for every elevation of the pole. Given the elevation of the pole of a certain region, and the declination of a star, the ascensional difference immediately appears, which according to the measure of northern or southern declination is to be added or subtracted. E ij
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70 LEXICON 326. ASTRO, ex Græcobarbaro dicitur secundus decanus Aquarij, sub dominatu Mercurij in sphæra barbarica, significator bonorum morum, formæ, intellectus, mansuetudinis cum modestia, liberalitatis, &c. 327. ASTRABISTER dictum est instrumentum quoddam Geometricum ad mensutandas altitudines, & profunditates, instar radij Latini 328. ASTRAEA dicta est ab Arato Virgo, cæleste sidus inter Leonem & Libram, muruato ex fabulis nomine, fingunt enim Poëtæ ipsam justitiæ antistitem aureo illo sæculo è cælo in terras migrasse, sed mortalium sceleribus offensam cælos repetiisse, vbi in cæleste illud sidus conuersa eorum facta de longè perpendit, & aqua lance dijudicat: hinc illi lances applicitæ: alio nomine dicitur trigone, Auseno, Isis; eius sideris qualitatem, numerum stellarum, quibus constat, naturam & alia: Vide in V. Virgo 329. ASTROCYNOS, & ASTROCYON Græcè appellatur Canis sidereus maior, alio nomine Sirius qui inter multas stellas quibus integratur duas peculiari consideratione dignas habet, alteram in capite quæ vocatur Isis, alteram in ore seu lingua apud Arabes Alhabor: de vtrisque suo loco. 330. ASTROLABIVM instrumentum Mathematicum, totam ferè cælestem doctrinam in plano rep[er]æsentans, vnde & planisphærium dictum est quasi sphæram in plano demonstret, ex eo enim perquam bellè astrorum motus colliguntur, distantiæ menturantur, ascensiones, descensiones, declinationes, & alia id genus intuitiue noscuntur. Fertur à primo parente Adam inuentum, vel saue ab Abraham: lieet postea successu temporis perfectiùs semper, & perfectiùs elaboratum prodietit. De eius fabrica, & vsu multi scripsêre, imprimisque Egnatius Dantes, & Ioannes Stoslerinus egregiis voluminibus. 331. ASTROLOGIA Græcè, Latinè Astrorum sermo seu scientia interpretatur, quæ & Astronomia promiscuè dicta est: Nisi quod vsus postea obtinunt, vt Astrologia vsurparetur pronotitia quadam coniecturali ex astrorum positu comparata, qua de rerum mutationibus, alijsque effectibus qui à cælorum positu ottum habent, pronunciatur. Astronomia verò pro ipsa astrorum scientia sumitur, quæ in eorum præcisa consideratione sistit, stellarum motus, naturas, magnitudines, affectiones scrutatur, ac dimetitur: vnde Astrologia supponit Astronomiam, atque in ea fundatur. Hæc enim pars est nobilior Geometriæ, quantitatem continuam, sed solùm altioris ordinis, & cælestem considerans; illa scientia experimentalis longo vsu a posteriori, & ex effectibus comparata, quæ nec scien-
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70 LEXICON 326. ASTRO, from Græco-barbarous usage, is called the second decan of Aquarius, under the dominion of Mercury in the barbaric sphere, signifying good morals, beauty, intellect, gentleness with modesty, liberality, etc. 327. ASTRABISTER was said to be a certain Geometric instrument for measuring heights and depths, like the Latin radius 328. ASTRAEA, called by Aratus Virgo, is a heavenly star between Leo and Libra, the name being taken from the fables; for the poets imagine that she, the minister of justice, migrated from heaven to earth in that golden age, but, offended by the crimes of mortals, returned to the heavens, where, changed into that heavenly star, she weighs their deeds from afar and judges them with a balance of water: hence scales are applied to her. By another name she is called trigone, Auseno, Isis; the quality of that star, the number of the stars of which it is composed, its nature, and other things: see under V. Virgo 329. ASTROCYNOS, and ASTROCYON, in Greek, is called the greater dog-star, otherwise Sirius, which among the many stars of which it is made up has two worthy of special consideration, one in the head called Isis, the other in the mouth or tongue, called by the Arabs Alhabor: on both, see the proper place. 330. ASTROLABIVM, a Mathematical instrument representing almost the whole of celestial doctrine on a plane, whence it is also called a planisphere, as though it were showing the sphere on a plane; for from it the motions of the stars are very neatly gathered, distances are measured, ascents, descents, declinations, and other things of that kind are known intuitively. It is said to have been invented by the first parent Adam, or perhaps by Abraham: although later, in the course of time, it was always elaborated more and more perfectly. Many have written about its construction and use, especially Egnatius Dantes and Ioannes Stoslerinus in excellent volumes. 331. ASTROLOGIA, in Greek, is interpreted in Latin as the discourse or science of the stars, and was used interchangeably with Astronomia: except that later usage came to prevail, whereby Astrologia was used for a certain conjectural foreknowledge derived from the position of the stars, by which changes in things and other effects that have their origin from the position of the heavens are announced. Astronomia, however, is taken for the science of the stars themselves, which rests in their exact consideration, investigates and measures the motions, natures, magnitudes, and properties of the stars: whence Astrologia presupposes Astronomia, and is founded upon it. For this is the nobler part of Geometry, considering continuous quantity, but only of a higher order and celestial; that is an experimental science, acquired long by use a posteriori and from effects, which neither scien-
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tiæ quidem nomen metetur, quandoquidem neque rem per causam scrutatur, neque certitudinem habet, quæ scientiæ animæ est, sed per conjecturas, & experimenta procedit. Hæc propriissimè, ac strictissimè scientia in summo certitudinis apicè sita. Quamobrem, etsi in nomine, seu potius nominis notione conueniant, in re tamen longissimè differunt. <332.> Porrò Astrologiæ objectum sunt naturales effectus à causis cælestibus producibiles, quatenus perspectâ rerum naturâ, corporumque cælestium inter se habitudine, ex iis, quæ alias experientia duce pluries euenisse Astrologus noscit, prudens colligit similes effectus ex simili causarum congressu etiam prodituros. Verum, quia inter naturales effectus alij sunt, qui merè à natura proueniunt, & quidem necessitò (posito divino, & vniuersali concursu, & causarum secundarum connexione) qualis est calor, qui ab igne naturaliter prouenit, nutritio Animalis naturaliter præstita per alimenta &c. alij, qui etsi naturaliter prodeant, originatiè tamen sunt à causa libera, liberè media, proportionata, & causas subordinatas ad talium effectuum productionem applicante; qualis est occisio hominis abs se, vel ab alio præstita, domus ædificatio, liberorum procreatio &c. alij, qui à causa libera liberè etiam secundùm substantiam proueniunt, vt studium, pietas, amor, odium, virtutes denique & vitia, quæ à natura non nisi valdè remotè ex qualitate temperamenti dependent; alij demum qui mixti ordinis sunt, pendent enim ex natura simul, & libera hominis voluntate, ita vt fiat ex iis quædam causarum confusio, atque mixtio, in qua effectus naturales sæpè humano artificio perueruntur, sæpè etiam adjuuantur, quales sunt plantarum insitio, terræ quantumuis rudis, & asperæ (idem, pro sui ratione, dic de ingenio) excolatio &c. idcircò varia est astrorum circa huiusmodi effectus actiuitas, varia etiam Astrologiæ de eorum productione diuinatio. Cum profectò quæ à natura purè, & absque vllor vel sanè paruo hominis artificio prouenint, necessitò etiam producantur, atque adeò certò per Astrologiæ præcepta prædici possint; quæ purè à libertate humana pendent, siue secundùm se tota, siue originatiuè, aut per sui magnam partem omninò liberè prodeant, sicque etiam ab Astrologo vel nullo modo, vel posita conditione, vel sanè valdè remotè ex debili quadam conjectura desumpta ex temperamento possint prædici; Quæ verò mixta sunt, possunt quidem ex parte præuideri, quâ videlicet ex naturali causarum connexione pendent, cum ea certitudine, aut probabilitate, quam causæ libetæ cum natura simul concurrentis maior, aut minor actiuitas, diligentia, obsistentia dat posse fieri. Hinc fallaces, E iiij
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this name indeed it merits, inasmuch as it neither examines the matter through its cause, nor has that certainty which belongs to the science of the soul, but proceeds by conjectures and experiments. This, most properly and most strictly, is science placed at the highest peak of certainty. Wherefore, although they agree in the name, or rather in the notion of the name, yet in reality they differ most widely. <332.> Moreover, the object of Astrology is natural effects producible from celestial causes, insofar as, the nature of things and the mutual relation of the celestial bodies having been observed, the Astrologer prudently infers from those things which experience, as guide, has several times known to have happened, that similar effects will also arise from a similar conjunction of causes. But because among natural effects some are such as arise purely from nature, and indeed necessarily (given the divine and universal concurrence, and the connection of secondary causes), such as heat, which naturally proceeds from fire, the nutrition of an animal naturally supplied by food, and so on; others, which although they proceed naturally, are nevertheless originally from a free cause, freely intermediate, proportioned, and applying subordinate causes to the production of such effects; such as the killing of a man by oneself or by another, the building of a house, the procreation of children, and so on; others, which proceed also from a free cause according to their substance, such as study, piety, love, hatred, and finally virtues and vices, which from nature depend only very remotely on the quality of temperament; others at last, which are of a mixed order, for they depend on nature and at the same time on the free will of man, so that a certain confusion and mixture of causes arises from them, in which natural effects are often perverted by human artifice, and often also assisted, such as the grafting of plants, the cultivation of soil however rough and uncultivated (the same, in proportion, may be said of the mind) and so on; therefore the activity of the stars regarding effects of this kind is various, and Astrology’s prediction of their production is also various. For certainly those things which proceed purely from nature, and without any or at least very little human artifice, must also necessarily be produced, and therefore can be predicted with certainty by the precepts of Astrology; those which depend purely on human freedom, whether wholly in themselves, or originally, or by a very large part of themselves entirely freely arise, can thus be predicted by the Astrologer either not at all, or on condition, or at least very remotely from some weak conjecture drawn from temperament; but those which are mixed can indeed be foreseen in part, namely insofar as they depend on the natural connection of causes, with that certainty or probability which the greater or lesser activity, diligence, or resistance of a free cause concurrent with nature allows to be assigned. Hence deceptive, E iiij
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Martis, aut Saturni, affert periculum combustionis. 276. ARANEA Rete, Voluellum in Asttolabio representans in plano omnem rationem primi mobilis sese in orbem rotando spatio quatuor, & viginti horarum. In ea videre est descriptos nedum polos, & omnes circulos, qui concipiuntur in primo mobili, sed etiam præcipuas stellas fixas suo loco secundùm longitudinem, & latitudinem, ascensionem rectam atque declinationem, quam habent, additis etiam ad earum plenam noritiam singularum nominibus. Eius inuentorem serunt fuisse Eudoxum quemdam Samium, qui etiam nomen indidit sumptum à reticula Araneæ cui est valdè persimilis: Arabicè dicitur albacantabat. 277. ARATEA sphæra dicitur globus Astronomicus vulgò Cælestis, in quo omnes stellæ fixæ suis quæque Asterismis inclusæ atque interstinctæ conspiciuntur vna cum positu ad æquatorem atque habitudine ad Zodiacum tam in longum, quam in latum: ita vt facili iure, huius instrumenti ope, possit quis stellam quamuis addiscere, locum in Zodiaco inuestigare, ortum & occasum noscere, ascensiones eruere, atque ad eam significatotum quemlibet per morum directionis deducere. Dicitur Arataa ab Arato antiquissimo poëta Græco eius inuentore, qui etiam Græcè elegantissimo carmine descripsit & explicauit, appellauitque librum Phanomena hoc est Apparentia. Quem posteà Germanicus Cæsar Augusti filius, Sextus Auienus Ruffus, & Marcus Tull. Cicero adhuc adolescens in latinum sermonem transtulerunt. 278. ARCHATAPIAS ex Græcobarb. dicitur in sphæra barbatica primus Decanus Piscium existens sub dispositione, ac dominatu Saturni, qui proinde dat ei significatum anxietatis, cogitationum profundarum, migrationis de loco ad locum, quærendi, & cumulandi opes &c. 279. ARCHITECTVRA ars est ex præceptis Geometricis comparata, qua traditur ratio extruendotum ritè quorumcunque ædificiorum humanæ vitæ commodis congruentium, ac penè ad vniuersi istius dispositionis idæam: Eius genera tria sunt ædificatio, Gnonomica, & Machinatio: Vide Vittuuium l.2.c.3. 280. ARCITENENS dictus est Sagittarius ab arcu, quem manibus gestat, vnde Sagittam eiaculare velle videtur, alio nomine Chyron, Centaurus &c. 281. ARCTOPHILAX Græcè hoc est Vesacustos appellatur fidus in Cælo propè Visam constitutum, quasi ad eam constituendam alio nomine Vociferator, Bubulcus, Bootes. Stellas habet iuxta Ptolemæum 23. at secundùm Keplerum 28. & Baierum 34. qui tamen inter eas annumerat etiam informes circa consu-
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It presents a danger of combustion on Tuesday or Saturday. 276. ARANEA: A web, representing the turning sphere in the Astrolabe, on a plane, the whole doctrine of the first mobile, revolving in a circle in the space of twenty-four hours. In it may be seen not only the poles and all the circles conceived in the first mobile, but also the principal fixed stars in their places according to longitude and latitude, right ascension and declination, which they have, with the names of each added for full knowledge of them. They say its inventor was a certain Eudoxus of Samos, who also gave it its name, taken from the spider’s little web to which it is very similar: in Arabic it is called albacantabat. 277. ARATEA sphere is called the astronomical globe, commonly the celestial one, in which all the fixed stars, each enclosed and interspersed in their asterisms, are seen, together with their position relative to the equator and their relation to the Zodiac, both in length and in breadth: so that, by this instrument’s aid, one may easily learn any star whatsoever, investigate its place in the Zodiac, know its rising and setting, determine its ascensions, and by that means draw forth any signification through the direction of the influences. It is called Aratea from Aratus, the most ancient Greek poet, its inventor, who also described and explained it in very elegant Greek verse, and called the book Phanomena , that is, Apparitions. This was later translated into Latin by Germanicus Caesar, son of Augustus, Sextus Avienus Rufus, and Marcus Tullius Cicero while still a young man. 278. ARCHATAPIAS, from barbarized Greek, is said in the sphere to be the first Decan of Pisces, existing under the disposition and dominion of Saturn, who therefore gives it the meaning of anxiety, deep thoughts, moving from place to place, seeking, and accumulating wealth, etc. 279. ARCHITECTURE is an art formed from geometric precepts, by which the method is taught of rightly constructing whatever buildings may be fitting for the needs of human life, and nearly for the idea of the arrangement of this whole. Its three kinds are building, gnomonics, and machinery: see Vitruvius, book 2, chapter 3. 280. ARCITENENS was the name given to Sagittarius from the bow he carries in his hands, as if he wished to shoot an arrow; by another name, Chiron, Centaur, etc. 281. ARCTOPHILAX, in Greek, that is, Bear-keeper, is called a faithful one placed in the sky near the Bear, as if appointed to guard it; by another name, Vociferator, Bubulcus, Bootes. According to Ptolemy he has 23 stars, but according to Kepler 28, and according to Bayer 34, who nevertheless also counts among them the unformed stars around the constel-
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62 LEXICON diameter verò 41. Si 21. quæ est quantitas semidiametri multi- plicetur per 66. Dimidium circumferentiæ producetur nume- sus areæ circuli prædicti 1186. Rectangulum enim compre- hensum sub semidiametro cuiusuis circuli, & dimidiara parre circumferentiæ eiusdem æquale est eidem circulo. 286. AREA item appellari solet circulus ille qui sub Sole, Luna alijsque astris efficitur ex haliruum copia ibi adunatorum, in quos eorum radij incidentes, quandam veluti coronam circa ipsum fidus efformare videntur: Qua de re vide quæ dicentur in V. Coronæ, nec non in V. Halones. 287. AREDIR Arab idem est ac pulsatio dispositionis & naturæ alicuius planetæ; quod tunc sit, cum aliquis Planeta repertus in alterius dignitatibus illum respicit aliquo radio: nam tunc ille dicetur transmittere suam dispositionem, & virtutem ei, in cuius dignitatibus reperitur. Et hæc transmissio à Latinis di- citur pulsatio. Aliter explicatum fuit in V. Aikia Dapha quod interpretatur pulsatio virtutis. 288. ARGENTVM, seu Argenticomus dicitur apud Astronomos species quædam noui Phænomeni, seu comætes de natura lo- uis, qui est adeò fulgidus vt vix in eum oculorum acies inten- di possit, vt proinde argenti, vnde nomen hausit, fulgorem & puritatem imitari videatur. Hic de nouo apparens Principibus indicat mutationem vitæ, ac regni, quæ, licet fiat in melius, non tamen erit absque perturbationibus, & animi angore. Si- gnificat etiam in vniuersum copiam frugum, bonamque aëris constitutionem, ac salubritatem. De hoc hæc habet Plin. Fis etiam candidus cometes argenteo crinesta refugens vt vix contueri liceat specieque humana Dei effigiem in se ostendens. Quæ verba suspicatur Fromendus spectare ad stellam Magorum, ac de ea voluisse Plinium loqui, quia fama percrebuerat in ludea visum Cometem fulgentissimum in cuius medio imago erat cuiusdam pueruli expressa. 289. ARGESTES Græcè dicitur ventus Occidentalis collateralis Fauonio spirans ab occasu æstuiali à nostris dictus Corne, ab aliis Scoron, & Olympias est natura frigidus, & humidus; licet ab initio siccus, vnde & procellas adducit (vnde ei nomen à Græcis) & niues & grandines facit. Per flat potissimum in æquinoctio autumnali. 290. ARGETENAR Arab. dicitur stella fixa quartæ magnirudinis in flexu Eridani propè Acarnar. 291. ARGION Græcè idem, quod Bootes: de quo suo loco. Hic in Horoscopo repertus, inquit Firmicus, facit hominem ab omni venationis studio alienum, sed qui tamen venationis fructu gaudat, canes ad hoc curriat, arma, retia, ac sagittas
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62 LEXICON diameter, moreover, 41. If 21, which is the quantity of the semidiameter, is multiplied by 66, half the circumference is produced; the number of the area of the aforesaid circle is 1186. For the rectangle enclosed under the semidiameter of any circle and half the circumference of the same is equal to that circle. 286. AREA is also the name given to that circle which is formed under the Sun, Moon, and other stars by the abundance of haloes gathered there, in which the rays falling upon them seem to form a kind of crown around the star itself: on this matter see what is said in V. Coronæ, and also in V. Halones. 287. AREDIR, in Arabic, is the same as the pulsation of the disposition and nature of some planet; which occurs when some planet found in the dignities of another looks upon it with some ray: for then it is said to transmit its disposition and virtue to that in whose dignities it is found. And this transmission is called by the Latins pulsation. It was otherwise explained in V. Aikia Dapha, which is interpreted pulsation of virtue. 288. ARGENTVM, or Argenticomus, is said by astronomers to be a certain kind of new phenomenon, or comet of a light nature, so bright that the eye can scarcely be directed toward it, and thus it seems to imitate the brightness and purity of silver, from which it takes its name. When appearing anew, it indicates to princes a change of life and of kingdom, which, although it may be for the better, will nevertheless not be without disturbances and anguish of mind. It also signifies in general an abundance of crops, good constitution of the air, and healthfulness. Concerning this, Pliny writes: “There is also a white comet, with silver hair streaming back, so that it can scarcely be looked at, and showing in itself, with human appearance, the likeness of a god.” Fromendus suspects that these words refer to the star of the Magi, and that Pliny wished to speak of it, because rumor had spread that in Judea a most brilliant comet had been seen, in the middle of which was expressed the image of a certain little boy. 289. ARGESTES, in Greek, is called the western collateral wind, blowing from the summer sunset; by our people called Corne, by others Scoron, and Olympias. By nature it is cold and moist, though at first dry, whence it brings storms (from which it gets its name among the Greeks), and makes snow and hail. It blows most especially at the autumnal equinox. 290. ARGETENAR, in Arabic, is called a fixed star of the fourth magnitude in the bend of Eridanus, near Acarnar. 291. ARGION, in Greek, is the same as Bootes: see it in its proper place. When found in the horoscope, says Firmicus, it makes a man entirely alien to every pursuit of hunting, though one who nevertheless rejoices in the fruits of hunting; he runs to dogs for this purpose, arms, nets, and arrows
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LEXICON Denique ea est Arithmeticæ facultatis dignitas, vt quemadmoduni obseruauit Philosophus in primo Physicorum, ipsa necessariò omnes Mathematicas scientias præcedat, ad earumque notitiam nos manducat, atque vt Platonis verbis vtar, Arithmeticam si quis ausert, omnes attes aufetuntur & nullæ manent, & omnes in totum peribunt. Verum si quis diuinam, & mortalem originem inspexerit, in qua pietas erga deos, & numerus cognoscitur, cognoscit, quantum numero opus sit: nam & tota Musica numeris opus habet in motibus, & sonis: & quod maximum est, numeri omnium bonorum causa sunt, ex quo cognosci possit, quod omne malum, & omnis motus rationis expers, & indecorus sine rythmo est, & inconcinus: & omnia quæ cum malo communionem habent esse absque numero oportet tandem statuere eum qui felix futurus est, & qui justum, & bonum, & pulchrum, & omnia huiuscemodi ignorat. A Plato: De Arithmeticæ inuentione vide Polydor. Virgil. lib 1. c. 18 & Rhodigin. lib 18 c. 34 302. ARMILLA olim dicebatur ornamentum militare, ad modum circuli, quo milites ex bello victores honoris causa ab Imperatoribus munerabantur, vt eo armum (sic enim audiebat antiquis simistrum brachium) ad fortitudinis indicium decorarent. Inde ad omne circulorum genus significandum hoc nomen translatum est: præcipuè verò apud Astronomos, apud quos circuli materiales sphæræ, sed potssimum suspensorum Astrolabij, vel alterius consimilis instrumenti positum ad illud perpendiculariter statuendum, quod Arabes Abalantica vocaure, Armilla antonomasticè dicta est: Inde etiam. 303. ARMILLARIS sphæra appellatur quæ pluribus circulis ex solidiori aliqua materia factis interstincta totam primi mobilis doctrinam continet, atque oculis exhibet ad differentiam Arataæ non ita pridem memoratæ, quæ vndequaque solida est, atque in ea circuli, & sidera fixa tantum delineata propriis quæque locis apparent. 304. ARNIG. Arab. Musicale dicitur instrumentum, quod ideò apud Astronomos Arabes sumitur pro ridicula, Lyra, seu Vulture cadente, cælesti sidere, de quo alibi sermo. 305. AROLABVM instrumentum Mathematicum ad venandas siderum affectiones. 306. ARPEEN Græcobarbar. dicitur tertius Decanus Libræ in sphæra barbarica sub dominaru Louis, habens significationem gulositatis, hilaritatis, carminum malorum saporum, &c. 307. ARTVRVS. Vide Arcturus. AS 308. ASANGES Chaldaicè, vel potius Mesanguo dicitur astrum
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LEXICON Finally, such is the dignity of the art of Arithmetic, that, as the Philosopher observed in the first book of the Physics , it necessarily precedes all the mathematical sciences, and leads us to the knowledge of them; and, to use Plato’s words, if anyone takes away Arithmetic, all the arts are taken away and none remain, and all will utterly perish. But if anyone considers its divine and mortal origin, in which reverence toward the gods and number are known, he will understand how much number is needed: for the whole of Music also has need of numbers in motions and sounds; and, what is greatest, numbers are the cause of all good things, from which it may be known that every evil, and every motion devoid of reason and indecorous, is without rhythm and discordant; and it must at last be established that all things which have communion with evil are without number, he who is to be happy, and who knows nothing of the just, the good, the beautiful, and all things of this kind. From Plato: on the invention of Arithmetic see Polydor. Virgil., book 1, c. 18, and Rhodigin., book 18, c. 34. 302. ARMILLA was formerly called a military ornament, in the form of a circle, with which soldiers, victorious in war, were rewarded by Emperors as an honor, so that they might adorn the arm (for so the ancients called the left arm) as an indication of bravery. From this the name was transferred to signify every kind of circle; especially among Astronomers, among whom the material circles of the sphere, but chiefly the rings of the suspended Astrolabe, or of another similar instrument set perpendicular to it, which the Arabs called Abalantica, was antonomastically called Armilla. Hence also. 303. ARMILLARY sphere is the name given to that which, being marked out by several circles made of some more solid material, contains and displays to the eye the whole doctrine of the first mobile, in distinction from the Aratea lately mentioned, which is solid throughout, and in which the circles and fixed stars only appear drawn in their proper places. 304. ARNIG. In Arabic, a musical instrument is called thus, which is therefore taken by Arab astronomers for a kind of ridiculous Lyre, or the setting Vulture, a heavenly star, of which there is mention elsewhere. 305. AROLABVM, a mathematical instrument for hunting the affections of the stars. 306. ARPEEN is called, in Greek-barbarous language, the third Decan of Libra in the barbaric sphere under the dominion of Louis, having the signification of gluttony, cheerfulness, bad-tasting songs, etc. 307. ARTVRVS. See Arcturus. AS 308. ASANGES, in Chaldean, or rather Mesanguo, is called a star
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70 LEXICON 326. ASTRO, ex Græcobarbaro dieitur secundus decanus Aquarij, sub dominatu Mercurij in sphæra barbarica, significator bonorum morum, formæ, intellectus, mansuetudinis cum modestia, liberalitatis, &c. 327. ASTRABISTER dictum est instrumentum quoddam Geometricum ad mensurandas altitudines, & profunditates, instar radij Latini 328. ASTRAA dicta est ab Arato Virgo, cæleste sidus inter Leonem & Libram, mutuato ex fabulis nomine, fingunt enim Poëtæ ipsam justitiæ antistitem aureo illo sæculo è cælo in teitas migrasse, sed mortalium seeleribus offensam cælos repetisse, vbi in cæleste illud sidus eouersa eorum facta de longè perpendit, & æqua lanee dijudicat: hinc illi lanees applicitæ: alio nomine dicitur trigone, Auseno, Isis; eius sideris qualitatem, numerum stellarum, quibus constat, naturam & alia: Vide in V. Virgo 329. ASTROCYNOS, & Astrocyon Græcè appellatur Canis sidereus major, alio nomine Sirius qui inter multas stellas quibus integratur duas peculiari consideratione dignas habet, alteram in capite quæ vocatur Isis, alteram in ore seu lingua apud Arabes Alhabor: de vtrisque suo loco. 330. ASTROLABIVM instrumentum Mathematicum, totam ferè cælestem doctrinam in plano repræsentans, vnde & planisphærum dictum est quasi sphæram in plano demonstret, ex eo enim perquam bellè astrorum motus colliguntur, distantiæ mensurantur, aleensiones, descensiones, declinationes, & alia id genus intuitiue noscuntur. Fertur à primo parente Adam inuentum, vel saue ab Abraham: licet postea successu temporis perfectiùs semper, & perfectiùs elaboratum prodierit. De eius fabriea, & vsu multi scripsêre, imprimisque Egnatius Dan- tes, & Ioannes Stroflerinus egregiis voluminibus. 331. ASTROLOGIA Græcè, Latinè Astrorum sermo seu scientia interpretatur, quæ & Astronomia promiscuè dicta est: Nisi quod vsus postea obtinuit, vt Astrologia vsurparetur pro notitia quadam coniecturali ex astrorum positu comparata, qua de rerum mutationibus, alijsque effectibus qui à exlorum positu ortum habent, pronunciatur. Astronomia verò pro ipsa astrorum scientia sumitur, quæ in eorum præcisa consideratione sistit, stellarum motus, naturas, magnitudines, affectiones serutatur, ac dimetitur: vnde Astrologia supponit Astronomiam, atque in ea fundatur. Hæc enim pars est nobilior Geometriæ, quantitatem continuam, sed solùm altioris ordinis, & cælestem considerans; illa scientia experimentalis longo vsu a posteriori, & ex effectibus comparata, quæ nec scien-
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70 LEXICON 326. ASTRO, from Græco-barbarous usage is called the second decan of Aquarius, under the dominion of Mercury in the barbaric sphere, a significator of good morals, beauty, intellect, gentleness with modesty, liberality, etc. 327. ASTRABISTER is the name given to a certain Geometric instrument for measuring heights and depths, in the manner of a Latin radius. 328. ASTRAA, called by Aratus Virgo, a celestial star between Leo and Libra, borrows its name from fables; for the poets imagine that she herself, the guardian of justice, in that golden age migrated from heaven to earth, but being offended by the crimes of mortals, returned to heaven, where in that celestial star she from afar contemplates their deeds turned upside down, and judges them in an equal scale: hence the scales are attached to her. By another name she is called trigone, Auseno, Isis; the quality of that star, the number of the stars of which it consists, its nature, and other things: See in V. Virgo 329. ASTROCYNOS, and Astrocyon in Greek, is called the great sidereal Dog, otherwise Sirius, which among the many stars of which it is made up has two worthy of special consideration, one in the head, called Isis, the other in the mouth or tongue among the Arabs Alhabor: concerning both in their proper place. 330. ASTROLABIVM, a Mathematical instrument, representing almost the whole of celestial doctrine on a plane, whence it is also called a planisphere, as if it demonstrates a sphere on a plane; for by means of it the motions of the stars are beautifully gathered, distances are measured, ascensions, descensions, declinations, and other things of that kind are known intuitively. It is said to have been invented by the first parent Adam, or perhaps by Abraham: although afterward over the course of time it came forth ever more perfectly and more perfectly worked out. On its construction and use many have written, and especially Egnatius Dan- tes, and Ioannes Stroflerinus, in excellent volumes. 331. ASTROLOGIA in Greek is interpreted in Latin as the discourse or science of the stars, and this has also been called Astronomy indiscriminately: unless later usage has prevailed, so that Astrology is used for a certain conjectural knowledge derived from the arrangement of the stars, by which one pronounces on changes in things, and other effects which arise from the arrangement of the stars. Astronomy, however, is taken for the science itself of the stars, which rests in their precise consideration, investigates and measures the motions, natures, magnitudes, and properties of the stars: whence Astrology presupposes Astronomy and is founded upon it. For this is the nobler part of Geometry, considering continuous quantity, but only of a higher order, and celestial; that science is experimental, gathered a posteriori over a long use, and from effects, which neither is scien-
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MATHEMATICVM. 79 temporis esse inueniuntur, Saturni initio Capricorni cum min. 35. Louis in grad. 7. minut. 27. Libræ: Martis in grad. 29. min. 29. Leonis: Solis in grad. 11. min. 4. Cancri. Veneris in grad 16 minut. 50. Geminorum: Mercutij tandem (cum in Luna eam assignare non sit) in grad. 1. min. 39 Sagittarij. Similiter oppositum Augis est in partibus signorum oppositis. Plura habes apud extractores Tabularum secundorum mo-bilium. AX <356.> Axis apud Astronomos audit linea quædam imaginaria, quæ ab uno Mundi cardine, seu polo per centrum telluris tran-siens, in alterum terminatur; circa quam totam Cælorum machinam intelligimus circumvolui. Et quoniam plures po-los, pro ratione motuum atque orbitarum secundorum mo-bilium, circa quos singula agitentur, conamur astruere, vt dicemus, cum fiet termo de polis; ideò plutes axes ab vno in alterum, ex dictis polis protensos concipi necesse est, qui omnes, per centrum telluris transite debeant, seque mutuò intersecare: ita vt nihil aliud axis sit, quàm mundi dia-meter, circa quam sphætiæ voluntur. Antonomasticè tamen accipitur pro insigniore, hoc est axe mundi ad eiusdem polos Arcticum, & Antarcticum terminante. AZ <366.> AZELFAGE Arab. dicitur cauda Cigni, stella fixa secundæ magnirudinis de natura Veneris, & Mercurij, existens nunc temporis in primo gradu Pilcium cum latitudine boreali gr. ferè 60. intrà Galaxiam. Hæc in horoscopo aut cum Luna maximè inclinare dicitur ad Venerea, quippe quæ habet natu-ra sua corpus humoribus replere, ac spectra producere. Est nunc Verticalis Florentiæ, Bononiæ, Placentiæ, aliisque Galliæ Cisalpinæ vrbibus, quæ sunt in eleuatione poli grad. 44. cum ipsa totidem ferè habeat declinationis borealis. Alio nomine, sed corrupto, vt notat Ricciolus, dicitur Deneb. Adsgege. AZEMENA Arab. idem sonat, ac corporis debilitas: Vnde pars Azemena apud Arabes Generhiacos audit ea pars quæ dirigitur pro corporis infirmiratibus. Absolutè autem sumpta sunt cerri quidam gradus signorum, in quibus reperta Luna, aut maleficus, adducit morbum aliquem incurabilem, seu inseparabilem, vt sunt cæcitas, surditas, membri debilitas, & similia; idque pro ratione signorum, & planetarum tam ibi existentium, quam eundem locum respicientium, habito etiam respectu ad situm mundi, in quem incidit talis gradus Por-ò gradus Azemene quos Arabes omnes, & nonnulli ex
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MATHEMATICVM. 79 times are found to be, Saturn at the beginning of Capricorn, with min. 35. Louis in grad. 7. minut. 27. Libra; Mars in grad. 29. min. 29. Leo; the Sun in grad. 11. min. 4. Cancer. Venus in grad. 16 minut. 50. Gemini: Mercury finally (since in the Moon it is not possible to assign it) in grad. 1. min. 39 Sagittarius. Likewise the opposite of the Augis is in the opposite parts of the signs. You have more at the extractors of the Tables of the second mobiles. AX <356.> Axis among Astronomers is called a certain imaginary line, which passing from one cardinal point of the World, or pole, through the center of the earth, ends at the other; around which we understand the whole machine of the Heavens to revolve. And since we attempt to establish more poles, according to the motions and orbits of the second mobiles, around which each of the things may be moved, as we shall say when the subject of the poles comes up, it is therefore necessary to conceive many axes extended from one to the other of the said poles, which all must pass through the center of the earth and mutually intersect one another: so that axis is nothing other than the diameter of the world, around which the spheres are turned. Yet it is taken antonomastically for the more distinguished one, that is, the axis of the world terminating at its Arctic and Antarctic poles. AZ <366.> AZELFAGE, in Arabic, is said to be the tail of Cygnus, a fixed star of the second magnitude, of the nature of Venus and Mercury, now situated in the first degree of Pisces, with a northern latitude of about 60 degrees, within the Galaxy. In a horoscope, or when the Moon is especially inclined to it, it is said to be favorable to Venusian matters, since by its nature it fills the body with humors and produces specters. It is now Vertical at Florence, Bologna, Piacenza, and other cities of Cisalpine Gaul, which are at a pole elevation of 44 degrees, since it itself has almost as much northern declination. Under another name, though corrupted, as Ricciolus notes, it is called Deneb Adsgege. AZEMENA, in Arabic, signifies the same as bodily weakness: whence the part Azemena among the Arabes Generhiaci is called that part which is directed toward bodily infirmities. Taken absolutely, however, there are certain degrees of the signs, in which, when the Moon or a malefic is found, some incurable or inseparable disease is brought on, such as blindness, deafness, weakness of a limb, and the like; and this according to the nature of the signs and of the planets both existing there and regarding that same place, with due regard also to the position of the world into which such a degree falls. Moreover, the degrees of Azemene, which all the Arabs, and certain of
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LEXICON mæus, neque à Gadibus Insula, vt placuit Straboni, Artemidoro, & Proclo: qui proprereà ab istis locis numerare incipiebant longitudines Ciuitatum, quia ignorabant verum Occidens, quod præcedenti tantum sæculo, tanto cum Christianæ Reipublicæ bono, ac detegensium laude repertum est. Siquidem, vt benè aduertit Iunctinus in sphæram Io. de Sacrobosco, cum verum Occidens constitui debeat in fine tetrae habitabilis ex opposito Orientis, atque ad angulos rectos polorum Mundi; consequenter ibi erit, vbi linea quædam concipiaur, diuidens æquatorem ad angulos rectos, & Colurum solstitiorum intersecans; quæ à nauigantibus linea diametri, seu diametet Mundi appellariur. < 374.> Porrò hæc linea comprehendit immediatè laudatas Insulas, parum vltia Promontorium Hieron, ad quinque gradus: vbi etiam acus nautica, seu sagitta magnetica se rectè vertit ad polos mundi, diuidens æquatiorem ad angulos rectos. Quod etiam oculatus testis probat à se expertum Gonzalus de Ouedo in summario de itineribus ad partes India Occidentalis cap. 84. qui regiones illas quatuor vicibus peragruit. Ait enim se, quoriscumque peruenit ad istud Meridianum, semper vidisse magnetis sagittam rectè se vertere diametraliter ad polos mundi. Et narrat lepidam historiam memoratu dignam, quod quoriscunque ei coniagit cum suis locijs per hanc lineam pertransire, omnes pediculi, quos ipsi habebant in capitibus, in vestimentis, aut vbiuis in nauibus, confestim tanquam mortui deueniebant, atque ipsi ab eorum molestia libetabantur: verum cùm posteà discedereat ab illis partibus Occidentalibus ac suo itinere Hispaniæ viam adorientes cum suis nauibus, redirent ad hanc lineam diametri, mox pediculi reuiuiscebant, vt priùs, ac semper multiplicabantur quò magis parribus nostris appropiabant. Ex quo portento atque ex rotaru recto acus magneticæ ad polos mundi comprehenderunt, ipsum esse verum Occidentis Meridianum; cum nullibi in alio Meridiano contingat id videre, quod in isto, qui nunc vulgò appellatur sancta Maria. Quapropter non abs re foret nouum catalogum Ciuitatum construere, atque earum longitudinem non ab Canariis, vt olim, sed ab Azorum Insulis compiare. Quem laude dignum laborem vtinam sapiens quis aggrederetur. < 375.> Azvbene Arab Latinè Cheles, leu Giasiæ Cancri stellæ fixæ sunt quartæ magnitudinis de natura Saturni, & Martis, quæ reuerà informes sunt circa constellationem Cancri, at reperiuntur nunc remporis in grad. 11. & 12. Leonis cum grad 3 & 6. latitudinis borealis: Sunt stellæ infensæ præsertim oculis, nec quicquam boni, siue in catdinibus genituræ,
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LEXICON mæus, not from the Isle of Gades, as Strabo, Artemidorus, and Proclus thought; for they began from those places to count the longitudes of cities because they did not know the true West, which only in the preceding century, to the great good of the Christian Commonwealth and to the credit of the discoverers, was found out. For, as Iunctinus rightly notes in the sphere of Io. de Sacrobosco, since the true West must be established at the end of the habitable earth opposite the East, and at right angles to the poles of the world, consequently it will be there where a certain line can be conceived, dividing the equator at right angles, and intersecting the solstitial colure; which by sailors is called the line of diameter, or the world’s diameter. < 374.> Moreover, this line immediately includes the aforesaid islands, a little beyond Cape Hieron, at five degrees; where also the nautical needle, or magnetic arrow, turns correctly to the poles of the world, dividing the equator at right angles. This is also proved by an eyewitness, Gonzalo de Oviedo, in the summary of journeys to the parts of the West Indies, chap. 84, who traversed those regions four times. For he says that whenever he reached that meridian, he always saw the arrow of the magnet turn straight diametrically to the poles of the world. And he tells a delightful and memorable story, that whenever he happened to pass with his companions through this line, all the lice that they had in their heads, in their clothes, or anywhere on the ships, would at once fall away as if dead, and they were freed from their annoyance; but when afterwards they departed from those western parts and, taking the route to Spain with their ships, returned to this line of diameter, the lice would quickly revive, as before, and always multiply the more they approached our regions. From this prodigy, and from the needle’s right turning toward the poles of the world, they concluded that this is the true meridian of the West; since nowhere else on any other meridian does one see what is seen on this one, which is now commonly called Santa Maria. Therefore it would not be amiss to construct a new catalogue of cities, and to compute their longitude not from the Canaries, as formerly, but from the Azores. Would that some wise man would undertake a labor worthy of praise. < 375.> Azvbene, in Arabic Cheles, or Giasiæ, the fixed star of Cancer, are of the fourth magnitude, of the nature of Saturn and Mars; they are in truth formless near the constellation of Cancer, but are now found at present at 11 and 12 degrees of Leo, with 3 and 6 degrees of northern latitude. They are stars especially hostile to the eyes, and bring nothing good, whether in the cardinal points of the nativity,
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84 LEXICON Cælesti Philosophia, ex stellis fixis proijcere radios ad planetas, eosque esse non minoris efficaciæ, quam ipsos radios planetarum: idque ob situm suum in Ecliptica, vbi cum omnibus planetis aliquando congreditur. Est nunc in gradu 21. Leonis. Ea in horoscopo, aut culmine Cæli, præsertim cum Ioue aut Venere, vel eorum benigno radio magnam tribuit felicitatem, gloriam, & honores, atque ab statu humili ad eminentem, ac sublimem euebit. 5. BATA-KAITOS Arab Venter ceti, Stella fixa tertia magnitudinis de natura Saturni, existens nunc in gradu 13 Arietis, cum latitudine australi grad. 15. de qua vide in V. Cetus, Balena. 6. BED-ALGENSE seu etiam Beldegensis Arab. dicitur dexter humerus Orionis, Stella fixa sub usa primæ magnitudinis de natura Martis, & Mercurij: Vide etiam in V. Orion. 7. BELLATRIX altera Stella item subrufa, & valde utilans secundæ tamen magnitudinis in sinistro humero eiusdem Orionis. Nomen accepit à bello, ad quod mirè propellit, & si quidem fuerit in horoscopo cum bono aspectu Martis, aut Iouis, facit Duces strenuos, magnatimos, peculorum contemptores. Observatione cautum est, Lunæ directiones ad hanc stellam rixam aliquam semper inducere, aut iter repentinum. Porrò hæ duæ stellæ Beldegensis, inquam & Bellatrix cum Marte exorienses maxime colores intendunt, vt notat Argolus in Astronomicis lib. 2. cap. 10 8. Beibenix sunt stellæ fixæ principaliores, quæ in singulis imaginibus cælestibus considerantur; præcipue velò corda iplarum, & quæ sunt primæ magnitudinis: vt regulus in Leone, Antares in Scorpio, Spica in Virgine, Alpharad in Hydra, &c. Vsus tamen obtinuit, vt omnes stellæ primæ magnitudinis in singulis Asterismis dispositæ vocentur corda ipsorum, & consequenter Beibenix: teste Hali super proposit. 29. Centiloquij, licet ego inter stellas Beibenias alias etiam secundi ordinis, & minoris conditionis apud alios connumeratas inuenenim. De stellis Beibeniis extat insignis tractatus Hermetis apud Iunctinum in fine commentar. in sphæram loanis de Sacrobosco. 9. BENNENAX ELKERD, vel Benenaim, id est N[atur]aurnum dicitur apud Arabes stella fixa secundæ magnitudinis posita in extremo caudæ Vrsæ majoris, de natura Martis in longitud. grad. 22 Virginiscum latitudine grad. 54. boreali. Aliàs dicitur primus equus Plancti BERENICES Cuma dicta etiam spicarum manipulus, fidus in Cælo propècaudam Leonis, & apud antiquos cum ea confu-
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84 LEXICON Celestial Philosophy: to cast rays from the fixed stars to the planets, and that these are no less efficacious than the rays of the planets themselves; and this on account of their position in the ecliptic, where at times they meet with all the planets. It is now at the 21st degree of Leo. It, in the horoscope, or at the zenith of the heavens, especially when joined with Jupiter or Venus, or by their benefic aspect, bestows great happiness, glory, and honors, and raises one from a low state to an eminent and sublime one. 5. BATA-KAITOS, Arab. “belly of the whale,” a fixed star of the third magnitude, of the nature of Saturn, now situated at the 13th degree of Aries, with southern latitude 15 degrees. See under V. Cetus, Whale. 6. BED-ALGENSE, or also Beldegensis, Arab., is called the right shoulder of Orion, a fixed star under the first magnitude, of the nature of Mars and Mercury. See also under V. Orion. 7. BELLATRIX, another star, somewhat reddish and very bright, of the second magnitude, in the left shoulder of the same Orion. It received its name from war, to which it wonderfully impels, and if it should be in the horoscope with a good aspect of Mars or Jupiter, it makes men vigorous commanders, magnanimous, contemptuous of wealth. By observation it has been noted that the Moon’s directions to this star always bring about some quarrel, or a sudden journey. Moreover, these two stars, namely Beldegensis and Bellatrix, rising with Mars very much intensify colors, as Argol notes in Astronomics, book 2, chap. 10. 8. Beibenix are the principal fixed stars which are considered in the several celestial images; especially the hearts of them, and those which are of the first magnitude: such as Regulus in Leo, Antares in Scorpio, Spica in Virgo, Alpharad in Hydra, etc. Usage, however, has obtained that all stars of the first magnitude arranged in the several asterisms are called their hearts, and consequently Beibenix: witness Haly on proposition 29 of the Centiloquium, although I have found among the Beibenian stars others also of the second rank, and of lesser condition, counted by others. Concerning the Beibeni stars there is an outstanding treatise by Hermes in Junctinus, at the end of the commentary on the Sphere of Johannes de Sacrobosco. 9. BENNENAX ELKERD, or Benenaim, that is, Saturn, is called among the Arabs a fixed star of the second magnitude, placed in the extreme tail of Ursa Major, of the nature of Mars, in longitude 22 degrees of Virgo, with latitude 54 degrees north. It is otherwise called the first horse of the Plancti. BERENICES, a cluster also called the sheaf of ears of grain, a faithful one in the sky near the tail of Leo, and among the ancients with it was con-
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MATHEMATICVM. 87 tercalaris transigerentur; quarius verò quicque centesimus esset Bissextilis Ita vt annus 1600. sit, vt antea Bissextilis; anni verò 1700. 1800. 1900. Bissextiles non essent, bene verò centesimus sequens hoc est 2000. Idque in perpetuum obseruando, nunquam Æquinoctia, & Solstitia à suis sedibus deturbarentur: Qua de te plura apud Clauium in Kalendario Gregoriano. 17. BIVMBRES hoc est binas habentes vmbras dicuntur populi habitantes in Zoua torrida citrà Tropicos ad æquatorem, vbi pro temporum varietate binam experiuntur vmbram, alteram ad Meridiem, alteram ad Septentrionem: Vide in V. Amphiscij. 18. BOLIDES apud Plinium, lib. 2. cap. 26. sunt species Cometarum Quale, inquit, Mucemensibus malis visum est. Quæ distant à facibus per hoc, quod istæ vestigia longa faciunt, priore ardente parte: Boles verò perpetua atdens longiorem trahit limitem: Hæc Plinius. 19. BOOTES, Bubulcus, Arctophilax Plaustri ductor dicitur si- dus in Cælo prope Elicen, seu Vrsam maiorem continens stellas 23. iuxta Ptolemæum, Keplerum autem 28. & ex Baiero 34. omnes ferè de natura Louis, & Saturni, inter cuius femora adest vna infornis clara, & rutilans primæ magnitudinis de natura Martis, & Louis nomine Arcturus Arabicè Alramech quasi Vociferator, vel Thequus, hoc est plorans, de qua satis dictum suo loco. Ea cum Ioue, inquit Stadius, magnas diuitias cum dignitate polliceur: sicut è contrà cum Saturno earum profligationem protendit: Vide etiam in V. Arctophilax. 20. BOREAS, ventus Septentrionali vicinus, ac lateralis spirans, ex parte ortus Solstitialis, sic dictus vel à nutrimento, quia sementem, fructus, & animantia valdè nutrit, vel cettè à boaru, quod flatus eius sit violentus reboans, ac sonorus. Est frigidus, & siccus, aërem purgans, & corruptioni resistens, sicut & reliqui Septentrionales venti. Aliquando accipitur etiam pro ipso vento cardinali, qui immediatè à Septentrione exsufflat; dicto à Græcis Aparctia, ob eius vicinirem, & similitudinem naturæ. Quid Borea flante, aggrediendum, quidue cauendum sit: Vide apud Plin lib. 18. cap. 33. Dictus est etiam Aquilo ab Aquilæ volatu, quem æmulari videtur, vt suo loco admonuimus. 21. BORRHAPELIOTES, ventus vnsus ex quatuor intermedijs medio loco exsufflans inter Septentrionem & Æquinoctialem ortum: à Nostris dictus est Græcus, cò quod per mediam Græciam transeat; Estque frigidus, & siccus, 111j
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MATHEMATICVM. 87 the intercalary days were regulated; and every fourth hundredth year would be a leap year, so that the year 1600 would be, as before, a leap year; but the years 1700, 1800, and 1900 would not be leap years, while the next hundredth year, that is 2000, would rightly be so. And by observing this forever, the equinoxes and solstices would never be displaced from their stations: on this matter see more in Clavius in the Gregorian Calendar. 17. BIVMBRES, that is, “having two shadows,” are called the peoples dwelling in the torrid zone, this side of the tropics, toward the equator, where according to the variation of the seasons they experience a double shadow, one toward the south, the other toward the north: see under V. Amphiscij. 18. BOLIDES, in Pliny, book 2, chapter 26, are a kind of comet. “Such a one,” he says, “was seen among the evil signs of Mucem.” They differ from torches in this, that the latter make a long trail, with the burning part in front; but bolides, burning continually, draw out a longer track: thus Pliny. 19. BOOTES, also called Bubulcus, Arctophilax, and the driver of the Wagon, is the constellation in the sky near Helice, or the Great Bear, containing 23 stars according to Ptolemy, 28 according to Kepler, and from Bayer 34; almost all are of the nature of Jupiter and Saturn, among whose thighs there is one very bright, and reddish, of first magnitude, of the nature of Mars and Jupiter, named Arcturus, in Arabic Alramech, as if “the Shouter,” or Thequus, that is, “weeping,” concerning which enough has been said in its place. With Jupiter, says Stadius, it promises great riches together with dignity; whereas with Saturn it portends their ruin: see also under V. Arctophilax. 20. BOREAS, a wind neighboring the north and blowing from the side of the solstitial rising of the sun, is so called either from nourishment, because it greatly nourishes seed, fruits, and living creatures, or certainly from boaru, because its blast is violent, roaring, and sonorous. It is cold and dry, purging the air and resisting corruption, as also do the other northern winds. At times it is also taken for the cardinal wind itself, which blows immediately from the north; by the Greeks called Aparctia, because of its closeness and similarity in nature. What should be undertaken and what avoided when Boreas blows: see in Pliny, book 18, chapter 33. It is also called Aquilo from the flight of the eagle, which it seems to imitate, as we noted in its proper place. 21. BORRHAPELIOTES, a wind one of the four intermediate winds, blowing from the middle position between the north and the equinoctial east: by ours called the Greek wind, because it passes through the middle of Greece; and it is cold and dry, 111j
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LEXICON 88 nubes generans, & aliquando nives 22. BORRHOLYS. CVS, ventus est item principalis, vnus ex quauior intermediis, qui à loco æquè inter Septentrionem &c Occasum interiecto perflat, à Noltris dicitur Magistralis quasi nauigationis Magister existat in mari Mediterraneo, vbi primum obseruatus fuit. Est natura sua humidus, nimbosus, procellosus, & in Æstate tonitruosus: in Autumno verò, aut vere violentus, repentinus, ac turbulenius. 23. BRIDEMIF, in tabulis Persicis dicitur Lupus, Fera, Bestia Centauri sidus videlicet ad australem plagam fere nobis inconspicum: de quo paulò ante dictum in V. Bestia. 24. BRINEK, siue Brinets apud Hermetem dicitur stella lucida Lyræ, primi honoris, alio nomine Vvega. 25. BRVMA ex Græco quasi breuis dies appellatur tempus solstitij hyemalis, quando dies sunt breuissimi, & noctes è contrà longissimæ in introitu Solis, ad primum gradum Capricorni: quod accidit post Gregorianam anni correctionem circà duodecimum kalendar. Ianuarij. Ipso brumali tempore Origanum aridum, & suspensum domi repente efflorescere, & murium jecora adaugeri testatur Cicero 2. de D minat. ac reipsa vel rustici experiuntur Democritus apud Plinium, talem futuram esse hyemem arbitratur, qualis fuerit Brumæ dies, & circæ eum terni. Portò Brumæ tempore quid Agricolis faciendum, vide apud ipsum Plinium lib. 18. cap. 26. 26. BVLTHO, Chaldaicè dicitur Virgo, sextum ab Ariete signum, Hebraicè autem Betulah, prout testatur kircherus in Oedipo Ægyptiaco. Vide in V. Virgo. 27. BVBVLCVS vide Bootes. CA 1. CABALLVS Barbarè dictus est vectisteres premens ac ligans rete, ac tympana in Astrolabio circà Clauum ex specie quam vtecumque oculis exhibet. A tabicè Alphæras Z. 2. CACODÆMON Græcè, Latinè malus genius dicta est duodecima domus ab horoscopo cadens ab angulo Medij Cæli, sic dicta à tristium, & exitialium rerum significatione: est enim significatrix carcerum, hostium occuliorum, aliarumque tribulationum, ac difficultatum. Consignificatus eius est Venus, & in ea gaudet Saturnus: qua ratione vide in V. Gaudium 3. CADENS apud Astronomos appellatur planeta quotiescunque in Cælesti figura reperitur in domibus cadentibus ab Angulis, quales sunt tertia, sexta, nona, & duodecima, quas Iulius Firmicus pigra, & abiecta figura loca nominat, eò quod in illis constituti planetæ plurimum debilitentur: licet reuerà
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LEXICON 88 generating clouds, and sometimes snow 22. BORRHOLYS. CVS, is also a principal wind, one of the four intermediate ones, which blows from a place equally between the North and the West. By our people it is called Magistral, as if it were the Master of navigation in the Mediterranean Sea, where it was first observed. By nature it is moist, stormy, squally, and in Summer thundery; but in Autumn, or in spring violent, sudden, and turbulent. 23. BRIDEMIF, in Persian tables is called Wolf, Wild Beast, Beast that is to say the constellation of Centaurus, lying almost invisible to us in the southern part; of which something was said a little before under V. Bestia. 24. BRINEK, or Brinets, is called by Hermes the bright star of Lyra, of the first honour, otherwise named Vega. 25. BRVMA, from the Greek as if “short day,” is the name given to the time of the winter solstice, when the days are shortest and the nights, on the contrary, longest, at the entrance of the Sun into the first degree of Capricorn: which happens, after the Gregorian correction of the year, around the twelfth day before the Kalends of January. Cicero testifies that in the very brumal season dry oregano, hung up at home, suddenly blossoms, and the livers of mice increase; and in fact even rustics experience it. Democritus, cited by Pliny, judges that such a winter will be as the day of Bruma has been, and the three days around it. Moreover, what should be done by farmers at the time of Bruma, see in Pliny himself, book 18, chapter 26. 26. BVLTHO, in Chaldean is called Virgo, the sixth sign from Aries; in Hebrew however Betulah, as Kircher testifies in the Oedipus Aegyptiacus. See under V. Virgo. 27. BVBVLCVS see Bootes. CA 1. CABALLVS, in barbarous speech, is the pressing and binding support of the net and the drums in the Astrolabe around the Claw, according to whatever form it displays to the eyes. In Arabic, Alphæras Z. 2. CACODÆMON, in Greek, in Latin called the evil genius, is the twelfth house falling from the horoscope from the angle of the Midheaven, so called from the signification of sad and ruinous things: for it signifies prisons, hidden enemies, and other tribulations and difficulties. Its co-significator is Venus, and Saturn rejoices in it: for which reason see under V. Gaudium 3. CADENS, among astronomers, a planet is called so whenever in a celestial figure it is found in the cadent houses from the angles, such as the third, sixth, ninth, and twelfth, which Julius Firmicus calls sluggish and abject places in the figure, because planets situated in them are greatly weakened: though in reality
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MATHEMATICVM. 89 nona, & terti illis non officiant, immò potiùs prosint, cum nonæ communiter tribuantur duæ fortitudinis partes, terræ verò vna. Ratio autem quare in istis planetæ non infortunentur; hæc, meo judicio esse potest, quia videlicet benigno aspectu aspiciunt horoscopum: nona quidem de Trino, terris de Sextili: & insuper nona est in magna altitudine à terra proxima decimæ, vbi planetæ puriores sunt, validiores ac liberi à terrenis vaporibus; & idcircò nona licet cadens euadit nihilominus fortunata; estque exceptis cardinibus potissimus locus vbi constituta Luminaria, aur pars fortunæ vim obtinere hilegialem, melius quam in vndecima, ob radij nempe fortitudinem, ac præcellentiam, quo horoscopum intuetur. CADENS item dicitur planeta, quando in Zodiaco reperitur in signo opposiro suæ exaltationis: qua de re vide in V. Casus. CACIAS ventus Orientalis spirans ab exortu solstiriali: sic dictus à Caci flumine Hellesponti per quod transir vnde & Hellespontium ab aliquibus appellatur. Est frigidior, & inconstantior Subsolano ob participarionem cum ventis Septentrionalibus, arque adeò flaru suo subinde molestus, nubifer ac plu- niosus. De eo notar Aristoteles, quod contrà naturam aliorum ventorum nubes non abs se propellit, sed ad se attrahit: Plura apud Erasinum in Adagijs. CÆNACVLVM, alijs Tenaculum, est species quædam Come- ræ criniti, magni, oblongi, ac lati instar Cænaculi, seu mensæ quadrilareræ, vnde & nomen hausit. Est de natura Lunæ, portendisque afflictionem populi sine discrimine, seditiones, bella, legum innouariones, &c. ex morbis induerit catarhos, paralises, hydropas, epylepsias, scabies, dolores colicos, obstructiones, & alios huius generis morbos. CALBEZ Arab. est Stella fixa secundæ magnitudinis in effusione aquæ Aquarij proxima Fomahand de natura Louis, & Saturni. Eius concremina est altera Stella nomine Alcalism eiusdem naturæ. CALCULATOR dicitur Latinè Regula, Dioptra, Alhida[n]da in medio Astrolabij collocata, ab officio, quo fungitur calculandi gradus altitudinis stellarum, quam per Astrolabium venamur: proenditur enim vsque ad limbum Astrabij in quo circulus descriptus est in 160. partes dislectus. CALLIPICA Periodus dicta est Lunaris Anni magni cum Cy- clo Solis decennouennali conuenientia, ab eius inuentore Callippo, qui flornit Olympiade 162. annis ferè 128. ante Christum: In ea enim 940 Lunares menses explentur, & dies 13878. ferè, quot ferè comprehendunt Cycli Solares decenno-
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MATHEMATICVM. 89 the ninth, and the third do not hinder them, but rather help them, since the ninth is commonly assigned two parts of fortitude, the earth one part. The reason why in these planets they are not made unfortunate, this, in my judgment, may be, namely because they look upon the horoscope with a benign aspect: the ninth indeed by a Trine, the earths by a Sextile: and moreover the ninth is at a great height, near the tenth from the earth, where the planets are purer, stronger, and freer from earthly vapors; and therefore the ninth, though falling, nevertheless turns out fortunate; and, except the angles, it is the chief place where, when the Luminaries or the part of fortune are placed, they can obtain a hilegial force, better than in the eleventh, on account, namely, of the strength and pre-eminence of the rays by which it regards the horoscope. A planet is also called CADENS, when in the Zodiac it is found in the sign opposite its exaltation: on this matter see in the V. Casus. CACIAS, an eastern wind blowing from the solstitial sunrise: thus called from the river Cacus of the Hellespont, through which it passes, whence also it is by some called Hellespontian. It is colder, and more changeable than Subsolanus because of its participation with the northern winds, and therefore its blast is at times troublesome, cloudy, and rainy. Aristotle notes of it that, contrary to the nature of other winds, it does not drive the clouds away from itself, but draws them toward itself: more on this in Erasinus in the Adagies. CÆNACVLUM, by others Tenaculum, is a certain species of comet of a long-haired kind, large, oblong, and broad like a cænaculum, or a rectangular table, whence it also takes its name. It is of the nature of the Moon, and portends affliction of the people without distinction, seditions, wars, innovations of laws, and the like; from diseases it brings catarrhs, paralyses, dropsies, epilepsies, scabies, colic pains, obstructions, and other illnesses of this kind. CALBEZ, Arabic. is a fixed star of the second magnitude in the water-spout of Aquarius, near Fomahand, of the nature of Venus and Saturn. Its companion is another star named Alcalism, of the same nature. CALCULATOR is called in Latin the Rule, Dioptra, Alhida[n]da placed in the middle of the Astrolabe, from the office by which it is used in calculating the degrees of the stars’ altitude, which we seek by means of the Astrolabe: for it is extended as far as the limb of the Astrolabe, in which a circle is drawn divided into 160 parts. CALLIPICA Period was called the agreement of the lunar great year with the nineteen-year Solar Cycle, from its inventor Callippus, who flourished in the 162nd Olympiad, about 128 years before Christ: for in it 940 lunar months are completed, and days 13878, nearly, as many as the nineteen-year Solar Cycles comprise
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MATHEMATICVM. 93 duos semicirculos, & deferentis Lunam, & æquantis, vide- tur quendam velui Draconem efformare, cuius pars lata Dra- conis ventrem repræsentat; intersectiones verò Caput, & Caudam. Portò huiusmodi intersectiones non semper loco < 22.> consistunt, sed mouentur, & ipsæ motu proprio in Zodiaco, retrogradè tamen non directè: in superioribus insensibiliter, ita vt nodus boreus Saturni nunc temporis sit in grad. 3. min. 20. Canci, Louis similiter in grad. 3. min 7. Canci; Martis in grad. 1. min. 17. Tauri: Nodus verò Austinus in locis oppositis: In reliquis autem tribus nodi sunt perpetuò varia- biles, ac præcipuè in Luna, cum ad dies singulos isti ferè tribus minutis retrocedant. Obseruant Astronomi nodos planetarum, præsertim Luna- < 23.> res, eorumque naturam considerant, & boreum quidem aiunt imitari natuam Louis, & Veneris; Austrinum verò naturam Saturni, & Martis; ad eosque dirigunt significatores non se- cus ac ad ipsa corpora planetarum: quod tamen improbat Titus in Cæsti philosophia. Ego re bene perpensa, non ne- < *> garem ipsa aliquam efficientiam saltem indirectam, vt cum Luna reperitur al cui maleficæ iuncta in nodis, atque in augu- lis, facit natum gibbosum, claudum, aut vrcunque contor- tum, vt habet Prolemaus lib. 3. cap. 17. Sed id prouenit eò quia in Ecliptica radius, aut coniunctio est validior, proinde- que Luna magis à malefica infestatur, quod & in Sole accidit, qui tamen semper est in Ecliptica. Et ideò caput dicitur esse de natura Mercurij, cum bonis bonum, cum malis malum, quia in Ecliptica planetæ fortiores sunt, & dum relicta austra- li parte, incipiunt accedere ad boream, boni bonitatem auges- cunt, mali malitiam: è contrà in nodo austrino planetæ des- cendunt à boreali plaga, atque accedunt ad Austrum, vbi debiliores euadunt; meritò igitur cauda Draconis cum bonis mala dicitur, cum malis bona, quia cum illis eorum bonita- tem minuit, cum istis eorumdem labefactat malitiam. Caput perhibetur esse Masculinum, Cauda ex minina: Hæc Arabicè appellatur anabibazon illud autem Casabibazon, vt in loco diximus. CAPVT Apollo fixa in capite præcedentis Geminorum Ara- < 24.> bicè Ras Algense, vel etiam Elgieurze de natura Martis & Mercurij: de qua alijs in locis dictum. CAPVT Herculis stella fixa in capite Herculis fulgens, non < 25.> quidem eius, qui & Hercules dicitur, & est alter etiam Gemi- norum dictus etiam Pollux, sed eius qui alio nomine Engo- nasis appellatur propè Ophiucum: de qua vide in V. Ras Al- gest.
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MATHEMATICUM. 93 two semicircles, both that carrying the Moon and that of the equator, seems to form something like a Dragon, whose broad part represents the Dragon’s belly; the intersections, however, the Head and Tail. Moreover, such intersections do not always remain in one place, but move, and themselves with their own motion in the Zodiac, though retrograde and not direct: in the superior planets imperceptibly, so that the north node of Saturn is now at 3 degrees 20 minutes of Cancer, of the Sun likewise at 3 degrees 7 minutes of Cancer; of Mars at 1 degree 17 minutes of Taurus: but the south node in opposite places. In the remaining three, however, the nodes are perpetually variable, and especially in the Moon, since these retreat by about three minutes each day. Astronomers observe the nodes of the planets, especially the lunar ones, and consider their nature, and indeed they say that the north node imitates the nature of the Sun and Venus; the south node, however, the nature of Saturn and Mars; and they direct significators to them no differently than to the bodies of the planets themselves: which, however, Titus in Cæsti’s philosophy disapproves. I, having weighed the matter carefully, would not deny that they have some efficiency, at least indirect, as when the Moon is found joined to some malefic in the nodes and in the angles, it makes the native hunchbacked, lame, or otherwise twisted, as Ptolemy has in book 3, chapter 17. But this happens because in the ecliptic the ray, or conjunction, is stronger, and therefore the Moon is more afflicted by the malefic, which also happens in the Sun, which nevertheless is always in the ecliptic. And therefore the head is said to be of the nature of Mercury, with the good good, with the bad bad, because in the ecliptic the planets are stronger, and while leaving the southern part and beginning to approach the north, the good increase goodness, the bad their wickedness; contrariwise, in the south node the planets descend from the northern region and approach the south, where they become weaker; therefore the Dragon’s tail is rightly said to be bad with the good, good with the bad, because with the former it lessens their goodness, with the latter it weakens their wickedness. The Head is said to be Masculine, the Tail feminine: this is called in Arabic anabibazon, that other casabibazon, as we have said in the proper place. CAPUT Apollo, a fixed star in the head of the preceding Gemini, in Arabic Ras Algense, or also Elgieurze, of the nature of Mars and Mercury: concerning which something has been said elsewhere. CAPUT Hercules, a fixed star shining in the head of Hercules—not, indeed, of that one who is also called Hercules and is likewise another of the Gemini, also called Pollux, but of the one who is by another name called Engonasis, near Ophiuchus: see concerning it under V. Ras Algest.
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96 LEXICON 36. Denique Tycho ipse postquam de huius stellæ situ, specie materia, productione multa disseruit, prædicit magnam per eam religionis alterarionem portendi, cuius mutationis tempus ex directionum regulis vsque ad annum 1592. protendit, & tunc dicit initia mutationum, & semina jacienda; inde dirigendo stellam ad locum maximæ conjunctionis, quæ proximè precessit in grad. 21. Piscium air directionem complendam in annis 48 à prima fulsione stellæ, hoc est anno 1632. Et quia stella hæc fuit verticalis Moscouix, idcirco existimat ex Moscouia primas occasiones rubarum, ac mutationum orituras, & affert nescio quod vaticinium Sybillæ Iuburinæ, quod refert etiam Cornelius Gemmæ lib. de divinæ natura characte ismis in eius rei comprobationem Verùm jam sumus ad ann. 1662. & ab termino directionis transacti sunt adhuc triginta anni, nec quicquam huius murationis comminaræ præsertim ex Moscouia vidimus: sed nec visuros speramus. Et hæc obiter dicta sunt de hac stella ex occasione Cassiopæ in cuius Asterismo apparuit: de eius tamen efformatione, loco, materia, aliisque ad nostrum institutum spectantibus iterum redibit sermo in V. Phanomenon. 37. CATABIBAZON, teste Valla, apud Arabes, seu Ægyptios idem sonar ac caput Draconis, seu nodus boreus Lunæ, sicuti Anabibazon idem, ac Cauda. 38. CATAÆGIS ventus est ex genere procellarum, quem (inquit Apuleius in lib. de Mundo) præfractum possumus dicere, qui de eas parte submissus inferiora repentinis impulsibus quattu Per quod opponitur Vortici, qui ex intimo aridæ humi exiliens ad suprema erigitur. 39. CATAPHORÆ dicuntur Græcè in Cælesti figura Domus cadentes ab Angulis, tertia, sexta, nona & duodecima; quemadmodum Anaphora quæ proximè succedunt Angulis, secunda, quinta, octava, & vndecima. 40. CATHALZE Arabicè vocatur linea meridiana subterranea descripta in Planisphærio, quæ constituit angulum lmi Cæli, qui etiam 41. CATOGÆVM, hoc est domus subterranea apud Græcos aliquando audit, sumpta analogia ad Carogæum, quod propriè, & vniuersaliter domicilium subterraneum significat. 42. CATHETVS incidentia apud Astronomos diciur linea recta ducta ex quousi puncto radij incidentis ad planum speculum, seu reflexium perpendiculariter. 43. CATHETVS vero reflexionis est linea recta ducta ex quousi puncto radij reflexi perpendiculariter ad planum speculum vsque ad occursum cum radio incidente per imaginationem. Eius
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96 LEXICON 36. Finally Tycho himself, after he had spoken at length about the position, appearance, matter, and generation of this star, predicts that a great alteration of religion is portended through it, the time of which change he extends, according to the rules of directions, up to the year 1592; and then he says that the beginnings of changes and the seeds are to be sown; from there, by directing the star to the place of the greatest conjunction, which had most nearly preceded in 21 degrees of Pisces, the direction would be completed in 48 years from the first shining of the star, that is, in the year 1632. And because this star was vertical to Moscow, therefore he thinks that from Moscow the first occasions of disturbances and changes would arise, and he adduces some prophecy of the Sibyl of Iuburina, which Cornelius Gemma also relates in his book De divinæ naturæ charactereismis in confirmation of this matter. But now we have reached the year 1662, and from the term of the direction thirty years have still passed, nor have we seen anything at all of this threatened change, especially from Moscow; but we do not even hope to see it. And these things have been said incidentally about this star, on the occasion of Cassiopeia, in whose asterism it appeared; but concerning its formation, place, matter, and other things pertaining to our subject, there will again be discussion in the fifth Phenomenon. 37. CATABIBAZON, according to Valla, among the Arabs, or Egyptians, has the same meaning as the head of the Dragon, or the northern node of the Moon, just as Anabibazon is the same as the Tail. 38. CATAÆGIS is a wind of the class of storms, which, as Apuleius says in his book De Mundo, we may call a violent one, which drives down from that part and by sudden blasts crushes the lower regions. By this it is opposed to the Vortex, which, springing up from the very depths of dry ground, rises to the highest parts. 39. CATAPHORÆ, in the celestial figure, are said in Greek to be the Houses falling away from the Angles, the third, sixth, ninth, and twelfth; just as Anaphoræ are those which next succeed the Angles, the second, fifth, eighth, and eleventh. 40. CATHALZE in Arabic is the subterranean meridian line drawn in a planisphere, which constitutes the angle of the tenth heaven, which also 41. CATOGÆUM, that is, an underground house, is sometimes called among the Greeks, the name being taken by analogy from Carogæum, which properly and universally signifies an underground dwelling. 42. CATHETUS of incidence among astronomers is called the straight line drawn from any point of the incident ray to the plane mirror, or reflection, perpendicularly. 43. CATHETUS of reflection, however, is the straight line drawn from any point of the reflected ray perpendicularly to the plane mirror, up to the meeting with the incident ray in imagination. Its
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MATHEMATICVM. 99 tus, & cum eo vnumquid factus. Qui sit, vt in Cazimi existens, fortis, & viribus auctus. combustus autem, aut sub radiis, infirmus, ac debilis habeatur. CE 59. CEGINVS dicitur apud quosdam finister humerns Bootis stella videlicet fixa tertiæ magnitudinis, de natura Marris, & Saturni existens in grad. 4. Libræ cum maxima latitudine boreali: quæ nunc, cùm habeat declinationis grad. ferè 40. consequenter sit verticalis Regno Neapolis, quod valdè obsequandum 60. CEGINVS etiam audit apud quosdam Cepheus, vt testis est Ricciolus in Almagesto: de quo mox in ista suo loco. 61. CENTAURVS, qui & Typhon sidus in cælo ad australem plagam nobis perpetuò larens; constans stellis 36 omnibus ferè de natura Marris, & Veneris: Ex quibus insignior est fulgens in summitare prioris pedis dextri primæ magnitudinis de natura Iouis, & Veneris. Is in horoscopo, inquit Materius, facit aurigam equorum cultorem, nutritorem, vel etiam domitorem: & si Mars benigno radio affulgeat, faciet inter fortissimos equires militare. Si verò in occasiu repertus fuerit, & hunc locum maleuolæ stellæ irradiauerint, natus, aut ex alio proiectus morieiur, aut quadrupedis imperu, vel equi calce percussus, aut ab aliquo equo projectus peribit: vel euerso curiu rrahentibus aquis misera morie lacerabitur. Hæc ille. In longitudine rorus est sub signo Libræ. 62. CENTILOQVUM Anionomasticè apud Astronomos audit insignis tractarus complectens centum sententias in breues aphorismos redactas, ac Prolemæo Astrologorum facilè principi ascriptus: qui & fructus librorum suorum hoc est Quadripartiri, & Almagesti indigitatur. Verùm magna controuersia est inter Astronomos, an is reuerà sit Prolemæi opus, an potiùs Hermetis Trismegisti, cuius aliera Aphorismorum Centuriacircumfertur. Hali Heben Rodoam Prolemæi Commentator in Commentar. super Quadrip. affirmar, illud non esse Ptolemæi, sed Hermeris: sed tamen aggressus Centiloquij commentationem, seu fuerit affectus magnificandi operis, quod explicandum suscipiebat, seu fuerit maior veri noritia comparata, Ptolemæi genuinum opus esse farerur. Secundò Hieronymus Cardanus post hæc rem benè considerans, ac dicta dictis obijciens, sententiæ vnitatem in ijs non esse comperijt. Ac tandem Argolus, alijque nostri temporis doctissimi viri pro liquidò habent, id Ptolemæi opus non esse, sed dicti G ij
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MATHEMATICVM. 99 ...and with it made one thing. Which is why, when it is in Cazimi, it is strong and increased in power. But when combust, or under the rays, it is held to be weak and feeble. CE 59. CEGINVS is called by some the finisher of the Horseman, namely a fixed star of the third magnitude, of the nature of Mars and Saturn, existing in the 4th degree of Libra with the greatest northern latitude: which now, since it has a declination of almost 40 degrees, consequently is vertical to the Kingdom of Naples, which is very noteworthy. 60. CEGINVS is also called by some Cepheus, as Ricciolus testifies in the Almagest: of whom more shortly in its place below. 61. CENTAURVS, which is also the constellation Typhon, is a star in the sky on the southern side, perpetually lying hidden from us; consisting of 36 stars, all almost of the nature of Mars and Venus. Among these the most notable is the bright star on the summit of the foremost right foot, of the first magnitude, of the nature of Jupiter and Venus. In the horoscope, says Materius, it makes a charioteer, a horseman, a groom, or even a tamer; and if Mars shines upon it with a benign ray, it will make one serve in the army among the bravest cavalrymen. But if it be found in the west, and malignant stars have irradiated this place, the native, either thrust out from elsewhere, will die, or, struck by the kick of a quadruped or horse, or cast down by some horse, will perish; or, if overturned, he will be torn to pieces by the waters drawing along a wheel. Thus he. In longitude it is wholly under the sign of Libra. 62. CENTILOQVVM, by antonomasia among astronomers, is the name of a celebrated treatise comprising a hundred sayings reduced to brief aphorisms, and ascribed by Ptolemy, easily the prince of astrologers: and it is also indicated as the fruit of his books, that is, of the Quadripartitum and the Almagest. But there is great controversy among astronomers whether it is truly the work of Ptolemy, or rather of Hermes Trismegistus, whose other Centuria of Aphorisms is circulated. Hali Heben Rodoam, Ptolemy's commentator in his commentary on the Quadripartitum, affirms that it is not Ptolemy's, but Hermes': yet when he set about commenting on the Centiloquy, whether from a desire to magnify the work he was undertaking to explain, or from having attained a greater knowledge of the truth, he declared it to be Ptolemy's genuine work. Secondly, Jerome Cardano, after considering the matter well, and objecting one saying to another, found that there was no unity of doctrine in them. And finally Argolus, and other most learned men of our time, hold it for certain that it is not Ptolemy's work, but that of the said
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Lexicon 100 Hermetis, aliàs Trutinæ ad indagandum verum conceptionis tempus inuentoris, quam postea in Centiloquio aphor. 51. expressam, & confirmatam videmus in hæc verba. In quo signo Luna est Genitura tempore, illud fac Ascendens, in conceptu; & in quo signo inuenta fuerit in conceptu, illud aut eius oppositum fac Ascendens in partu. Ex quo liquet vt tantum absit, quod hic fructus librorum Ptolemæi sit, vt is ne verbo quidem id explicet siue in Quadripartito, vbi de rectificatione Genituræ agit, siue in alio librorum suorum loco. Vtcumque se res habeat, certum est, dictum Centiloquium magnæ esse auctoritatis, magnique nominis, idque siue à Ptolemæo ipso à suis operibus excerptum sit, siue à quous alio Ptolemæi gloriam affectante, cæteris omnibus id genus operibus antecellere. Quod etiam Angelicus Doctor 3. contra Gentes cap. 84. suo testimonio confirmauit. Sic enim ait: Verum est, quod Ptolemaus in Centiloquio dicit; Cum fuerit Mercurius in natiustate alicuius in alqua domorum Saturni, & ipse fortis in esse suo, dat bonitatem intelligentia fundiciùs in rebus. Et hæc obiter dicta sint de Auctore, & auctoritate Centiloquij, quod nos D. Thomam sequuti semper sub Ptolemæi nomine citabimus. 65. Centrum Græcè, Latinè punctum significat in medio sphætæ vel Circuli collocatum, ad quod ductæ lineæ à superficie, aut peripheria, omnes inueniantur æquales. Differt autem à puncto præcisè sumpto, quia hoc definitur ab Euclide cuius pars nulla est, ac præscindit ab eo, quod sit principium figuræ mediatum, vel non; Centrum autem semper appellat cujusuis rei medium, quod concipiatur indivisibile, licet subinde punctum ferè semper pro centro accipiatur, ac pro centro nil aliud veniat, quàm punctum in medio sphætæ aut circuli constitutum. Hinc terra in Mundi meditullio collocata, atque ad cælorum immensitatem relara, instar puncti cum sit, Mundi centrum vocatur. Vnde Cicero 1. Tusculan. Persuadens, inquit, Mathematico terram in medio Mundi sicutum ad vnserse Cals complexum quasi puncto instar obserere, quod Centrum alij vocant. Porrò quandocumque Mathematici stellarum motus, situs, distantias, apparentias, aliaque id genus supputare volunt, semper id à centro stellæ ad centrum alterius corporis aggrediuntur: sicque veras lumina-rium defectiones, quas, & Eclipses vocant, à centris lumina-rarium computant, ac rationem habent vtriusque semidia-metri, nec non telluris, ad cuius centrum, non ad superficiem rectè eiacularus à sidere radius terminatur. Hinc patallaxes, hinc differentia illa veri motus, & apparentis: de quibus om-nibus suo loco.
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Lexicon 100 Hermes’ trutina, or balance, for discovering the true time of conception of the inventor, which we later see expressed and confirmed in the Centiloquium, aphorism 51, in these words. In which sign the Moon is at the time of nativity, make that the Ascendant at conception; and in which sign she shall be found at conception, make that, or its opposite, the Ascendant at birth. From this it is clear that this product is so far from being from Ptolemy’s books that he does not explain it even by a word, whether in the Quadripartitum, where he treats of the rectification of the nativity, or in any other place in his books. However the matter may stand, it is certain that the said Centiloquium is of great authority, and of great name, whether it was excerpted by Ptolemy himself from his works, or by some other person aiming at Ptolemy’s glory; it surpasses all other works of this kind. This was also confirmed by the Angelic Doctor in 3 Contra Gentiles, chapter 84, by his testimony. For thus he says: It is true what Ptolemy says in the Centiloquium: When Mercury is, in the nativity of anyone, in one of Saturn’s houses, and he himself is strong in his own being, he gives soundness of understanding in things. And let these words be said in passing about the Author and the authority of the Centiloquium, which we, following St. Thomas, shall always cite under Ptolemy’s name. 65. Centrum, in Greek, in Latin signifies punctum, a point placed in the middle of a sphere or circle, to which lines drawn from the surface, or periphery, are all found to be equal. But it differs from a point strictly taken, because the latter is defined by Euclid as having no part, and it abstracts from whether it is the principle of a figure, mediately or not; whereas centrum always denotes the middle of any thing, conceived as indivisible, although in practice a point is almost always taken for a center, and by center nothing else is meant than a point placed in the middle of a sphere or circle. Hence the earth, placed in the middle of the world and comparable to the immensity of the heavens, being as it were a point, is called the center of the world. Whence Cicero, in book 1 of the Tusculans, says, persuading the mathematician that the earth in the middle of the world, as it were, is enclosed by the whole complex of the heavens almost like a point, which others call the center. Moreover, whenever mathematicians wish to calculate the motions, positions, distances, appearances, and other things of this kind of the stars, they always begin from the center of one star to the center of another body: and thus they compute the true eclipses of the luminaries, which they also call eclipses, from the centers of the luminaries, and take account of both semidiameters, as well as of the earth, toward whose center, not toward its surface, a ray shot rightly from a star terminates. Hence the parallax, hence that difference between true motion and apparent motion: concerning all of which, in their proper place.
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LEXICON piscium, aut sanè ijs mercandis, ac sale, alijsque liquamini- bus, vt fieri assolet, condendis, ac vendendis. In occasu verò periculum facit, quo natantes, vel in fluuo, vel in mari à Cracodilis, vel alijs huiusmodi bestiis lacerentur. CH 71. CHAKITICHI Græcè dicitur in cælesti figura sexta domus ab horoscopocadens, ab angulo lmi cæli, hoc est mala for- tuna: eò quod est significatrix malorum, atque infirmita- tum, & nullam cum horoscopo societatem haber. Ascribitur ei color niger, ex membris humanis venter cum intestinis. Consignificatorem haber Mercurium, & gaudet in ea Mars, qui imbi repertus, experientia teste, Medicinæ studijs facit intentum. 72. CHAMÆLSON sidus in cælo ad polum Antarcticum nobis innisum contans stellis nouem infimæ conditionis, à nouis Astronomis detectum atque alijs imaginibus recens adjun- ctum. Eius caput incidit in colurum æquinoctiorum. Totum verò sidus est in longitudine sub signis Scorpij, & Sagittarij, ac ferunt esse directè oppositum Vræ minori. 73. CHASMA, teste Plinio, lib. 2. cap 26. est Cæli quidam hiatus statis temporibus apparens, qualis est, quem nunc satis conspicuè videmus in pectore Cigni, in loco vbi noua stel- la apparuit anno 1600. ac tandem post aliquot menses eua- nuit. Hunc idem Plinius fallo in genere Cometarum col- locat. 74. CHELÆ sunt Scorpionum, & Cancerum brachia, quæ postea ab Astronomis acceptæ sunt ad significandas chelas Scorpij sideris, seu veriùs Lances australem, & borealem: (quandoquidem antriqui vt in loco dicemus pro vno tantùm sidere computabant & Libram, & Scorpium, & insuper istæ dux stellæ modo in longitudine sunt in Scorpionis signo) vtraque autem est secundæ magnitudiuis de natura Martis, & Saturni, quarum prior nempe lanx australis est vna ex stel- lis regijs; & ideò in horoscopo reperta, aut cum luminaribus, præsertim si bono beneficium radio fulciatur, ad magna euehit, atque honores, & diuitias pollicetur. 75. CHELISERIAM dicta est ab aliquidbus Lyra, Fidicula, Vul- tur cadens sidus ad borealem plagam: de quo fusè in suo loco. 76. CHELEVB, seu Chelub. Arab. dicitur Perseus, Inachides & Cyllenius: de quo vide suo loco. CHELIDONIVS ventus est anniuersarius spirans verno tem-
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of fish, or indeed for trading in them, and for salting and seasoning with other liquors, as is usually done, and selling them. But in the west it is dangerous, where those swimming, either in a river or in the sea, may be torn by crocodiles or other such beasts. CH 71. CHAKITICHI is called in Greek in the celestial figure the sixth house, falling from the horoscopus, from the angle of the lower heaven, that is, bad fortune: because it signifies evils and infirmities, and has no fellowship with the horoscopus. Black is assigned to it, and among the human members the belly with the intestines. It has Mercury as a co-significator, and Mars rejoices in it; found there, experience testifies, it makes one intent on the studies of Medicine. 72. CHAMÆLSON is a star in the sky near the Antarctic pole, resting on nine stars of the lowest condition, discovered by the newer Astronomers and recently added to other figures. Its head falls on the colure of the equinoxes. The whole star is in longitude under the signs of Scorpio and Sagittarius, and they say it is directly opposite the Lesser Bear. 73. CHASMA, according to Pliny, book 2, chapter 26, is a certain gap of the heavens appearing at fixed times, such as the one which we now quite clearly see in the breast of Cygnus, in the place where a new star appeared in the year 1600 and then disappeared after some months. The same Pliny wrongly places this among the class of comets. 74. CHELÆ are the arms of Scorpions and Crabs, which were later adopted by astronomers to signify the claws of the star of Scorpio, or more truly the southern and northern scales: (inasmuch as the ancients, as we shall say in the proper place, counted Libra, Scorpio, and also these two stars as only one constellation) both are of the second magnitude, of the nature of Mars and Saturn, of which the former, namely the southern scale, is one of the royal stars; and therefore, when found in the horoscope, or with the luminaries, especially if supported by a benefic ray, it carries one to great things and promises honors and riches. 75. CHELISERIA is called by some Lyra, Fidicula, Vultur, the falling star on the northern side: of which more fully in its place. 76. CHELEVB, or Chelub, in Arabic, is called Perseus, Inachides, and Cyllenius: see in its place. CHELIDONIVS is an anniversary wind blowing in the springtime
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MATHEMATICVM. 101 pore ab exortu vespertino Arcturi, omnium ventorum minis- timus, ac suauissimus, qui postea conueritur in Fauoniums nomen hausit ab aduentu hyrundinum, quæ eò potissimum tempore ad nos adueniunt: quamobrem & Ornihiac dictus est. CHENEN, in sphæra barbarica dicitur tertius decanus, Sagittarij manus sub dominatu Saturni, obstinationis in proposito, contradictionis, dexteritatis in malo Rixarum, & factorum abominabilium. CHIRON, Centaurus, Typhon, fidus in cælo ad australem plagam, de quo non multo antè dictum est in Verbo Centaurus. Ab aliquibus etiam accipitur de Sagittarij signo, vno ex duobus Zodiaci, cuius in loco mentio erit. CHORDA apud Geometras est linea recta arcui subtensa, quæ diuidat circulum in duas partes inæquales, sicque per centrum minimè transeat (in quo differt à diametro) sed vel suprà, vel infra sit, relinquens in circulo æquabilia spatia, seu portiones ipsius, quarum maior sit quæ centrum complectitur, minor verò quæ comprehenditur sub ipsa chorda. Nomen sortita est à similiudine quam habet ad chordam arcui venatorio subiensam, vnde Sagitia per arcum ejaculatur. Porrò dimidium chordæ sinus rectus appellatur, & semilles rectarum, prout in loco dicemus. Huius ope, ac tabularum sinuum tangentium, & secantium tota triangulorum doctrina resoluitur: per eam enim venamur quantitatem arcus, cui subtenditur, atque alterius ad alteram proportionem. Vide fusiùs in V. Simus. CHOREVTE, teste Hygino, appellantur à Græcis duæ stellæ Visæ minoris, quæ polari æquales in magnitudine, ac splendore, eam circumdant, & circumdantes, choreas veluti ducere, eique gestire, ac subfamulati videntur. CHOROGRAPHIA pais est Geographiæ, quæ particularium tantum prouinciarum, aut regnorum descriptionem tradit, cum tamen Geographia sit vniuersalis descriptio totius terræ habitabilis. CHRISEVS Cometes. Vide Rosa. CHRONICVS idem sonat ac Temporalis, quid importet. Vide in V. Achronicus. CRONOCRATOR Græcè, Latinè interpretatur temporis dominus. Apud Astronomos Chronocratores dicuntur planeæ, qui fuerint temporum dispositores. Rhodiginus Chronocratorem appellat luminare temporis, vt Solem de die, Lunam de nocte. Aben Ragel, alijque Astrologi diuidunt æratem hominis in septem partes pro singulis eius statibus, ac singu- G iiij
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MATHEMATICVM. 101 that is, from the evening rising of Arcturus, the mildest of all winds, and the sweetest, which afterward turns into Favonius; it took its name from the arrival of swallows, which come to us chiefly at that time: wherefore it is also called Ornihiac. CHENEN, in the barbaric sphere, is said to be the third decan, the hand of Sagittarius under the rule of Saturn, of stubbornness in purpose, contradiction, skill in evil, quarrels, and abominable deeds. CHIRON, the Centaur, Typhon, a fixed star in the sky toward the southern quarter, of which something was said not long before under the word Centaurus. By some it is also taken for the sign of Sagittarius, one of the two of the Zodiac, mention of which will be made in its place. CHORDA, among geometers, is a straight line subtended by an arc, which divides the circle into two unequal parts, and thus does not pass through the center at all (in which it differs from the diameter), but lies either above or below it, leaving in the circle equal spaces, or portions of it, of which the larger is that which encloses the center, the smaller indeed that which is contained under the chord itself. It received its name from the likeness it has to a bowstring under the hunting bow, whence the arrow is shot through the arc. Moreover, half the chord is called the right sine, and the semichords of straight lines, as we shall say in its place. By its aid, together with tables of sines, tangents, and secants, the whole doctrine of triangles is resolved: for by it we hunt the quantity of the arc to which it is subtended, and the proportion of one to another. See more fully under Sine. CHOREVTE, according to Hyginus, are the two stars of the Lesser Bear, which, equal to the pole in magnitude and brightness, surround it, and, by surrounding it, seem as though they were leading dances and rejoicing around it, and as though they were attendants upon it. CHOROGRAPHIA is a part of Geography that gives the description only of particular provinces or kingdoms, whereas Geography is the universal description of the entire inhabited earth. CHRISEVS Comet. See Rosa. CHRONICVS means the same as Temporal, what it imports. See under Achronicus. CRONOCRATOR in Greek, in Latin, is interpreted as lord of time. Among astronomers, Chronocrators are called the planets that have been the regulators of times. Rhodiginus calls the Chronocrator the luminary of time, as the Sun by day, the Moon by night. Aben Ragel, and other astrologers, divide a man’s life into seven parts according to each of its states, and singu- G iiij
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MATHEMATICVM. 105 tissimo ruens. Eo potissimum infestatur Gallia Narbonensis, vt auctor est Gellius, & in Italia vbs nomine Beneuentum olim ab ipso Maleuentum dicta, vt explicar Procopius lib. 1. sic inquiens Quondam Prisci Maleuentum dixere: id namque 90. Oppidum, Dalmatia ex aduerso oppositum est, in continentique situm. in quod spiritus violentior quidam, & aceibs simus (Circus nempe ventus) ingruere consueust: quis vstque vbs flare caperet, non foris ster agere, sed domi se quisque conservare laborat. Nam venti huius est violentia, vt vel equissem cum equo simul arreptum sublimem mox deferat, diuque per aerem circumactum, & quocumque tulerit c[on]s[ui]s projectum interimat: vnde & Maleuensum, & in edito positum ex eo vento toleratu difficili sortitum est nomen. Hueusque Procopius de ea vrbe, quæ postea boni ominis ergo Beneuentum appellari exp[er]it. CIRCITORES & Vigiles dictæ sunt duæ stellæ secundæ magnitudinis in Vrsæ minoris corpore extremæ, quæ polarem circumstant, & quasi custodes ambiunt, vnde a Græcis, vt habet Hyginus Choreuta etiam appellatæ sunt, quasi choreas circâ eam ducentes. CIRCULVS, & Circus à Mathematicis sic definitur. Est figura 92. plana, unâ tantùm lineâ contenta, in cuius medio punctus sit, à quo omnes lineæ ad circumferentiam ducta aqua es sim[us]. Differt à sphæra, quæ non est figura plana, sed perfectè rotunda, neque vnica linea terminatur, & circumscribitur, sed lata quædam superficie vndequalque concluditur. Differt etiam ab Ellipsi, quæ, quamuis figura plana sit, vnaque linea circumscribitur (in quo conuenit cum circulo) quia tamen in ea non datur punctum, à quo duci possint æquales lineæ ad ipsam circumferentiam, seu lineam terminantem, ideò circulus dici non potest, neque orbicularem formam retinet, sed oualem. CIRCULVS rectus in sphæra dicitur Meridianus, vnsus ex sex 93. circulis majoribus, ad differentiam horizontis, qui (præterquam in sphæra recta, & sub æquatore) semper est obliquus atque obliquè ex ea emergunt sidera; cum alias ad Meridianum, vbiuis locorum semper ascendant rectè. Complectitur autem hic circulus in cælesti figura decimam, & quartam domum: quæ proinde constituuntur per ascensiones rectas: atque hic circulus consideratur immobilis in situ Mundi. CIRCULVS rectus etiam dicitur æquator æquè distans à polis 94. mundi, hoc est grad. 90. hinc inde, atque adeò in medio sphætæ collocatus: de quo plura diximus suo loco, sicut è contia. CIRCULVS obliquus appellatur Zodiacus ad differentiam cir. 95.
Transcription: Translated (English)
MATHEMATICVM. 105 very violently rushing in. For this reason chiefly Gaul Narbonensis is troubled by it, as Gellius relates; and in Italy the city under the name Beneventum, once called by this very wind Maleventum, as Procopius explains, book 1. Thus he says: “Once the ancients called it Maleventum: for that city is opposite Dalmatia and situated on the mainland. Into it a certain violent and very sharp spirit (namely the Circius wind) is accustomed to rush; so that whoever can endure to remain there, labors not to go outside, but to stay safely at home. For the violence of this wind is such that it will snatch up even a horse together with its rider and immediately carry him aloft, and having long whirled him through the air, will destroy him, flinging him wherever it pleases.” Hence it received the name both of Maleventum, and, from that wind and from being set on a height, a name difficult to endure. Thus far Procopius concerning that city, which afterward was called Beneventum for the sake of a good omen. CIRCITORES and Vigiles are the names given to two stars of the second magnitude, at the ends of the body of Ursa Minor, which surround the pole and, as it were, encircle it as guards; whence, according to the Greeks, as Hyginus has it, they are also called Choreutae, as if leading dances around it. CIRCULUS, and Circus, is thus defined by mathematicians. It is a plane figure contained by a single line, having a point in its middle, from which all lines drawn to the circumference are equal. It differs from a sphere, which is not a plane figure but perfectly round, and is not bounded and described by a single line, but enclosed on every side by a certain broad surface. It also differs from an ellipse, which, although it is a plane figure and is enclosed by one line (in which it agrees with the circle), nevertheless has no point from which equal lines may be drawn to its circumference, or bounding line; therefore it cannot be called a circle, nor does it retain a circular form, but rather an oval one. CIRCULUS rectus in a sphere is called the Meridian, one of the six major circles, as distinct from the horizon, which (except in a right sphere and under the equator) is always oblique, and the stars rise obliquely from it; whereas otherwise they always ascend directly to the Meridian, wherever the place may be. This circle in the celestial figure comprises the tenth and fourth houses, which are therefore established by right ascensions; and this circle is considered immovable in the position of the world. CIRCULUS rectus is also called the equator, equally distant from the poles of the world, that is, 90 degrees on either side, and thus placed in the middle of the sphere; of which we have spoken more fully in its proper place, as opposed to the other. CIRCULUS obliquus is called the Zodiac, in distinction from the cir. 95.
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106 LEXICON culi recti, cùm is semper obliquè ascendat, tam in sphæra recta quàm in obliqua, cùm alias æquator in sphæra recta, æqualiter semper ascendat, & in obliqua, si non rectè saltem æqualiter, & Zodiaco rectiùs. 96. CIRCULI alitudinum vocantur circuli paralleli ad horizontem vsque ad summum verticem, eò quia eorum ope venamur altitudines siderum, & elevationem suprà horizontem. Arabicè dicuntur Almiscanscharath: vide quæ sub hoc vocabulo fusè diximus. 97. CIRCULI horarij sunt circuli ducti per polos mundi, ac partes oppositas horizontis, quibus venamur quantitatem diei ac noctis, horas planetarias, arcus semidiurnos, ac seminocturnos planetarum, atque elevationem policiuscumque sideris ad mentem Ptolemzi ad verum circulum positionis habendum. 98. CIRCULI positionum sunt circuli transeuntes per communes intersectiones horizontis, & Meridiani, atque per centrum stellæ, quibus potissimùm vtuntur Rationales ad eius situm in mundo venandum, ad quos reducuntur etiam circula domorum. 99. CIRCULI verticales sunt circuli transeuntes per verticem alicuius loci, sese ibi mutuò intersecantes, ac tandem ad oppositas horizontis partes terminantes, quibus iuquirimus locorum longitudines, ac distantiam siderum à quacumque horizontis parte, nec non ab inuicem per latum. Arabicè Azimutha: de quibus suo loco dictum. 100. CIRCUMFERENTIA. Vide Peripheria. 101. CIRCVMVALLATIO, teste Valla, idem valet apud Astronomos, ac Obsessio; estque cum planeta medius inter duos, ita circumdatur, ac vallo quasi obsiderur, vt vim suam exerere minimè valeat, neque aliorum aspectus recipere. Hæc obsessio ab infortunis alicui benefico, aut promiscuæ naturæ intenrata, pessima est: à beneficis verò erga maleficum optima: quippe quæ ita eius vires debilitat, vt nil ferè operari valeat planeta obsessus, sed tota eius actiuitas ab illis absumatur, aut sanè labefactatur. 102. CIRNECIR apud Hermetem in lib. de judicijs & significationibus stellarum Beibeniarum, audit stella fixa lucida lancis borealis, secundæ magnirudinis de natura Louis, & Mercurij, existens nunc temporis in grad. 15 Scorpij cum tot ferè grad. latitudinis borealis. Hæc in horoscopo (inquit idem Hermes) facit fortunatum Regem, amatorem aliaris Dei, malorum persecutorem, magni nominis apud exteros, ac poësis cultorem.
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106 LEXICON straight circles, since it always ascends obliquely, both in the right sphere and in the oblique, whereas the equator otherwise, in the right sphere, always ascends equally, and in the oblique, if not rightly, at least equally, and the Zodiac more rightly. 96. CIRCLES of altitudes are called circles parallel to the horizon up to the highest zenith, because by their help we hunt the altitudes of the stars, and their elevation above the horizon. In Arabic they are called Almiscanscharath: see what we have said at length under this word. 97. HOUR circles are circles drawn through the poles of the world, and the opposite parts of the horizon, by which we hunt the quantity of day and night, planetary hours, semidiurnal and seminocturnal arcs of the planets, and the elevation of any star according to Ptolemy’s view, by taking the true circle of position. 98. CIRCLES of position are circles passing through the common intersections of the horizon and the meridian, and through the center of the star, which the Rationalists use chiefly to hunt for its place in the world; to these are also reduced the circles of houses. 99. VERTICAL circles are circles passing through the zenith of a given place, mutually intersecting there, and finally terminating at the opposite parts of the horizon, by which we inquire into the longitudes of places and the distance of stars from any part of the horizon, as well as from one another in breadth. In Arabic, Azimutha: of which it has been spoken in its proper place. 100. CIRCUMFERENCE. See Peripheria. 101. CIRCVMVALLATIO, according to Valla, has the same meaning among Astronomers as Obsessio; and it is when a planet, lying between two others, is thus surrounded and, as it were, besieged by a rampart, so that it is by no means able to exercise its power, nor receive the aspects of the others. This siege, when imposed by infortunes upon a benefic, or upon one of mixed nature, is worst; but by benefics against a malefic it is best: for it so weakens its powers that the besieged planet can hardly do anything at all, but all its activity is consumed by those others, or truly is weakened. 102. CIRNECIR, in Hermes’s book on the judgments and significations of the Beibeniæ stars, is the name of a bright fixed star in the northern scale, of the second magnitude, of the nature of Jupiter and Mercury, now existing in the 15th degree of Scorpio with almost so many degrees of northern latitude. This, in the horoscope (says the same Hermes), makes a fortunate king, a lover of the other God, a persecutor of evil men, of great name among foreigners, and a cultivator of poetry.
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CLIMA Græcè, Latinè audit spatium siue in cælo, siue in 103, terra contentum inter duos parallelos, quod quia semper minor, ac minor concihi potest, ideò & plura Climata in infinitum. Nihilominus tamen nunc temporis accipitur pro tanto terræ, aut cæli, cui terra subest, spatio, per quantum sensibiliter variari potest ortus, & occasus signorum, nec non diesum, ac noctium artificialium quantitas, & longitudo. Differentia igitur semihoræ, qua augeatur maximi diei artificialis, aut maximæ noctis quantitas, visa est veteribus condigna portio, ac sensibilis assignanda cuilibet Climatis. Et quoniam non omnem tertam habitabilem existimabant, sed solum sub Zonis temperatis, quæ sunt inter tropicos, & circulum seu Arcticum, seu Antartcticum (partes enim æquatori vicinas propter nimium calorem, & quæ sub circulis Arctico, & Antartico continentut, ob nimium frigus inhabitabiles credidetunt) ideò vniuersam Zonam temperatam, quæ est ad botealem plagam in septem climata diuisctunt incipiendo à primo parallelo versus æquatorem, seu Tropico Cancri, vbi maximus dies est horarum 15, vsque ad circulum Arcticum, singulis sua nomina, à celebri aliquo loco, quem pettansit parallelus, qui per medium climatis describitur, tribuentes. Sed quoniam Recensiores, expetientia duce, comprobavere, totam ferè terræ molem habitablem esse, & adhuc, si vlla pars inhabitabilis poter, satis esset ad rationem climatum, vt maximorum dierum quantitas augeatur, ant minuarur; ideò rem meliùs auspicati, ac Ptolemæum sequuti, describunt in superficie terræ circulos parallelos ab æquatore versus Polum, tanta inter se distantia, quanta requiritur, vt vniuscuiusque maximus dies differat horæ quadrante ab die maximo alterius parallelis ita vt vnumquodque clima tribus parallelis definiatur. Atque hac ratione constituunt viginti t[em]tia climata, hinc citra æquatorem ad Polum boreum (totidem consequenter trans illum ad Austrum) atque intra quadrangintanouem parallelos includunt, singulis parallelis horæ, vt dictum est, quadrantem assignantes. Primùm clima includit Insulam Taprobanam, & sinus <104.> Aualicum, & Aduliticum, ac definitut tertio parallelo ab æquatote, vbi Polus attollitur gr. 8. min 34. ac maximus dies artificialis est hor. 12. min. 30. latitudo eius est grad. 8. min. 34.
Transcription: Translated (English)
CLIMA, in Greek, in Latin, signifies a space, whether in the heavens or on the earth, contained between two parallels, which, because it can always be conceived smaller and smaller, therefore there are likewise more and more Climata without end. Nevertheless, nowadays it is taken for so much of the earth, or of the heaven beneath which the earth lies, as the rising and setting of the signs, as well as the quantity and length of artificial days and nights, can sensibly vary. Therefore the difference of half an hour, by which the length of the greatest artificial day, or of the greatest night, increases, seemed to the ancients a fitting and sensible portion to be assigned to each Clima. And because they did not think every part of the earth habitable, but only that under the temperate Zones, which are between the tropics and either the Arctic or Antarctic circle (for they believed the regions near the equator, because of excessive heat, and those contained under the Arctic and Antarctic circles, because of excessive cold, to be uninhabitable), therefore they divided the whole temperate Zone, which is toward the northern region, into seven climata, beginning from the first parallel toward the equator, or the Tropic of Cancer, where the longest day is 15 hours, up to the Arctic circle, assigning to each its own name from some celebrated place which the parallel passing through the middle of the clima describes. But since later writers, guided by experience, have proved that almost the whole mass of the earth is habitable, and that even if any part were uninhabitable, it would be sufficient for the purposes of climata that the quantity of the greatest days should increase or decrease; therefore, taking a better course, and following Ptolemy, they describe on the surface of the earth parallel circles from the equator toward the Pole, at such distances from one another as are required so that the greatest day of each may differ by a quarter of an hour from the greatest day of the other parallel, so that each clima is defined by three parallels. And in this way they establish twenty-nine climata, here on this side of the equator to the northern Pole (and consequently as many across it to the South), and include within forty-nine parallels, assigning to each parallel, as has been said, a quarter of an hour. The first clima includes the island of Taprobana, and the sinus Aualicus and Aduliticus, and is defined by the third parallel from the equator, where the pole is elevated 8 degrees 34 minutes, and the longest artificial day is 12 hours 30 minutes. Its latitude is 8 degrees 34 minutes.
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105. LEXICON 105. Secundum elima (quod est primum antiquorum) amplectitur quartum, quinrum, & sexrum parallelum; ita tamen vt hic definiat maximum diem hor. 13. min 15. ac loca illi subjecta deprimantur infra polum grad 20. min. 33. eiusque medium transit per Meroen Insulam, à qua, muruaro nomine, à Græcis Diameros dictum est, sub hoc elimare continenrur Insulæ fortunatæ, pars Arabiæ, Nubi populi, Goa celeberrima Vrbs, arque Indiarum Emportum, Insula sancti Thomæ, & plurimæ alia prouinciæ, latitudo eius est grad. 7. min. 50. 106. Tertium elima dictum Diasynoës quia eius principium est ab Synoë, & amplectitur Prolemaidam, Ægyptium, maioremque partem Regni Chinensis, ac terminarut octauo parallelo, vbi altitudo Poli est grad. 27. min. 36. & dies maxima est hor. 13 min. 45 est larum gr. 7. min 3. 107. Quartum elima definitur decimo parallelo, & amplectitur Persidem, & reliquam partem Ægypti, & quia transit per mediam Alexandriam Diallexandros est appellatum, eius finis habet diem maximam hor. 14. min. 15. Polusque super loca illi subjecta, eleuatur gr. 33. min. 45. amplitudo eius est grad. 6. min. 9. 108. Quintum elima dictum Diarhodos quia transit per Rhodum Insulam, conrinet Phæniciam Cyprum, Cretam, Smyrnam, & Hellespontum, definirurque duodecimo parallelo, sub quo dies maxima est hor 14. min. 45 & altitudo Poli est gr. 39. minut. 2. hora eius latitudo est grad. 5. min. 17. 109. Sextum elima appellatur Diaromes quia transit per Romam, & sub se habet Bizantiam, Massiliam, Hispaniam, Regnumque Neapolis, est latum gr. 4. min 30. atque extenditur vsq[ue] ad quartumdecimum parallelo, vbi eleuatio Poli est gr. 43. min. 32. & dies maxima est hor. 15. min. 15. Seprimum elima, quod dicitur Diapontos quia transit per Pontum continet intrà se Venerias, Mediolanum, sinitimasque vrbis Vngariam, & Galliæ magnam parrem & clauditur parallelo 16. in latitudine grad. 3 min. 48. sub eleuatione Poli gr. 47. min. 20. vbi maxima dies artificialis est hor. 15. minut. 45. Octauum elima nomine Diaborystenes quia transit per Borystenis ostia amplectitur Podoliam, Germaniam supetiorem, Poloniam, aliasque plures Seprentrionis prouincias; estque larum gr. 3. min. 13. vlrimus eius terminus claudiur parallelo 18. vbi dies maximus est hor. 16. min. 15. sub eleuatione Poli gr. 50. min. 49. 110. Nonum elima incipit à Mattide palude (vbi climatum ter-
Transcription: Translated (English)
105. LEXICON 105. The second climate, which is the first of the ancients, embraces the fourth, fifth, and sixth parallels; yet so that here it has the maximum day of 13 hours 15 minutes, and the places subject to it are depressed beneath the pole by 20 degrees 33 minutes, and its middle passes through the island of Meroe, from which, by the name of Muruaro, it was called by the Greeks Diameros. Under this climate are contained the Fortunate Islands, part of Arabia, the Nubian peoples, Goa, the most famous city, and the emporium of India, the island of Saint Thomas, and many other provinces; its latitude is 7 degrees 50 minutes. 106. The third climate, called Diasynoës because its beginning is from Synoë, embraces Prolemaidæ, Egypt, and the greater part of the Chinese Empire, and ends at the eighth parallel, where the height of the Pole is 27 degrees 36 minutes and the maximum day is 13 hours 45 minutes; its breadth is 7 degrees 3 minutes. 107. The fourth climate is defined by the tenth parallel and embraces Persia and the remaining part of Egypt, and because it passes through the middle of Alexandria it is called Diallexandros; its end has a maximum day of 14 hours 15 minutes, and the Pole over the places subject to it is elevated 33 degrees 45 minutes; its extent is 6 degrees 9 minutes. 108. The fifth climate, called Diarhodos because it passes through the island of Rhodes, contains Phoenicia, Cyprus, Crete, Smyrna, and the Hellespont, and is defined by the twelfth parallel, under which the maximum day is 14 hours 45 minutes and the height of the Pole is 39 degrees 2 minutes; its breadth is 5 degrees 17 minutes. 109. The sixth climate is called Diaromes because it passes through Rome, and it has beneath it Byzantium, Marseilles, Spain, and the Kingdom of Naples; it is 4 degrees 30 minutes wide and extends as far as the fourteenth parallel, where the elevation of the Pole is 43 degrees 32 minutes and the maximum day is 15 hours 15 minutes. The seventh climate, which is called Diapontos because it passes through Pontus, contains within it Vienna, Milan, the neighboring city, Hungary, and a large part of Gaul, and is closed by the sixteenth parallel; in latitude it is 3 degrees 48 minutes, under an elevation of the Pole of 47 degrees 20 minutes, where the greatest artificial day is 15 hours 45 minutes. The eighth climate, by the name Diaborystenes, because it passes through the mouths of the Borysthenes, embraces Podolia, Upper Germany, Poland, and many other northern provinces; and it is 3 degrees 13 minutes wide. Its last limit is closed by the eighteenth parallel, where the longest day is 16 hours 15 minutes, under an elevation of the Pole of 50 degrees 49 minutes. 110. The ninth climate begins from the Mattian marsh (where the climate is...
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110 LEXICON 123. Vigesimum climatatum min. 11. amplectitur extrema Nor- uegiz loca, siniturque parallelo 42. sub quo dies maxima est hor. 22. min. 15. in altitudine Poli gr. 66. 124. Vigesimum-primum climat transit per Sueciam, & conrine- tur intra parallelum 42 & 44. cuius medium habet diem ma- ximam hor. 22. min. 30. estque in altitudine Poli. gr. 66. min. 6. amplitudo eius est min. 17. 125. Vigesimum-secundum clima transit per mediam Albam, Russiam; estque in altitudine Poli gr. 66. & min à 14. vsque ad 25. cuius medium habet diem maximam constantem hor. 23. finis verò cadit sub parallelo 46. vbi dies maxima est hor. 23. min. 15. tota eius latitudo est min. 11. 126. Vigesimum-tertium clima, quod est vltimum complectitur partem Islandiæ, & vicinas Insulas sub parallelis 46. 47. & 48. cuius principium habet diem maximam hor. 23. min. 15. me- dium hor 23. min. 30. finis hor. 23. min 45 in altitudine Poli grad. 66 min 28. estque latum solis min. 5. 127. Tandem parallelo 49. terminantur omnia climata vbi dies maximus est hor 24. ita vt ibi Sol incipiat non occidere, sed circulariter ferri; vt propterea populi ea loca inhabitantes vo- centur Perisc 1, hoc est Circumbrasiles quia vmbra illorum est versatilis, & circum circà se vertit, quod accidit ab hoc pa- rallelo vsque ad polum, sub quo dies vnis naturalis integra- tur ex integro anno, sex enim mensibus Sol nunquam occi- dit, cùm reperiatur in semicirculo boreali, qui nunquam sub terra sit, & è contrà dum est in semicirculo australi, qui semper sub terra latet, spatio item sex mensium facit longis- simam noctem: quæ tamen, neque nox dici potest, cùm ha- beat ferè semper lucem crepusculinam valdè claram ob Solis vicinitatem. 128. Porto quæ diximus de parallelis ad æquatorem constituen- tibus diuersa climata in nostra plaga Septentrionali conci- pienda sunt etiam in altero Hemisphætio versus polum An- tarcticum, vbi totidem climata constituenda sunt in eadem amplitudine, arque in eadem poli Antarcticci eleuatione, cum eadem prorsus quantitate dierum ac de nostris regioni- bus diximus, quæ vtique climata nominari possunt vel à præcipuis locis, per quæ transeunt, vel sanè (vt de Polo sit) ab oppositis. 129. Hic autem, etsi obiter, non erit fortè injucundum dis- quirere quod clima ex modo numeratis sit temperatius, atque habitationi hominum accommodatius. Auicennas lib. 1. Pen. cap. 1. opinatur quod sub æquatore vbi incipit primum clima sit locus habitationis omnium temperatissimus, quia, inquit,
Transcription: Translated (English)
110 LEXICON 123. The twentieth climate extends to the farthest parts of Norway, and is bounded by parallel 42, under which the longest day is 22 hours 15 minutes, at the elevation of the Pole 66 degrees. 124. The twenty-first climate passes through Sweden, and is contained between parallels 42 and 44; its middle has the longest day, 22 hours 30 minutes, and is at the elevation of the Pole 66 degrees 6 minutes. Its breadth is 17 minutes. 125. The twenty-second climate passes through the middle of Alba and Russia; and is at the elevation of the Pole 66 degrees and from 14 minutes to 25 minutes, the middle of which has a constant longest day of 23 hours. Its end, however, falls under parallel 46, where the longest day is 23 hours 15 minutes; its whole width is 11 minutes. 126. The twenty-third climate, which is the last, includes part of Iceland and the neighboring islands under parallels 46, 47, and 48; its beginning has the longest day of 23 hours 15 minutes, the middle 23 hours 30 minutes, the end 23 hours 45 minutes, at the elevation of the Pole 66 degrees 28 minutes, and it is 5 minutes wide in solar distance. 127. Finally, all climates are terminated by parallel 49, where the longest day is 24 hours, so that there the Sun begins not to set, but to move in a circle; and therefore the peoples inhabiting those regions are called Perisc 1, that is, Circumbrasiles, because their shadow is shifting and turns around itself, which occurs from this parallel to the pole, under which a natural day is completed by an entire year; for six months the Sun never sets, since it is found in the northern semicircle, which is never beneath the earth, and conversely while it is in the southern semicircle, which always lies hidden beneath the earth, for the space of six months it makes the longest night: which, however, can scarcely be called night, since it has almost always a very clear twilight light on account of the nearness of the Sun. 128. Moreover, what we have said about the parallels to the equator, constituting different climates in our northern region, must also be understood in the other hemisphere toward the Antarctic pole, where an equal number of climates must be established in the same extent and in the same elevation of the Antarctic pole, with exactly the same quantity of days as we have said of our regions; and these climates can certainly be named either from the principal places through which they pass, or indeed, as regards the Pole, from the opposite places. 129. Here, however, although only in passing, it will perhaps not be unpleasant to inquire which climate among those now numbered is the most temperate and best suited to human habitation. Avicenna, book 1, Pen, chap. 1, thinks that under the equator, where the first climate begins, is the most temperate place for habitation of all, because, he says,
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MATHEMATICVM. 118 rectitudo Solis supra verticem minus malum operatur, & minus mutat aërem, quam Solis propinquitas apud nos, qui sumus in majori latitudine, ibi enim non tantùm temporis consillic in hemisphærio, vt illud possit æquè, ac nostrum nimium ex eius radijs incalescere: & prætereà id probat experientia, & ex nostris qui illuc appuli, ad nos postea remearunt, testimonia dicentium sub æquatore esse temperatum aërem, fæcundissimam terram, iucundissimamque habitationem. Auerroës putat quintum clima, sub quo ipse erat, esse omnium temperatissimum. Manardus Ferrariensis epist. 7. sextum sub quo terrariam laudat. Albertus Magnus è contrà septimum, vbi Ratisbona, cuius ipse erat accola, & Episcopus, cæteris omnibus anteponit: quia, inquit, homines hic pulcherrimi, proceri corporis, justæ staturæ, & venusti coloris. Reuerà vnusquisq[ue] sibi plaudit, & patriæ amore illectus, atque aëri assuefactus, in ea plus jucunditatis inspicit, quàm in reliquis regionibus: vnde meritò ille cecinit: Nescio, qua natale solum dulcedine cunctos Ducit, & immemores non sinit esse sui. <130.> Sed enim dicendum est vnum quemque veritate coactum suum clima laudasse, idque illis cæteris omnibus temperatius esse; non absolutè, vt optimè obseruauit Galenus, sed respectu suorum habitatorum qui ibi nati, ibi assuefacti, ibi aërem sibi naturalem respirant, ibi etiam suæ temperiei accommodam quisque trahit moram, inuenit similitudinem. Sola igitur habitatio à primordijs constitutionis acquisita, vel longo vsu facta jam connaturalis est animantibus accommodata; alienæ verò incommodæ, & intemperatæ. Sic Lusitani, olim qui, <131.> acquisitis à suo Rege in India Orientali postubus, & castris præsediarij milites mittebantur vix tres aut quatuor menses ibi moram trahentes, cum climatis contrarietatem ferre non possent, miserè extinguebantur, vt postea cautum sit, non nisi pueros, & adolescentes eò mittere, quò aëri assueti, rem patriam, suaque iura in alienis regionibus tutarentur. Idipsum videre est in reliquis animantibus cuique regioni proprijs, quæ in alias asportata, aut vim generatiuam, amittunt, aut in totum etiam extinguuntur. Vt in elephantis, qui in Africa sunt in loco sibi connaturali, si in Italiam ducuntur, viuunt quidem, sed generare non possunt; si vlteriùs in Germaniam, aut alias Septentrionis ptouncias, non modò non speciem propagare, sed & ne vita quidem diu frui possunt: & hæc de climatum ratione satis sint dicta. <132.> CLIMACTERICVS, ex etymo Græco, petinde est, ac Latinè scalaris: Apud Astronomos verò, Physicos, aliosque passim
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MATHEMATICVM. 118 the directness of the Sun above the zenith produces less harm, and changes the air less, than the nearness of the Sun among us, who are in a higher latitude; for there there is not so much time of sunlight in the hemisphere that it could warm it as much as ours is excessively warmed by its rays. And besides, experience proves this, and the testimony of those of our people who landed there and afterward returned to us, saying that beneath the equator the air is temperate, the earth most fertile, and the dwelling most pleasant. Averroes thinks that the fifth climate, under which he himself was, is the most temperate of all. Manardus Ferrarensis, epist. 7, praises the sixth climate, under which he says the earth is fruitful. Albertus Magnus, on the other hand, prefers the seventh, where Regensburg, of which he himself was a resident and bishop, to all the rest: because, he says, the men here are most beautiful, of tall body, of proper stature, and of pleasing complexion. Truly, everyone applauds himself, and, drawn by love of his homeland and accustomed to the air, sees more delight in it than in other regions; whence he rightly sang: I know not by what sweetness native soil draws everyone, And does not allow them to be forgetful of it. <130.> But in truth it must be said that each, compelled by the truth, has praised his own climate, and that it is more temperate than all the others; not absolutely so, as Galen very well observed, but in respect to its own inhabitants, who are born there, accustomed there, breathe the air natural to them there, and there each draws, as it were, a dwelling suited to his own temperament and finds a likeness. Therefore only habitation acquired from the beginnings of constitution, or made by long use, is now natural and suited to living beings; foreign habitats, however, are unsuitable and intemperate. Thus the Portuguese, who formerly, when garrisons and posts had been acquired by their King in the East Indies, as frontier soldiers were sent there, staying scarcely three or four months, since they could not endure the contrariety of the climate, miserably perished; so that afterward it was provided that only boys and youths should be sent there, so that, accustomed to the air, they might defend the fatherland and their own rights in foreign regions. The same may be seen in the other animals proper to each region, which, when carried into others, either lose their generative power or are even extinguished altogether. As in elephants, which are in Africa in a place natural to them: if they are led into Italy, they indeed live, but cannot breed; if farther into Germany or other provinces of the North, they not only cannot propagate their species, but cannot even enjoy life for long: and let this be enough said concerning the nature of climates. <132.> CLIMACTERICVS, from the Greek etymology, is the same as, in Latin, scalaris: but among astronomers, physicians, and others, commonly
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COELVM dicitur pars illa, & potior Vniuersi, quæ est super omnia elementa, substantiæ, vt fert communior Philosophorum sententia, ab hac sublunari diuetiæ, formæ, vt creditur, incorruptibilis, quamque communiter Ætheta appellarunt, amplectiturque corpora ipsa cælestia, astra, planetas, atque orbes deferentes in quibus ista fixa esse intelliguntur. Dicitur cælum à cælando, vt habet Ambrosius lib. 2 examiner. eò quod impressa stellarum lumina habeat, quasi cælarium varijs imaginibus opus. Quinque autem cæli proprietates communiter enumerantur. Lumen, situs, incommutabilitas motus, & natura, quæ à Philosophis quinta nuncupatur essentia. Quod ad lumen attinet, id manifestum est esse præcipuam cæli proprietatem, qua in hæc inferiora influit per motum localem qui lumen ipsum applicat, & pro siderum adinuicem habitudine aut intendit, aut remitit. Non quod omnes cæli partes sint luce præditæ (cum hac prærogatiua sola fulgeant astra) sed quod sit sua natura pellucidum, & astrorum lumen in se recipiat, & transfundat. Quoad situm is est cæteris omnibus præcellentior: quò enim magis aliquid rem ouetur à terra, eò est purius, & nobilius. De incommutabilitate verò nemo est qui dubitet, quandoquidem sola corpora cælestia neque alterari, neque corrumpi queunt; vt notat Philosophus in libris de cælo. Quoad morum, is circularis est, continuus ac perpetuus; motus autem elementorum rectus est, irregularis, & citò finem habet. Tandem natura cæli, siue ea simplex sit, siue composita, longè ab omni sublunarium rerum natura discedit, & est cæteris omnibus præstantior, ac diuinior. Porrò cælorum numerum pro motuum diuersitate constituebant antiqui, cum enim viderent omnia astra rapidissimo motu ferri ab Oriente in Occidentem, ac insuper aliqua ex ipsis contrario motu, & quidem singulis proprio versus Orientem cieri, seu potius ab motu vniuersitatis retardari; ideò & plures motus, & plures cælos admiscent: Et quidem Ionstonus de adm. cal. cap. 2. hæc habet: In orbis variè distinxere astronomi, placuere Eudoxo XXIII Callippo XXX. Prolemao XXX. Regiomontano XXX. II. Aristoteli XCVII D. cum esse commun: est opinso At enim Fracastorius LXX. cælos poluit omnes terræ concentricos: septem in Luna, in Mercurio vndecim, totidem in Venere, in Sole quatuor, in Marte nouem, in Ioue vndecim, in Saturno decem, supra Firmamentum sex, & Firmamentum, quod Aplanem vocat ex septem orbibus constans, H
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HEAVEN is said to be that part, and the nobler part of the universe, which is above all the elements, a substance, as the more common opinion of the philosophers holds, distinct from this sublunary world, of a form, as is believed, incorruptible, and it embraces the heavenly bodies themselves, the stars, the planets, and the carrying spheres in which these are understood to be fixed. It is called heaven from cælando , as Ambrose has in book 2 of the Exameron , because it has the impressed lights of the stars, like a work of a sky vault adorned with various images. Five properties of heaven are commonly enumerated: light, position, immutability, motion, and nature, which by philosophers is called the fifth essence. As for light, it is manifest that this is the chief property of heaven, by which it flows into these lower regions through local motion, which applies the light itself, and either strengthens or diminishes it according to the relation of the stars to one another. Not that all parts of the heaven are endowed with light, since only the stars shine with this privilege, but because by nature it is transparent and receives and transfuses the light of the stars within itself. As to position, it is superior to all the rest: for the more anything is removed from the earth, the purer and nobler it is. As for immutability, no one doubts it, since the heavenly bodies alone can neither be altered nor corrupted, as the Philosopher notes in the books On the Heavens . As for motion, it is circular, continuous, and perpetual; but the motion of the elements is straight, irregular, and quickly comes to an end. Finally, the nature of heaven, whether simple or composite, departs far from the nature of all sublunary things, and is more excellent and more divine than all the rest. Moreover, the ancients determined the number of the heavens according to the variety of motions; for when they saw all the stars carried with the swiftest motion from East to West, and furthermore some of them also moved with a contrary motion, and indeed each with its own proper motion toward the East, or rather were slowed by the motion of the universe, therefore they admitted both many motions and many heavens. And indeed Iohnstonus, de adm. cal. cap. 2, says: “Astronomers have variously distinguished the spheres; Eudoxus preferred 23, Callippus 30, Ptolemy 30, Regiomontanus 32, Aristotle 97; the common opinion is that there are 8.” But Fracastorius thought there were 70 heavens, all concentric with the earth: seven in the Moon, eleven in Mercury, as many in Venus, four in the Sun, nine in Mars, eleven in Jupiter, ten in Saturn, six above the Firmament, and the Firmament, which he calls Aplanes , consisting of seven orbs.
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IX. LEXICON Verùm hæc omnia gratis & absque vllor fundamento conficta ni cælorum nomine orbis, concentricos, & epicyclos velimus intelligere. Decem igitur omninò sunt cæli mobiles si ii solidi sunt (vt taceam de Empyreo, quod fides docet omninò immobile ac firmum, quippe quod sedes Beatorum est) ex quibus septem totidem planeis assignarunt; octauum Firmamentum seu Cælum stellatum in quo fixa constituuntur: Nonum verò cùm non nisi per motum dignoscerent, essetque prætereà pellucidum ac transparens, Christallinum dixerunt, ac tandem decimum primum mobile, quod secum reliquos rapit, atque ab Oriente in Occidentem spatio vigintiquatuor horarum circumvoluitur, & rotatur. 136. At enim si physicè loquamur (vt bene ostendit Titus in cælesti Philosophia) omnia quæcumque sidera vno tantùm motu, qui est raptus & primi mobilis agitantur ab Oriente in Occidentem; neque alius propius cuique motus vlterius admittendus. Quod autem singula non quotidie cum ijsdem partibus primi mobilis occidant, sed vicissim loca permutent, atque in præcedentibus semper conspiciantur, quæ successiuè occidunt, ac proinde videantur motu proprio, & contrario præcedentes partes acquirere; id non à vero motu, sed poriùs à motus morositate, ac mobilium resistentia, & ponderositate procedit. Quod vel ex eo patet, quia propius est, ac contiguus primo mobili stellatus Orbis validiùs ab eo trahitur, ac citiùs quàm cæleri inferiores motum diuturnum vniuersitatis absoluit. Inde Saturnus; mox Iupiter, & sic per ordinem progrediendo, omnes quò magis à primo mobili remouentur eò magis eius impulsui resistunt, ita vt Luna quæ postrema omnium est, ac teriæ vicinior, tantùm resistat, vt singulis diebus modò vndecim, modò quindecim gradus retrò remaneat, quod nos proprium motum in Zodiaco vocitamus; reuerà tamen est quædam retardatio, & morositas, qua impulsui primi mobilis resistit. Igitur hac ratione Luna non est dicenda omnium planetarum velocissima, sed tardissima: Saturnus non seguis, ac piger, sed longè plus alijs expeditior: ac tandem Firmamentum velocitate proximè accedit ad primum mobile, eò quia non remanet retrò nisi quatuor tantum minutis; ac motum suum circularem ab Oriente in Occidentem circà tellurem (præter quem alium reuerà non habent) citiùs compleat: inde Saturnus, mox Iupiter: denique serius omnibus Luna. Quia verò id non officit communi v sui loquendi, ac verè sidera hac morositate permutant loca, situm suum, & consistentiam in Zodiaco; ideò admittitur, dici posse duplex huiusmodi motus, quo post inueteratam consuetudinem
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IX. LEXICON But all these things are invented for nothing, and without any foundation, unless we wish to understand by the name of heavens the spheres, concentric spheres, and epicycles. Therefore there are altogether ten mobile heavens, if they are solid (I say nothing of the Empyrean, which faith teaches to be altogether immovable and firm, since it is the dwelling-place of the Blessed), of which they assigned seven to the planets; the eighth, the Firmament, or starry heaven, in which the fixed stars are placed; the ninth, since they recognized it only by motion, and since it was moreover pellucid and transparent, they called the crystalline; and lastly the tenth, the first mobile, which carries the rest with it, and is revolved and rotated from East to West in the space of twenty-four hours. 136. But if we speak physically (as Titus shows well in Celestial Philosophy), all the stars whatever are moved by only one motion, namely the carrying motion of the first mobile, from East to West; and no other further motion is to be admitted as proper to each of them. But the fact that the individual stars do not set each day with the same parts of the first mobile, but instead exchange places in turn, and are always seen in the parts that precede those which set successively, and therefore seem by a proper and contrary motion to acquire the preceding parts; this proceeds not from a true motion, but rather from the slowness of the motion, and from the resistance and heaviness of the mobile bodies. This is clear even from the fact that the starry sphere, being nearer and contiguous to the first mobile, is drawn by it more strongly, and sooner completes the long motion of the whole universe than do the lower heavens. Hence Saturn; then Jupiter, and so on in order: the farther they are removed from the first mobile, the more they resist its impulse, so that the Moon, which is last of all and nearer to the earth, resists so much that each day it remains behind sometimes eleven, sometimes fifteen degrees, which we call proper motion in the Zodiac; yet in truth it is a certain retardation and slowness, by which it resists the impulse of the first mobile. Therefore, for this reason, the Moon is not to be called the swiftest of all the planets, but the slowest; Saturn not sluggish and lazy, but far more swift than the others; and finally the Firmament comes nearest in speed to the first mobile, because it falls behind by only four minutes, and completes its circular motion from East to West around the earth more quickly (apart from which, in truth, they have none other); then Saturn, then Jupiter; finally, slowest of all, the Moon. But because this does not conflict with common speech, and because the stars really change their places, position, and consistency in the Zodiac by this slowness, therefore it is permitted to say that there may be a twofold motion of this kind, by which after long-established custom
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MATHEMATICVM. 121 tur. Vide Vitellion in Ops. lib. 1. CONCENTRICVM appellatur etiam omne id quod habet 138. idem centrum cum alio: sicut è contrà Eccentricum, quod habet diuersum centrum. Hinc apud Astronomos concentrici vocantur illi orbis coelestes, quorum centrum idem est cum centro mundi: Eccentrici verò ij, qui licet terram circumdent, eorum tamen centrum diuersum est à centro mundi: Vtrumque autem diuiditur in Concentricum, & Eccentricum simpliciter, & Concentricum & Eccentricum secundum quid. Concentricum simpliciter est quando vtraque superficies orbis, & concaus, & conuexa est cumcentrica cum centro mundi: similiter Eccentricum simpliciter, quando neutra superficies habet centrum mundi pro suo centro. Eccentricum secundum quid est, quando Orbis secundùm vnam tantùm superficiem, scilicet concanam, aut conuexam est concentricus mundo, secundùm alteram verò est Eccentricus: cuiusmodi est Orbis augem deferens, qui proinde partim Concentricus, partim Eccentricus est. CONDITIONARIVS apud Astronomos dicitur planeta sequens 159. conditionem temporis: vt si diurnus de die sit supra terram, nocturnus verò de nocte lustret superius hemisphærium. Præcipuè autem id in luminaribus vsurpatur: vnde & luminare conditionarium absolusè dicitur illud, cui competit prærogariua hylegij, & cæteris omnibus antefertur, vt Luna de nocte post Solis occasum: Sol in spatijs crepusculinis, aut interdiu, &c. CONFINIVM, teste Valla, idem importat, ac fines, seu termini planerarum: est que cum plures planetæ fuerint in ijsdem, aut in aliorum terminis constituti. CONGRESSVS Coniunctio. Vide in V. Coitus 160. COODROMVS, Græcè dicitur planeta, præsertim Luna solitaria, cùm nulli alij applicat, siue corpore, siue radio. Quod est ratio quædam notabilis detrimenti in planetis maximè promiscuis, quales sunt Luna, & Mercurius, qui aliorum semper radio, & subsidio gaudent. Hæc autem passio à Latinis dicitur Feralissas. CONSTELLATIO est congeries plurium stellarum in certam 162. quandam formam, & imaginem redacta, quales sunt omnes Asterismi, atque Imagines octauæ sphæræ. Antiqui enim Astronomi ad fixarum naturam explicandam, earumque numerum distinguendum, ac memoriâ retinendum, colligarunt eas in plures imagines, quarum singulæ, sui consideratione, nos prudenter ad earum naturæ noritiam manuducerent: Qua de re vide quæ fusiùs dicemus in V. Imagines Coelestes. CONTACTVS, teste Valla, est conjunctio partilis duorum
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MATHEMATICVM. 121 tur. See Vitellio in Ops. lib. 1. CONCENTRIC is also called whatever has the same center as another; as, on the contrary, ECCENTRIC is that which has a different center. Hence, among astronomers, concentric are called those celestial spheres whose center is the same as the center of the world: eccentric, on the other hand, are those which, although they surround the earth, nevertheless have a center different from the center of the world. But both are divided into Concentric and Eccentric simply, and Concentric and Eccentric in a certain respect. Concentric simply is when both surfaces of the sphere, both concave and convex, are concentric with the center of the world; similarly, eccentric simply, when neither surface has the center of the world as its center. Eccentric in a certain respect is when the sphere, according to one surface only, namely the concave or the convex, is concentric with the world, but according to the other it is eccentric: such is the sphere carrying the apogee, which therefore is partly concentric, partly eccentric. CONDITIONAL, among astronomers, is said of a planet following 159 the condition of the time: as if a diurnal one by day is above the earth, but a nocturnal one by night traverses the upper hemisphere. But this is especially used of the luminaries: whence a conditional luminary absolutely is said to be that to which the prerogative of the hyleg belongs, and which is preferred before all the others, as the Moon by night after sunset; the Sun in the twilight intervals, or by day, etc. CONFINIUM, according to Valla, imports the same as the boundaries or limits of the planets: and it is when several planets are found established in the same terms, or in those of others. CONGRESSUS: Conjunction. See under V. Coitus 160. COODROMUS, in Greek, is said of a planet, especially a solitary Moon, when it applies to no other, either by body or by ray. This is a certain notable cause of detriment in the planets, especially the promiscuous ones, such as the Moon and Mercury, which always enjoy the ray and support of others. This affection, however, is called by the Latins Feralissas. CONSTELLATION is a collection of several stars reduced into a certain 162 form and image, such as are all the asterisms and the images of the eighth sphere. For the ancient astronomers, in order to explain the nature of the fixed stars and distinguish their number, and to keep them in memory, gathered them into several images, each of which, by its own consideration, might prudently lead us to the knowledge of their nature: on this matter see what we shall say more fully under V. Celestial Images. CONTACT, according to Valla, is the partial conjunction of two
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124 LEXICON cum numerò gradum, quem obtinebat horoscopus, tenerent etiam domus succedentes in consequentibus signis; ac proinde gradus, qui incidebat in cuspidem domus decimæ non semper erat idem, ac qui ex amussi cadebat in lineam meridianam (qui solus dirigendus erat per ascensiones rectas) sed quandoq[ue] longè diuersus, ac distans. Vnde ad eum dignoscendum, seorsim signabant in decima, hoc vocabulo prænotantes: Cor cali. 171. Cor Hydræ. Arab Aiphirad, stella fixa primæ (alijs secundæ) magnitudinis de natura Saturni, & Venetis, existens in gr. ferè 23. Leonis cum latitud ne australi totidem ferè graduum. Hæc cum sui naturæ mixtæ ex contrarijs qualitatibus, Saturninis tamen prædominantibus, affect humorum insitam in ipsa natura corruptionem, præsertim cum malo radio Venetiis, aut Saturni: Et si in alicujus ortu cum Anxæreta fuerit, portendit venenum. Oritur Romæ cum gr. 2 Virginis. 172. Cor Leonis, Regulus, Basiliscus. Arabicè Kalb eleced, stella fixi, seu primæ, seu secundæ magnitudinis, sed tamen ob sui præstantiam inter primas, & præcipuas computata, de natura Martis, & louis consistens in Ecliptica, atque in longirudine in gr. 25. Leonis priuni mobilis. Est princeps, & potissima inter stellas regias, quæ in horoscopo, medio Cæli, aur cum luminatibus reperia, amplam fortunam, magnosque semper honores pollicetur. Nihilominus est etiam abscindentis naturæ ob participationem cum Marte, vt proinde in horoscopo, aliquam semper afferat corporis discretiam. Oritur Romæ atque in cæteris Orbis partibus (cùm enim consultat ferè in Ecliptica, paruam differentiam importat) cum gr. 25. Leonis, cum eodemque mediat Cælum, & occidit: Vide amplius in V. V. Basiliscus, & Regulus. 173. Cor Scorpij, Græcè Antares, stella fixa Regia, sed tamen violenta primæ magnitudinis de natura Martis, & louis, existens nunc temporis in gr. 5. Sagittarij, cum totidem ferè latitudinis meridionalis. Est item venenosæ naturæ, abscindens & humorum corruptrix. Ea tamen in horoscopo reperta cum Luna, inquit Stadius, immensas tribuit diuias, facit ductorem militum, atque ad magnos honores euehit Si verò cum Marte, aut cum Saturno fuerit, bella, & labores portendit, grauesque causas irarum. Est opposita ex diametro Pallilitio, seu oculo australi Tauti, primæ item magnitudinis, ac regiæ; vt proinde mirum non sit, si in præcipuis figuræ cardinibus reperta magna promittat, quippe quæ significationes cum illa commiscet. Oritur Romæ cum gr. 8. Sagittar. occidit verò cum 28 Scorpij. IN CORDE SOLIS dicitur esse planeta, cùm non distiterit ab eo
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124 LEXICON with the number of degrees which the horoscope occupied, the succeeding houses in the following signs would also hold them; and therefore the degree that fell upon the cusp of the tenth house was not always the same as that which, from the plumb line, fell upon the meridian line (which alone was to be directed by right ascensions), but sometimes very different and distant. Hence, in order to recognize it, they marked it separately in the tenth, noting this word: Cor cali. 171. Cor Hydræ. Arabic Aiphirad, a fixed star of the first (by others of the second) magnitude, of the nature of Saturn and Venus, situated in about 23 degrees of Leo, with southern latitude of about the same number of degrees. This, as its nature is mixed from contrary qualities, though with Saturnine qualities predominating, affects the humors, and by an inborn corruption in its own nature, especially with an evil ray of Venus or Saturn. And if in someone’s nativity it is with Anxæreta, it portends poison. It rises at Rome with 2 degrees of Virgo. 172. Cor Leonis, Regulus, Basiliscus. In Arabic Kalb eleced, a fixed star either of the first or second magnitude, yet because of its excellence counted among the first and chief ones, consisting of the nature of Mars and Jupiter, lying in the Ecliptic, and in longitude at 25 degrees of the first mobile Leo. It is the prince and most powerful among the royal stars, which, if found in the horoscope, Midheaven, or with the luminaries, promises ample fortune and great honors at all times. Nevertheless it is also of a cutting nature, because of its participation with Mars; thus in the horoscope it always brings some bodily discrepancy. It rises at Rome and in the other parts of the world (for since it is almost fixed in the Ecliptic, it makes little difference) with 25 degrees of Leo, and with the same it culminates and sets: see more in V. V. Basiliscus and Regulus. 173. Cor Scorpij, in Greek Antares, a royal fixed star, yet violent, of the first magnitude, of the nature of Mars and Jupiter, now located at 5 degrees of Sagittarius, with nearly the same southern latitude. It is also of a poisonous nature, cutting and corrupting the humors. Yet if found in the horoscope with the Moon, says Stadius, it grants immense wealth, makes a commander of soldiers, and raises one to great honors. But if with Mars or with Saturn, it portends wars and labors, and grave causes of anger. It is directly opposite Pallilitio, or the southern eye of Tauti, also of the first magnitude and royal; so it is no wonder if, when found in the principal angles of a figure, it promises great things, since it mingles its significations with that star. It rises at Rome with 8 degrees of Sagittarius; it sets with 28 degrees of Scorpio. IN CORDE SOLIS a planet is said to be, when it has not departed from it
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MATHEMATICVM. 115 plus min. 19 quantum videlicet importat aggregatum semidia- metrorum disci solaris, & ipsius Planetæ. Apud Arabes dicitur esse in Cazimi. Vide sibi. CORONA Austr[ia]na sidus est in cælo ad australem plagam (sic < 175.> dicta ad differentiam Septentrionalis) alio nomine Rota Ixionis, constans stellis tredecim, omnibus ferè de natura Saturni, & Martis, atque existens nunc temporis in longitudine in principio Libræ. Ea in horoscopo ob stellarum inibi consistentium malignitatem tantumdem malorum affert, quantum boni deceiunt stellæ de natura louis, & Veneris, oppositis vtique rationibus. CORONA Septentrionalis dicta Gnossia, Ariadnes &c. Sidus < 176.> in cælo ad borealem plagam propè Bootem constans stellis 8. at Keplero, & Baiero oculatoribus omninò 10 ob sui pulchritudinem, splendorem, varietatem, ferè omnium quæ sunt in cælo siderum celeberrimum, atque omnium ferè nationum summis laudibus decantatum. Quippe quæ apud Persas dicitur Piramis, hoc est sertum pupilla, apud Arabes Alphecca seu Alphesalid est aperitio, aperit enim suo exortu iucunditatem Veris, & prata floribus cælum ipsum tribuit æmulari: ad quod fortè allusisse visus est bellè Muretus, cùm cecinit: Esse rosas cali meriò quis dixeris Astra? Astra, sed & terra dixeris esse Rosas. Inter præcipuas stellas est quæ Arabicè dicitur Mumir, id est pupilla secundæ magnitudinis de natura Veneris, & Mercurij existens nunc temporis in gr. 18. Scorpij cum latitudine boreali gr. ferè 41. De ea horoscopante ita eleganter cecinit Mandlius lib. 5. Astronom. Clara Ariadnea quondam monumenta corona Et molles tribuent artes, hinc dona puella. Namque nescens: illic oriens est ipsa puella. Ille colet nitidis gemmantem floribus hortum, Pallentes violas, & purpureos byacinibus, Vernantisque rosæ rubicundo sanguine florem: Aut varios nettet flores, sertisque locabit. Effingesque suum similes: in mutua pressos Incoquet, atque Arabum siluis mulcebit odoreo Et medios unguenta dabit referentia status Vt sic adulserio succorum gratia major. Hæc ille; quibus olim ego ipse piè ludens in Diui Stephani < 177.> Proromartyris adornandis laudibus vsus sum: dictaque est Panegyris, editaque Patauij anno 1657. Porrò corona hæc non adeò innocens atque amabilis, vt non aliquid mali afferatam producit ventos, & pluuias, & tempestates in mari faciti
Transcription: Translated (English)
plus min. 19, namely, as much as the aggregate imports of the semidiameters of the solar disk and of the planet itself. Among the Arabs it is said to be in Cazimi. See there. CORONA Austr[ia]na is a star in the sky on the southern side (so called in distinction from the Northern) otherwise named the Wheel of Ixion, consisting of thirteen stars, almost all of the nature of Saturn and Mars, and at present being in longitude at the beginning of Libra. In the horoscope, because of the malignity of the stars situated there, it brings as much evil as good the stars of the nature of Jupiter and Venus would effect, with contrary reasons indeed. The NORTHERN CORONA, called Gnossia, Ariadne's, etc., is a star in the sky on the northern side near Boötes, consisting of 8 stars; but according to Kepler and Bayer, as observers, 10 altogether, on account of its beauty, brilliance, variety, almost the most famous of all the stars that are in the sky, and praised with the highest commendations by almost all nations. For among the Persians it is called Piramis, that is, the crown of the pupil; among the Arabs it is Alphecca or Alphesalid, meaning opening, for by its rising it opens the delight of Spring, and makes the meadows with flowers rival the heavens themselves: to which Muretus perhaps seemed to have elegantly alluded when he sang: Who would say that the stars are roses of the sky? The stars, but you would also say that roses are the earth. Among the principal stars is one which in Arabic is called Mumir, that is, the pupil of the second magnitude, of the nature of Venus and Mercury, being at present in 18 degrees of Scorpio, with northern latitude of about 41 degrees. Of it, when making a horoscope, Mandlius sang thus elegantly in book 5 of the Astronomica: The clear memorials of Ariadne's crown, And gentle arts shall they bestow; hence gifts to the girl. For, knowing it not: there arises there the girl herself. There shall he tend a garden sparkling with bright flowers, Pale violets and hyacinths, and the flower of roses blooming with ruddy blood; Or he shall weave various flowers, and shall place them in garlands. And you will fashion your own likenesses: pressed in mutual embrace He shall prepare them, and with the woods of the Arabs shall soothe them with fragrance, And in the midst shall give perfumes reflecting the couch, So that thus through love the grace of juices may be greater. Thus he; with which words I myself once, while piously playing, made use in adorning the praises of the Divine Stephen, Protomartyr; and it was called a Panegyric, and published at Padua in the year 1657. Moreover, this crown is not so innocent and lovable that it does not bring something bad; it produces winds, rains, and storms at sea. It causes
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126 LEXICON atque eius ortus matutinus cum Sole facit aërem frigidum, tu bidum, & veniosum. 178. CORONÆ in plural dicuntur ab aliquibus circuli altitudinem, Arabicè Almicantharath. Paralleli nempè ad horizontem atque ad verticem terminantes, quorum ope siderum altitudines dimenmur, cò quia singuli instar coronæ circumdare videntur verticem, aut horoscopum. Vide in V. Almicantharath. 179. CORONÆ etiam Latinè dicuntur, quæ à Græcis Halones, species quæ tam accensionum, quæ in sublimi videntur circà corpora p[er]ta stellarum, præcipuè verò circà luminaria: eas fieri inquit Vitellon in vapore leuitet condensato. Vapor enim iste à sidere attractus in ea aëris regione, quæ sideri immediatè subest ab incidentibus eius radijs illustratur, & fulgorem illum facit, similem prorsus ei, quem videmus in Atmosphæra circà horizontem in aurora, & post Solis occasum, & vocamus lucem crepusculinam H s affine est parelium, quod est Solis reuerberatio in nube rotida; ita vt alium Solem repræsentet. Porrò coronæ hujusmodi circà Solem semper ventorum præsagia sunt, ex ea parte spirantium: vnde ipsæ dissipari coeperint. 180. CORPVS Geometricè definitur, quod sit magnitudo, quæ potest tribus diametris sese ad angulos rectos intersecantibus mensurari: per quod explicatur tria dimensio, qua constituitur corpus in suo esse longum, latum, & profundum. 181. CORVS, siue Caurus ventus est Occidentalis, lateralis, Fauonio spirans ab oriu solstitiali, Aquiloni directè oppositus, sic dictus à siccitate: est enim ab initio siccus, licet posteà euadat frigidus, & humidus: Flare solet in æquinoctio autumnali cum maxima violentia, adducens procellas niues, grandines, atque interdum fulgura. Eò potissimum infestatur Apulia: eius spitauerit sereno cælo, nubila plerumque spectantur in Oriente. A Græcis Argestes dicitur à procellis, quas excitat, item & Sciron à rupe quadam vnde spirat, nec non & Olympias à monte Olympo. 182. CORVS fidus in cælo ad australem plagam circà Colurum æquinoctiorum sub signo Libræ continens stellas septem de natura Veneris, & Saturni, quatum præcipua est quæ in aladextra malignantis naturæ Arabicè algorab 1erriæ magnitudinis, quæ Romæ oritur cum gr 13 Libræ, occidit verò cum 7 Virgin. 183. COSMICS idipsum sonat Græcè, ac Latine Mundanus: sed potissimum vsurparur de oriu, & occasu siderum maruino. Et ortus quidem cosmicus est, quando signum, aut stella mane vnà cum Sole suprà horizontem ascendit: vt Romæ canis major Sirus, verbi gratiâ dicitur oriri cosmicè; quia mane circà Kalendas Augusti cum Sole emergit ex horizonte. Impropriè
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126 LEXICON and its morning rising with the Sun makes the air cold, dry, and windy. 178. CORONÆ in the plural are called by some the circles of altitude, Arabic Almicantharath. Namely, the parallels terminating at the horizon and at the zenith, by whose means the altitudes of the stars are measured, because each seems to surround the zenith, or the horoscopos, like a crown. See under V. Almicantharath. 179. CORONÆ are also called in Latin what the Greeks call Halones, kinds of appearances seen high in the sky around the bodies of the stars, especially around the luminaries: Vitellio says that these arise in a vapor lightly condensed. For that vapor, drawn by the star into that region of the air which lies immediately beneath it, is illuminated by the incident rays and produces that glow, quite similar to that which we see in the atmosphere around the horizon at dawn and after sunset, and which we call crepuscular light. It is akin to a halo, which is the sun’s reflection in a round cloud; so that it represents another sun. Moreover, crowns of this kind around the Sun are always omens of winds, from the quarter whence they are blowing: from which they begin to be dispersed. 180. A BODY is defined geometrically as a magnitude that can be measured by three diameters intersecting one another at right angles; by which is explained the three-dimensional nature, whereby a body is constituted in its being as length, breadth, and depth. 181. CORVS, or Caurus, is a western wind, a cross wind, blowing from the solstitial rising of Favonius, directly opposite to Aquilo, so called from dryness: for it is dry at first, although later it becomes cold and damp. It is wont to blow in the autumnal equinox with the greatest violence, bringing storms, snow, hail, and sometimes thunder. Apulia is especially afflicted by it: its blowing in a clear sky is usually accompanied by clouds seen in the East. By the Greeks it is called Argestes from the storms it raises, and also Sciron from a certain rock whence it blows, and likewise Olympias from Mount Olympus. 182. CORVS is a fixed star in the sky on the southern side around the equinoctial Colure, under the sign of Libra, containing seven stars of the nature of Venus and Saturn, the chief of which is the one at the right hand of the malignant nature, Arabic algorab, of the magnitude of the first, which rises at Rome with 13 degrees of Libra, but sets with 7 degrees of Virgo. 183. COSMICS in Greek signifies the same as Mundane in Latin: but it is chiefly used of the rising and setting of a morning star. And cosmic rising is when a sign, or a star, in the morning together with the Sun rises above the horizon: as at Rome the Greater Dog, Sirius, for example, is said to rise cosmically; because in the morning around the Kalends of August it emerges from the horizon with the Sun. Improperly
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VERO DICUNTUR ORIHI COSMICÈ OMNIA ASTRA, QUÆ INTERDIU SUPRA NOSTRUM LIEMISPHÆRIUM ASCENDUNT, SOLE ADHUC IPUSUM TENENTE. OCCASUS AUTEM COSMICUS PROPRIÈ, & RIGOROSE DICITUR QUANDO STELLA AUT SIGNUUM ALIQUOD MANÈ OCCIDIT, ATQUE INFRÀ HORIZONTEM DEPRIMITUR, DUM SOL CODEM TEMPORE IN CARDINE ORIENTALI ORITUR, & EMERGIT: AT ENIM IMPROPRIÈ DICUNTUR ETIAM OCCIDERE COSMICÈ EA OMNIA SIDERA, QUÆ DE DIE SUBTER OCCIDUUM CARDINEM LABUNTUR. Hujusmodi ORTUS, & OCCASUS SIDERUM PASSIM MENTIONEM FACIUNT POËTÆ, AC PRÆSETTIM VIRGIL. IN GEORG. COSMOGRAPHIA DICITUR ARTIFICIOSA MUNDI DESCRIPPIO, SEU DELINEATIO CÆLOURUM SIMUL, TERRÆQUE RATIONEM CONTINENS, & CONNECTENS. Eius quippe munus est indicare, quorum CÆLI SPATIUM QUIBUSVIS TERRÆ EXTANTIS PARTIBUS CORRESPONDEAT, & E CONTRÀ: REGIONES & OPPIDA, AMNES & MARIA, MONTES & VALLES ENUMERARE, LOCORUM TERMINOS CONSTITUERE, QUÆ LONGITUDO, QUÆ LATITUDO GEOGRAPHICA, QUÆ ITEM GNOMONUM DIFFERENTIA, VMBRARUMQUE PRO LARICUDINE LOCORUM PROJECTIO, VUDE LONGITUDO, VEL DIERUM BREUITAS, HORARUMQUE INTERUALLA EXPISCARI POSSINT, STATUERE & EXPlicARE. DOCER INSUPER QUÆ SIDERA SINT POLIS SINITIMA, QUÆVE IN ARCTON, QUÆVE IN MERIDIEM ÆSTANT: CORUMDEM ORTUS & OCCASUS PRO DIUERSIS LOCORUM POSITIONIBUS CENSET: DENIQUE, VT VNO VERBO DICAM, EST ASTRONOMIÆ, GEOMEIRIÆQUE SUMMA AD PTAXIM REDACTA, & COMPLANATA. EI ADEO AFFINIS EST GEOGRAPHIA, VT SÆPENUMERO TUM AB SCRIPTORIBUS EXTERIS, TUM ETIAM AB IPSIS PROFESSORIBUS VNA ALTERIUS NOMINE APPELLEUR, AC SÆPISSIMÆ CONFUNDANTUR. REUERÀ TAMEN COSMOGRAPHIA EST SCIENTIÆ ABSTRACTIOR, ATQUE VNIUERSALIOR: PROCEDIT ENIM CERTIORIBUS, & VNIUERSALIORIBUS PRINCIPIJS PER CERTA QUÆDAM PRINCIPIA AB GEOMETRIA DESUMPTA: GEOGRAPHIA VERO, QUIA MAGIS AD PRAXIM TENDIT, ESTQUE REBUS VTI DE FACTO SUNT, & MUTAZIONI SUBJACENT ALLIGATA, EST ETIAM CUM IPSIS REBUS, DE QUIBUS AGIT, MUTATIONI OBNOXIA, & COSMOGRAPHIA INCONSTANTIOR. NAM SÆCULOURUM DECURSU, MULTIFARIAQUE ILLUSTRIUM SCRIPTORUM TRADITIONE, NEC SEMPER CONSONA SIBI, NEC CERTA EST, CUM LOCORUM ENUMERATIONI HISTORIAM ARTEXAT, ATQUE VT PLURIMUM, QUÆ CIUITATUM, QUÆ GENTIUM, QUÆ NATIONUM, QUÆ POPULORUM ORIGO FUERIT, VNDEQUE REBUS INDITA NOMINA SINT EXPPLICAT: TUM & INSIGNIA QUÆQUE NATURÆ OPERA ENARRAT, ATQUE IN TERRÆ SITU DESCRIBENDO VBERIOR ESSE SOLET QUAM SUA PARENS GEOGRAPHIA: VT PROSECTO HÆC DIFFERENTIA INTER HAS NOBILISSIMAS SCIENTIAS DIGNOSCATUR, VT QUEMADMODUM GEOGRAPHIA RERUM VSUI, AC PRUDENTIBUS, ITA COSMOGRAPHIA ACCOMMODATIOR SIT EARUMDEM PERITIÆ, ATQUE HOMINIBUS SAPJENTIBUS. COZIMON, & CÆSMON APUD ÆGYPTIOS APPELLANTUR NODI LUNA-
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The rising of all stars is properly called cosmic when they ascend above our hemisphere by day, while the sun is still holding the same position. But a cosmic setting is properly, and strictly speaking, when a star or some sign sets in the morning and is driven below the horizon, while the sun at the same time rises and emerges in the eastern angle; yet improperly, those stars are also said to set cosmically which by day sink below the western angle. Poets everywhere make mention of such risings and settings of the stars, especially Virgil in the Georgics . Cosmography is the artful description, or delineation, of the world, containing and connecting at once the reckoning of the heavens and of the earth. For its function is to indicate to which parts of the earth’s extent the space of the heavens corresponds, and conversely; to enumerate regions and towns, rivers and seas, mountains and valleys; to establish the boundaries of places; to set forth what longitude, what geographical latitude, what also the difference of gnomons and the projection of shadows according to the width of places, from which the length of days, or their brevity, and the intervals of hours may be ascertained; and to explain these things. It further teaches which stars are near the poles, which toward the north, which toward the south; it judges their risings and settings according to the different positions of places. Finally, in a word, it is astronomy and geometry reduced to practice and made plain. It is so closely related to geography that very often, both by foreign writers and by the professors themselves, the one is called by the name of the other, and they are most frequently confused. Yet in truth cosmography is the more abstract and more universal science: it proceeds from more certain and more universal principles through certain principles drawn from geometry. Geography, however, because it tends more toward practice and is attached to things as they are in fact and are subject to change, is also with the things themselves of which it treats liable to change, and more unstable than cosmography. For in the course of the ages, and through the manifold tradition of illustrious writers, which is not always consistent with itself nor certain, as it interweaves history with the enumeration of places, and for the most part explains what was the origin of cities, peoples, nations, and populations, and whence the names were given to things; then it recounts each and every work of nature worthy of notice, and in describing the situation of the earth is usually fuller than its parent geography. Thus indeed may this difference between these most noble sciences be recognized: geography is suited to the use of things and to prudent men, whereas cosmography is more suited to the knowledge of those things and to wise men. Among the Egyptians, COZIMON and CÆSMON are called the nodes of the moon-
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125 LEXICON res, caput videlicet, & cauda Draconis: de quibus abundè di- ximus suo loco. CR 186. CRATER, Patera, Vena, Vas, &c. dicitur fidus ad austra- lem plagam supra corpus Hydræ, Arabicè Pharmaz vel Elkis, seu etiam Eluarad, constans stellis septem secundùm Prole- mæum; at juxtà Keplerum octo, & ex Baieri obseruarionibus vndecim, quæ omnes ferè sunt de natura Saturni, & Veneris. Earum præcipua est, quæ in fundo vasis terriæ magnitudinis; quæ in horoscopo alicujus reperta (inquit Firmicus) faciet, vt ille campos colat, & fontes, aut riuos, seu fluuios ab alueo suo ad alia loca deducat. Is etit quoque vinearum amator, & qui infæcundis arboribus fæcundos inserat surculos. Inde meri genialis amor, studiumque bidendi. Subdit perbelle Pontanus in sua Vrania. Quod si reperta fue- rit in occasu, sine vllo maleficarum aspectu, portendit mor- tem inter epulas, & ebrietates: cum malo vero radio malefi- carum, præsettim Saturni, præfocationem in aquis, aut in dolio vinario: Hæc Firmicus. 187. CREPUSCULVM dicitur dubia illa, & suboscuta lux, quæ mane ante Solis ortum, & vespere post illius occasum conspi- citur in partibus horizontis ad Orientem, & Ocidentem (cre- perum enim Antiquis idem sonabat, ac dubium) Vnde & ma- tutinum, & vespertinum Crepusculum appellatur. Absolutè tamen sumitur p[otes]t vespertino, quoniam matutinum proprio nomine Aurora postmodum dicta est: de qua suo loco dictum. Causa huius suboscuræ lucis est interfusa circà tellutem vapo- rum congeries, quam rectè Atmosphæram vocamus, quæ cum aëtem crassiorem suis halitibus reddat, inde est, vt is solares radios non exquisitè transmittat, sed aliquatenus deti- neat, ac reflectat; proindeque conspicuus reddatur, ac lucem Solis acceptam vniuersæ reræ communicet. Porro quoniam æstra non influunt, nisi per lumen, & juxtà majorem, aut mi- norem lucis intentionem, & extensionem diuersimodè agunt in hæc inferiora, vt luculenter in loco probarum est; ideò 188. acutissime P. Titus in Celesti Philosophia demonstret, Solem in spatijs crepusculorum repertum dirigendum esse non in circulis horarijs, seu positionis, in quibus sunt proporrio- nales distantiæ à cardinibus, sed in circulis parallelis ad hori- zontem, in quibus jugiter, & successiue magis, ac magis sem- per intenditur aut remirtitur gradus lucis vsque ad primum pa- rallelum, seu ipsum finitorem, in quo Sol constitutus classi- me micat; vel vlrimum paralelum depressionis gr. 18. sub fini- tore, vbi desinit illa lux, & incipit spatium noctis obscurum; nisi
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125 LEXICON res, namely the head and the tail of the Dragon: concerning which we have spoken at length in their proper place. CR 186. CRATER, a bowl, basin, vessel, and the like, is said of the fixed star in the southern part above the body of Hydra, in Arabic Pharmaz or Elkis, or also Eluarad, consisting of seven stars according to Ptolemy; but according to Kepler, eight, and from Bayer’s observations, eleven, all of which are almost of the nature of Saturn and Venus. The principal of these is the one in the bottom of the vessel, of earthy magnitude; which, if found in someone’s horoscope (says Firmicus), will make him cultivate fields, and lead springs, streams, or rivers from their channels to other places. He will also be a lover of vineyards, and one who grafts fruitful shoots onto barren trees. Hence the pure love of festivity, and the delight in drinking. Pontanus very neatly adds in his Urania, that if it be found in the west, without any aspect of the malefics, it portends death amid banquets and drunkenness; but with an evil ray of the malefics, especially Saturn’s, strangling in waters, or in a wine-vat: this is Firmicus. 187. CREPUSCULVM is that doubtful and dim light which is seen in the morning before sunrise, and in the evening after sunset, in the parts of the horizon toward the East and West (for with the ancients creperum signified the same as doubtful). Hence it is called both morning and evening twilight. Yet it can absolutely be taken for the evening twilight, since the morning twilight afterward was called by the proper name Aurora: concerning which it has been spoken in its place. The cause of this dim light is the mass of vapors spread around the earth, which we rightly call the Atmosphere; since by its exhalations it makes the air denser, the result is that it does not exquisitely transmit the sun’s rays, but holds them back somewhat and reflects them; and therefore it becomes visible, and communicates the light received from the Sun to the whole of the earth. Moreover, since the stars exert influence only through light, and according to the greater or lesser intensity and extension of light act differently upon these lower things, as has been clearly proved in its place, therefore 188. Father Titus most acutely demonstrates in Celestial Philosophy that the Sun, when found in the spaces of twilight, must be directed not in the hourly circles, or circles of position, in which the distances from the cardinal points are proportional, but in circles parallel to the horizon, in which the degree of light is continually and successively more and more increased or diminished, all the way to the first parallel, or the horizon itself, in which the Sun, standing there, shines most brightly; or to the last parallel of depression, 18 degrees below the horizon, where that light ends and the dark space of night begins; unless
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MATHEMATICVM. 173 stat lineis curuis, vt sunt trianguli, & quadranguli considerati in cælestibus, qui omnes sunt curuilinei, cum efformentur ex arcubus circulorum: Qua de re vide in V. Angulus. CVSRTS Latinè dicitur quidquid in acumen desinit. Hinc 202. quia Cæli diuisio in duodecim domicilia ratione atcuum cir-culorum, ea in quasdam veluti cuspides terminat, hinc factum est, vt apud Astronomos singularum domotum initia Cus-pides appellarentur. Et quatuor quidem puncta ottus, & occasus, Medij Cæli, & Imi, Cardines seu Anguli diceten-tur, reliqua verò domorum initia simplex cuspidum vocabulum retinerent. Porrò singulatum domorum spatium tri-ginta æquatoris gradibus mensuratur, facta ex æquo diuisio-ne: quæque Zodiaci pars intercipitur intrà singularum do-morum spatia, constituere dicitur talem domum, quæ etsi, vt modo dixi comprehendat spatium interjectum inter vnam & alteram cuspidem, eius tamen initium computatur à quin-que præcedentibus gradibus æquatoris, & p[ro]tenditur v[er]sque ad grad. 25. eiusdem domus s ira vt planera, qui reperitur in grad. 20. Leonis verbi gratiâ in Zodiaco, habeatque præ-tereà ascensionis rectæ grad. 141. atque in angulum Medij Cæli incidant grad. 24. eiusdem Leonis, etsi non peruene-rit ad lineam meridianam, atque ad cuspidem domus deci-mæ, nihilominus dicetur, & reputabitur esse in decima do-mo. CY CYCLVS Græcè, Latinè circulus absolutè dicitur: magis 203. tamen pressè accipi solet pro integra revolutione certi cu-jusdam numeri annorum per orbem, donec ad initium re-deat: vnde & Cyclus solaris, & Cyclus lunaris, & Cyclus de-cennouemmalis aurei numeri, quorum vsus, & sermo frequens in Kalendarijs. CYCLVS SOLARIS est revolutio annorum 28. ad inueniendam 204. literam Dominicalem; eò quod istæ post 28. annos eodem ptorsus ordine, ac priùs, redeunt. Hoc Cyclo vtebatur Ec-clesia ante correctionem Gregorianam ad inueniendam lite-ram Dominicalem: sed postea longè facilius, & expeditius inuenitur, vt videri potest apud Clauium in Computed Eccle-siastico. Nihilominus si quis hoc cyclo solari voluerit vti ad literam Dominicalem reperiendam, facili negotio id poterit. Siquidem anno Domini exhibito adijciantur nouem, & nu-merus inde compositus diuidatur per 28. nam numerus, qui ex diuisione relinquirur, erit numerus Cycli solaris. Quod si ni-bil ex quotiente remaneat; signum est, quod tunc numerus 1 iij
Transcription: Translated (English)
MATHEMATICVM. 173 is marked by curved lines, as are the triangles and quadrangles considered in the heavens, which are all curvilinear, since they are formed from arcs of circles: On this matter see under V. Angulus. CUSPIS is said in Latin of whatever ends in a point. Hence 202. because the division of the heavens into twelve houses, by reason of the arcs of circles, ends in certain points, it has come about that among Astronomers the beginnings of the individual houses were called Cuspides. And indeed the four points, of rise and setting, of the Midheaven, and of the Lower Heaven, are called the Cardines or Anguli dicentes, while the beginnings of the remaining houses retain the simple name of cusps. Moreover, the space of each house is measured by thirty degrees of the equator, the division being made equally; and whatever part of the Zodiac is intercepted within the spaces of the individual houses is said to constitute such a house, which, although, as I said, it comprises the space lying between one cusp and another, nevertheless its beginning is reckoned from the five preceding degrees of the equator, and extends as far as degree 25 of the same house, so that a planet, which is found in degree 20 of Leo, for example, in the Zodiac, and moreover has 141 degrees of right ascension, and degree 24 of the same Leo falls into the angle of the Midheaven, although it has not yet reached the meridian line and the cusp of the tenth house, nevertheless it will be said, and reckoned, to be in the tenth house. CY CYCLE, in Greek, is called, in Latin, circulus absolutely; 203. however, it is more strictly taken for the complete revolution of a certain number of years around the circle, until it returns to the beginning: hence the solar cycle, the lunar cycle, and the nineteen-year cycle of the golden number, whose use and frequent mention are found in calendars. THE SOLAR CYCLE is the revolution of 28 years for finding 204. the Dominical letter; because these return in exactly the same order after 28 years as before. The Church used this cycle before the Gregorian correction to find the Dominical letter: but afterward it is found much more easily and conveniently, as may be seen in Clavius, in the Computus Ecclesiasticus. Nevertheless, if anyone wishes to use this solar cycle to find the Dominical letter, he can do so easily. For if nine be added to the year of our Lord given, and the number thus formed be divided by 28, the number remaining from the division will be the number of the solar cycle. But if nothing remains from the quotient, it is a sign that then the number 1 iij
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154 LEXICON Cycli erit integra reuolutio annorum 18. Numerus autem quotiens, indicat quot reuolutiones Cycli solaris à Christi ortu, vsque ad annum propositum, excursæ sint. Alium item modum inueniendi huius Cycli solaris in digitis manus: vide apud eundem Clauium in restitutione Kalendarij. 205. CYCLVS lunaris est reuolutio, & successio 19. annorum, quibus expletis, redeunt lunationes ad pristinam in Kalendario sedem, hoc est ad locum vbi erant prius, & concordat annus lunaris cum solari: qua de re fusè diximus in V. Annus Metonicus. 206. CYCLVS Aurei Numeti. Vide in V. Aureus Numerus. 207. CYCLVS Bpactarum. Vide in V. Bpacta. 208. CYGNVS, vel rectiùs Cygnus olor Gallina, Ouidio Miluus, sidus in cælo ad borealem plagam secùs Aquilam intrà Galaxiam continens stellas septemdecim iuxta Ptolemæum, & duas informes circa alas, at Keplero sunt 27. & Baiero omninò 37. omnes de natura Veneris, & Mercurij; inter quas præcipua est Cauda, Arabicè Azelfage, vel corruptè Deub Adigege: de qua alibi dictum. Totum verò sidus, dicitur Eldegiagich hoc est gallina, sicut etiam HiereZim, id est Rosa, vel lilium redolens. In huius pectore anno 1600. apparuit noua stella, quæ diù manens; tandem anno 1621. sensim euanuit, relinquens in suo loco quemdam hiatum, qui ad hæc vsque tempora cernitur. De ea multi scripser, & nos non nihil dicemus, in V. Phanomenon. Porrò Cygnus in horoscopo; inquit Pontanus in Vrania, inclinat ad aucupium, ad insidias auibus parandas, nec non etiam ad cantus eorumque voces imitandas. 210. CYLINDER, seu Cylindrus est figura Geomettica solidà, oblonga quidem, sed ad latus vndequaque rotunda; ita vt circulis æquè distantibus, & circulari superficie contineatur: Vnde est, quod cylindri bases sint circuli ipsi in extremis cylindri positi. Hinc quæuis columna cylindrica dici potest. Nomen hausit ex Græco ἀπὸ τεῦ ἀυλιθρεῖν, quod Latinè voluere interpretatur. 211. CYNOSVRA Græcè, quasi cauda Canis dicitur sidus in cælo Polo mundi arctico proximè adjacens, quod nos Vrsam minorem vocamus ad differentiam maioris, quæ non multò post sequitur, & capite versus huius minoris caudam voluitur. Constat stellis conspicuis omninò septem, vnde & Septentrionis nomen sortitum est, idque etiam toti plagæ, quæ ab æquatore vsque ad Polum protenditur, impertiuit.
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154 LEXICON The cycle is the complete revolution of 18 years. The number how many times indicates how many revolutions of the solar Cycle, from the birth of Christ up to the proposed year, have been made. Another way of finding this solar Cycle on the fingers of the hand is also found in the same Clavius in the restoration of the Calendar. 205. CYCLE of the lunar cycle is the revolution and succession of 19 years, after which the lunations return to their original place in the Calendar, that is, to the place where they were before, and the lunar year agrees with the solar: about which we have spoken at length in V. Metonic Year. 206. CYCLE of the Golden Number. See V. Golden Number. 207. CYCLE of the Epacts. See V. Epact. 208. CYGNUS, or more correctly Cygnus olor, the Hen, in Ovid the Kite, a constellation in the sky on the northern side near Aquila, within the Galaxy, containing seventeen stars according to Ptolemy, and two shapeless ones around the wings; but according to Kepler there are 27, and according to Bayer altogether 37, all of the nature of Venus and Mercury; among which the principal one is the Tail, in Arabic Azelfage, or corruptly Deub Adigege: of which something has been said elsewhere. The whole constellation, however, is called Eldegiagich, that is, hen, just as also HiereZim, that is, Rose, or fragrant lily. In its breast, in the year 1600, there appeared a new star, which, after remaining for a long time, finally in the year 1621 slowly disappeared, leaving in its place some kind of gap, which can be seen even to these times. Many have written about it, and we shall say something about it, in V. Phenomenon. Moreover, Cygnus in the horoscope, says Pontanus in Urania, inclines to bird-catching, to laying snares for birds, and also to songs and the imitation of their voices. 210. CYLINDER, or Cylindrus, is a solid geometric figure, indeed oblong, but round on every side; so that it is enclosed by equally distant circles and a circular surface: whence it follows that the bases of cylinders are themselves circles placed at the ends of the cylinder. Hence any column may be called cylindrical. The name was taken from the Greek ἀπὸ τεῦ ἀυλιθρεῖν, which in Latin means to turn around. 211. CYNOSURA in Greek, so called as it were the tail of the Dog, is a constellation in the sky lying very near the Arctic Pole of the world, which we call the Little Bear in distinction from the Greater, which follows not much later and turns with its head toward the tail of this lesser one. It consists of seven conspicuous stars, whence it also derived the name of the North, and this too it gave to the whole region, which extends from the equator to the Pole.
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118 LEXICON Ptolemæus in 2. Quadrip. cap. 15. diuidens vnumquodque si- gnum in tres partes æquales, vbi earumdem explicat qualita- tes, non tamen singulis planetis assignat; sed potius id fecisse videtur ratione fixarum in ea parte existentium, quam quod peculiare in ipsis præcisis fixis intelligat. Sed quidquid sit de istorum decanorum vi, ac potentia certum est Ptolemæum, cum de facie sermonem habet primo Quadrip. cap. 30. non de planetarum decanis intelligere, sed de ea configuratione ipso- rum ad Luminaria, quam habent domus istorum, ad illorum domicilia, & nos supra Almugeam diximus appellari. Cæterum quemadmodum decani dicuntur tertia queque partes signorum singulis planetis per ordinem attributæ, ita etiam 8. DECVRIONES vocantur ipsi Planetæ prædictis partibus, seu signorum decanis præsidentes. 9. DECLINATIO apud Astronomos dicitur deuiatio stellæ, siue cuiuslibet pariis cæli ab æquatore versus polorum alterutrum, quæ proinde ab eo denominationem sumit: ita vt si ad polum arcticum deflectat, eius declinatio borealis dicatur, si ad au- strum, australis. Hinc prima puncta Arietis, & Libræ nullam habent declinationem, quia immediatè incidunt in æquato- rem: puncta verò tropica maximam quam possit Zodiacus habere, hoc est gr. 23. cum dimidio, quia tantumdem etiam ab æquatore huiusmodi puncta elongantur. Planetæ maiore. a declinationem habere nequeunt, quam gradus Zodiaci, quem perlustrare possunt, computata etiam latitudine: sic Sol qui semper est in Ecliptica, maiorem declinationem habere nequit, quam ipsa puncta tropica quæ maximè ab æquatore deuiant; hoc est gr. 23. min. 30. E contrà fixa, quæ extra Eclipticam diuagandiur, tantam declinationem habere possunt, quanta est paralleli, sub quo degunt; ita vt ea pertingere possit ad gr. 90 si ad ipsum polum immediatè accedant, & recidant, vt fortassè accidet in stella polari proximè succedente sæculo, quæ nunc temporis est in declinatione gr. 87. min. 20. Ex declina- <10.> tione sideris colligitur quantitas eius arcus diurni, ac nocturni, elevatio supra horizontem, distantia à vertice, circulus positionis, & alia huiusmodi, quæ valdè necessaria sunt ad res Astronomicas perficiendas. 11. DECVRITVS figura, est Cæli constitutio inspecta tempore accedentis morbi vt volut aliqui, vel sanè ingrauescentis; cum profectò natura reluctans, viribus impar, tandem consterni- tur, atque in lecto petit decumbere. Vt proinde non momentum accedentis morbi, qui sensum, & ferè impercibiliter in- trat, sed tempus consternationis & decubitus præcipiat Hippo- crates Medicorum facilè princeps obseruandum esse, atque
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118 LEXICON Ptolemy in the 2nd book of the Quadripartite, chapter 15, dividing each sign into three equal parts, where he explains their qualities, does not, however, assign them to individual planets; but rather seems to have done this by reason of the fixed stars existing in that part, rather than because he understands anything special in those very specific fixed stars. But whatever may be the force and power of these decans, it is certain that Ptolemy, when he speaks of the face in the first Quadripartite, chapter 30, understands not planetary decans, but that configuration of the planets themselves to the Luminaries, which the houses of these have to the domiciles of those, and which we said above is called Almugeam. Moreover, just as decans are called the third parts of the signs, assigned in order to each planet, so also 8. DECURIONS are called the planets themselves presiding over the aforesaid parts, or decans of the signs. 9. DECLINATION among astronomers is called the deviation of a star, or of any part of the heaven, from the equator toward either pole, and thus takes its name from it: so if it inclines toward the arctic pole, its declination is called northern; if toward the south, southern. Hence the first points of Aries and Libra have no declination, because they fall immediately on the equator; but the tropical points have the greatest that the Zodiac can have, that is 23 degrees and a half, because such points are likewise so far removed from the equator. The planets cannot have a greater declination than the degree of the Zodiac which they can traverse, latitude also being taken into account: thus the Sun, which is always in the Ecliptic, cannot have a greater declination than the tropical points themselves, which deviate most from the equator; that is, 23 deg. 30 min. In contrast, fixed stars, which move outside the Ecliptic, can have as much declination as there is of the parallel under which they dwell; so that it may reach 90 degrees if they come immediately to the pole itself and fall there, as perhaps will happen in the next century to the polar star, which at present is in declination 87 deg. 20 min. From the declination of a star are gathered the magnitude of its diurnal and nocturnal arc, its elevation above the horizon, its distance from the zenith, its circle of position, and other things of this kind, which are very necessary for accomplishing astronomical matters. 10. DECURITUS is a figure, that is, the constitution of the heavens observed at the time of an approaching disease, as some say, or indeed of one growing worse; when nature, resisting, unequal to the forces, is at last overthrown and seeks to lie down in bed. Therefore Hippocrates, easiest prince of physicians, notes that one should pay attention not to the moment of the disease's onset, which enters imperceptibly and almost unnoticed, but to the time of prostration and lying down, and
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138 LEXICON realem plagam in trianguli formam: Arabicè Mulatum. Prolemæus ei assignat stellas quatuor, Keplerus verò, & Baierus quinque omnes de natura Mercurij: vnde in horoscopo reper tum nato sublime tribuit ingenium. Romæ oritur cum grad. 21. Piscium: occidit cum 10. Tauri. 17. Deneb, Arabicè idem sonat, ac cauda: vnde Deneb Adigege dicitur cauda Cygni: Deneb Algedi, cauda Capricorni: Deneb Elecer, cauda Leonis, Deneb Kaytos, cauda Ceti, &c. Vide de singulis suo loco. 18. DESCENSIO: Vide in V. Ascensio. 19. DETRIMENTVM est genus quoddam debilitatis planetæ, quando reperitur in signo, quod diametraliter opponitur ei, in quo ipse obtinet domicilium, vt Sol in Aquario, Luna in Capricorno, & sicut domicilium est potissima inter dignitates essentiales, ita & detrimentum inter debilitates essentiales est maxima. DI 20. DIAGONIVS, apud Græcos significat lineam ab angulo in angulum rectà producta. Hinc septem climata vetetum, quas certis lineis parallelis definiebant, ex composito Dia, & loci per cuius medium pertransibat ducta linea, nomine denominabant, sic primum clima quod per Meroen pertransibat Diameroes; secundum quia per Syenen, Diafyenen; tertium quia per Alexandriam Dialexandros; quartum, quia per Rhodum, Dianhodos; quintum quia per Romam, Diaromes; sextum quia per Pontum, Diapontos; septimum quia per Borysthenen Diaborysthenes dicta sunt. De quibus omnibus, nec non de alijs à recensioribus adjectis: vide in V. Cl ma. 21. DIAGRAMMA, apud Geometras significat figuram vtcumque lineis efformatam, siue ea triangularis sit, siue quadrangularis, siue recti-linea, siue curui- linea, siue mixta, cuiusmodi sunt omnes figuræ quæ in sex libris elementorum Euclidis ob oculos exhibentur. 22. DIAMETER Græcè, Latinè dimetiens dicitur linea ab vno extremo in alterum potensa, qua eorum distantiam dimetimur. Eam præcipuè venamur in circulo, quem in duas partes æquales secat, ac necessario transire debet per eius centrum. Vnde & definitur ab Euclide. Est recta quadam linea per centrum ducta, & ex vtraque parte in circulo peripheriam terminata, qua circulum bifariam secat. Sicut è contrà linea à centro ad peripheriam ducta semidiameter dicitur: Vide fusiùs in V. Dimetiens. 23. DIASACCORA Arab. Græcè Discora apud Ptolemæum in Quadrip. ex versione Arabica Hali significat Genituram duorum masculorum, & vnius femellæ, cuius significatores sunt Saturnus, Iupiter, & Venus.
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138 LEXICON a real region in the form of a triangle: in Arabic, Mulatum. Ptolemy assigns it four stars; Kepler, however, and Baier, five, all of the nature of Mercury: whence, in a horoscope, it bestows a lofty talent upon the native found under it. At Rome it rises with 21 degrees of Pisces; it sets with 10 of Taurus. 17. Deneb, in Arabic, signifies the same as a tail: whence Deneb Adigege is called the tail of Cygnus; Deneb Algedi, the tail of Capricorn; Deneb Elecer, the tail of Leo; Deneb Kaytos, the tail of Cetus, etc. See each separately in its place. 18. DESCENSIO: See under Ascensio, V. 19. DETRIMENT is a certain kind of debility of a planet, when it is found in a sign diametrically opposite to that in which it has its domicile, as the Sun in Aquarius, the Moon in Capricorn, and just as domicile is the chief among the essential dignities, so detriment is the greatest among the essential debilities. DI 20. DIAGONIVS, among the Greeks, signifies a line drawn straight from angle to angle. Hence the seven climates of the ancients, which they defined by certain parallel lines, were named from a combination of Dia and the place through the middle of which the line passed; thus the first climate, which passed through Meroe, was called Diameroes; the second, because through Syene, Diafyenen; the third, because through Alexandria, Dialexandros; the fourth, because through Rhodes, Dianhodos; the fifth, because through Rome, Diaromes; the sixth, because through Pontus, Diapontos; the seventh, because through Borysthenes, Diaborysthenes. Of all these, as well as those added by later writers: see under Cl ma. V. 21. DIAGRAMMA, among geometers, signifies a figure formed in whatever way by lines, whether it be triangular, quadrangular, rectilinear, curvilinear, or mixed, such as are all the figures displayed before our eyes in the six books of Euclid's Elements. 22. DIAMETER, in Greek; in Latin, dimetiens, is called a line extended from one end to the other, by which we measure their distance. We especially seek it in the circle, which it divides into two equal parts, and must necessarily pass through its center. Hence it is also defined by Euclid as a certain straight line drawn through the center, and terminated on either side at the circumference of the circle, by which it cuts the circle in half. In contrast, a line drawn from the center to the circumference is called the semidiameter: see more fully under Dimetiens, V. 23. DIASACCORA, Arabic; in Greek, Discora, in Ptolemy's Quadrip. from the Arabic version of Hali, signifies a nativity of two males and one female, whose significators are Saturn, Jupiter, and Venus.
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140 LEXICON 26. Dies apud Astronomos est mensura temporis, quo Sol motu primi mobilis raptus integrè circà tellurem voluitur; hoc est spatium viginti-quatuor horarum: tantùm enim temporis insumit, quousque redeat ad idem punctum, seu circulum positionis, vnde discesserat, additâ ea parte, quam ipse motu suo in Zodiaco acquisiuit. Nam primum mobile citiùs revolutiorem suam absoluit, nempè spatio 21 horarum, ac ferè 56. minutorum, itaut integra primi mobilis revolutio præcedat singulis diebus revolutionem Solis quatuor ferè minutis. Et hic est dies naturalis complectens diem, ac noctem artificialem, quod est temporis spatium, quo Sol vtrunque hemisphætium, & superius, & inferius perlustrat. Dies naturalis semper, & vbique æqualis est: non sic artificialis, qui solum sub æquatore seruat æqualitatem, & cum nocte etiam æquè pottionem diei naturalis diuidit: At extrà illum quò magis accedit ad tropicos, ac polus super regionem attollitur, eò inæqualior est, & longior quidem nocte, si Sol ad eum polum decliner, breuior, si ad oppositum Vnde & sub Polo immediatè degentibus, Sole in siguis borealibus existente, accidit dies longissima sex mensium tantumdemq[ue] noctis, eo alteram Zodiaci partem perlustrante: ita vt in his regionibus integra Solis revolutio in Zodiaco duret vna die naturali, & vns dies naturalis sit integer annus. Porrò diei naturalis initium Astronomi computant à Metidie in Meridiem. Similiter Hispani & Galli, aliæque Nationes. Itali à Solis occasu. Chaldæi; atque Ægyptij à Solis ortu. Tandem Ecclesia in jeunijs, ritibus, festisque seruandis à media nocte. Sed de hac re satis pro nostro instituto. 27. DIFFERENTIA Ascensionalis est arcus æquatoris interceptus inter ascensionem, vel descensionem rectam, & obliquam eiusdem sideris aut cuiuscumque partis Zodiaci. Cùm enim diuersimodè ascendant in sphæra recta, & in obliqua (quæ enim habent declinationem borealem citius oriuntur, & serius occidunt; & è conttà quæ australem serius ascendunt, citiusque descendunt ijs qui habent horizontem obliquum, quam qui habent tectum) ideo hæc diuersitas in gradibus æquatoris coascendentibus, vel condescendentibus computata vocatur differentia Ascensionalis: Vide in V. Ascensio. 28. DIGITVS Eclipticus apud Astronomos est duodecima pars disci Solaris, vel Lunaris, quem ideò in tot partes diuiserunt (quas alij Vncias appellant) vt innotesceret, quota pars alterius Luminarium eclipsum patientis obscuretur. Si enim tres digitis disci Lunaris in telluris vmbram immerguntur, dicere tur quarta pars Lunæ obscurata; si sex, dimidium; si duodecim, signum est quod totum corpus lunare obscuretur. Sed enim hic
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140 LEXICON 26. A day, among astronomers, is a measure of time in which the Sun, carried by the motion of the first movable, revolves completely around the earth; that is, the span of twenty-four hours: for it takes so much time until it returns to the same point, or circle of position, from which it had departed, together with that part which it itself acquired by its motion in the Zodiac. For the first movable completes its swifter revolution in the space of 21 hours and nearly 56 minutes, so that the complete revolution of the first movable precedes each day the Sun’s revolution by nearly four minutes. And this is the natural day, comprising the artificial day and night, which is the span of time in which the Sun traverses both hemispheres, both upper and lower. The natural day is always, and everywhere, equal: not so the artificial day, which preserves equality only under the equator, and there also shares the natural day equally with the night; but outside it, the more it approaches the tropics and the pole is raised over the region, the more unequal it is, and indeed longer than the night if the Sun inclines toward that pole, shorter if toward the opposite. Hence also for those living immediately under the pole, when the Sun is in the northern signs, there occurs a day of six months and the same amount of night, while it traverses the other part of the Zodiac: so that in these regions the complete revolution of the Sun in the Zodiac lasts one natural day, and one natural day is a whole year. Moreover, astronomers calculate the beginning of the natural day from midday to midday. Likewise the Spaniards and the French, and other nations. The Italians from sunset. The Chaldeans and Egyptians from sunrise. Finally, the Church, in keeping fasts, rites, and feasts, from midnight. But enough on this matter for our purpose. 27. Ascensional Difference is the arc of the equator intercepted between the right and oblique ascension or descension of the same star or of any part of the Zodiac. For since they ascend in different ways in the right sphere and in the oblique one (those with northern declination rise sooner and set later; and conversely those with southern declination rise later and descend sooner for those who have an oblique horizon than for those who have a level one), therefore this diversity, calculated in the degrees of the equator that rise or set together, is called Ascensional Difference: see in V. Ascension. 28. An Ecliptic Digit, among astronomers, is the twelfth part of the solar or lunar disc, which for that reason they divided into so many parts (which others call inches) so that it might be known what fraction of the other luminaries suffering an eclipse is obscured. For if three digits of the lunar disc are immersed in the earth’s shadow, it may be said that a fourth part of the Moon is obscured; if six, half; if twelve, it is a sign that the whole lunar body is obscured. But here
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M A T H E M A T I C V M. 141 aduertendum, quod quando Luna totaliter eclipsatur, cum aliqua mora in tenebris, quia vmbra terræ, vel, vt volunt Astronomi recensiores penumbra Atmosphere incidens in cor- pus Lunare est maior ipso disco Lunari, ideò ad dignoscendam Eclipsis magnitudinem vltà duodecim digitos, dicuntur eclipsati tor digiti, quot sunt inter circumferentiam Disci ecli- psati & vmbræ, penumbræue eclipsantis, vt si post totalem obscurationem Luna tam profundè vmbram subintret, vt si forte eius diameter foret quindecim digitorum, adhuc tota obscurearetur, & intraret totam vmbram telluris, tunc dicerentur quindecim digiti eclipsati. Ar quoniam Lunæ corpus Solem eclipsantis per interpositionem inter ipsum, & nos vel non adæquat vel sanè non superat corpus Solare, ideò in Solis ecli- < 29.> psi ad mensurandam eius magnitudinem, non considerantur nisi duodecim tantum digiti, qui si fortè obscurentur omnes, tunc nulla pars disci Solaris erit conspicua, sed rorum erit in tenebris. Eiusmodi erit mira, & portentosa Solis eclipsis, quæ accidet anno 1684. die 12. Iulij, hora circiter tertia post Me- ridiem. Portò hanc diametri obscurandæ tam in Sole, quàm in Luna quantitatem Astronomi venantur ab distantia Lunæ à capite, vel cauda Draconis, quam ideò argumentum verum latitudinis Lunæ appellant: quò enim propiùs ipsa accedit ad suos nodos, eò maior erit obscuratio in Eclipsi; etsi tempore veræ conjunctionis, aut oppositionis cum Sole, ipsa fuerit in eodem puncto cum suis nodis, hoc est omnis latitudinis expert, & in Ecliptica, tunc sanè totalis erit obscuratio, vel Solis, vel Lunæ, prouea fuerit conjunctio, vel oppositio. DIGNITAS, apud Astronomos est quædam prærogatiua pla- < 30.> netæ qua ex eius habitudine ad Solem, loco in Zodiaco, aut in Mundi situ, moru, & configuratione ad alios, viribus auge- rur, & plurimùm roboratur. Ea multiplex est, & in duplici differentia. Aliæ sunt essentiales dictæ, non quia sint cæteris potiores, sed quia conveniunt planetis ratione essentia, & na- < *> turæ ipsorum, eo quia confortmentur cum dictis locis in primis qualitatibus passiuis, & actiuis, & hæc conformitas non ex accidente, sed ab intrinseco semper illis, & primariò insit. Aliæ accidentales, quæ non pet se, & primariò illis compe- tunt, sed extrinsecus & veluti ex accidente, vt ex situ Mundi aut ex accidentalibus passionibus, vt mox dicemus. Dignitates essentiales quinque statuit Ptolemæus 1. Quadrip. c. 15. Domi- cilium nempe, altitudinem, seu exaltationem, trigonum, ter- minum, & personam: de quibus suis in locis recurrerfermo. Accidentales etiam plures enumerantur: potissima verò est situs Muudi, hoc est quod sit in Angulo, vel succedente domo;
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It is to be noted that when the Moon is totally eclipsed, and remains for some time in darkness, because the shadow of the Earth, or, as more recent astronomers say, the penumbra of the atmosphere falling upon the lunar body, is greater than the lunar disc itself, therefore, in order to determine the magnitude of an eclipse beyond twelve digits, the eclipsed digits are said to be as many as there are between the circumference of the eclipsed disc and the shadow, or penumbra, causing the eclipse; thus, if after total obscuration the Moon were to enter the shadow so deeply that, if by chance its diameter were fifteen digits, it would still be wholly darkened and enter the whole shadow of the Earth, then it would be said that fifteen digits were eclipsed. But since the body of the Moon eclipsing the Sun by interposition between it and us either does not equal or certainly does not exceed the solar body, therefore, in a solar eclipse, in order to measure its magnitude, only twelve digits are considered; if all of these should perhaps be obscured, then no part of the solar disc will be visible, but all will be in darkness. Such will be the wondrous and portentous eclipse of the Sun, which will occur in the year 1684, on the 12th of July, at about the third hour after midday. Moreover, astronomers ascertain this quantity of the diameter to be obscured, both in the Sun and in the Moon, from the distance of the Moon from the head or tail of the Dragon, which on that account they call the true argument of the Moon’s latitude; for the more closely it approaches its nodes, the greater will be the obscuration in the eclipse. And although at the time of a true conjunction or opposition with the Sun it should be in the same point with its nodes, that is, devoid of all latitude and in the ecliptic, then certainly the obscuration will be total, whether of the Sun or of the Moon, according as there is conjunction or opposition. DIGNITY, among astronomers, is a certain prerogative of a planet, by which, from its relation to the Sun, its place in the Zodiac, or its position in the world, and by its motion and configuration with respect to the others, its powers are increased and greatly strengthened. It is manifold, and of a twofold distinction. Some are called essential, not because they are superior to the others, but because they belong to the planets by reason of their essence and nature, since they are in harmony with the said places in the primary passive and active qualities, and this conformity is not by accident, but is always and primarily inherent in them from within. Others are accidental, which do not belong to them per se and primarily, but extrinsically and, as it were, by accident, as from the position of the world or from accidental passions, as we shall presently say. Ptolemy sets down five essential dignities in Book 1 of the Quadripartite, chapter 15: namely domicile, altitude or exaltation, trigon, term, and face; about these there will be discussion in their proper places. Several accidental dignities are also enumerated; but the chief one is the position of the world, that is, whether it is in the angle or in the succeeding house;
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MATHEMATICVM. 143 dicta loca, ac proinde metiri tempus quod requititur quoad- vsque alter ad alterum deuoluatur. Cuius motus auctor & regu- lator est Sol per suum realem motum, non quidem illum annu[m], quo integro circulo Zodiaci peragrato regreditur ad idem pun- ctum, vnde discesserat, sed singulas illas lationes diurnas sin- gulis annis competentes, quibus adæquat motum primi mobi- lis; eo pacto, ac progressionum suo motu regulatrix est Luna: Et sicut hæc per suum motum progressium ordinat, disponit, ac regit in viuentibus humidum radicale; ita Sol motu illo di- rectionis regit calorem vitalem; qui proinde aliud principium naturalem non habet quàm Solem ipsum omnis caloris, & vitæ fontem, vt propterea mirum non sit, si eo male affecto in cælestibus per concursum cum astris prauis, malè etiam habeat in terrestribus vita, quæ in calore innato consistit; hicque à motu Solis directorio totam suam virtutem, ac subsistendi potentiam recipit. Sed quia vt aliàs ex Ptolemæo meminimus, non modò Sol, & Luna, sed etiam vtiusque horoscopus, & cæli culmen se habent vt subjectum passibile respectu aliorum siderum occursantium, quibus malè vel benè affectis ea etiam, quæ ab ipsis pendent benè vel malè habeant necesse est, inde sit, vt quandocumque hæc in sideta occursantia impingunt motu directionis, noui effectus in viuentibus exerantur circà eorum significata. Itaque duo loca concipienda sunt in cælo in quacumque directione: quorum alter dicatur significator, & se habeat vt subjectum passibile, eò quia significat in genere aliquid, vt vitam, morbos, fortunas &c. & recipiat in se im- pressiones siderum occursantium, alter se habeat vt causa effi- ciens, & dicatur Promissor, qui decernat, & promittat bona vel mala in illa re quam denotauerit significator, implenda pro reimpore, quo ipse ad eumdem locum peruenerir: & ab hoc munere, ne ipsa quidem luminaria excludenda sunt, quibus non repugnat pro diuersa consideratione, & habitudine diuersa- rum etiam causarum vices subire, idque ex eminenti eorum virtute. Sic igitur significator, & locus passibilis in hoc casu gerit vicem creditoris recepturi aliquid à Promissore, & loco occursante; qui se haber vt causa efficiens, statis temporibus, quibus expletis promissio adimpleatur, arque effectus in lucem exear per realem causarum congressum. Hæc itaque tempora nos directione merimur: & hæc temporis inquisitio vocatur, directio. Quomodo autem fiat huiusmodi causarum congressus, & quonam pacto expleto tempore directionis locus vns intelligarut realiter ad alterum deuolurus eo videlicet tempore, quo prodit effectus, paulò fusiùs explicandum est, eò maximè, quia diximus omnem directionis motum à Sole pendere, ac perfici
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MATHEMATICVM. 143 the aforesaid places, and therefore to measure the time required until one is carried over to the other. The author and regulator of this motion is the Sun by its real motion, not indeed that annual motion by which, having traversed the whole circle of the Zodiac, it returns to the same point from which it departed, but those individual daily motions proper to each year, by which it makes equal the motion of the primum mobile; in like manner the Moon, by its motion, is the regulator of the progressions: and just as the Moon, by its progressive motion, orders, disposes, and governs the radical moisture in living things, so the Sun by that motion of direction governs the vital heat, which therefore has no other natural principle than the Sun itself, the fountain of all heat and life. For that reason it is no wonder if, when the Sun is ill affected in the heavens through conjunction with evil stars, life also fares ill in earthly things, since it consists in innate heat; and this life receives from the Sun’s directing motion all its power and ability to subsist. But because, as we have elsewhere remembered from Ptolemy, not only the Sun and Moon, but also the horoscope of each and the culmination of the heavens stand as a passive subject in relation to the other encountered stars, by which, if they are ill or well affected, those things also which depend on them must necessarily fare well or ill, hence it comes about that whenever these strike upon the encountered stars by the motion of direction, new effects are produced in living things concerning their significations. Therefore two places must be conceived in the heavens in any direction: of which the one is called the significator, and stands as a passive subject, because it signifies in general something, such as life, diseases, fortunes, and so forth, and receives into itself the impressions of the encountered stars; the other stands as an efficient cause, and is called the Promissor, which decrees and promises good or evil in that matter which the significator denotes, to be fulfilled at the time when it shall have come to the same place: and from this office even the luminaries themselves are not to be excluded, to which it is not repugnant, according to different consideration and the different relation of causes, to undergo vicissitudes, and this by reason of their eminent virtue. Thus the significator, and the passive place in this case, plays the role of a creditor about to receive something from the Promissor and the encountered place, which stands as an efficient cause, at fixed times, when these are completed, so that the promise may be fulfilled, and the effect may come to light through the real conjunction of causes. These times therefore we measure by direction; and this inquiry into time is called direction. But how such a conjunction of causes takes place, and in what manner, when the time of direction is completed, one place is understood to be really about to devolve upon the other, namely at that time when the effect appears, must be explained somewhat more fully, especially because we have said that every motion of direction depends on the Sun, and is accomplished
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144 LEXICON per motum primi mobilis, qui cùm sit rapidissimus, ac spatio vnius diei integre circà tellurem roterur, ac proinde videatur ad paucas horas singulas eius partes fer i ad situm significatorum: vt propterea non absuerint qui cixerint omnes motus directionis statim post natalem moru horatio minote spatio quam vna die compleri: In quo profecto casu non apparet ratio mensuræ ad annos, neque vlla similitudo causarum ad suos effectus, vt benè aduettit Titus lib. 3. cap. 3. Quapropter ipse aliam rationem diluendæ huius difficultatis excogitauit. ait enim: Dum Sol circa Mundum fertur latione diurna, seu motu ruptus; Primum mobile vna cum omnibus astris, quæ tanquam fixa sub ipso censentur esse, quia velocius monetur hoc motu, quam Sol, successiuè non nihil præcurrit ipsum Solem; ita vt in fine vnius integra dies repersatur præcessisse uno gradu ferè, quantum scilicet decimus esse motum Solem contra ipsum primum Mobile. Dum ergo Sollatione vniuo integra dies præordinat caïorem vitalem ad unum annum, astris præcurrendo appropinquans sitibus positionum prorogatorum, per gradem ferè, & sim iter su cessiue sequentibus diebus: dum autem appropinquent, applicant etiam ad jam iaritates quibus præordinant naturales effectus ad actum sturos vna cum ipsi vita principiis: Vt exempli gratiâ, si in aliqua Gevesi, sit Sol in Meridie, dum circumfertur ad Occasum, Imum, & Orsum, primum Mobile successiuè paulatim antecedit, ita vt vbi Sol ad Meridiem exquisitè peruenerir, inueniatur primum Mobile cum omnibus astris præcessisse per gradum ferè; quantum decimus Solem fuisse motum contra ipsum. Dico igitur tali modo fieri mo um directionis. Hæc Titus, quibus innuere videtur, motum directionis expleri non quidem, vt illi volebant minori spatio vnius diei ad singula momenta, quibus loca occursantia attingunt situm significatorum, sed ad singulos dies post natalem ratione præcessionis primi mobilis ad motum Solis, vnde in eius sententia, si locus occursans ver. gra. distet à loco prorogatorio per quindecim fere gradus, quia primum mobile vt dictum est præcedit Sol vno ferè gradu ad dies singulos, ideò ad hoc vt quindecim isti gradus adæquentur, & Sol reperiatur in eodem signo cum primo mobili requiri adhuc quindecim dies, quibus expleris intelligatur completa directio, & deuolutus occursans ad situm Prorogatoris. Tunc autem, subdit, præordinantur potentia naturales effectus ad singulos annos. Per morum istum qui sit ad singulos dies, ita vt singulæ diurnæ lationes singulis annis respondeant. Quod ideò directionem prius definierat, quod sit velox quidam mo[ti]us, quo in nato calestes causa breui tempore præordinant potentia effectus naturales ad actum ituros in diuturno vita decursu. Verum
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by the motion of the first movable, which, since it is the swiftest, and in the space of a single day revolves entirely around the earth, and therefore seems to carry each of its parts to the place of the significators within a few hours: so that it was not without reason that some said that all motions of direction are completed immediately after birth in a space smaller than one day. In which case, indeed, no ratio of measure over years appears, nor any likeness of causes to their effects, as Titus well notes, lib. 3, cap. 3. Wherefore he himself devised another way of dissolving this difficulty. For he says: While the Sun is carried around the world by its daily course, or by a constant motion, the Primum Mobile, together with all the stars which are thought to be fixed under it, because it is moved by this motion more swiftly than the Sun, successively goes somewhat ahead of the Sun; so that at the end of one whole day it is found to have gone ahead by nearly one degree, namely as much as the tenth of the Sun’s motion against the first movable. Therefore, while the Sun by its annual course completes one whole year, approaching the positions of the projected places by preceding the stars by nearly a degree, and so successively on the following days: and while they approach, they also apply to those nativities by which natural effects are preordained to come into act together with the very principles of life. Thus, for example, if in some nativity the Sun is at midday, while it is carried around to the setting, the lower meridian, and the rising point, the Primum Mobile successively advances little by little, so that when the Sun has exactly reached midday, it is found that the Primum Mobile with all the stars has gone ahead by nearly one degree; as much, namely, as the tenth part of the Sun’s motion against it. I say, therefore, that the motion of direction is brought about in this way. This is Titus, by which he seems to indicate that the motion of direction is not completed, as they wanted, in a lesser space than one day for individual moments, when the places that make contact reach the place of the significators, but for each day after birth, by reason of the precession of the first movable relative to the motion of the Sun; whence, in his opinion, if an occurring place, for example, is distant from the prorogatory place by about fifteen degrees, since the first movable, as has been said, precedes the Sun by nearly one degree for each day, therefore in order that these fifteen degrees may be made equal, and the Sun may be found in the same sign with the first movable, another fifteen days are still required; when these have elapsed, let the direction be understood to be complete, and the occurring point carried to the place of the prorogator. Then, he adds, the natural effects are preordained in potency for individual years. By this motion, which occurs day by day, so that the several daily courses correspond to the several years. He had therefore previously defined direction as a certain swift motion, by which, in the native, celestial causes in a short time preordain the natural effects in potency to come into act in the long course of life. However
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MATHEMATICVM. 149 < 37.> Verum hæc explicatio, etsi alioqui ingeniosa, & quæ, fateor, mihi aditum præbuït ad huius arcani, ni fallor, uoritiam comparandam, non euacuat difficultatem: non enim tradit, quonam pacto fiat huiusmodi præordinatio, & qui fiat, vt cum causæ omnes post quindecim v.g. dies congrediantur, & completæ reducantur ad actum, effectus nihilominus non nisi post quindecim annos elucescat, & eius vix vmbra quædam, tunc temporis quando causæ suam virtutem promunt, appareat? Plus enim, vt ille ait, nocet præsens musca, quàm ab sens leo. Ergò si post quindecim dies expletur motus directionis, & causæ ponuntur in actu proximo ad agendum, tunc quidem, & non post tantum temporis interuallum prodire debet effectus. < 38.> Sciendum igitur est, Solem, qui vt diximus est regula omnis motus directionis, spatio 24. horarum conficere integtam, ac perfectam reuolutionem circà tellurem: ita vt ea expleta ponatur in eodem circulo positionis, ac situ mundi, in quo, pridie erat, cùm primum ab eodem puncto moueri expit, motu primi mobilis ductus: At enim, cum ipse interim motu proprio, eoque contrario moueatur in Zodiaco, & consequenter etiam in æquatore singulis diebus ferè gradum vnum, indè est, vt etiamsi expleta vnica reuolutione spatio 24. hor. redeat ad eundem circulum positionis, non tamen ibi ponitur cum eodem gradu æquatoris, cum quo pridie erat, sed cum alijs, & alijs successiuè, quos ipse acquirit in dies singulos per proprium motum progrediendo secundùm successionem signorum. Similiter etsi ponatur in eodem circulo positionis, non tamen ponitur in eodem puncto eiusdem circuli, cum motus eius diurnus ratione sui motus proprij non sit circularis, sed spiralis, vnde ratione declinationis, quam successiuè acquirit vel deperdit, modò ponitur infra, modò suprà, sed in eodem circulo. Interim primum mobile, & æquator perficit suam reuolutionem circà tellurem minori temporis spatio quàm ipse Sol; nempè in horis 23. & minutis ferè 56. ex quo fit, vt dum Sol ponitur in eodem circulo positionis, in quo pridie erat, ipse vlterius præcesserit ferè integro gradu, vt supra explicatum est, cuius situm Sol, vt ad amussim acquirat, requiritur spatium ferè quatuor minutorum temporis; quæ singulis diebus competentia inferunt in vno anno diem vnum naturalem præcessionis: ita vt dum æquator in vno anno facit 366. reuolutiones circà tellurem, eodem tempore Sol inueniatur perfecisse tantùm 365. circuitiones, vna videlicet minus. Vt igitur & ipse acquirat hoc quod acquisiuit æquator, ponaturque non modo in eodem circulo positionis, sed in eodem puncto præcisè, accum eodem gradu æquatoris, opor- K
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MATHEMATICVM. 149 < 37.> But this explanation, although ingenious enough in itself, and which, I confess, has given me access to the means of, if I am not mistaken, grasping the truth of this hidden matter, does not remove the difficulty: for it does not explain by what means such a preordination is made, or how it happens that, although all the causes come together, say, after fifteen days, and, when completed, are reduced to act, the effect nevertheless does not become apparent until after fifteen years, and scarcely even a shadow of it appears at the time when the causes display their power? For, as the saying goes, a present fly does more harm than a lion in the distance. Therefore, if after fifteen days the motion of direction is completed, and the causes are placed in the immediate act of acting, then indeed the effect ought to emerge then, and not after so long an interval of time. < 38.> It must therefore be known that the Sun, which, as we said, is the rule of every motion of direction, in the space of 24 hours accomplishes a complete and perfect revolution around the earth: so that, once this is completed, it is placed in the same circle of position and the same state of the world in which it was the day before, when it first began to move from the same point, drawn by the motion of the primum mobile. But since, in the meantime, it moves by its own motion, and that in the contrary direction, in the Zodiac, and consequently also in the equator by nearly one degree each day, it follows that, although after a single revolution in the space of 24 hours it returns to the same circle of position, it is nevertheless not placed there with the same degree of the equator with which it was the day before, but with different and different ones successively, which it acquires each day by advancing through its own motion according to the succession of the signs. Similarly, although it is placed in the same circle of position, it is nevertheless not placed in the same point of that circle, since its daily motion, in respect of its own proper motion, is not circular, but spiral; hence, with respect to the declination which it successively acquires or loses, it is now placed below, now above, but in the same circle. Meanwhile the primum mobile and the equator complete their revolution around the earth in a shorter span of time than the Sun itself; namely, in 23 hours and nearly 56 minutes. From this it follows that, while the Sun is placed in the same circle of position in which it was the day before, the equator itself has already advanced nearly a whole degree further, as explained above, to whose position the Sun, in order to acquire it exactly, requires a space of nearly four minutes of time; these, being due each day, produce in one year one natural day of precession: so that while the equator in one year makes 366 revolutions around the earth, in the same time the Sun is found to have completed only 365 circuits, one fewer. Therefore, in order that it too may acquire what the equator has acquired, and be placed not only in the same circle of position, but precisely in the same point, with the same degree of the equator, it is necessary that K
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148 LEXICON cum apud omnes Professores passim obuia sit: sit enim aut per ascensoria tempora & distantiam à meridiano vtriusque tam significatoris, quam promissoris, aut per ascensiones seu re- ctas, seu obliquas vtriusque, sumptas ad rationem eius, ad quem sit deductio. De qua re fusè agit Titus lib. 3. cauestos Phi- losophia, à cap. 14. vsque ad cap 16. & fusiùs adhuc, atque ex professo in primo mobis, æradens etiam quomodo Sol in spatijs crepusculinis non sit dirigendus in circulis hotarijs, in qui- bus fiunt proportionales distantiæ à cardinibus, sed in circulis paralelis ad horizontem, in quibus quamcumque declinationem habeat seriat semper eumdem erga nos gradum intensionis lucis, secundùm quam omnem suam activitatem exerit. Solum hic ex eodem Tito, ac doctrina superiùs tradita, quæ non nihil à communi discrepat, exponere volo modum adæ quando arcum directionis ad expiscandos præcisè annos, & menses effectuum. Igitur arcus directionis elicitus addatur ascè- sioni rectæ Solis, ac deinde in tabula ascensionum rectarum requirendus gradus Eclipticæ huic summæ competens: postea computandi dies, & horæ, quas Sol insumpsit à puncto nati- uitatis quousque ad dictum gradum peruenerit; nam dies qui præcesserunt, annos, singulæ binæ horæ, menses denotant, post quos apparebit effectus promissus per directionem. DIRECTVS dicitur planeta, cum motu suo proprio in Zo- diaco fertur in consequentiam signorum: sicut è contrà Re- trogradus, cùm mouetur à consequentibus in antecedentia signa. Esse autem directum, est species quædam dignitatis ex accidente planetæ aduenientis. Nam cum motu suo perductus contrà motum primi mobilis ab Occidente in Orientem nitat- tur; inde sit, vt seriùs occidat quàm ipsæ primi mobilis par- tes, ac proinde diutiùs supra terram consistat, plus temporis consequenter habeat ad illam suis qualitatibus imbuendam. Vide in V Auclus numero. DISCORA Græcè apud Ptoleimæum 3. Quadrip. cap. 7. ex Ver- sione Arabica Hali, significat Genitutam duorum masculorum, & vnius femellæ, in quam conveniant Saturnus, Iupiter, & Venus. DISCVS Græcè proptiè patinam rotundam exprimit: inde hoc vocabulum ad omnem figuram rotundam, & planam si- gnificandam aptatum est: Quamobrem, & corpora lumina- rtum, quæ quamuis perfectè sphætica, & rotunda, tamen ob nimiam distantiam plana videntur, & referunt quandam disci figuram, discus Solatis, & discus Lunatis sunt appellata; in quorum visa planitie diametrum Astronomi concipiunt, quam in æquales partes diuidunt omninò duodecim, quas & vncias,
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148 LEXICON which is commonly found among all Professors: for it is either by the ascensional times and distance from the meridian of both the significator and the promissor, or by the ascensions, whether right or oblique, of both, taken according to the ratio of the one to which the deduction is made. On this matter Titus treats at length in book 3 of Cauestos Philosophia , from chapter 14 to chapter 16, and even more fully, and expressly, in the first mobile, also showing how the Sun in crepuscular spaces is not to be directed in the horizon circles, in which proportional distances from the cardines are made, but in circles parallel to the horizon, in which, whatever declination it may have, it always retains the same degree of light-intensity toward us, according to which it exerts all its activity. Here I wish only, from the same Titus and the doctrine given above, which differs somewhat from the common view, to explain the method of finding, exactly, through the arc of direction, the years and months of effects. Therefore, let the arc of direction obtained be added to the Sun’s right ascension, and then in the table of right ascensions the degree of the ecliptic corresponding to this sum is to be sought; afterward compute the days and hours which the Sun has spent from the point of nativity until it has reached the said degree; for the days that have passed denote years, and every two hours denote months, after which the promised effect by the direction will appear. DIRECT is said of a planet when, by its own proper motion in the Zodiac, it is carried onward in the sequence of the signs: just as, on the contrary, Retrograde, when it moves from the succeeding signs to the preceding ones. To be direct, however, is a certain kind of dignity arising incidentally to the planet. For, being carried by its own motion contrary to the motion of the first mobile from West to East, it thereby sets later than the parts of the first mobile itself, and consequently remains longer above the earth, and therefore has more time to imbue that with its qualities. See in V Auclus, number. DISCORA in Greek, according to Ptolemy in Quadrip. 3, chapter 7, from the Arabic version of Haly, signifies the nativity of two males and one female, in which Saturn, Jupiter, and Venus agree. DISCUS in Greek properly expresses a round dish: hence this word has been adapted to signify any round and flat figure. For this reason the bodies of the luminaries, which, although perfectly spherical and round, nevertheless appear flat because of their great distance, and present a certain disc-like shape, have been called the disc of the Sun and the disc of the Moon; in whose apparent flatness astronomers conceive a diameter, which they divide into equal parts, altogether twelve, which also [they call] ounces,
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MATHEMATICVM. 177 natura sua humido, & frigido, humidi radicalis origini, si- gnum quoque humidum & frigidum, quale est Cancer, tri- buendum erat. E contrà Saturnus omnis interius author, cali- di innari, radicalisque humoris destructor, & inimicus oppo- sitas hisce luminarium sedes occupare debebar, nempe Capri- cornum, & Aquarium cæteris humidiores, & quæ maxime di- stant à nostro vertice, sicut longe distar Saturnus à terra. Ex quibus Capricornus ob conformitatem naturæ (est enim vt ille natura frigidus & siccus) prima sedes foret. Mars etiam na- tura maleficus, cum vitam à luminaribus originatam sua ma- lignitate concuriat, eas domos sibi vendicare debebar, quæ hostili radio domos luminarium infestarent, idecircò attributa sunt ei signa Arietis, & Scorpij, quæ de quadraro signa lumi- narium intuerentur: E contrà benefici, ea loca haberent, quæ amicitiæ vinculo locis luminarium necterentur: ideò Ioui fortunæ maiori eæ domus assignandæ erant, quæ amicitiæ per- fectæ nexu, nempe radio trino cum locis luminarium vniuen- tur, Sagirrarius, inquam, & Pisces. Veneri autem fortunæ minori Taurus, & Libra, quæ easdem domos respiciunt de Sextili. Tandem Mercurio, qui est omnium planeratum pro- ximior luminaribus; quippe à Sole nunquam corpore elon- garur plus gr. 28. Lunæ verò est contiguus ratione orbis, eæ domus daræ sunt, quæ proxime accedunt ad luminarium do- mos, videlicet Gemini, & Virgo: Et hæc est ratio domicilio- rum, ac distributionis conuenienter factæ pro singulis pla- neris. Domus item vocatur duodecima quæque Cæli pars in situ < 53.> mundi considerata: diuidunt enim Astronomi superius, atque inferius hemisphærium in quatuor quadrantes, duos quos vo- cant Orientales, à linea videlicet horizontali ad lineam meri- dianam suprà terram, & ab occasu ad lineam Imi cæli; reli- quos duos, quos Occidentales appellant à linea Meridiana ad occasum; atque ab Imo cæli ad Ortum. Hos autem quadrantes in ternas partes dispescunt: Ptolemæus quidem per binas horas temporales, rationales verò per duos circulos magnos tran- seuntes per communes intersectiones horizontis, & Meridiani, quorum ope diuiditur æquatuor in duodecim partes æquales, singulis domibustriginra æquatoris gradus attribuentes, nulla Zodiaci habita ratione, sed eo, vt jacer sub æquatore in partes siue æquales, siue inæquales, quæ videlicet intercipiuntur intrà fines horum circulorum, tributo. Et has intercapedines Dodecatemorias, domos, angulos succedentes, & cadentes ab angulis Astronomi appellarunt; quasum ordo esset inuer- sus, & contrà motum pruni mobilis ordinatus: ita vt prima X iiiij
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MATHEMATICVM. 177 Since its own nature is moist and cold, to the origin of the radical moisture a moist and cold sign also ought to have been assigned, such as Cancer. On the contrary, Saturn, as the planet inherently bringing cold, the destroyer and enemy of radical moisture, ought to occupy the opposite seats of these luminaries, namely Capricorn and Aquarius, the more moist signs after the others, and those which are farthest from our zenith, just as Saturn is far distant from the earth. Of these, Capricorn, because of conformity of nature (for it is by nature cold and dry), would be the first seat. Mars also, being by nature a malefic, since by his malignity he corrupts life originating from the luminaries, ought to claim those houses for himself which would vex the houses of the luminaries with a hostile ray; therefore the signs of Aries and Scorpio were assigned to him, which behold the signs of the luminaries in a square aspect. On the contrary, the benefics should have those places which are joined to the places of the luminaries by a bond of friendship; therefore to Jupiter, the greater fortune, those houses ought to be assigned which are united to the places of the luminaries by the bond of perfect friendship, namely by the trine ray, that is, Sagittarius and Pisces. To Venus, the lesser fortune, Taurus and Libra, which regard the same houses by sextile. Finally, to Mercury, who is nearest to the luminaries of all the planets—for from the Sun he is never separated by more than 28 degrees, and indeed he is contiguous to the Moon by the nature of his orbit—those houses are given which approach most closely to the houses of the luminaries, namely Gemini and Virgo. And this is the reason for the domiciles, and for the distribution suitably made for each of the planets. A house is also called every twelfth part of the sky considered in the position of the world. For astronomers divide both the upper and the lower hemisphere into four quadrants, two of which they call eastern, namely from the horizontal line to the meridian line above the earth, and from the west to the line of the lowest heaven; the other two, which they call western, from the meridian line to the west, and from the lowest heaven to the east. These quadrants they divide into three parts: Ptolemy indeed by means of two temporal hours, while the more rational do so by means of two great circles passing through the common intersections of the horizon and the meridian, by whose aid the four are divided into twelve equal parts, assigning to each house thirty degrees of the equator, with no regard to the zodiac, but only to what lies beneath the equator in parts, whether equal or unequal, that is, those which are intercepted within the bounds of these circles. And astronomers have called these intervals dodecatemories, houses, succedent and cadent houses from the angles; whose order would be inverted and arranged contrary to the motion of the first mobile: so that the first X iiij
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152 LEXICON domus esset horoscopus, quæ comprehenderet quinque gradus æquatoris supra terram, & vigintiquinque sub terra: secunda domus diceretur non quam mox acquirunt sidera motu diurno lara, sed quæ proximè succederet Orienti sub terra: inde tertia, quæ propè esset Meridiano subterraneo, post quarta, Meridianus ipse subterraneus, & Imum cæli, & sic de singulis, incipiendo à quinque gradibus æquatoris præcedentibus cuspidem vsque ad triginta secundùm successionis ordinem, hoc est 25. à cuspide. Quare autem totum cælum, seu mundi ambitus in duodecim non plus, nec minus partes, seu domicilia sit dissectus, vatiæ suppetunt rationes, quarum potissima desumitur ratione aspectuum, & ex dignitate duodenarij numeri. Cùm enim is solus præ cæteris diuidi possit in duas, tres, quatuor, sex, ac duodecim partes æquales jure is erat præ cæteris eligendus, qui commodè omnes aspectus ad cardines exhibere posset, cæteris numeris ad eam rem minimè congruentibus. Portò duodecim cæli domorum significata, proprietates, & accidentia, si quis ediscere volet, proprias cuiusque dictiones suis in locis consulat. 54. DOMINVS anni, secundùm Arabes dicitur is planeta, qui in signo profectionali horoscopi dominium obtinet, ac jus domicilij: Vt si horoscopus, exempli gratia, hoc anno profectione transeat in signum Arietis, Mars dicetur anni dominus; sequenti verò anno erit Venus, quia signum profectionale horoscopi est Taurus, in quo jus domicilij habet ipsa Venus, &c. Hunc plutimi faciunt in anni revolutionibus antiquiores Arabes, contendentes suis nugis eum esse maximæ auctoritatis, atque efficacix in rebus illo anno euenientibus decernendis; quæ prorsus delitamenta sunt. Ea in præsenti refellere, neque instituti mei est, neque rei dignitatis. Id vnum moneo, quod eriamsi è re foret illum admittere in profectionibus annuis colligendis, id faciendum esse, non per æqualem illum motum, ac profectionem locorum hylegialium per singula Zodiaci signa, tribuendo cuilibet anno solari signum vnum, quemadmodum hucusque Astronomi omnes tradiderunt, sed eo modo, quem nuper ex veris philosophiæ principijs inuenit ingeniosissimus, atque amicissimus P. Titus; nosque in loco vbi profectionum sermo inciderit, explicabimus. 55. DOMINVS genitura, apud Genethliacos dicitur is planeta, qui totius genitutæ sibi arrogat vniuersale dominium, quicque alijs præstat in judicio temperamenti, morum (quantum naturales animi propensiones appellant) affectionum corporis, & similium, vade natus in vniuersum, nomen Iouialis, Sarus-
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152 LEXICON The first house would be the horoscope, which includes five degrees of the equator above the earth, and twenty-five below the earth; the second house would be said to be, not that which the stars immediately acquire by diurnal motion, but that which next succeeds the East under the earth; then the third, which would be near the subterranean Meridian; after that the fourth, the subterranean Meridian itself, and the Imum cæli, and so on with each of the others, beginning from the five degrees of the equator preceding the cusp up to thirty, according to the order of succession, that is, 25 from the cusp. But as to why the whole heaven, or circuit of the world, is divided into twelve, neither more nor less, parts, or domiciles, various reasons are available, of which the chief is drawn from the doctrine of aspects, and from the dignity of the number twelve. For since it alone, more than the others, can be divided into two, three, four, six, and twelve equal parts, it was rightly to be chosen above the rest, since it could conveniently exhibit all the aspects to the angles, whereas the other numbers were by no means suited to that purpose. Moreover, if anyone wishes to learn the significations, properties, and accidents of the twelve houses of heaven, let him consult the proper terms of each in their respective places. 54. LORD OF THE YEAR, according to the Arabs, is said to be that planet which, in the profectional sign of the horoscope, obtains lordship and the right of domicile. Thus, if the horoscope, for example, in this year by profection passes into the sign of Aries, Mars will be called the lord of the year; but in the following year it will be Venus, because the profectional sign of the horoscope is Taurus, in which Venus herself has the right of domicile, and so on. The older Arabs place great value on this in revolutions of the year, contending in their trifles that it is of the greatest authority and efficacy in determining the events that will happen in that year; which are altogether delights. To refute these here is neither my purpose nor required by the dignity of the subject. I note only this much: even if it were useful to admit it in the calculation of annual profections, it ought to be done not by that equal motion, and the profection of hylegial places through each sign of the Zodiac, assigning to each solar year one sign, as all astronomers have hitherto taught, but in that manner which the most ingenious and dear to me Father Titus has lately discovered from the true principles of philosophy; and I shall explain it in the place where the discussion of profections occurs. 55. LORD OF THE GENITURE, among the Genethliacs, is said to be that planet which arrogates to itself universal dominion over the whole nativity, and surpasses the others in judgment regarding temperament, morals (so far as natural inclinations of the mind are called), affections of the body, and similar things; whence the native, in general, is called Jovial, Sarus-
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MATHEMATICVM. 155 nini, Mercurialis, sortitur. Ad quem præcisè pertineat hoc jus, non adhuc benè compertum. Iulius Firmicus magni no- minis author, quique floruit circa annos Christi 310. eum planetam huic dominio præficit, qui præest signo, in quod proximè ingreditur Luna post editum fætum: exceptis ta- men ab hac prærogatiua luminatibus, vtpote vniuersalibus te- rum significatotibus. Sic exempli gratiâ posito, quod Luna genituræ tempore in Ariete reperiatur, genituræ domina erit Venus, eò quod Tauri signo, in quod proximè ingrediur Luna post natiuitatem, Venus dominatur. Sed demus Lunam Geminos possidere; tunc profectò prætermisssis Cancro, & Leone luminarium domicilijs, transiur ad Virginem, cui præest Mercurius, qui propterea totius genituræ vniuersale dominium sortieit. Hæc Firmæcimens, cui subscribit Ponta- nus, & non pauci ex recensioribus. Reuera tamen id nec vali- da ratione deductum, nec cum effectibus consonat. Et scimus Firmicum Latinè magis, quàm Philosophicè scripsisse, vt aduertiteriam Iunctinus; vnde & eius scripta propter sermo- nis elegantiam ab Ecclesia permissa sunt, cum alias multa ibi absona, Arabum superstitionibus inuoluta confarcinauerit: sicut & Pontanum, Poëtam magis, quàm Astrologum egisse. Alij absolutè eum, huic dispositioni præficiunt, qui fuerit dominus ascendentis, vel in ascendente partiliter repetius. Et sanè, nulli dubium, ascendentis dominum, siue Almurhem, ac Planetam in eo repertum plurimùm posse in decernenda complexionemati: at in alijs, non ita clarè. Alij eum statuunt genituræ dominum, in cujus finibus tempore natiuitatis Sol reperiatur in geniura diurna, Luna verò in nocturna. Com- munior tamen sententia insistens Ptolemæi præceptis, in ijs quæ habet lib. 3. Qu. drip. cap. 11. (vbi agit de Aphææ ele- ctione, quando luminaria vitæ moderationem fortui ne- queunt) docenus, vt is eligatur in Aphetam, ex quinque erraticis, qui cum sit in locis idoneis, plures prærogatiuas habuerit in locis luminarium, ascendentis, medij cæli, & partis fortunæ (alij pro parte fortunæ ponunt locum præcedentis lu- minarium conjunctionis, aut oppositionis) ita & ipsi illum planetam præficiunt vniuersali rerum dominio, qui in omni- bus hisce locis plures prærogatiuas habens, cæteris anteibit; atque eum qui, facto scrutinio, proximus illi erit in numero dignitatum, in huius domini participationem admittunt, exclusis semper luminaribus. Ego sanè, omnibus perpensis, ratione, & experientia du- ctus, ijs assentiri cogot, qui existimant eum planetam in hoc negotio præficiendum esse, qui cæteros vincet in fortitudine;
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MATHEMATICVM. 155 ...ninus, Mercurialis, obtains it. To whom precisely this right belongs has not yet been well ascertained. Julius Firmicus, an author of great name, who flourished around the year of Christ 310, assigns this lordship to that planet which rules the sign into which the Moon next enters after birth; excepting, however, from this prerogative the luminaries, as universal significators of things. Thus, for example, supposing that at the time of nativity the Moon is found in Aries, Venus will be lady of the nativity, because she rules Taurus, the sign into which the Moon next enters after birth. But let us suppose the Moon to occupy Gemini; then, passing over Cancer and Leo, the domiciles of the luminaries, it will go on to Virgo, over which Mercury presides, and therefore Mercury obtains the universal rule of the whole nativity. Such is the opinion of Firmicus, to which Pontanus subscribes, and also not a few of the more recent writers. Yet in truth this is neither drawn from sound reasoning nor in agreement with the effects. And we know that Firmicus wrote more in Latin than philosophically, as Iunctinus observes; whence his writings, on account of the elegance of their language, have been permitted by the Church, although elsewhere he has stuffed them with many absurd things, wrapped up in Arabian superstitions; just as Pontanus acted rather as a poet than as an astrologer. Others absolutely assign this disposition to that planet which is lord of the ascendant, or is partilely found in the ascendant. And indeed there is no doubt that the lord of the ascendant, or Almurhem, and the planet found therein, can do very much in determining temperament; but in other matters, not so clearly. Others establish as lord of the nativity that planet in whose bounds the Sun is found in a diurnal nativity, but the Moon in a nocturnal one. The more common opinion, however, adhering to the precepts of Ptolemy, in those things which he has in Book 3, Qu. drip., chapter 11 (where he treats of the choice of the Apheta, when the luminaries cannot moderate the fortune of life), teaches that from the five wandering stars that one is to be chosen as Apheta which, being in suitable places, has the greater prerogatives in the places of the luminaries, the ascendant, the midheaven, and the part of fortune (others place in the part of fortune the place preceding the conjunction or opposition of the luminaries); and thus they also assign to that planet universal dominion over things which, having more prerogatives in all these places, will surpass the others; and the one who, after examination, is next to it in number of dignities, they admit into participation in this lordship, always excluding the luminaries. I myself, indeed, considering everything, and led by reason and experience, am compelled to agree with those who think that the planet to be set over this matter is the one which surpasses the others in strength;
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MATHEMATICVM. 157 DORYPHORIA Græcè idem sonat, ac Latinè securitas, & comitatus 1 (Arabes Ductoriam vocant) quod nos exemplo à Principibus sumpto, qui multo satellitum famulatu comitati incedunt, Satellitum planetarum ad luminaria cælestium lum- minum principes, nominamus. Et quemadmodum Regem fa- mulatus præcedit, Reginam verò subsequitur, ita ad hoc sa- tellitium luminaribus adornandum, debent quinque erraticæ Solem præcedere, sicque esse ab illo Orientales, Lunam verò subsequi, atque esse ab illa Occidentales. Quomodo autem fiat hic famulatus, satellitium, ac Doryphoria, aliter expli- cant Arabes, aliter Græci. Hi enim docent, tunc planetam facere Doryphoriam Soli, quando fuerit separatus ab illo, & extrà eius radios ad triginta gradus, quando mane apparuetit, in qua re valdè dissentiunt, & confunduntur. Aliqui enim inquiunt planetam infrà 16. gradus nullo pacto facere Doty- phoriam, quia vel est sub radijs, vel combustus. Alij verò id non attendunt, sed vbique sit intrà triginta gradus, etiamsi combustus, docent ipsum facere satellirium. Alchabitius tenet, quod infrà 60. gradus intelligi debeat hæc distantia, cum pla- netæ fuerint extrà radios; eo modo, quo dictum est, & figu- ra sexangula inueniatur: sed in alio capite dicit, quod quando planetæ fuerit in angulo, seu in sua similitudine, & Sol in sua similitudine in altero angulorum, tunc fiat Doryphoria. Ara- bes verò docent, quod non tantum ex præsentia, sed etiam ex radio cum luminaribus fiat Doryphoria: ita quod Sol verbi gratiâ sit in aliquo angulorum, & respiciatur ab erraticis per sextilem, trigonum, aut quadratum, nihiloseciùs fiat Dory- phoria. Quid in tanta controversia determinandum sit, non est animus pro nunc explicare. Est enim res magni momenti, & à multis inftà explicandis dependet; quibus traditis liqui- dò apparebit, quid requiratur, quidue sufficiat ad verum sa- tellitium luminaribus adornandum. Vnde cum iterum redibit sermo in V. Satellitium jactis jam fundamentis, facile erit ædificium struere, nouamque hanc doctrinam mentibus inge- rere, ac tenacius implantare. Pro nunc sufficiat p[er]tæmittere tanquam dicendorum basim, idque pro certo supponere, ad satellitium requiri, vnionem, & familiaritatem erraticarum cum Sole aut Luna (vt optimè probat Titus in Cæleste Philoso- ~~phia) Cùm enim id sit accessus virium ad luminaria, ac veluti vectigal mutuari luminis, quod à lateronibus ipsis soluatur; nisi in ea distantia fuerint, qua eorum virtus vniri possit, at- que ad luminaria transmitti, Satellitium facere, ac Dorypho- riam minimè poterunt. Porrò quanta sit cælestis hæc consti- tutio, quantiue momenti ad dignitates, & imperia decer-
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MATHEMATICVM. 157 Doryphoria in Greek means the same as securitas and comitatus in Latin; the Arabs call it ductoria. We, taking our example from princes, who proceed accompanied by a great retinue of attendants, name the satellites of the planets the princes of the celestial lights. And just as the retinue goes before a king, but follows a queen, so, for this adornment of the luminaries, the five wandering stars ought to go before the Sun, and thus be eastern from him, but follow the Moon, and thus be western from her. But how this retinue, this satellite-service, and this doryphoria come to be, the Arabs explain in one way, the Greeks in another. For the latter teach that a planet makes doryphoria to the Sun when it has separated itself from him and is beyond his rays by thirty degrees, when it appears in the morning; in this matter they differ greatly and are confused. Some indeed say that a planet within 16 degrees by no means makes doryphoria, because it is either under the rays or combust. Others, however, do not consider this, but everywhere within thirty degrees, even if combust, teach that it makes satellite-service. Alchabitius holds that this distance ought to be understood within 60 degrees, when the planets are beyond the rays, in the manner stated, and the hexagonal figure is found; but in another chapter he says that when the planet is in an angle, or in its own likeness, and the Sun is in his own likeness in another of the angles, then doryphoria is made. The Arabs, however, teach that doryphoria is made not only by presence, but also by aspect with the luminaries: so that, for example, if the Sun is in one of the angles and is aspected by the wandering stars by sextile, trine, or square, doryphoria is nevertheless made. What should be determined in so great a controversy is not my intention to explain for the present. For this is a matter of great importance, and much depends on the explanations to be given below; once these have been set out, it will clearly appear what is required and what suffices for the true adornment of the luminaries with a satellite retinue. Hence, when the discourse returns again in V. Satellitium, the foundations having now been laid, it will be easy to build the structure and to implant this new doctrine in minds more firmly. For the present let it suffice to set this down as the basis of what is to be said, and to assume as certain that satellite-service requires the union and familiarity of the wandering stars with the Sun or the Moon (as Titus proves best in Cæleste Philosophiā). For since this is an approach of powers to the luminaries, and as it were a borrowing of light to be repaid by the planets themselves, unless they are at that distance in which their power can be united and transmitted to the luminaries, they can by no means make satellite-service or doryphoria. Moreover, how great is this celestial constitution, and of what importance it is to dignities and empires,
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MATHEMATICVM. 159 natura Saturni, retinuit nomen Dubbe. Kircherus in Oedipo refert plaustrum hunc, seu Vrsam ab Arabibus Christianis vocari Naasch Laazar, hoc est feretrum Lazari, pio quidem affectu, quo abjectis poëtarum figmentis, non à fabulis, sed à sacrarum paginarum penu desumpta sideribus nominæ indiderunt, quod postea audio fecisse de toto firmamento, eiusque imaginibus cælestibus nescio quem Iacobum chillerum appingendo singulis astris nomina sanctorum, & præsertim Zodiacum appellando ex nominibus duodecim Apostolorum: sed de hac re fusiùs in V. Imagines Ca'estes. Dvctio, idem est apud aliquos, ac Directio: significat < 69.> enim deductionem Promissorum ad loca Significatorum, atq[ue] artificiosam mensuram itineris, quod motu primi mobilis perficit Promissor, quousque ad locum Significatoris perueniat. Quod quomodo fiat, satisfictum est in V. Directio. Dvctoria, Arab. idem quod Græcè Doryphoria, de qua < 70.> non longè ante dictum. Sed enim eam aliter explicat Alchabitius. Est enim inquit Ductoria vt planeta sit in suo Hayχ, id est in parte sibi propria, & in aliquo angulorum ascendentis, & aliquod luminarium: similiter sit in loco sibi consimili in quadrante, videlicet in aliquo angulo, ita quod planeta in die sit Orientalis à Sole, in nocte Occidentalis à Luna. Hali verò super proposit. 16. Centiloquij dicit quod ad Ductoriam requiritur, vt superiores quidem sint Orientales à Sole, at verò inferiores sint Occidentales; quoniam isti cùm Occidentales sunt, & illi cùm Orientales crescunt lumine, atq[ue] adeò fortiores, validioresque euadunt. Quid in hac re sit dicendum explicabimus in V. Satellitium. Dvodenaria planetarum, siue domorum, est vna ex superstitiosis, < 71.> ac vanis Arabum considerationibus super duodecim Zodiaci signa, ac cælestes domos in situ mundi; quemadmodum Nouenaria, Alfridaria &c. Itaque in quolibet signo vel domo inuenire satagunt dominum duodenariæ, atque ad id præstandum diuidunt vnumquodque signum in duodecim partes æquales; ita vt quælibet pars constet duobus gradibus &c dimidio: quo facto dicunt, quod dominus primæ duodenariæ est dominus illius signi; dominus secundæ duodenariæ est planeta succedens per ordinem descendendo, & sic de reliquis. Sic verbi gratia domiuius primæ duodenariæ Arieris est Mars: secundæ Sol: terriæ Venus: quartæ Mercurius: quintæ Luna: sextæ Saturnus: septimæ Iupiter: octauæ iterùm Mars, & sic sequendo. Et hæc est explicatio duodenariæ quam tradit Ioannes de Saxonia in Alchabitium. Cùm igitur, subdit, volueris scire duodenarias planetarum, vel domorum, vide quantum
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MATHEMATICVM. 159 The nature of Saturn retained the name Dubbe. Kircher, in Oedipus, reports that this wagon, or Bear, is called by Christian Arabs Naasch Laazar, that is, the bier of Lazarus, with a pious sentiment indeed; for, rejecting the fictions of poets, they gave the stars names taken not from fables but from the storehouse of the sacred pages. I hear that afterward someone, I know not what Jacobus Chillerus, did the same for the whole firmament and its heavenly images, attaching to each star the names of saints, and especially calling the Zodiac from the names of the Twelve Apostles; but of this matter more fully in V. Imagines Caelestes. Dvctio, among some is the same as Directio: for it signifies <69.> the bringing of the Promissors to the places of the Significators, and an artificial measurement of the journey, which the Promissor accomplishes by the motion of the primum mobile, until it arrives at the place of the Significator. How this is done has been sufficiently explained in V. Directio. Dvctoria, in Arabic, is the same as the Greek Doryphoria, of which <70.> something was said not long before. But Alchabitius explains it otherwise. For, he says, Ductoria is when a planet is in its own Hayχ, that is, in its proper part, and in one of the angles of the ascendant, and of one of the luminaries; likewise when it is in a place akin to itself in the quadrants, namely in one of the angles, so that the planet by day is Oriental from the Sun, and by night Occidental from the Moon. Hali, however, on proposition 16 of the Centiloquium says that for Ductoria it is required that the superior planets indeed be Oriental from the Sun, but the inferior ones Occidental; because when these are Occidental, and those Oriental, they increase in light and thus become stronger and more vigorous. What is to be said in this matter we shall explain in V. Satellitium. Dvodenaria of the planets, or of the houses, is one of the superstitious <71.> and vain considerations of the Arabs concerning the twelve signs of the Zodiac and the celestial houses in the state of the world; just like Nouenaria, Alfridaria, and the like. Accordingly, in each sign or house they strive to find the lord of the duodenaria, and for this purpose divide each sign into twelve equal parts, so that each part consists of two degrees and a half; once this is done, they say that the lord of the first duodenaria is the lord of that sign; the lord of the second duodenaria is the planet following in descending order, and so on with the rest. Thus, for example, the lord of the first duodenaria of Aries is Mars; of the second, the Sun; of the third, Venus; of the fourth, Mercury; of the fifth, the Moon; of the sixth, Saturn; of the seventh, Jupiter; of the eighth, Mars again, and so on in order. And this is the explanation of the duodenaria which John of Saxony gives in his Alchabitius. When, therefore, he adds, you wish to know the duodenaries of the planets or of the houses, see how much
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MATHEMATICVM: 163 < 6.> Opinatur autem Ricciolus in Almagesto, Eclipses non tam calamitates in mundum importare quàm bona, eaque maxima, licet nobis ignota, aur inconsiderata, qui eius conditionis su- mus, vt ad mala potius quæ in natuta sunt, oculos admoueamus, quàm ad plurima beneficia, quæ vel ex malis ipsus habemus. Neque enim, inquit, si aliquidbus incommodæ sunt Eclipses, credendum est nulli omninò natura sublunarium prodesse: & sanè sicut noctis, & hyemis vicissitudines suas habens in natura opportunitates; ita subtractio Lunaris luminis eo tempore, quo plenum alsoquin tetras illustraturum fuisset, & obstructio radsorum Solarium ad attemperandos, aut interrumpendos influxus pertinere videtur. Hæc ille & sanè non sine maxima probabilitare. < 7.> Hic autem quoniam de luminarium defectionibus agitur, non erit ab te aliqua etiam de eclipsi, seu obscuratione aliorum cælestium corporum per interpositionem inferiorum, exponere. Equidem eo modo, quo Sol obscuratur, possunt & quinque erraticæ, possunt quinimò & fixæ, eandem defectionem pati, qua eorum lumen & influentia per inferiores intercipiantur. < 8.> Quod quando accidit præsertim in tribus superioribus, atque hæc luminis inhibitio sit ab ipsis luminaribus, qui cum corpore magni sint diu planetam superiorem tenent occultatum, eiusque radios, & influentias diu à nobis auertunt, tunc quidem grande aliquid; idque non ita obuium expectandum est. Talis fuit obscuratio, immò & occultatio Iouis per interpositionem corporis Lunaris ante annum 1648. de qua variè pronunciatum ab nostris Astronomis, & quia effectus isti incidebant in Poloniam, quæ suberat signo, in quo celebrata fuit: ideò nil mirum si ab eo tempore ea tam malè sit bellis vexata. < 9.> At enim eo modo quo obscuratur Luna per hoc quod incidat in vmbram terræ, aut alterius planetæ nullus eorum poterit obscurari. Patet, quia licet telluris vmbra pertingat ad orbem Veneris, ac proinde tangere possit, & Venerem, & Mercurium, sic etiam vmbra Mercurij ad orbem Veneris; nihilominus vmbra illa non rectè sursum porrigitur, nisi quando Luna, aut alius planeta est in oppositione Solis: At isti planetæ, Venus scilicet, & Mercurius nunquam elongantur à Sole plusquam vnum, aut duo signa, quî sit, vt neque in vmbram conicam terræ possint incidere, neque in Lunæ, neque in alterius alter, atque adeò nec etiam eclipsari. ECLIPtica est linea in medio Zodiaci collocata, hinc inde sex gradus latitudinis relinquens, per quam Sol perpetuò incedit neque ad dextam, neque ad sinistram vnquam declinans, seu melius definiri potest ecliptica, quod sit Circulus magnus in calo aqualiter distans à polis Zodiaci, non secùs ac aquator à L ij
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MATHEMATICUM: 163 < 6.> However, Ricciolus in the Almagest thinks that eclipses bring into the world not so much calamities as goods, and very great ones too, though unknown to us or unconsidered by us, who are of such a condition that we direct our eyes more to the evils which are in nature than to the many benefits which we even derive from evils themselves. For, he says, if eclipses are in some respects inconvenient, it should not be believed that nature among sublunary things is of no benefit at all; and indeed, just as the alternation of night and winter has its own conveniences in nature, so the subtraction of lunar light at the time when otherwise it would have fully illuminated the darkness, and the obstruction of solar rays, seems to belong to the moderation or interruption of influences. Thus he speaks, and indeed not without great probability. < 7.> But here, since we are dealing with the failures of the luminaries, it will not be irrelevant for you to explain something also about the eclipse, or obscuration, of other heavenly bodies by the interposition of lower ones. Indeed, in the same way that the Sun is obscured, the five wandering stars, and even the fixed stars too, can undergo the same failure, by which their light and influence are intercepted by inferior bodies. < 8.> And when this happens, especially in the three superior planets, and this inhibition of light comes from the luminaries themselves, which, being of a great body, keep the superior planet hidden for a long time and turn its rays and influences away from us for a long time, then certainly something great, and not so ordinary, is to be expected. Such was the obscuration, indeed even the concealment, of Jupiter through the interposition of the lunar body before the year 1648, about which our astronomers pronounced variously; and because these effects fell upon Poland, which was under the sign in which it was celebrated, therefore it is no wonder if from that time it has been so badly harassed by wars. < 9.> But in the same way that the Moon is obscured by falling into the shadow of the Earth, or of another planet, none of them can be obscured. It is clear, because although the shadow of the Earth reaches to the orbit of Venus, and therefore can touch both Venus and Mercury, and likewise the shadow of Mercury extends to the orbit of Venus, nevertheless that shadow is not properly carried upward unless the Moon, or another planet, is in opposition to the Sun. But those planets, namely Venus and Mercury, never move more than one or two signs away from the Sun; how then should they be able to fall either into the conical shadow of the Earth, or into that of the Moon, or of another, and thus not even be eclipsed. The ecliptic is a line placed in the middle of the Zodiac, leaving on either side six degrees of latitude, along which the Sun perpetually moves, never declining either to the right or to the left; or better, the ecliptic may be defined as a great circle in the sky equally distant from the poles of the Zodiac, no differently than the equator from the poles of the
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MATHEMATICVM. 167 naria isthæc præ cæteris potissimam vim obtinet) in signis, ac domibus constitutio: vt si celeritate sit opus sint in mobilibus signis, si stabilitate, ac firmitate vt ædificationes, in fixis. Prætereà vt planeta rei aggrediundæ naturalis significator, liber sit à maleficis, atque in suis dignitatibus, bonorumque aspectibus constitutus. Tandem, vt signum ascendens tempore operis incundi sit de natura propositæ rei, vt pro itineribus. signa mobilia, & pro navigationibus quidem aqvea, pro terrestribus terrea, aut fixa: pro prælijs aut rixa feliciter ineunda in horoscopo sint signa aut fidera Martialia, vt Bellatrix, Pallilitium, Regulus, &c. Pro Navigationibus item inauspicari sunt congressûs Lunæ cum Marte, aut sideribus prædictis de eiusdem natura, ortus, & occasus Arcturi, Orionis, Hædorum, Delphini, & Sirij: experientia enim nunquam fallens edocuit hæc tempestates inducere. Similiter quoad Potiones sumendas generaliter Ver est tempus maximè accommodatum: hyems & æstas, ac præcipuè dies caniculares in opportuni. In specie verò Luna quæ humoribus præsidet sir benè affecta, lumine minuta magis, quàm aucta, libera à maleficis, nec non à Sole, eorumque prauis aspectibus: ac sit in signo de natura humorum qui purgandi sunt vt si attrabilis euacuanda sit, Luna constituatur in signis terreis; si flaua in signis igneis; si phlegma in signis aqueis: Aries tamen, Gemini, Cancer, Leo, & signa ruminantia parum idonea sunt ad potiones sumendas, quia cum partibus superiotibus præsint: eas sursum euocant, & vomitum cienr, vt experientia jugis testatur. Ni fortè Vomitoria præbeantur, in quo casu ea signa dera opera sunt perenda. Attendendus etiam est ipsius Lunæ cum planetis aspectus, qui vt dixi maleficarum, quicunque tandem sint semper portionum effectus, impediunt. Sol è contrà, & Venus per benignos aspectus adjuuant: Iupiter non est adeò idoneus, quia naturam nimium roborat, qui sit, vt medicamentum in nutritionem poriùs abeat, quam in excretionem. Vniuersaliter autem planeta cui humor euacuandus subditur, non sit potens in angulo, aut suis dignitatibus necesse est, sed potiùs debilis, & sub terra, si enim fortis, & supra terram humorem auget, sursum euocat, purgationique obsistit. Sic si phelgma purgare velis, non sit fortis, eo tempore quo medicina sumitur Venus, sed Mars: si flauam bilem è contrà Mars debilis sit & sub terra, Luna verò, aut Venus potentes, &c. Vbi aduertendum est aliam esse rationem signorum, aliam siderum. Nam in bile euacuanda, cauenda est quidem vt dixi fortitudo Martis illam augentis, ac roborantis, at eligendum est in horoscopo & in Luna signum igneum ob conformitatem naturæ, eò quia se L iiij
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MATHEMATICVM. 167 That arrangement, however, which has the greatest force above the others, is the placing of signs and houses: so that if speed is required, one should use movable signs; if stability and firmness, as in building, fixed signs. Furthermore, let the planet that is the natural significator of the matter to be undertaken be free from malefics, and placed in its own dignities and in good aspects. Finally, let the ascendant sign at the time the work is begun be of the nature of the matter proposed, as for journeys, movable signs; and for voyages, watery signs; for land travel, earthy or fixed signs; and for battles or quarrels to be happily undertaken, let Martial signs or stars be in the horoscope, such as Bellatrix, Pallilitium, Regulus, etc. For voyages, too, the conjunctions of the Moon with Mars, or with the aforesaid stars of the same nature, and the rising and setting of Arcturus, Orion, the Haedi, the Dolphin, and Sirius, are to be regarded as unfavorable: for experience, which never fails, has taught that these bring on storms. Likewise, as regards potions to be taken, Spring is generally the most suitable time; winter and summer, and especially the dog days, are unfavorable. In particular, the Moon, which presides over humors, should be well affected, decreasing in light rather than increasing, free from malefics, and also from the Sun and their evil aspects; and it should be in a sign of the nature of the humors that are to be purged. Thus, if black bile is to be evacuated, let the Moon be placed in earthy signs; if yellow bile, in fiery signs; if phlegm, in watery signs. Aries, Gemini, Cancer, Leo, and the ruminant signs are, however, little suited to taking potions, because, since they preside over the upper parts, they draw them upward and provoke vomiting, as constant experience shows. Unless, perhaps, emetics are being given, in which case those signs are deliberately to be sought. Attention must also be paid to the Moon’s aspect with the planets, which, as I said, whatever they may be, always hinder the effects of potions if they are malefic. The Sun, on the contrary, and Venus help by their benign aspects; Jupiter is not so suitable, because he strengthens the nature too much, so that the medicine tends rather to nourishment than to evacuation. Generally, however, the planet to which the humor to be evacuated is subject should not be powerful in an angle, or in its dignities; rather it must be weak, and below the earth, for if it is strong and above the earth it increases the humor, draws it upward, and hinders the purgation. Thus, if you wish to purge phlegm, Venus should not be strong at the time the medicine is taken, but Mars should; if yellow bile, on the contrary, Mars should be weak and below the earth, while the Moon or Venus should be powerful, etc. Here it must be noted that the rationale of the signs is one thing, and that of the stars another. For in evacuating bile, as I said, one must avoid the strength of Mars, which increases and reinforces it; but in the horoscope and in the Moon one should choose a fiery sign, because of the conformity of nature, since it is by that same nature that it
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170 LEXICON tiora, eò magis resistunt, ac morantur: vt patet in ipsis sphæris cælestibus. Vnde etiam intelligi potest, & has omnes fluidas esse, vt elementa sunt, & eò fluidiores, ac puriores, quo à centro magis elongantur. Et vnico tantùm motu cieri ab Oriente in Occidentem raptas à primo orbe; licet quæ ab eo sunt magis remotæ, magis impulsui dato sua ponderositate resistant, ac retro in partibus Orientalioribus maneant, prout diximus in V. Calum. Cæterùm non negaverim multos ex recensioribus inter elementa Ignem minimè connumerare, quia & aliquos omnia elementa negare: inter quos est Auerfa tom. 2. Philosoph. quast. 41. sect. 2. 25. ELEMENTA Geometrica, Antonomasticè audiunt Libri quindecim Geometricorum principiorum Euclidis Geometrarum Principis, & Magistri: eò quia sine ipsis nullum opus Mathematicum aggredi, nullum effatum percipi potest; sicut enim is qui legere vult (inquit Claiius in Prologom.) Elementa literarum discit prius, & illis affiduè repetitis vtitur in vocibus omuibus exprimendis, sic qui alias disciplinas Mathematicas desiderat sibi reddere familiares elementa hæc Geometrica plenè, ac perfectè calleat prius necesse est. Quandoquidem horum elementorum ope, omnis in cælo siderum ratio auspicatur, eorum motus, situs, distantia, altitudo, quantitas internoscitur. Ab ijs omnis in cælo, omnis in terra dimensio habetur: ac denique ingens hoc Dei, ac Naturæ opus, Vniuersi, inquam, istius machina non sine Geometricorum horum elementorum auxilio intelligi, & contemplari potest. Iure igitur hæc prima Geometriæ principia elementa Geometrica dicta sunt. 26. ELEVATIO apud Astronomos significat præcellentiam, ac prædominium vnius planetæ super alium, quando videlicet duo, vel plures concurrunt adinuicem, & conueniunt ad vnam, eandemque rem significandam: tunc qui alijs, viribus atque activitate prævaler, dicitur super illos eleuatus. Pontanus in 27. Commentar. super Centiloqu. hanc dicendi formam non probat, quia eleuare, inquit, apud Grammaticos indicat depressionem potiùs, quàm præeminentiam: Verùm nescio, an satis benè discurrat: cùm Eleuo propriè significet sursum leuo, siue in altum tollo: quod idipsum prorsus est, quod explicare volumus in planetis se super alios eleuantibus, vt mox dice[mus]. Quod autem quandoque per translationem accipiarur pro rei diminutione, quæ verbis fiat eam vituperando, id non officit propriæ notioni. Sed quidquid sit de modo loquendi, certum est in re, Eleuari apud Astronomos nil aliud significare quàm extollentiam vnius planetæ super alium: quod
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170 LEXICON the more they resist and delay: as is clear in the celestial spheres themselves. Whence it can also be understood that all these are fluid, as the elements are, and the more fluid and pure, the farther they are removed from the center. And they are moved by a single motion, driven from East to West, carried along by the first orb; although those which are farther removed from it resist the given impulse more by their own heaviness, and remain behind in the more eastern parts, as we said in V. Calum. Moreover, I would not deny that many of the more recent writers do not at all count Fire among the elements, because some even deny all the elements: among whom is Auerfa, tom. 2. Philosoph. quast. 41. sect. 2. 25. The Geometrical ELEMENTS, by antonomasia, are so called in the fifteen books of Euclid’s Geometrical Principles, Euclid, Prince and Master of geometers; because without them no mathematical work can be undertaken, no statement can be understood; for just as one who wishes to read, as Claiius says in the Prologom., first learns the elements of letters, and by repeatedly using them refers to all the voices to be expressed, so he who desires to make the other mathematical disciplines familiar to himself must first thoroughly and completely master these geometrical elements. Since by the aid of these elements, all the account of the stars in the heavens is begun, and their motion, position, distance, altitude, and quantity are discerned. By them every measurement in heaven, every measurement on earth, is obtained; and finally this vast work of God and Nature, I mean the machine of the Universe, cannot be understood and contemplated without the help of these geometrical elements. Therefore these first principles of geometry were rightly called geometrical elements. 26. ELEVATION among astronomers signifies the preeminence and predominance of one planet over another, when, namely, two or more come together and agree in indicating one and the same thing: then the one which prevails over the others in strength and activity is said to be elevated above them. Pontanus in 27. Commentar. on the Centiloqu. does not approve this manner of speaking, because to elevate, he says, among grammarians indicates depression rather than preeminence: but I do not know whether he reasons sufficiently well; since elevo properly signifies to raise upward, or to lift on high: and this is exactly what we wish to explain in planets elevating themselves above others, as we shall soon say. But if at times it is taken by translation to mean a diminution of a thing, expressed by words that disparage it, that does not affect the proper meaning. But whatever may be said about the manner of speaking, it is certain in fact that to be elevated among astronomers means nothing other than the raising of one planet above another: which
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172 LEXICON tur, vt alibi obseruatum est. Neque in ista efficientia vnum aliud vincere potest, ac vires illius deprimere, nisi fuerit in se fortis, atque armis validioribus præmuuitus. Quandoquidem quando sidera sunt inter se configurata agunt ad inuicem, ac repatiuntur: quod est validius, magis agir, & minus repatitur; quod est infirmius minus agir, & magis repatitur: Vnde est quod quæ sidera viribus præualent, dum alijs viribus imminutis aur corpore, aut radio copulantur, in illa agant, virtutem eorum altetent, atque actiuitatem diminuanr. Quare, vt suprà habet Ptolemæus, si benefici super malesicos eleuentur, bonum est; nam qualitates eorum maleficas deprimunt, & instringunt: si malefici super beneficos extollantur, noxium est: quippe corrumpunt eorum bonitatem, vt ipsa bonitas noxia har. 30. Hinc benè dixit Argolus faciendum esse scrutinium, & quod inuenietur vincere aliud in numero fortitudinum (cùm aliàs intercedat inrer illa aliqua familiaritas, vt dictum est) illud dicetur super aliud eleuatum. Ordo autem, & præcellentia fortitudinum est primò situs in nobiliori cardine, & domo quoad mundum, siue maior propinquitas ad cardinem, ad quem feruntur; itaq[ue] vt hæc comparatio ad cardines præcæreris sit attendenda, cum sit omnibus prærogatiuis validior. Secundò Orientalitas à Sole, Occidentalitas à Luna. Tertiò quod sit in domo, altitudine, triplicitate, ac terminis suæ naturæ. Quartò maior ad polum arcticum propinquitas, si fuerint supra terram; ad antarcticum verò si fuerint sub terra. Quintò ascensio suprà terram, & descensio sub terra secundùm latitudinem, secundùm declinationem, & secundùm situm in mundo Sextò familiaritas siderum consimilis naturæ, & cum capite Draconis. Septimò cursus, velocitas. Octauò descensio ab Apogæo tam Eccentrici quàm Epicycli: & si qui sunt alij modi, quibus sidera augeant suas vires, omnes sunt arrendendi; quia eleuatio, vt verbo concludam, aliud non requirit quàm familiaritatem, & maiorem virium instructionem. Hanc Arabes suo vocabulo Mamareh planetarum vocant: de qua plura habet Albumasar in fine sui introductorij. 31. ELHABOR Arab. Canis maior Sirius, vide Alhabor. 32. ELHAMMEL Arab. vt habet Kircherus in Oedipo, dicitur signum & constellatio Arietis: sicut etiam 33. ELHAVT item apud Arabes, vt testatur idem Kircherus significatur signum & constellatio Piscium. Quemadmodum 34. ELKAVS est signum & constellatio sagittarij: necnon. 35. ELGEDI Signum & constellatio Capricorni. Vide sub propriocujusque nomine.
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172 LEXICON …thus, as has been observed elsewhere. Nor in that efficacy can one overcome the other, and depress its forces, unless it is strong in itself and fortified with stronger arms. For when the stars are configured with one another, they act upon one another and are acted upon in turn: that which is stronger acts more and is less acted upon; that which is weaker acts less and is more acted upon. Hence it is that those stars which prevail in force, when joined by body or ray to others diminished in force, act upon them, lessen their virtue, and diminish their activity. Therefore, as Ptolemy has above, if benefics are elevated above malefics, it is good; for they depress and restrain their evil qualities: if malefics are raised above benefics, it is harmful; for they corrupt their goodness, so that goodness itself becomes harmful. 30. Hence Argolus rightly said that an examination must be made, and that what is found to prevail over another in the number of strengths (since there is otherwise some familiarity between them, as has been said) will be said to be elevated above the other. The order, however, and preeminence of strengths is, first, position in the nobler angle and house with respect to the world, that is, greater proximity to the angle toward which they are directed; and thus this comparison ought to be observed with respect to the angles, since it is stronger than all prerogatives. Second, orientalness from the Sun, occidentalness from the Moon. Third, that it be in its own domicile, exaltation, triplicity, and terms according to its nature. Fourth, greater nearness to the Arctic Pole, if they are above the earth; but to the Antarctic, if they are below the earth. Fifth, ascension above the earth and descension below the earth according to latitude, according to declination, and according to position in the world. Sixth, the familiarity of stars of similar nature, and with the head of the Dragon. Seventh, course and speed. Eighth, descent from the Apogee of both the Eccentric and the Epicycle. And if there are any other ways by which stars increase their powers, all must be considered; because elevation, to conclude in a word, requires nothing other than familiarity and a greater endowment of forces. The Arabs call this by their own term Mamareh of the planets: on which Albumasar has more in the end of his Introduction. 31. ELHABOR, in Arabic, the Great Dog, Sirius; see Alhabor. 32. ELHAMMEL, in Arabic, as Kircher has in his Oedipus, is said of the sign and constellation of Aries; as also 33. ELHAVT, likewise among the Arabs, as the same Kircher testifies, signifies the sign and constellation of Pisces. In the same way 34. ELKAVS is the sign and constellation of Sagittarius; likewise. 35. ELGEDI, the sign and constellation of Capricorn. See under each proper name.
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MATHEMATICVM. 169 rei quisque in radice nativitatis ab siderum constitutione addictus est, eique se dedat constituendum planetæ, vel signo illi quod talem significationem facit in ascendentie. < 23.> Denique in quacumque Electione, ea semper ineatur cum Luna per ea signa mear, in quibus Iupiter, Venus, aut pars for- tunæ reperiebantur tempore nativitatis, aut benigno radio res- piciatur à dictis planetis, sintque loca rerum significationi idonea: Experientia enim compertum est, quidquid boni & for- tunæ vnicuique obuenit, id potissimum obuenire, eò quia Luna per loca beneficarum transiit: sicut è contrà quidquid mali, ex ingressu eiusdem in loca in radice à maleficis infesta. < 24.> ELEMENTVM absolutè dicitur id, quod quavis in re prima radix est, & initium, ex quo alia componuntur. Vnde in vniuersi istius ambitu, quæ sunt prima rerum semina, ex quibus reliqua corpora coagmentantur, Elementa dicuntur; Ignis videlicet, Aër, Aqua, Terra, atque ex ijs elementaris regio quæ infrà cælum omnia elementa, & ex ijs mixta complecti- tur, dicta. Quare autem quatuor tantùm, & nec plura, nec pauciora elementa rerum assignata sint, explicat Philosophus 2. de Generas & corrupt. cap. 4. Quia videlicet quatuor tan- tùm sunt primæ qualitates tangibilium, nempe caliditas, sic- citas, frigiditas, & humiditas, quæ adinuicem copulata, om- nem rerum tam simplicium, quàm mixtarum complexionem, ac temperiem comprehendunt. Quot enim sunt possibiles com- binationes harum primarum qualitatum in vno, eodemque subiecto, tot elementa assignantur: quippe oppositarum, vt caloris, & frigoris, humiditatis, & siccitatis impossibilis est combinatio. Tot igitur sunt Elementa. Quapropter & Prole- mæus in prima parte Quadrip. omnes altorum influxus ad quatuor Elementorum qualitates reducit; quasi elementa ipsa ex cælorum, & siderum moribus suæ distinctionis originem trahant. Porrò, vt modò dixi, elementa inter se certo ordine constituta efficiunt regionem elementarem, prout ab Ætherea discernitur, quæ tamen vna cum ipsis hoc Vniuersum consti- tuunt. Et in Vniuersi quidem ipsius centro existit Terra omni- nò immobilis, & cæteris elementis glauor: inde Aqua: mox Aër: denique Ignis, qui immediatè subest concauo Lunæ An autem elementa (excepta Terra) moueantur cuculanter ab Oriente in Occidentem moru vniuersitatis, & primi mobilis: vnde Oceani morum non Lunæ, sed primi mobilis raptui tribuendum esse sunt qui affirmant apud Clauium in sphæram Io. de Sacrobosco: & nos in loco diximus. Quod autem non exquisitè rapiantur, id prouenit ex eorum resistentia, & elon- gatione à primo mobili; quò enim glauora sunt, ac siu remo-
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MATHEMATICVM. 169 Everything in the root of nativity is bound by the constitution of the stars, and one should commit himself to that planet, or to that sign, which gives such a signification in the ascendant. < 23.> Finally, in whatever Election, it should always be undertaken while the Moon passes through those signs in which Jupiter, Venus, or the Part of Fortune were found at the time of nativity, or is aspected by those planets with a benign ray, and let the places be suitable to the signification of the matter. For experience has shown that whatever good and fortune befalls each person, it chiefly befalls because the Moon has passed through the places of the benefics; just as, on the contrary, whatever evil occurs comes from her entrance into places in the nativity that are afflicted by malefics. < 24.> An ELEMENT is absolutely said to be that which in any thing is the first root and beginning, from which other things are composed. Hence, within the scope of this whole universe, those things which are the first seeds of things, from which the remaining bodies are joined together, are called Elements; namely Fire, Air, Water, Earth, and from these the elemental region, which beneath heaven embraces all elements and mixtures from them, is called. But why only four, and neither more nor fewer, elements should be assigned to things is explained by the Philosopher, 2 De Generatione et Corruptione, cap. 4. Namely, because there are only four primary qualities of tangible things, namely heat, dryness, coldness, and humidity, which, joined to one another, comprehend every complexion and temperament of things, both simple and mixed. For as many as are the possible combinations of these primary qualities in one and the same subject, so many elements are assigned; since the combination of opposites, as of heat and cold, humidity and dryness, is impossible. Therefore there are so many Elements. Wherefore Ptolemy also, in the first part of the Quadripartitum, reduces all heavenly influences to the qualities of the four Elements; as though the elements themselves derive the origin of their distinction from the habits of the heavens and the stars. Moreover, as I just said, the elements, arranged among themselves in a certain order, form the elemental region, as it is distinguished from the ethereal, which nevertheless together with them constitutes this Universe. And in the very center of the Universe there exists the Earth, wholly immobile, and the heaviest of the other elements; then Water; next Air; finally Fire, which lies immediately beneath the concavity of the Moon. But whether the elements, except for the Earth, are moved circularly from East to West by the motion of the universe and of the first movable sphere—whence the motion of the ocean, they say, should be attributed not to the Moon but to the dragging of the first movable sphere, as is affirmed by Clavius in the sphere of Io. de Sacrobosco, and we have said in the proper place. But that they are not carried off exactly is due to their resistance and their distance from the first movable sphere; for the heavier they are, and as if more re-
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176 LEXICON 50. ENNEATICI Dies, vel Anns sunt Nouenarij quicque recurrentes dies, vel anni, à puncto Natiuitatis, vel initio morbi, in quibus profectò semper aliquam naturæ alterationem experimur, atque accessionem morbi, sicut & in septenarijs, ac manifestiùs quando ambo conveniunt, & septenarij, & nouenarij. Cuius rei, vti effectus patens est, & manifestus, ita & ratio, & origo obscura nimis, & adhuc non benè nota. Qua de re fusè egimus in Verbo Critici dies. 51. Eosphorvs Grecè Latinè Luci er dicitur apud Astronomos Venus matutina, atque Orientalis à Sole, à Græco verb[us] Eos, quod Orientalis sonat: sicut econtra Hesperus appellatur Vespertina, & quando est Occidentalis à Sole. E P 52. Epacta (quasi Epiaucta hoc est superexcescentia) nil aliud est, quam excessus anni communis solaris supra annum lunarem duodecim lunationum in diebus vndecim singulis annis: Cum enim annus communis solaris constet diebus 365. Lunaris verò diebus 354. consequenter lunaris terminatur, & anteuertit solarem diebus vndecim, qui fit vt Nouilunia, tot etiam diebus præcedant finem anni solaris. Et quia id singulis quibusque annis accidit, inde etiam est, vt singulis decem, & nouem annis solaribus Luna compleat vicesies duodecim integras lunationes, seù superet vnum annum communem solarem, quo circuitu expleto conueniat cum Sole: atque ita semper procedendo in infinitum, singulis annis primis à dicta conuentione reperiatur Luna præcedere Solem diebus vndecim; secundo anno diebus 22. sicque Epacta istius anni sit 22. tertio anno præcedat diebus 31. sed cum diebus 30. fiat vna integra lunatio, ideò ea prætermissa, immò potius admissa, atque in numerum integra lunationis computata. Epacta, seu præcessio lunationum sit dierum 3. qui ad triginta supersunt: quarto verò anno sit dierum 14. & sic de singulis. Progrediuntur igitur Epactæ omnes per continuum augmentum dierum vndecim, abjectis tamen 30. semper cum abijci possunt. Numerumque istum vocamus Epactum, quia epactat Lunæ defectum, atque inseruit ad ejus æratem ad dies singulos dignoscendam. Quippe si addatur Epactæ currenti eo anno numerus dierum mensis, qui transierunt, nec non Calendarum quæ præcesserunt, incipiendo à mense Martio, vsque ad præsentem mensem in quo hæc scrutari volumus, inclusiùè; statim elucent in producto numero dies ætatis Lunæ à præcedenti coitione cum Sole, demptis prius triginta, si fortè cum numerum excesserint, quia isti sufficiunt ad vnam integram lunationem constituendam. Procedit
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176 LEXICON 50. ENNEATICI. Days, or years, are the recurring nine-day periods, or nine-year periods, from the point of birth or the beginning of a disease, in which we certainly always experience some alteration of nature and an increase of the disease, just as in septenaries, and more manifestly when both coincide, both the septenaries and the enneatics. Of this matter, as the effect is evident and manifest, so too is the reason and origin exceedingly obscure, and as yet not well known. We discussed this at length under the word Critici dies . 51. Eosphorus, in Greek, in Latin is called Lucifer by astronomers, the morning and eastern Venus from the Sun, from the Greek word Eos , which means eastern; just as conversely it is called Hesperus, the evening one, when it is western from the Sun. E P 52. Epacta (as though Epiaucta , that is, superabundant) is nothing other than the excess of the common solar year over the lunar year of twelve lunations, by eleven days each year. For since the common solar year consists of 365 days, while the lunar year consists of 354 days, consequently the lunar year ends earlier than the solar year by eleven days, so that the new moons precede the end of the solar year by as many days. And because this happens each year, it is therefore also the case that every nineteen solar years the Moon completes twelve full lunations twenty times, or surpasses one common solar year, after which cycle it agrees with the Sun; and thus always proceeding to infinity, in the first year from the said conjunction the Moon is found to precede the Sun by eleven days; in the second year by 22 days; and thus the epact of that year is 22. In the third year it precedes by 31 days; but since one full lunation is made up of 30 days, that being omitted, indeed rather admitted and counted among the full lunations, the epact, or precedence of the lunations, is 3 days, which remain beyond thirty. In the fourth year it is 14 days, and so on for each year. Therefore all epacts advance by a continuous increase of eleven days, however always subtracting 30 whenever they can be subtracted. And we call this number the epact, because it adds to the Moon’s deficiency and is inserted so that her age may be known day by day. For if to the current epact there be added the number of days of the month that have passed, as well as the calends that have preceded, beginning from the month of March up to the present month in which we wish to investigate this, inclusively, immediately the days of the Moon’s age since the preceding conjunction with the Sun become clear in the resulting number, after first deducting thirty, if perhaps they have exceeded that number, since these suffice to constitute one complete lunation. Procedit
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178 LEXICON ipso deferente, atque ejus centrum eccentricè circà tellurem moueretur vna cum ipso Orbe eccentrico, & adhuc corpus planetæ circà ipsum in ejus circumferentia moueretur, qui dictus est Epicyclus. Et hunc tertium omnibus planetis præterquam Soli attribuerunt: licet Ptolomæus in Almagesto demonstret, quod apparentiæ in Sole saluari possint ponendo in eo circulum eccentricum tantum, vel coucentricum cum Epicyclo, tamen magis abbrobat eccentricum. Etenim planetæ modo apparent majores, modò minores; etiam in eadem altitudine supra horizontem: modo velocius mouentur, modò segniùs: modo videntur consistere, modò etiam retrocedere: quæ omnia talia sunt, quæ neque concipi possunt, neque explicari, nisi per orbes eccentricos, & Epiclycos. Et quoniam in Sole non videmus tantam motus diuersitatem, quanta est in reliquis planetis, qui omnes excepta Luna, modò videntur stare, modò celerius progredi, modò retrogredi in Zodiaco; ideò in ipso duos quidem priores circulos ponimus, Epicyclum, verò sine quo optime saluare eius apparentias possumus, remouemus. In Luna verò, etsi non tanta morus diuersitas dignoscatur quanta in reliquis quinque erraticis, neque etiam habeas retrocedere in Zodiaco; quia tamen in eodem loco eccentrici sui constituta, puta in Apogæo, vel Perigæo non semper habet eandem aspectus conformitatem; ideo necesse fuit, concipere, vt in eodem loco eccentrici sui sit nihilominùs modò terræ vicinior, modo ab ea remorior; quod vtique saluare minimè possumus, ni ponamus, & in ea vnum Epicyclum, in cujus Apogæo appareat minor, in Perigæo major, etiam cum alias est in Apogæo sui eccentrici. Sed de hac re vide quæ latiùs haber Clauius in Sharam Ioannis Sacro Bosco. 57. EPIGIVS ex Græco idem sonar, ac humi repens. Per translationem vsurparur ab Astronomis in Planeta, qui reperiatur in ima abside sui deferentis, vel Epicycli, in quo sit terræ proximior. 58. EPIMA in sphæra Barbarica dicitur secundus Decanus Capricorni manens sub dominatu Martis, præbens genium quærendi de rebus, quæ sciri non possunt, & sciscitandi de ijs, quæ ad finem perduci nequeunt. 59. EPITRION apud Prolomæum lib. 1. cap. 11. vbi agit de aspectibus signorum, idem sonat ac sesquitertium. 60. EPOCHA Græcè, Latinè radix. Est initium certi cuiusdam temporis apud antiquos, vnde incipiebar motus aliquis, aut rei computus numeraræ, vt Olympiades apud Græcos, ac indictiones & lustra apud Romanos. Significat etiam, reste Rhodigino, ascensiones planetarum in Zodiaco, positusque stellarum adinqvicem.
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ipso deferente, and its center moved eccentrically around the earth together with the eccentric orbit itself, and yet the body of the planet moved around it on its circumference, which was called the Epicyclis. And this third was attributed to all the planets except the Sun: although Ptolemy in the Almagest shows that the appearances in the Sun can be preserved by positing in it only an eccentric circle, or a concentric one with an epicycle, nevertheless he approves the eccentric more. For the planets sometimes appear larger, sometimes smaller; even at the same altitude above the horizon: sometimes they move more quickly, sometimes more slowly; sometimes they seem to stand still, sometimes even to go backward: all such things are of a kind that can neither be conceived nor explained except by eccentric orbits and epicycles. And since in the Sun we do not see such diversity of motion as is in the rest of the planets, which all, except the Moon, sometimes appear to stand still, sometimes to advance more swiftly, sometimes to move backward in the Zodiac; therefore in it we place indeed the two former circles, but remove the Epicyclis, without which we can most easily preserve its appearances. In the Moon, however, although no such diversity of motion is discerned as in the other five wandering stars, nor do you observe retrogression in the Zodiac; yet because, when placed in the same place of its own eccentric, namely in the Apogee or Perigee, it does not always have the same conformity of aspect; therefore it was necessary to conceive that, in the same place of its eccentric, it is nevertheless sometimes nearer to the earth, sometimes farther from it; which certainly we can by no means preserve unless we also posit in it one epicycle, in whose Apogee it appears smaller, in Perigee larger, even when otherwise it is in the Apogee of its eccentric. But on this matter see more fully what Clavius has in the Sharah of John of Holywood. 57. EPIGIVS, from Greek, means the same as creeping on the ground. By translation it is used by astronomers for a planet that is found in the lowest apse of its deferent or epicycle, in which it is nearest to the earth. 58. EPIMA in the Barbaric sphere is called the second decan of Capricorn, remaining under the dominion of Mars, and providing a disposition for seeking out things that cannot be known, and for inquiring into matters that cannot be brought to completion. 59. EPITRION, in Ptolemy book 1, chapter 11, where he treats of the aspects of the signs, has the same meaning as sesquitertian. 60. EPOCHA, in Greek, in Latin radix. It is the beginning of a certain fixed time among the ancients, from which some motion or numerical reckoning of a thing would begin, as the Olympiads among the Greeks, and the indictions and lustrums among the Romans. It also signifies, according to Rhodiginus, the ascensions of the planets in the Zodiac, and the positions of the stars relative to one another.
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186 LEXICON quidam ad terram simul, & ad erraticas stellas, & ad Solem, Lunam vel partes Zodiaci. Datis igitur his duobus familiaritatum generibus, statim elucet, quibus modis configurari possint planetæ, quæue sint harum configurationum differentiæ, < 5.> quas ingeniosè hausit Keplerus ex harmonicis chordarum consonantijs, quæ cùm sint octo, vnìsona, tertia minor, tertia maior, quarta, quinta, sexta minor, sexta maior, & octaua (vt experjri est in chorda subtensa, quæ in dictis tantum distantijs consonantiam habet) consequenter, tor etiam sint, necessè est, familiaritatum differentiæ quas possunt contrahere ad inuicem sidera in certa, ac determinata distantia, nempe Conjunctio, Sextilis, Quintilis, Quadratus, Trinus, Sesquicuadratus, Biquintilis, & Oppositio. Et quoniam radij siderum quidam sunt à centro sideris producti vsque ad oppositionem, quæ est diametralis, profectò exceptra conjunctione, & oppositione, omnes isti radij cùm hinc inde ad fidus proijciantur, & à dextris, & à sinistris, duplices sunt, ac proinde vna cum illis duobus quatuordecim genera familiaritatum inuenientur: quibus si adjungatur etiam duplex semiquadratus alter à dextris, & alter à sinistris, qui cùm participet rationem quadrati, in morbis habet vim indicandi de futura crisi, vt ego sæpiùs obseruaui, & testatur etiam Argol. de diebus criticis; vtiqve sexdecim omninò erunt, & constituent figutam sexdecim laterum: de qua sermo est in Centiloquio propos. 60. < 6.> Præterea adsunt antiscia, seu vt alij vocant paralleli tam primarij, quàm secundarij, tam in Zodiaco, quàm in Mundo; quæ cùm sit species quædam familiaritatis resultans ex æquidistantia, ac proinde pati astrorum potentia; conuenienter reducuntur ad conjunctionem, si ea quidem sint eiusdem declinationis, aut hemisphætij, atque ad oppositionem si diuersæ. Sed de hac re vide Titum in Cælesti Philosophia lib 2. cap. 2. nosque fusiùs agemus in V. Paralleli. < 7.> Favonius, ventus vnus ex quatuor Cardinalibus spirans ab occasu æquinoctiali, directè oppositus subsolano, sic dictus à favendo, quod cunctis faueat, vel potiùs à fouendo, quod omnia foueat: quippe qui temperie quadam caloris, & humidi cedit cunctis animantibus opportunus, ac salutatis. Vnde & Plinius eum Genitalem mundi spiritum nominat, quo planca hyberno frigore adusta remissum, animalia recreantur, & Venere m sobolis desiderio appetunt, & alibi, eo flante equas in Lusitania concipere testatur. Hinc jure à Græcis Zephyrus dicitur, hoc est vitam afferens. Spirar porissimum in Italia æstatis tempore lenissimè post Meridiem, adducens serenitatem ma-
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186 LEXICON certain to the earth at the same time, and to the erratic stars, and to the Sun, Moon, or parts of the Zodiac. Therefore, these two kinds of familiarities being given, it is immediately clear in what ways the planets may be configured, and what the differences of these configurations are, <5.> which Kepler ingeniously drew from the harmonic consonances of strings, which, since they are eight in number—unison, minor third, major third, fourth, fifth, minor sixth, major sixth, and octave (as can be experienced in a stretched string, which has consonance only in the said distances), consequently there must likewise be as many kinds, namely the differences of familiarities that the stars can contract with one another at fixed and determinate distances, namely Conjunction, Sextile, Quintile, Square, Trine, Sesquiquadrate, Biquintile, and Opposition. And since the rays of the stars are in some cases projected from the center of the star up to opposition, which is diametral, certainly, apart from conjunction and opposition, all these rays, when cast to a star on both sides, both to the right and to the left, are double; and therefore together with those two there will be found fourteen kinds of familiarities: to which if there is also added the double sesquiquadrate, one on the right and another on the left, which, since it participates in the nature of the square, in illnesses has the force of indicating a future crisis, as I have often observed, and as Argol also testifies in the critical days; certainly there will be sixteen in all, and they will form a figure of sixteen sides: of which there is discussion in the Centiloquium, proposition 60. <6.> Moreover, there are antiscia, or, as others call them, parallels, both primary and secondary, both in the Zodiac and in the World; and since this is a certain kind of familiarity resulting from equidistance, and therefore from the suffering power of the stars, they are fittingly reduced to conjunction, if they are of the same declination, or hemisphere, and to opposition if different. But on this matter see Titius in Celestial Philosophy, book 2, chapter 2; and we shall treat it more fully in V. Paralleli. <7.> Favonius, one of the four Cardinal winds, blowing from the western equinox, directly opposite Subsolanus, so called from favouring, because it favors all, or rather from nourishing, because it nourishes all: indeed, with a certain tempering of heat and moisture, it is fitting and salutary to all living creatures. Hence also Pliny calls it the generative spirit of the world, by which the plants, burned by winter cold, are refreshed, living creatures are revived, and they yearn for offspring with desire of Venus; and elsewhere he testifies that, with it blowing, mares in Lusitania conceive. Hence by the Greeks it is rightly called Zephyrus, that is, bringing life. It blows most especially in Italy in summer time, very gently after midday, bringing serenity ma-
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MATHEMATICVM. 187 ximam, cum non minori corporum salubriate. Hyeme verò niues, & pluuias generat, & quandoque etiam repentinis flatibus matia concurit, corporibusque humorum ingerit commotionem. FE FERA Lupus, bestia Centauri &c. in Tabulis Persicis Bride- <8.> mis, sidus in cælo ad australem plagam sub Centauto, constans stellis seu 19. vt vult Ptolemæus, seu 20. vt obseruasse testatur Keplerus, & Baierus, omnibus ferè de natura Saturni, & parum Martis; quarum præcipuæ duæ in posteriori pedes, tertiæ magnitudinis. Ex in horoscopo semper infaustæ sunt, ac malorum nunciæ, licet in nostro hemisphærio non oriantur, nisi tantùm duæ posiræ in extremo pedis sinistri, idque fiat ad modicum tempus & parùm suprà horizontem attollantur. Oriuntur enim Romæ cum gr. 2. & 12. Sagittatij, occiduntque cum gt. 7. & 25. Virginis. FERALIA, signa sunt quæ ferinam speciem referunt, qualia <9.> sunt Leo, & vltima pars Sagittarij, quibus annumerati possunt & sidera extrà Zodiacum, vt Lepus, Centaurus, &c. Quibus non ab re hoc nomen inditum, seu potiùs adjecta ferarum forma; quia videlicet nescio quid cum illis habent affine: bestiis illis præsunt, in hominum genituris aut feram edi, aut ferinam naturam ingerunt; præsertim si luminaria in ipsis reperiantur, & in cardinibus duo malesici, vt notat Ptolemæus lib. 3. cap. 8. FERALIS, apud Astronomos dicitur planeta, quando fuerit 10: <10.> in loco, vbi nullam cum reliquis familiaritatem habet: quod quidem maximum est detrimentum, & potissimè arrenditur in Luna, quæ proinde in eo casu appellatur Agrestis, cursu vacua, &c. FERDARIÆ, Vide Fridaria. 11. FI FICARES, apud Babylonios nuncupatur Cepheus, constellatio <12.> in firmamento prope Bootem, quod vocabulum apud nos idem sonat ac succensus. FIDICVLA Lyra, Vultur cadens, &c. dicitur sidus in cælo 13: <13.> ad borealem plagam ferè verticalis Italiæ, constans apud Ptolemæum stellis tantummodò decem, quot videlicet chordæ sunt in Lyra, seu Spalterio decachordo. At verò Keplerus in eo considerat stellas 11. & Baierus adhuc 13 quæ omnes sunt de natura Veneris, & Mercutij. Inter has præcipua est quæ proprio nomine apud Arabes appellatur Vega, Vagiah, & Brinek, seu Brinett, fixarum omnium (excepto Sitio) maxima, & fulgentissima, existens nunc in gr. 11. Capricorni cum declin-
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MATHEMATICVM. 187 as to the zenith, with no less salubrity of bodies. In winter it produces snow and rains, and sometimes even with sudden gusts it stirs up the air, and brings disturbance to bodies’ humors. FE FERA Lupus, the beast of Centaurus, etc., in the Persian Tables Bride- mis, a star in the sky toward the southern region under Centaurus, consisting of stars, either 19, as Ptolemy says, or 20, as Kepler and Bayer attest to have observed, almost all of the nature of Saturn, and somewhat of Mars; the two principal of which are in the posterior feet, of the third magnitude. From a horoscope they are always inauspicious, and messengers of evil, although in our hemisphere they do not rise except only the two placed at the end of the left foot, and that only for a short time and when they are raised only a little above the horizon. For in Rome they rise with gr. 2 and 12 of Sagittarius, and set with gt. 7 and 25 of Virgo. FERALIA, are signs which present a wild-beast appearance, such as Leo and the last part of Sagittarius, to which may be added the stars outside the Zodiac, such as Lepus, Centaurus, etc. The name was not wrongly given to them, or rather the shape of beasts was added; because, namely, they have something akin to them: those beasts govern, in men’s nativities, either producing a wild beast or imparting a bestial nature; especially if the luminaries are found in them, and in the angles two malefics, as Ptolemy notes book 3, ch. 8. FERALIS, among astronomers, is said of a planet when it is in a place where it has no familiarity with the rest: which is indeed a great detriment, and is especially noticed in the Moon, which in that case is called Agrestis, course-vacant, etc. FERDARIAE, see Fridaria. 11. FI FICARES, among the Babylonians is the name of Cepheus, a constellation in the firmament near Bootes, a word which among us means the same as “kindled” or “set on fire.” FIDICVLA, Lyra, Vultur cadens, etc., is called a star in the sky toward the northern region, almost vertical to Italy, consisting according to Ptolemy of only ten stars, namely as many as there are strings in the Lyre, or ten-stringed psaltery. But Kepler considers in it 11 stars, and Bayer still 13, all of which are of the nature of Venus and Mercury. Among these the principal is the one which by its proper name among the Arabs is called Vega, Vagiah, and Brinek, or Brinett, the largest and brightest of all the fixed stars (except Sirius), existing now at gr. 11 of Capricorn with declin-
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188 LEXICON natione boreali, grad. 35. quî fir, vt jam modo sit verticalis Siciliæ, quod maximè aduerrendum. Ea partiliter in secunda domo, aut cum loue, Venere, & parte fortunæ reperta immensas diuitias pollicetur; sicut etjam in medio cæli magnam fortunam in honoribus, atque in opificio. Vide amplius eius decreta in horoscopo sub V. Lyra. 14. FIGVRA ex Euclide lib. 1. d. 14. definitur esse quantitas, quæ sub aliquo, vel aliquibus terminis clauditur. Quantitas enim secundùm variam extemorum positionem, vatiam etiam dicitur figuram subire, etsi alioqui in seipsa inuariata remaneat: vnde intelligitur aduenire quantitati jam in suo genere constitutæ, quoniam illam modificat, facitque vt extensio parrium, quam alias ex se haber quantitas, seruet aliquem ordinem in partibus ritè dispositis, vnde se habet per modum qualitatis afficiens illas, ac superficiei terminum dicens. Hinc figura angularis, lateralis, rectilinea, curuilinea, triangularis, quadrangularis, solida, plana &c. de quibus suo loco. 15. FIGVRÆ Isoperimentra apud Geometras sunt duæ, vel plures figutæ, quæ ad inuicem comparatæ perimetros, id est circumferentias habent æquales. Deriatur enim hoc vocabulum à Græco isos quod est aquale; peri quod est circum & Metros quod est Mensura: quasi figutæ æqualium circumdantium mensuratum. Hinc figuræ omnes, quæ æquales ambitus continent Isoperimetra sunt. Vt quadratum sex pedes habens in ambitu, dicitur Isoperimentum triangulo siue rectilineo, siue curuilineo, siue mixto, quod pariter sex pedes habeat in circuitu: ita ut quatuor lineæ quadrati ambitum constituentes, si in vnam, eandemque lineam aprentur, inueniantur æquales tribus rectis lineis trianguli, aut lateribus omnibus cuiuscunque figuræ in rectum quoque & continuum positis. Plura qui volet, consulat Clauium in Euclidem, qui easdem delineatas exhibet oculis conspiciendas. 16. FIGVRA sexdecim laterum, est complexus omnium aspectuum, seu radiorum, quos ab vno puncto in quo est significator in principio morus, acquirere potest, dum per suam realem viam incedit, quousque torum circulum compleat, atque ad eundem locum radicalem redeat, in quo erat ab initio motus. Iius potissimum menzionem facit Ptolemæus, siue quicumq; alius sit auctor Centiloquij in Verbo 60. monens, in morbis dijudicandis considerandam esse Lunæ peragrationem in figura sexdecim laterum; & prout ea ibi benè vel malè fuerit affecta, præcipir, benè, vel malè de morbo pronuntiandum. Et sanè inde exorti critici dies, dectetorisque: sicut etiam indicatiui, quos sedulò obseruant ex Hippocratis
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188 LEXICON in the northern sign, 35th degree, which is such that it is now vertical to Sicily, which is especially to be noted. If it is partly in the second house, or with Jupiter, Venus, and part of Fortune, it promises immense riches; likewise also in the midheaven great fortune in honors and in work. See more of its decrees in the horoscope under V. Lyra. 14. FIGURE, from Euclid, book 1, def. 14, is defined as a quantity which is enclosed under some one or several boundaries. For quantity, according to the various position of its extremities, is also said to assume various figures, although in itself it remains unchanged: whence it is understood to belong to quantity already constituted in its own kind, since it modifies it and makes it so that the extension of the parts, which quantity otherwise has of itself, preserves some order in the parts duly arranged, whence it stands in the manner of a quality, affecting them, and setting the boundary of the surface. Hence angular, lateral, rectilinear, curvilinear, triangular, quadrangular, solid, plane, etc., figures, of which in their place. 15. ISOPERIMETER FIGURES among geometers are two or more figures which, when compared with one another, have equal perimeters, that is, circumferences. For this word is derived from the Greek isos, which means equal; peri, which means around; and metros, which means measure: as if figures measured by equal circumferences. Hence all figures which contain equal bounds are isoperimeters. Thus a square having six feet in perimeter is called isoperimetric with a triangle, whether rectilinear, curvilinear, or mixed, if it likewise has six feet in circumference: so that the four lines constituting the perimeter of the square, if stretched into one and the same line, are found equal to the three straight lines of the triangle, or to all the sides of any figure likewise placed in a straight and continuous line. Whoever desires more should consult Clavius on Euclid, who presents the same figures drawn for the eye to behold. 16. FIGURE of sixteen sides is the complex of all the aspects, or rays, which from one point in which the significator is at the beginning of the motion, it can acquire while proceeding by its real course, until it completes the entire circle and returns to the same radical place in which it was at the beginning of the motion. Of this Ptolemy makes particular mention, or whoever else may be the author of the Centiloquium in Saying 60, warning that in judging diseases one must consider the Moon’s passage in the sixteen-sided figure; and according as it shall there be well or badly affected, one must pronounce well or badly upon the disease. And indeed from this there arose the critical days, and the prognostic ones: likewise the indicative, which they diligently observe from Hippocrates
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MATHEMATICVM. 189 præceptis Medici peritiores, ex Lunæ uidelicet peragratione ad loca quæ aliquam habeant configurationem cum loco radicali, in quo erat initio morbi. Igiturum sexdecim positus habere potest Luna ad locum suum radicalem, prout totidem sunt genera familiarisatum, quæ contrahere possunt ad inuicem sidera, & non ita pridem detexit Keplerus, atque ex modulis harmonicis confirmavit. Ea sunt sextilis per distantiam 60. graduum, seu sexiæ partis circuli. Simiquadratus per distantiam 45. graduum seu per octauam patrem circuli. Quintilis per quintam partem, & distantiam gr. 72. Quadratus per integrum quadrantem 90. graduum. Trinum per iertiam partem, & gr. 120. Sesquiquadratus per distantiam trium ex octo partibus, hoc est per gr. 135. Biquintilis, per distantiam duarum ex quinque partibus, hoc est per gr. 140. ac tandem oppositio, quæ est distantia semicirculi, & gr. 180. quæ vice versa iterum dextrorsum numerata, & loco oppositionis, si addatur reditus Lunæ ad locum suum radicalem, profecto inuenientur omninò sexdecim, quæ constituunt figuram hanc sexdecim laterum, cuius peragrationem obseruandam in Luna præcipit centiloquij Auctor ad morborum judicium proferendum. Porrò ex his aspectibus, alij boni sunt, alij mali. Mali, semiquadrati, quadrati, sesquiquadrati, & oppositio sicut etiam reditus, seu conjunctio cum loco suo radicali. In bonis, ac benignis aspectibus morbi non accipiunt incrementum; inimo potius natura vires ad illum pellanduni: in malis è contrà morbus reuiuiscit, & aduersus naruram, ijsdem ferè armis, quibus prius eam oppugnauerar, vitibus auctus insurgit. Inde conflictus, & pugno, vnde judicium pendet, atque sentenria, quam Græci crisim appellant. Hinc dies critici, atque indicatiui omnes infausti, quibus Luna ad suos hostiles radios peruenit. Et si quidem natura ob præcedentes radios ad suum locum benignos inueniatur ità uiribus roborata, vt in die critico sustinere possit insultum; pugna, & crisis in bonum cedet; sin minus, præualebit morbis, ipsaque prosternetur. Quoniam autem seuquadrati, & sesquiquadrati imperfecti radij sunt, & perfectorum ptodromi, (sunt enim quadrati, & oppositionis participatio,) ideò vera crisis accidir in quadratis, oppositione, & reditu Lunæ ad locum suum radicalem: diesque illi, in quibus accidit, dicuntur absolure critici, & indicatiui; ij vetò in quibus Luna peruenit ad suos semiquadratos, & sesquiquadratos, dicuntur rantum indicatiui, eoquia sunt veluti indicium pugnæ critico die futuræ. Ideò rectè monet centiloquij auctor in morbiis, inspiciendos esse, nedum críticos dies, sed & reliquas Lunæ peragrationes in figura sexdecim laterum, quo-
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MATHEMATICVM. 189 by the precepts of the physician, more experienced, namely from the Moon’s passage to those places which have some configuration with the radical place, in which it was at the beginning of the illness. Therefore the Moon can have sixteen positions with respect to its radical place, just as there are the same number of familiarities which the stars can contract with one another, and which not long ago Kepler discovered, and confirmed by harmonic ratios. These are the sextile, by a distance of 60 degrees, or one sixth of the circle. The semisquare by a distance of 45 degrees, or one eighth of the circle. The quintile by one fifth part, and a distance of 72 degrees. The square by the whole quadrant, 90 degrees. The trine by one third part, and 120 degrees. The sesquiquadrate by a distance of three out of eight parts, that is, 135 degrees. The biquintile, by a distance of two out of five parts, that is, 140 degrees; and finally the opposition, which is the distance of a semicircle, 180 degrees, which conversely again, counted rightward, and in place of opposition, if the Moon’s return to its radical place be added, certainly there will be found altogether sixteen, which constitute this figure of sixteen sides, whose passage the Author of the Centiloquium bids us observe in the Moon for giving judgment on diseases. Moreover, of these aspects, some are good, others bad. Bad are the semisquares, squares, sesquiquadrates, and opposition, as also the return, or conjunction with its radical place. In good and benign aspects the diseases do not gain increase; indeed rather nature brings forth strength to drive it away: in bad aspects, on the contrary, the disease revives, and against nature, with nearly the same weapons by which previously it had attacked her, strengthened by forces it rises up. Hence conflict, and battle, from which judgment depends, and the sentence, which the Greeks call crisis. Hence critical days, and indicative ones, all unlucky, on which the Moon reaches its hostile rays. And if indeed nature, because of the preceding rays, is found so strengthened in its favorable place with forces that it can withstand the assault on the critical day; the battle and crisis will turn to good; if not, the disease will prevail, and it itself will be overthrown. But since the semisquares and sesquiquadrates are imperfect rays, and the forerunners of the perfect ones, (for they are participation in the square and opposition,) therefore the true crisis occurs in the squares, opposition, and return of the Moon to its radical place: and those days in which it occurs are called absolute critical and indicative days; but those days in which the Moon reaches its semisquares and sesquiquadrates are called only indicative, because they are as it were an indication of a battle that will occur on the critical day. Therefore the author of the Centiloquium rightly warns that in diseases, not only critical days should be examined, but also the remaining passages of the Moon in the figure of sixteen sides, in which-
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190 LEXICON niam ex aliorum aspectuum ratione collegi potest, quintæ sint naturæ vires, quantæ etiam morbi, vnde judicium proferri possit, quis tandem succumbere, quis præualere debeat: Ex quibus habes male pronunciasse Gallucium in theatro mundi & temporis, nec- non Henricum Alstedium in sua Enciclopedia, figuram hanc diuidendam esse in sexdecim latera æqualia: non enim in æqualibus spatijs, sed in configuratione consistit hæc vis, vt ipsimet notant. <17.> FINIS, seu, Termine apud Astronomos sunt certi quidam limites, & partes signorum Zodiaci, in quibus planetæ ratione habitudinis ad suas domos habent certam prærogatiuam, ac dignitatem, quæ vna est ex quinque essentialibus. Alij sunt apud Ægyptios, alij apud Ptolæmeum: sed magis probantur qui apud Ægyptios atque eorum distributionis convenientissimam rationem affert. Titus in cælesti Philosophia. Portò tabulam terminorum, tam secundum Ægyptios, quam secundum Ptolomæum hic non exscribo, quoniam ea passim obuia est apud omnes scriptores. <18.> FINITOR apud Latinos audit quod Græci horizontem appellant: Circulum nempe maximum in sphera dirimentem superius hæmisphærium ab inferiore, inde dictum, quod visum finiat: Comprehendit enim quidquid supra terram visibile est; ita ut quæ sidera ad finitorem Orientalem pertingunt, dicantur oriri, quæ verò Occidentalem tenent, occidere. Duplex est alter rationalis, seù naturalis, alter sensibilis: Primus diuidit sphæram seù totum cælum in duas partes æquales; vt proinde si concipiatur aliqua superficies eum terminans, ea transire debeat per centrum terræ: secundus est circulus conceptus ad terræ superficiem elevatus, ita ur cum ea vnam planitiem efformare concipiatur; comprehendatque totum id, quod remotis omnibus impedimentis, oculorum acies circumducta conspicere potest. Sed de hac re vide Fusius in Verbo Horizon. Ab alijs dicitur etiam Finiens. <19.> FIRMAMENTVM dicitur communiter octauus otbis, & cælum stellarum, in quo stellæ omnes inerrantes fixæ sunt, atque in varios Asterismos tributæ. Nouem hausit ab eo, quod sit quasi firmamentum ac vallum, vel sanè quia in eo sidera firmiter semper adhærent, nec locum permutant in eo, sicut eandem ob causam ipsæ stellæ fixæ dicuntur, vt mox infra. Alij inter quos Blacanus, illud existimant dictum ab firmitate, seu soliditate qua præditum esse credunt: sic enim inquit Blacanus lib. 8. cap. 6. de mundi fabrica. Si qua pars cali duritæ, ac firmitate prædita est, proculdubio erit firmamentum: Videmus enim stellas in eo affixas atque ad inuisem immotas, omnes
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190 LEXICON from the reasoning of other aspects one can gather what the forces of the fifth nature are, as well as what the diseases are, from which a judgment may be made as to which must finally yield and which prevail: From these you have that Gallucius in the theater of the world and of time, and also Henricus Alstedius in his Encyclopedia, have wrongly stated that this figure must be divided into sixteen equal sides: for this power does not consist in equal spaces, but in configuration, as they themselves note. <17.> FINIS, or Termini among the astronomers are certain limits, and parts of the signs of the Zodiac, in which the planets, by reason of their relation to their houses, have a certain prerogative and dignity, which is one of the five essentials. Some are according to the Egyptians, others according to Ptolemy; but those are more approved which are found among the Egyptians, and Titus in Celestial Philosophy gives the most fitting reason for their distribution. Moreover, I do not transcribe here the table of terms, both according to the Egyptians and according to Ptolemy, since it is commonly found among all writers. <18.> FINITOR among the Latins is what the Greeks call the horizon: namely, the great circle in the sphere dividing the upper hemisphere from the lower, so called because it limits sight: for it comprises whatever is visible above the earth; so that the stars reaching the eastern boundary are said to rise, while those occupying the western are said to set. There are two kinds, one rational, or natural, the other sensible: the first divides the sphere, or the whole heaven, into two equal parts; so that if some surface be conceived as bounding it, that surface must pass through the center of the earth: the second is a circle conceived as raised above the surface of the earth, so that it is imagined to form one plane with it; and it encompasses all that, with all impediments removed, the range of the eyes can perceive when they are turned around. But on this matter see Fusius in the word Horizon. It is also called by others Finiens. <19.> FIRMAMENTVM is commonly called the eighth orb, and the heaven of the stars, in which all the wandering stars are fixed, and distributed into various Asterisms. Nouem derived it from the fact that it is, as it were, a firmament and rampart, or indeed because the stars in it always adhere firmly and do not change their place there, just as for the same reason the fixed stars themselves are said to be fixed, as noted below. Others, among whom is Blacanus, think it is so called from the firmness, or solidity, with which it is believed to be endowed: thus Blacanus says in book 8, chapter 6, of the fabric of the world. If any part of the heaven is endowed with hardness and firmness, it will doubtless be the firmament: for we see the stars fixed in it and immovable to our view, all
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MATHEMATICVM. 201 bus mundi, vnde etiam sunt configurationes ad horoscopum. Quare sicuti Sol non habet configurationes ad horoscopum nisi in mundo acceptos, ita & Luna non habet configurationes ad partem forunæ, nisi tantùm in mundo. Ex his liquidò constat, quomodo supputanda sit pars fortu- < 38.> næ quod pluribus modis fieri potest: faciliùs tamen, & sem- per eodem modo, si sumatur vera distantia Solis ab horoscopo per ascensiones Climatis, auferendo semper ascensionem obli- quam Solis sumptam in eleuatione horoscopi ab ascensione obliqua ipsius horoscopi, & quæ superest differentia addatur ascensioni rectæ Lunæ, nam vbi cadit numerus graduum pro- ductorum in ascensionibus rectis, cum declinatione Lunæ, & numero, & regione eadem, ibi erit ascensio recta, & verus locus partis forrunæ, siue ea cadat in Zodiaco, siue extra, quod parum refert, quandoquidem in hoc casu Zodiacus materiali- ter se habet, & perinde est, ac si non esset. Locetur autem in exleisti figura vbi cadit talis ascensio recta, cum tali declina- tione. Quod si cui placeat, & locum illi in Zodiaco date, tam in < 39.> longum quàm in latum, id fiat per rabulas sinuum, quærendo quis gradus Zodiaci respondeat tam in longum, quàm in latum ad datam ascensionem rectam cum tali declinatione, eo pror- sus modo, ac practicatur in stellis fixis. Similiter directiones partis forunæ vtroque motu, & recto, < 40.> & conuerso fieri possunt ad familiaritates astrorum acceptas tantum in mundo: Recto quidem, si pars forunæ considere- tur immobilis in suo circulo horario, siue positionis expectans siderum corpora & aspectus, quæ ad ipsam motu vniuersitatis ferantur: Conuerso verò, si constituantur sidera, & aspectus occurssantes, immobiles, arque interim sors motu raptus ad eadem deuoluantur. Eius significata vide in V. horoscopus Lu- naris. Pari ratione, & aliæ partes quinque extrahi possunt pro nu- < 41.> mero reliquarum quinque erraticarum, quæ nihil aliud sunt quàm singulorum planetarum horizontia, & loca in situ mundi considerata, vnde emergunt planeræ, quando Sol emergit ab Oriente, ita vt eam semper habitudinem habeant isti planeræ ad suas partes, quam Sol ad suum horoscopum, acceptam in suis cuiusque parallelis eo prorsus pacto, ac dictum est de Luna, quæ proinde eandem habebunt declinationem, ac planetæ vnde extrahuntur. Hac sanè consideratione habita, non omninò inanes fortè reperienur partes ab Arabibus excogitatæ, & sin- < 42.> gulis rerum significationibus attributæ; licet quæ passim cir- cumferantur, & inanes sint & fictitiæ, tum quia extrahuntur
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MATHEMATICVM. 201 ...of the world, whence there are also configurations to the horoscopos. Wherefore, just as the Sun has no configurations to the horoscopos except those accepted in the world, so also the Moon has no configurations to the part of fortune except only in the world. From these things it is clearly established how the part of fortune should be computed, which can be done in several ways; more easily, however, and always in the same way, if the true distance of the Sun from the horoscopos is taken by the ascensions of the climate, always subtracting the oblique ascension of the Sun, taken at the elevation of the horoscopos, from the oblique ascension of the horoscopos itself, and the difference that remains is added to the Moon’s right ascension; for where the number of degrees produced in right ascensions falls, together with the Moon’s declination, and with the same number and region, there will be the right ascension and the true place of the part of fortune, whether it falls in the Zodiac or outside it, which matters little, since in this case the Zodiac is only material, and it is as though it were not. But let it be placed in the displayed figure where such a right ascension falls, with such a declination. If anyone prefers, however, that a place be given to it in the Zodiac, both in length and in breadth, let this be done by means of sine tables, by asking which degree of the Zodiac corresponds, both in length and in breadth, to the given right ascension with such a declination, in precisely the same way as is practiced for fixed stars. Similarly, the directions of the part of fortune, in both motions, both direct and converse, can be made to the familiarities of the stars accepted only in the world: direct, indeed, if the part of fortune is considered immobile in its own hour circle, or circle of position, waiting for the bodies and aspects of the stars, which are carried toward it by the motion of the universe; conversely, if the stars and aspects are set as meeting, immobile, while in the meantime fortune, carried along by motion, is rolled toward them. See its significations in V. horoscopus Lunaris. In like manner, the other five parts can also be drawn out for the number of the remaining five wandering stars, which are nothing other than the horizons of the individual planets, and places considered in the state of the world, whence the planets emerge, when the Sun emerges from the East, so that these planets always have toward their own parts the same relation which the Sun has to its horoscopos, taken in each of their own parallels, in precisely the manner already said of the Moon, and therefore they will have the same declination as the planets from which they are extracted. Having truly made this consideration, perhaps the parts devised by the Arabs and attributed to the significations of individual things will not be found altogether empty; although those commonly circulated are both empty and fictitious, partly because they are extracted...
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LEXICON in partibus Zodiaci, qui hac in re locum non habet, tum etiam quia plures singuntur quam numerus planetarum postulet, atque accipiuntur à domibus ad planetas, & è contrà, vel etiam à planeta ad planetam, cùm reuerà tantum per habitudinem ad Solem accipiendæ sint, nec aliud esse possint, quàm ea habirudo planetæ ad locum vnde discesserat, Sole in Oriente constituto, quam habet Sol ad ipsum Orientem, vnde manè emerserat. Igitur ad calculandas istas partes accipiatur semper distantia Solis ab horoscopo, vt de fortunæ parte dictum est, eaque adijciatur ascensioni rectæ planetæ, cuius horoscopum quærimus, nam locus productus erit ascensio recta illius partis, & verus horoscopus planetæ quem quærimus, habens eandem declinationem planetę, cuius est pars, dirigendus eodem modo, ac diximus de parte fortunæ pro suis cuiusque significatis. FOVEA, Græcis Ipogon dicitur ab Astronomis quarta pars domus ab horoscopo & cardo Imi cæli ab inferiore situ, & loco; ac potissimè eò quod sit veluti fouea planetarum, vt proinde non ab re ab aliquibus constituatur inter præcipuos An[n]eretas, ad cuius lineam directus vitæ significator, seu ascendens, seu luminare in ascendente repertum, vltimam vitæ periodum faciat. Quod tamen ego ex Titi placitis haud probare possum, quippe erius consideratio sit tantùm in mundo, neque aut cardo Imi cæli, aut ascendens loco mouetur, vt alter in alterum impingat, neque moderatores planetæ motu suo reali, qui est idem ac primi mobilis ferri possunt ab Oriente ad Ium cæli, quin transeant prius per medium cæli & occasum: quem enim motum habent ad partes Orientaliores est cuique proprius in Zodiaco, cuius respectus materialiter tantùm habetur ad cardines mundi, ac perinde est, ac si non esset. Sed de hac re alibi satis. Cæterùm huius domus significata vide in V. Ium cæli. FRACTIONES dicuntur ab Arithmeticis, atque etiam ab Geometris partes minimę aliarum partium quantitatis, seu continuæ, seu discretæ. Vt sunt minuta in gradibus, secunda in minutis; terria in secundis &c. De modo eas inueniendi ex radice quadrata, lege lunctinium in Commentar. ad spæram Io. de Sacrobosco pag. mihi 360. FRIDARIE, seu Afridarie apud Arabes est quædam temporaria potestas planetarum participantium cum domino decenniorum in gubernatione vitæ nati, ita vt si natiuitas sit diurna, primum decennium sibi vendicet Sol, cum participatione tamen aliorum planetarum per septimam partem, hac videlicet ratione vt Sol gubernet solus septimam partem decennij, quæ comprehendit vnum annum solarem, mens. 5. & dies circiter qua-
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LEXICON in partibus of the Zodiac, which in this matter has no place, and also because more are assigned than the number of the planets requires, and they are taken from houses to planets, and conversely, or even from planet to planet, whereas in truth they are to be taken only by relation to the Sun, and can be nothing else than that relation of the planet to the place from which it departed, the Sun being placed in the East, which the Sun has to that same East from which it rose in the morning. Therefore, in calculating these parts, let the distance of the Sun from the horoscope always be taken, as was said of the Part of Fortune, and let this be added to the right ascension of the planet whose horoscope we seek; for the resulting place will be the right ascension of that part, and the true horoscope of the planet we seek, having the same declination as the planet whose part it is, is to be directed in the same way as we said of the Part of Fortune, according to the significations of each. FOVEA, called Ipogon by the Greeks, is, according to the astronomers, the fourth part of the house from the horoscope and the cardo of the lower heaven from the lower position and place; and especially because it is as it were the pit of the planets, so that therefore it is not without reason placed by some among the chief Anaretæ, toward whose line, if the significator of life, whether the ascendant or the luminary found in the ascendant, be directed, it makes the last period of life. This, however, I cannot approve from the teachings of Titius, since its consideration is only in the world, and neither the cardo of the lower heaven nor the ascendant is moved in place, so that one should strike into the other, nor can the planetary rulers by their real motion, which is the same as that of the primum mobile, be carried from the East to the lower heaven without first passing through the midheaven and the setting point: for that motion which they have toward the more eastern parts is proper to each in the Zodiac, and in relation to which they are considered materially only with respect to the cardines of the world, and therefore it is as if it were not. But enough about this elsewhere. In any case, see the significations of this house under V. Ium cæli. FRACTIONS are called by arithmeticians, and also by geometers, the smallest parts of other parts of quantity, whether continuous or discrete. Such are minutes in degrees, seconds in minutes, thirds in seconds, etc. For the method of finding them from the square root, read Lunctinium in the Commentary on the Sphere of John of Sacrobosco, page 360 in my copy. FRIDARIE, or Afridarie among the Arabs, is a certain temporary power of the planets participating with the lord of the decennials in the governance of the life of the native, so that if the nativity is diurnal, the Sun claims for itself the first decade, with the participation however of the other planets by a seventh part, namely in this way: that the Sun governs alone a seventh part of the decade, which contains one solar year, 5 months, and about days like-
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MATHEMATICVM. 205 Olim multa fuit de hoc Circulo disceptatio: Aristoteles 5. illum volebat in aëris regione consistere; sed id falsitatis euincitur; quippe hac ratione non semper cerneretur ex qua- cunque terræ plaga transire per easdem stellas firmamenti, vt patet de ignitis cometis, qui in aëre generantur. Alij opinati sunt esse partem firmamenti continuam, cæteris densiorem, ita ut Solis lumen accipere possit, non tamen ità densam, vt fixæ. Sed tamen nostro æuo ferè in compertissimo est, cum aliquid non esse, quam congeriem plurium stellularum in- uicem collucentium, quæ ob multitudinem, vicinitatem, exilitatem, atque ob oculis nostris distantiam distinctè con- spici nequeunt, sed apparent, vt confusa quædam nubes subalbicans, eo modo quo sunt duæ nubiculæ ad polum An- tarcticum, atque omnes stellæ, quas dicimus nebulosas, & nunc ope Telescopij, ac testimonio nuntij siderei scimus esse plures stellas in vnum colligatas. Roberatur id eò potissimum, quod noua Phænomena in cælo enata non nisi in Galaxia visa sunt; vt noua stella quæ in sede Cassiopeæ anno 1572. appa- ruit, ac duos integros annos durauit; quæ item anno 1600. visa est in pectore Cygni, ac postea sensim euanuit, relicto in loco vbi erat quodam hiatu, qui etiam nùm visibilis est, ac taudem quæ anno 1604. in genu Serpentarij clarè enituit, & post annum discessit. Preterquam idipsum etiam credendum existimo de septima Pleiadum, quæ non nisi statis tempori- bus etiam lippis oculis se conspicabilem reddit, quæ cætero- qui ità latet, vt ab aliquibus cælo gratis affixa credatur. Qua- propter haud imprababile est, eas aliud planè non extritille, quam plures stellulas loco dimotas, atque in vnum collectas ad certum tempus, ex quo vnum numero Astrum in tanta di stantia peruisus illusionem æstimaretur: idque maximè locum habet si cælum ipsum cum Tychone ponamus fluidum, per cuius expansum facilè concipi possit vagus iste minutarum stellatum discursus. Porrò Galaxia varios & miros habet ef- fectus, quorum plurimos refert Plinius lib. 18. cap. 29. GALGAL Hammasaloth teste Kirchero in Oedipo Ægyptia- <6.> co dicitur apud Hebreos Zodiacus, hoc est sphæra signo- rum: GALLINA, Olor, &c. fidus in cælo intrà Galaxiam consti- <7.> tutum. Vide in V. Cygnus. GARBINVS vulgò Italorum dicitur ventus vns ex quatuor <8.> intermedijs spirans ex æquo inter meridiem & occasum. Gix- cis Notolybicus, vide eius qualitates sub hoc Vocab. GAVDINM apud Astronomos est species quædam dignitatis, <9.> & fortitudinis planeris accidens ab extrinsecio, cum profecto
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MATHEMATICVM. 205 There was once much dispute about this Circle: Aristotle wanted it to stand in the region of the air; but that is proved false, since by that reasoning it would not always be seen to pass from any part of the earth through the same stars of the firmament, as is evident from fiery comets, which are generated in the air. Others thought it to be a continuous part of the firmament, denser than the rest, so that it could receive the Sun’s light, yet not so dense as the fixed stars. But in our age it is almost certainly known that it is not one thing, but a gathering of many little stars shining on one another, which, because of their multitude, proximity, smallness, and their distance from our eyes, cannot be distinctly perceived, but appear as some confused whitish cloud, in the same way as the two little clouds near the Antarctic pole, and all the stars which we call nebulous; and now, with the aid of the Telescope and the testimony of the stellar messenger, we know that there are many stars gathered into one. This is especially confirmed by the fact that new phenomena arising in the sky have been seen only in the Galaxy; such as the new star which appeared in the seat of Cassiopeia in the year 1572 and lasted a full two years; likewise the one seen in the breast of Cygnus in the year 1600, and afterward gradually faded away, leaving in the place where it was a certain gap, which is still visible; and also that which in the year 1604 shone clearly in the knee of Serpentarius, and after a year departed. Besides this, I think it must also be believed concerning the seventh of the Pleiades, which reveals itself to sight only at fixed times, even to weak eyes, and otherwise lies so hidden that by some it is believed to be fixed in the sky for no reason. Wherefore it is not improbable that they brought forth nothing else than many little stars moved from their place and gathered into one for a certain time, from which one star in number, at such a great distance, would be judged by the illusion of sight: and this especially holds if, with Tycho, we suppose the sky itself to be fluid, through whose expanse that wandering course of minute stars may easily be conceived. Moreover, the Galaxy has various and remarkable effects, many of which Pliny recounts in book 18, chapter 29. GALGAL Hammasaloth, according to Kircher in Oedipus Aegyptiacus, is called among the Hebrews the Zodiac, that is, the sphere of the signs: GALLINA, Cygnus, etc. a fixed star situated in the sky within the Galaxy. See under V. Cygnus. GARBINVS is the name commonly used by the Italians for a wind blowing from one of the four intermediate directions, equally between south and west. Gixcis Notolybicus; see its qualities under this word. GAVDINM among astronomers is a certain kind of dignity, and an accidental strength belonging to the planets from an external source, when indeed
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108 LEXICON < 14.> Losophi definiere Naturæ caloris permanentiam vel sensitivi spiritus operationem. Ideò aliqui instans natuitatis dixerunt punctum exitus nati ex vtero: Verum quia id successuè fit, & per partes, ita vt quandoque integræ horæ labantur, sæ pè etiam integrum diem fætus consistat per dimidium sui corporis intrà vterum Matris, per reliquam medietatem extrà, adhuc sub quæstione erit, quale dicendum sit verum natiuitatis momentum, ad quod cæleste thema etigi debeat. Titus in Cælesti Philosophia more suo erudissimi rem expendens, reiectis aliorum sententijs, ex intimis Philosophiæ principijs concludit id esse, cum fætus incipit fieri independens à sua causa proxima, proindeque destitui eius ministerio, & immediaro influxu. < 14.> Sed id etiam exploratum habere, perdifficile est. Perpensis igitur singulorum opinionibus, mihi maximè arridet opinio Cardani dicentis tunc puerum nasci dicendum, cum primum aerem per os respirare incipit extrà matris vterum. Quandoquidem cum vitæ principalis operatio sit halitus, vnde viuens sustentatur, & quo deperdito, vita sinitur, id iure optimo dicendum erit vitæ principium, quo quis non genitricis ope, sed suo Marte incipit respirationis beneficio frui, atque aërem illum haurire, qui cum ob sui facilitatem, subtilitatem, & continui (nisi etiam materiei velimus dicere) vnitatem, præstò sit ad cælorum impressiones suscipiendas, iure spiritus Mundi, ac cælestium qualitatum vehiculum appellatur. Quaproptet etsi puer non adhuc ex vtero Matris emersus sit, modo caput extra illum habeat, & respirare incipiat, sat est, vt viuere dicatur, atque in lucem editus. Econttâ, sit quamuis extrà vterum positus, lotus, pannis inuolutus &c. nunquam propriè viuere dici poterit, donec prima vitæ semina excipiat, adeoque cælorum influxus per aeris aspirationem non illi communicentur. Atque hæc de hoc argumento satis. Hinc. < 15.> GENETLIACVM dicitur quod ad Genesim spectat; quique ex natalitio themate de hominum vita fortunaque pronunciant, Genethliaci appellantur. < 16.> GENIGVLATOR, seù Ingeniculus dicitur Hercules Græco nomine Engonasis, fidus in cælo ad Borealem plagam, sic dictum, quod eius imago representet hominem in genua pronolutum, atque altero pede erecto Draconis caput gestientem opprimere. De eo vide iam dicta in V. Engonasis, ac dicenda in Hercule. < 17.> GENNA, teste Othone dicitur ab aliquibus Luna, cum post conjunctionem cum Sole recessit ab eo per grad. 15. vel sanè 17. quantum videlicet sufficit, vt è radijs ipsius emergat. Vide Vallam. GENZAHAR
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108 LEXICON < 14.> Losophi define the permanence of natural heat, or the operation of the sensitive spirit. Therefore some have called the moment of nativity the point of the infant’s خروج from the womb: but since this happens successively and by parts, so that sometimes entire hours pass, and often even for a whole day the fetus remains with half its body inside the mother’s womb and the other half outside, it will still remain in question what should be called the true moment of birth, to which the celestial theme ought to be cast. Titus, in the Celestial Philosophy, examining the matter in his usual learned manner, rejecting the opinions of others, concludes from the deepest principles of philosophy that this is when the fetus begins to become independent of its nearest cause, and consequently to be deprived of its ministry and immediate influence. < 14.> But to have this also ascertained is very difficult. Therefore, weighing the opinions of each, the view of Cardanus pleases me most, who says that the child should then be said to be born when he first begins to breathe air through the mouth outside the mother’s womb. For since the principal operation of life is breath, by which the living being is sustained, and with its loss life ceases, that will rightly be called the beginning of life by which one, not with the help of the mother but by his own effort, begins to enjoy respiration and to draw in that air, which, because of its ease, subtlety, and unity of the whole continuum (unless we wish also to call it matter), is ready to receive the impressions of the heavens and is therefore rightly called the vehicle of the World-Spirit and of celestial qualities. Wherefore, although the child has not yet emerged from the mother’s womb, if only he has his head outside it and begins to breathe, that is enough for him to be said to live and to have been brought into the light. On the contrary, even if he is placed outside the womb, bathed, wrapped in cloths, etc., he can never properly be said to live until he receives the first seeds of life, and so the influxes of the heavens are not communicated to him through the inhalation of air. And enough of this argument. Hence. < 15.> GENETLIACVM is said of that which pertains to Genesis; and those who pronounce concerning the life and fortune of men from the natal theme are called Genethliacs. < 16.> GENIGVLATOR, or Ingeniculus, is the Greek-named Hercules Engonasis, a fixed star in the sky toward the northern region, so called because its image represents a man crouched on his knees, and with one foot raised seeking to crush the head of the Dragon. See what has already been said under V. Engonasis, and what will be said under Hercules. < 17.> GENNA, according to Otho, is by some called the Moon, when after conjunction with the Sun it has moved away from him by 15 degrees, or indeed 17, as much as is sufficient for it to emerge from his rays. See Valla. GENZAHAR
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LEXICON in eam partem, quæ in planorum consideratione versatur, & generali vocabulo retento Geometria strictiùs audit; & in eam qua corporum solidorum doctrina traditur, ac proprio, & peculiari nomine Stereometria appellatur. Rursus quæ ex- lestium corporum affectiones solummodò speculatur, Astro- nomia dicitur, quæ in terræ descriptione versatur, Geogra- phia. Itaque Geometria vniuersè hunc sibi scopum præsigit, vt plana, aut solida, vel constituat, vel constituta inter se comparet, aut diuidat, ac proinde corpora præcisè ac superfi- cies speculatur. Eius laudes, arque vtilitates Clauius in Prolo- gomenis ad Commentar. in Elementa Euclidis. GL 22. GLOBVS Latinè idem, quod sphæra Græcè, definitur enim à Theodosio, quod sit Corpus solidum vnicæ superficie conten- tum in medio habens centrum à quo omnes linea ad superficiem ducta sint æquales. Differt à circulo quod iste sit figura plana vnicâ lineâ circunducta comprehensa; globus autem sit cor- pus sphæricum omnis dimensionis capax. Differt etiam ab Or- be propriè dicto, quod is vnicam tantum habet superficiem, exteriorem nempe, atque conuexam, qua clauditur, & fini- tur, cum aliàs concipiatur ex integro solidus vsque ad cen- trum; qualia dici possunt corpora planetarum, globus ter- restris, &c. Orbis autem etsi alioqui solidus intelligatur, ta- men eius solidiras, seu crassities compræhenditur duabus su- perficiebus, altera interiore concaua, altera exteriore conue- xa, quales sunt omnes cæli, & deferentes corpora planeta- rum, aëris regio, &c. Id autem propriè, nam sæpè vocabula confunduntur. Quinimò nunc temporis vsus obtinuit, vt globi nomine pressiùs veniret vtraque mundi Mappatam ex- lestis, quam terrestris, in quarum vna descripta essent om- nia sidera, ac cælestes imagines, circuli, sphæræ longitudi- nes, latitudines, declinationes cuiuscumque partis cæli cum suo horizonte, ac Meridiano adaptandis ad quascumque poli elevationes, cuius ope ortus, & occasus siderum, cæli media- tio, aliaque vnico intuitu haberentur: in altera descriptus esset totus terræ, marisque ambitus cum suis circulis paralle- lis, vnde locorum longitudines, latitudines, distantia inter se, proindeque vniuersa penè Geographia commodè addisci possit. GN 23. GNASCH Hebræo nomine dicitur Vrsa minor, fidus ad po-
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LEXICON in that part which deals with the consideration of plane figures, and with the general term retained it is more strictly called Geometry; and in that part where the doctrine of solid bodies is treated, it is called by its proper and particular name, Stereometry. Again, that which merely speculates on the properties of heavenly bodies is called Astronomy, that which deals with the description of the earth, Geography. Thus Geometry generally sets before itself this aim: to construct planes or solids, or, having constructed them, to compare them with one another, or to divide them; and therefore it speculates precisely on bodies and surfaces. Its praises and usefulness are discussed by Clavius in the Prolegomena to the Commentary on Euclid’s Elements. GL 22. GLOBUS is the same in Latin as sphæra in Greek; for it is defined by Theodosius as a solid body enclosed by a single surface, having in its midst a center from which all lines drawn to the surface are equal. It differs from a circle in that the latter is a plane figure enclosed by a single line; whereas a globe is a spherical body capable of every dimension. It also differs from an orb properly so called, because the orb has only one surface, namely the outer and convex one by which it is enclosed and bounded, while otherwise it is conceived as solid throughout to the center; such may be said to be the bodies of the planets, the terrestrial globe, etc. But an orb, although otherwise understood as solid, has its solidity or thickness comprehended by two surfaces, one inner and concave, the other outer and convex; such are all the heavens and the spheres carrying the bodies of the planets, the region of the air, etc. This is properly so, for the terms are often confused. Indeed, nowadays usage has prevailed so that by the name of globe there is more precisely meant either map of the world, celestial or terrestrial, in one of which would be described all the stars and celestial figures, circles, spheres, longitudes, latitudes, declinations of any part of the sky with its horizon and meridian adapted to whatever elevation of the pole, by the aid of which the rising and setting of the stars, the midpoint of the heavens, and other things would be had at a single glance; in the other would be described the whole extent of the earth and sea with their parallel circles, from which the longitudes and latitudes of places, their mutual distances, and therefore almost the whole of Geography, may conveniently be learned. GN 23. GNASCH is called by a Hebrew name the Lesser Bear, a fixed star near the po-
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LEXICON 214 si in dies singulos milliaria 40. conficeret. Qui huius rei curiosus extuerit, videat Clauium loco citato, & Blancanum in < 30.> spharamuodi, lib. 4. cap. 5 Considerantur eriam ab Astronomis, præsertim antiquioribus, certi quidam gradus in signis, quos vocant vacuos, plenos, lucidos, tenebrosos, masculinos, fæmininos, pureales, fumosos, felices, infelices, augentes fortunam, vel minuentes, nescio prudenti ne ratione, an potius Arabum vanitate, ac figmento. Hos ego gradus, eorumque distributionem olim deridebam; vel eò maximè quod à recentioribus silentio obuoluuntur. Verum quia postmodum inueni Angelicum Doctorem D. Thomam eorum mentionem fecisse in opuscul. de Faso, nec proptereà improbasse (vt alias solet grauissimus vir in rebus superstitionem olentibus) placuit eos & hic inserere, neq[ue] approbando, neque improbando, sed solùm ad operis complementum, atque vt curiosorum desiderio satisfacerem. Eorum aliqua ratio elucer ex fixarum natura in illis incidentium, aure proportionalibus distantijs ad puncta cardinalia, vnde sidera influere incipiunt primas qualitates, quales sunt fines secundùm Ægyptios, vt nos dicemus in V. Termini. irem gradus fæminini, & masculini, &c. aliorum non item, cuiusmodi sunt gradus puteales, pleni, vacui, fumosi, lucidi, tenebrosi. Fortassis vocantur pleni, ac lucidi, in quibus stellæ fixæ corporaliter incidunt; sicut è contrà tenebrosi, & vacui qui nullis circà stellis præditi sunt. Licet & hoc quidem præsenti tempore obseruare superuacaneum foret ob Firmamenti peculiare motum, quo stellæ jam non in eadem longitudine sunt, proindeque in ijsdem Zodiaci gradibus, ac tempore Ptolemæi, sed longe antecessetunt ad grad. ferè 28. Quapropter & nouam graduum constitutionem construere oporter. Sed & eorum, qui felices, vel infelices vocantur non spernendam rationem affert Cardanus in Commentar. ad lib. 1. Quadresp. text. 61. Vbi enim, inquit, conueniunt fines vtriusque benefica, ij iure cateris feliciores censendi sunt, ob vtriusque mixtam naturam: contrà infelices habentur qui sunt contermini finibus maleficarum; quia ambæ concurrunt ad eos infortunandos. Sic septimus gradus Arietis, quia est finis terminorum Louis, & initium Veneris, felix jure optimo nuncupatur. E contrà grad. 26. eiusdem Arietis infelix; quia ibi fines vtriusque maleficæ conjunguntur: sic discurrendum de reliquis, vt videre est in sequenti tabella.
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LEXICON 214 if he were to travel 40 miles each day. Whoever is curious about this matter should look at Clavius in the place cited, and Blancanus <30.> Spharamuodi, book 4, chapter 5. Astronomers, especially the older ones, also consider certain degrees in the signs, which they call void, full, bright, dark, masculine, feminine, dusty, smoky, fortunate, unfortunate, increasing fortune or diminishing it, I know not whether by prudent reasoning, or rather by the vanity and fiction of the Arabs. I used to mock these degrees and their distribution; especially because the more recent writers pass them over in silence. But because later I found that the Angelic Doctor, St. Thomas, had mentioned them in the little work de Fato , and had not thereby disapproved them (as that most serious man usually does in matters smelling of superstition), it seemed good to insert them here also, neither approving nor disapproving, but only to complete the work and to satisfy the desire of the curious. Some reason for them may be seen from the nature of the fixed stars falling upon them, by proportional distances to the cardinal points, whence the stars begin to influence the primary qualities, such as the bounds according to the Egyptians, as we shall say in V. Termini ; likewise the feminine and masculine degrees, etc., but not the others, such as the void, full, empty, smoky, bright, and dark degrees. Perhaps they are called full and bright where the fixed stars physically fall; just as, on the contrary, dark and void are those which are not adorned with any stars around them. Although even this would now be superfluous to observe because of the special motion of the firmament, by which the stars are no longer in the same longitude, and therefore not in the same degrees of the Zodiac as in the time of Ptolemy, but have advanced far beyond, to about degree 28. Wherefore a new arrangement of the degrees would also have to be constructed. Cardan also gives a not inconsiderable reason for those which are called fortunate or unfortunate, in his Commentary on book 1 of Quadresp. , text 61. For where, he says, the bounds of the two benefics coincide, they are by right to be judged more fortunate than the others, because of the mixed nature of both; conversely, those are considered unfortunate which border on the bounds of the malefics, because both concur to bring them misfortune. Thus the seventh degree of Aries, because it is the end of the terms of Jupiter and the beginning of Venus, is rightly called fortunate. On the other hand, the 26th degree of the same Aries is unfortunate, because there the bounds of both malefics are joined: thus one must proceed with the rest, as may be seen in the following table.
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MATHEMATICVM. 235 Tabula Graduum Felicium, & Infelicium. 31. In Ariete. felix grad. 7. Infelix 26. In Tauro. felix nullus Infelix 26. In Geminis. felix 15. Infelix 25. In Cancro. nullus felix, neque infelix. In Leone. felix 20. Infelix nullus. In Virgine. felix 14. Infelix 24 & 30. In Libra. felix 12. Infelix nullus. In Scorpione. felix 15. Infelix nullus. In Sagittario. felix 9. Infelix 25. In Capricorno. nullus felix Infelix 25. In Aquario. felix 21. nullus infelix. In Piscibus. felix 9. Infelix 30. Eò quia, vt disci, contermini sunt unibus beneficarum, aut malesicarum. Hac etiam, vel sanè ex consimili ratione repertos crediderim gradus augentes fortunam: suntque gr. 19. Arietis: item gr. 3. 15. 27. Tauri: 11. Geminorum: 1. 2. 3 4. Cancri. 2. 5. 7. 19. Leonis. 3. 14. 20. Virginis. 3. 5. 21. Libræ. 7. 18. 20. Scorpij. 13. 20. Sagittarij. 12. 13 14. 20. Capricorni. 7. 16. 17. 20. Aquarij: tandem gr. 13. & 20. Piscium. Minuentes fortunam sunt ijsdem ac puteales. Sequuntur Gradus Lucidi, & Tenebrosi. In Ariete grad. lucid 27. tenebrosi 2. 6. 11. In Tauro grad. lucidi. 6. 14. 25. tenebr. 2. & 29. In Geminis grad. lucid 2. 10. 20. tenebr. 6. 29. In Cancro grad. lucid. 7. tenebr. 13. 19. 24. In Leone grad. lucid. null. tenebr. 6. 15. 28. In Virgine grad. lucid. 7 14. tenebr. 3. 20 29. In Libra gr. lucid. 3. 14. 24. tenebr. 3. & 20. In Scorpione gr. lucid. 6 & 17. tenebr: 2. 21 29. In Sagittario grad. lucid. & tenebr. nulli. In Capricorno gr. lucid. 9. & 17. tenebr. 4. 13. 21. 28. 111)
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MATHEMATICVM. 235 Table of Happy and Unhappy Degrees. 31. In Aries, lucky degree 7. Unlucky 26. In Taurus, no lucky degree Unlucky 26. In Gemini, lucky 15. Unlucky 25. In Cancer, no lucky, nor unlucky. In Leo, lucky 20. Unlucky none. In Virgo, lucky 14. Unlucky 24 & 30. In Libra, lucky 12. Unlucky none. In Scorpio, lucky 15. Unlucky none. In Sagittarius, lucky 9. Unlucky 25. In Capricorn, no lucky Unlucky 25. In Aquarius, lucky 21. No unlucky. In Pisces, lucky 9. Unlucky 30. For this reason, as may be learned, they are adjacent to the lines of benefic or malefic ones. For this reason also, or truly from a similar cause, I should believe the degrees increasing fortune to have been found: and they are degrees 19 of Aries; likewise degrees 3, 15, 27 of Taurus; 11 of Gemini; 1, 2, 3, 4 of Cancer; 2, 5, 7, 19 of Leo; 3, 14, 20 of Virgo; 3, 5, 21 of Libra; 7, 18, 20 of Scorpio; 13, 20 of Sagittarius; 12, 13, 14, 20 of Capricorn; 7, 16, 17, 20 of Aquarius; and finally degrees 13 & 20 of Pisces. The degrees diminishing fortune are the same as the pit degrees. There follow the Lucid and Dark Degrees. In Aries, lucid degree 27; dark 2, 6, 11. In Taurus, lucid degrees 6, 14, 25; dark 2 & 29. In Gemini, lucid 2, 10, 20; dark 6, 29. In Cancer, lucid 7; dark 13, 19, 24. In Leo, lucid none; dark 6, 15, 28. In Virgo, lucid 7, 14; dark 3, 20, 29. In Libra, lucid 3, 14, 24; dark 3 & 20. In Scorpio, lucid 6 & 17; dark 2, 21, 29. In Sagittarius, lucid degrees and dark none. In Capricorn, lucid 9 & 17; dark 4, 13, 21, 28. 111)
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LEXICON In Aquario gr. lucid. 7. 17. 28. tenebr. 3. 12. In Piscibus gr. lucid. 10. 20. 27. tenebr. 3. 16. 30. Gradus Puteales. 35. In Ariete. 6. 11. 16. 23. 29. In Tauro. 5. 12. 24. 25. In Geminis. 2. 12. 17. 26. 30. In Cancio. 12. 17. 23. 26. 30. In Leone 6. 13. 15. 22. 23. 28. In Virgine. 8. 13. 16. 21. 25. In Libra. 2. 7. 20. 30. In Scorpione. 9. 10. 21. 23. 27. In Sagittario. 7. 12. 15. 24. 27. 30. In Capricorno. 2. 7. 17. 22. 24. 28. In Aquario. 1. 12. 17. 24. 29. In Piscibus. 4. 9. 24. 27. 28. Puteales dicuntur eò quia in ijs planeta existens videtur esse in puteo. Gradus Vacui & Pleni. 36. In Ariet. gr. vac. 3. plen. 8. vac. 17. plen. 20. vac. 26. plen. 30. In Taur. vac. 3. pl. 11. vac. 13. pl. 21. vac. 26. pl. 30. In Gem. vac. 6. pl. 12. vac. 11. pl. 18. vac. 20. pl. 29. vac. 30. In Caner. vac. 6. pl. 12. vac. 11. pl. 18. vac. 20. pl. 29. vac. 30. In Leon. vac. 6. pl. 14. vac. 20. pl. 30. In Virgin. vac. 5. pl. 9. vac. 11. pl. 17. vac. 21. pl. 27. vac. 30. In Libr. vac. 6. pl. 5. vac. 13. pl. 16. vac. 24. pl. 27. vac. 30. In Scor. vac. 3. pl. 8. vac. 14. pl. 20. vac. 22. pl. 27. vac. 30. In Sagitt. vac. 6. pl. 8. vac. 11. pl. 19. vac. 23. pl. 30. In Capric. vac. 7 pl. 10. vac. 15. pl. 20. vac. 24. pl. 30. In Aquar. vac. 4. pl. 7. vac. 13. pl. 19. vac. 22. pl. 30. In Pisc. vac. 6. pl. 12. vac. 15. pl. 19. vac. 25. pl. 28. Atque hi sunt gradus quos minus inanitatis habere credendum est, quàm alij penè innumeris, quos Arabes confinxerunt, sunt etiam gradus Azemene, hoc est debilitatis corporis, quos in loco retulimus, necnon masculini, ac fæminini: de quibus sermo etiam fuit in V. Fæminimum. 37. Græcvs, apud nos vulgò dicitur ventus intermedius inter Septentrionem, & Subsolanum, eò quod per medium Græciam transeat. Græcis Borrhapeliores, directè oppositus Garbino, seu Notolybico. Est natura sua frigidus, & succus ob vicinitatem Boreæ, adducens aliquando niues. 38. Grvs, sedus in cælo ad polum antarcticum à recensoribus de nouo cum alijs vndecim, detectum, & hoc nomine præsignatum. Continet intra se stellas tredecim, quarum præcipua est, quæ in oculo secundæ magnitundis: sed est eadem, quæ
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LEXICON In Aquarius, bright degrees 7, 17, 28; dark 3, 12. In Pisces, bright 10, 20, 27; dark 3, 16, 30. Pit-like degrees. 35. In Aries. 6, 11, 16, 23, 29. In Taurus. 5, 12, 24, 25. In Gemini. 2, 12, 17, 26, 30. In Cancer. 12, 17, 23, 26, 30. In Leo. 6, 13, 15, 22, 23, 28. In Virgo. 8, 13, 16, 21, 25. In Libra. 2, 7, 20, 30. In Scorpio. 9, 10, 21, 23, 27. In Sagittarius. 7, 12, 15, 24, 27, 30. In Capricorn. 2, 7, 17, 22, 24, 28. In Aquarius. 1, 12, 17, 24, 29. In Pisces. 4, 9, 24, 27, 28. They are called pit-like because in them a planet existing seems to be in a pit. Degrees of Empty and Full. 36. In Aries: empty degree 3, full 8, empty 17, full 20, empty 26, full 30. In Taurus: empty 3, full 11, empty 13, full 21, empty 26, full 30. In Gemini: empty 6, full 12, empty 11, full 18, empty 20, full 29, empty 30. In Cancer: empty 6, full 12, empty 11, full 18, empty 20, full 29, empty 30. In Leo: empty 6, full 14, empty 20, full 30. In Virgo: empty 5, full 9, empty 11, full 17, empty 21, full 27, empty 30. In Libra: empty 6, full 5, empty 13, full 16, empty 24, full 27, empty 30. In Scorpio: empty 3, full 8, empty 14, full 20, empty 22, full 27, empty 30. In Sagittarius: empty 6, full 8, empty 11, full 19, empty 23, full 30. In Capricorn: empty 7, full 10, empty 15, full 20, empty 24, full 30. In Aquarius: empty 4, full 7, empty 13, full 19, empty 22, full 30. In Pisces: empty 6, full 12, empty 15, full 19, empty 25, full 28. And these are the degrees which must be believed to have less emptiness than the others, almost innumerable, which the Arabs have devised; there are also degrees of Azyme, that is, of weakness of the body, which we have mentioned in their place, as well as masculine and feminine; of which there was also discussion in V. Feminine. 37. Greek, among us commonly called the intermediate wind between the North and Subsolanus, because it passes through the middle of Greece. Among the Greeks, Borrhapelios, directly opposite to Garbino, or Notolybicos. In its nature it is cold, and it brings moisture on account of its nearness to Boreas, sometimes bringing snow. 38. Grus, a constellation in the sky near the south pole, newly discovered by the revisers together with eleven others, and designated by this name. It contains within itself thirteen stars, of which the principal is the one in the eye of the second magnitude; but it is the same as the
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M A T H E M A T I C V M. 217 in cauda piscis Rotij: In longitudine totum est sub signo Aqva- rij, nobis perpetuò inconspicuum. HA HADRONITHO Demalushe, Chaldaicè dicitur Zodiacus, 1. hoc est Orbis signorum, teste Kirchero in Oedipo Ægygiaco. HAIA, id est serpens dicitur apud Hebræos Hydra sidus, 2. teste Kyrchero, in Oedipo. liem Hackasa. HALON, seu Halones, Græcè dicuntur circuli illi, qui sæpè 3. numero apparere solent circà sidera fulgorem quemdam crassum præseferentes, ad instar radiorum, qui sanè aliud non sunt, quàm densati quidam vapores, & adhuc non resoluti, in eam aëris regionem conuenientes, quæ subest sideri quod circumire videntur, qui posteà ab eius radijs illustrantur nihilò seciùs ac circa horizontem Atmosfera à radijs Solis, vel jamjam emergentis, vel infra finitorem depressi. Hos & areas vocauere Prisci, quia, inquit Seneca, rotunda sunt loca rerendis frugibus destinata, quibus isti valdè consimiles. Memo- rabilis Halonis suo tempore apparentismeminit Plinius, nec- 4. non & aliorum duorum Suetonius, atque Dio, ex quibus histo- riam accipiens Cornelius Gemma lib. 2. de diuinis Natura cha- racterism. cap. 8 hæc habet: Sub imperium augustis Cæsaris, vt author est Plinius, ingens circulus circa Solem seu radiantibus stel- lis insignis corona apparuit: deside & alij duo, vt ex Suetonio pa- tet, atque Dione; quorum alter Iridis elegantissima formam, al- ter ex spicis triticeis sertum præseferebat. His affinia sunt parzlia, fouex, virgæ, & alia: de quibus suo loco. Vide etiam quæ di- ximus sub V. Circuli. HALYSIS non multum discrepat ab Halone: est enim teste 5. Apuleio lib. de mundo catena quædam ( illius verbis vtor) lu- minis clarioris per Solis ambitum in se reuertens: aitque inter hanc & iridem illud interesse, quod Iris multicolor est, & semicirculo figurata procul à Sole, atque Luna; Catena cla- rior est, astrumque ambit orbe incolumi, corona non disco- lori. HAMMEL, seu El. Hammel, prout in loco adnotauimus, di- 6. citur apud Arabes signum, & constellatio Arietis, teste Kir- chero in suo Oedipo Ægyptiaco: sicur etiam HAMMOSCHLVSCH, hoc est tripartitus dicitur apud Hebræos 7. Triangulus: sidus de quo vide in V. Delteton. HAVT, & Ehaus signum, & constellario Piscium. 8. HAPSI apud Astronomos dicuntur nubeculæ quædam, seu 9. maculæ pendulæ sub Luna in eius defectione nascentes, & sus- pensæ sub illa, de quibus testatur Vendelinus in præf. ad Eclips. p. 3. sæpè à se visas nubes qualdam pendulas sub Luna adhuc in
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M A T H E M A T I C V M. 217 in the tail of the fish Rotij: in length it is entirely under the sign of Aqvarius, to us perpetually invisible. HA HADRONITHO Demalushe, in Chaldaic, is called the Zodiac, 1. that is, the Circle of signs, according to Kircher in the Oedipus Ægyptiacus. HAIA, that is, serpent, is what the Hebrews call the star Hydra, 2. according to Kircher, in the Oedipus. liem Hackasa. HALON, or Halones, the Greeks call those circles which often 3. appear in great number around the stars, presenting a certain thick brightness, like rays; and these are in truth nothing other than some condensed vapors, not yet resolved, coming together in that region of the air which lies beneath the star that they seem to encircle, and which afterward are illuminated by its rays no less than around the horizon the atmosphere is by the rays of the Sun, whether just rising or already depressed below the boundary. The ancients also called these areas, because, says Seneca, they are round places assigned for ripened crops, to which these are very similar. Pliny remembered a memorable appearance of Halones in his time, 4. and Suetonius and Dio also mention two others, from whose history Cornelius Gemma, lib. 2. de divinis Natura characterism. cap. 8, has these words: Under the rule of Augustus Caesar, as Pliny is author, a huge circle around the Sun, or a radiant crown distinguished by shining stars, appeared: and two others also, as is clear from Suetonius and Dio; of which the one presented the form of a most elegant rainbow, the other a garland made of ears of wheat. Related to these are parzlia, fouex, virgæ, and others: about which in their place. See also what we said under V. Circuli. HALYSIS differs little from Halon: for it is, according to 5. Apuleius, lib. de mundo, a certain chain (I use his own words) of brighter light, returning upon itself around the course of the Sun; and he says that the difference between this and the rainbow is that the rainbow is multicolored and figured as a semicircle, far from the Sun and the Moon; the Chain is brighter, and surrounds the star with a whole orb, a crown not multicolored. HAMMEL, or El. Hammel, as noted in the place, is said 6. among the Arabs to be the sign and constellation of Aries, according to Kircher in his Oedipus Ægyptiacus: likewise also HAMMOSCHLVSCH, that is, tripartite, is said among the Hebrews 7. of the Triangle: a star of which see under V. Delteton. HAVT, and Ehaus, sign and constellation of Pisces. 8. HAPSI among astronomers are called certain little clouds, or 9. hanging spots, arising beneath the Moon in its eclipse, and suspended below it, of which Vendelinus testifies in the preface to Eclipses, p. 3, that he has often seen certain hanging clouds beneath the Moon while still in
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LEXICON 218 tenebris constituta, quasi aqua multa grauidas, quæ aliquando, ob figuram, quam præseferunt vmbiæ more arcuatam exquisitissimè imitantur initium, & finem Eclipsis à penumbræ terræ realiter factæ, qua in re ait, deceptos fuisse Tychonem & alios sæpissimè in Eclipsium lunarium obseruatione. 10. HAYZ, siue, vt alij scribunt A hayz, apud Arabes est qui-dam accessus fortitudinis, ac dignitatis factus planetæ, eò quod existat in signo sibi sexu conformi, atque in situ mundi in loco sibi conditionario, vt si masculinus, & diurnus de die reperiatur suprà terram, & in signo masculino; si nocturnus & masculinus de nocte reperiatur suprà terram, & in signo masculino. Similiter si planeta sit foeminæ conditionis, constituatur in signo foeminino, & suprà terram de nocte, sub tetram interdiù, & si diurnus suprà terram de die. Sic Saturnus, exempli gratiâ, existens in Leone in decima (Sole suprà terram existente) dicitur esse in suo Hayz; eò quia cùm sit masculus, & diurnus, reperitur in signo sibi in sexu conformi, scilicet masculino, & de die etiam suprà terram. Mars autem ad hoc vt ibidem dicatur in suo Hayz, debet habere Solem sub terra, cùm ipse sit planeta nocturnus. Si verò planeta seruet quidem conditionem temporis, at non actu reperiatur in loco sibi idoneo in situ mundi, vt esset si Saturnus de nocte reperitur sub terra, & in signo masculino, Luna de die sub terra, & in signo foeminino; tunc sanè dicetur esse in suo lumine, quia est in loco sibi proportionato, minimè verò in suo Hayz. 11. HADI duæ sunt stellæ perniciosæ, horridæque (quales appellat Plin. lib. 18 c. 36.) in sinistra manu Aurigæ consistentes de natura Martis, & Mercurij, quartæ magnitudinis, in longitudine nunc temporis in gr. 12. & 14. Geminorum. De ijs in Oriente repertis in alicuius natiuitate, sic petbellè cecinit Pontanus in Vransælib. 3. Promittunt igitur duros à fronte Cæsones Nascentes Hadi, turpi sed inertia mentem Occupat, & molles languent in pectore curæ. Triste supercilium, molls sed degener vmbra: Est animus luxu languens, & deside somno Frons ficta, obsceni mores, petulansque ibido. Armorum, & deses fuga, nobiliumque laborum. Hinc mortem sibi conciscunt, infamis vt vmbra Erret letheos non transmittenda per amnes. Quod aliter explicat Firmicus in hæc verba. Si Hædi, inquit, in alicuius natiuitate in horoscopo reperti fuerint; natus aliud ex fronte pollicetur, aliud latenter in moribus exlabit: Brit enim austera facie, prolixa barba, obstinata fronte; ita vt Ca-
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LEXICON 218 set in darkness, as though heavy with much water, which sometimes, because of the figure which they present, they most exquisitely imitate in the arched form of the cloud; the beginning and end of an Eclipse, from the earth’s penumbra actually produced, in which matter he says that Tycho and others were deceived most often in the observation of lunar Eclipses. 10. HAYZ, or, as others write, A hayz, among the Arabs is a certain increase of strength and dignity made of a planet, because it exists in a sign conforming to its sex, and in the position of the world in a place suitable to it, as if a masculine and diurnal planet is found by day above the earth, and in a masculine sign; if nocturnal and masculine, by night above the earth, and in a masculine sign. Likewise, if a planet is of feminine condition, let it be placed in a feminine sign, and above the earth by night, beneath the earth by day, and if diurnal above the earth by day. Thus Saturn, for example, being in Leo in the tenth house (the Sun being above the earth) is said to be in its Hayz; because, since it is masculine and diurnal, it is found in a sign conforming to it in sex, namely masculine, and also by day above the earth. Mars, however, in order that there it may be said to be in its Hayz, must have the Sun below the earth, since it is a nocturnal planet. But if a planet indeed keeps the condition of time, yet is not actually found in the place suitable to it in the position of the world, as if Saturn were found by night below the earth, and in a masculine sign, the Moon by day below the earth, and in a feminine sign; then truly it will be said to be in its light, because it is in a place proportionate to itself, but by no means in its Hayz. 11. HADI are two pernicious and dreadful stars (such as Pliny calls them, book 18 ch. 36.) standing in the left hand of Auriga, of the nature of Mars and Mercury, of the fourth magnitude, in longitude at the present time at 12 and 14 degrees of Gemini. Of them, when found in the East in someone’s nativity, Pontanus sweetly sang thus in Vransæ lib. 3. They promise hard heads from birth, therefore Hadi, but foul idleness occupies the mind, and soft cares languish in the breast. Sad is the brow, but a weak and degenerate shade: the spirit is languishing in luxury, and in idle sleep the brow is false, the manners obscene, and wanton desire. From arms, and from noble labors, is a sluggish flight. Hence they take their own lives, so that the infamous shade may wander, not to be carried across the Lethean rivers. Which Firmicus explains otherwise in these words. If the Hædi, he says, are found in the horoscope in someone’s nativity; the native promises one thing from the brow, another secretly slips out in his character: for Brit with a stern face, a long beard, a stubborn brow; so that Ca-
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MATHEMATICVM. 219 ronis prorsus institutum mitari videatur: sed rotum hoc fucato mentietur affectu. Quippe in t t infecus erit lascius, & qui la- tenter amorum illecebris semper exæstuet, &c. Nascuntur etiam sub hoc sidere ouium pastores, quique siluestri sistula modulaires, rustic i catminis dulcissimos modulos edant. Si verò in occasu fuerint cum piauo aspectu Saturni; nati in ipso vitæ momento moriuntur, aut in ipso nascenti lumine constituti deficientibus Matris viribus strangulantur; aut tumescen- tibus faucibus acerbum illis mortis infertur exitium. Quod si Mars cum ipsis in occasu fuerit, omni beneuolarum testimonio destitutus, plecti factiet natos, aut religionis causa exuri. Hæc Firmicus, quæ tamen cautè intelligenda sunt. Sed quoad aëris mutationem Hædi exorientes ventos ciere solent, plu- uias violentas adducere, & tempestate in mari excitare. Vnde inimicum nauigantibus fidus canit Germanicus. HELIACVS ortus, & occasus, stellæ apud Astronomos signi- <12.> ficat eius emerstonem è radijs Solis, ita vt fiat conspicua, aut cum in illos immergitur, & ampliùs videri nequit, siue id fiat ob Solis approximationem, vel elongationem ab ea, siue ipsius stellæ ad Solem, quod locum habet tantummodo in planetis. Quod fit ad distantiam plus minus 17. graduum in Luna, in cæteris autem ferè vnius signi. Ortum heliacum Aquarij sic describit Ouidius lib. 2 Factorum dum cecinit: Iam leuis obliqua subsedit Aquarius una: Proximus as-ereos excope Piscis equos. Mense etenim Februario Sol existit in Aquario, eumque proptereà suo splendore occultat: verùm cùm sub finem Fe- bruarij Pisces ingreditur, incipit Aquarius paulatim è Solis ra- dijs emergere, sicque mane ante Solis ortum fieri conspicuus. E contra occasum heliacum Canis intellexit Virgilius lib. 1. Georg quando dixit: Candidus auratis aperit cum cornibus annum Taurus, & aduerso cedens Canis occidit astro. Quia cùm olim Canis maior existeret in Geminis, Sole sibi appropinquante in Tauro, occidebat heliacè; cùm priùs enim eslet conspicuus, jam inde incipiebat occultari, atque in Solis radijs iminegi; ita vt ampliùs videri non posset. HELIAC Græco nomine, sicut etiam Callisto, & Megisto dici- <13.> tur Vrsa maior, sidus in exlo propè polum arcticum ex aduerso Cassiopææ, sic dictum à circumuolutione, quod diei, no- ctisque spatio breui circumlatione circa polum voluatur. Habet stellas apud Prolemæum omninò 35 hoc est 27. intra imaginem inclusas, octo autem extrà vagantes, & informes, licet Baic- rus in eo numeret tautùm 32. Cùm Keplerus obseruasse se di-
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MATHEMATICVM. 219 would seem to imitate the very institution of a foreign land: but with this painted feeling it will deceive. For he will be lascivious in t t infecus, and one who will always boil secretly with the enticements of love, etc. Under this star are also born shepherds of sheep, and those who with a woodland pipe give forth the sweetest measures of rustic song. But if they are at the setting together with an evil aspect of Saturn, those born die at the very moment of life, or, placed in the very light of birth, are strangled as the mother’s powers fail; or, with their throats swelling, a bitter end of death is brought upon them. But if Mars also has been at their setting, deprived of every testimony of goodwill, it will make those born be punished, or burned for the sake of religion. Thus Firmicus, which nevertheless must be understood cautiously. But as far as change of air is concerned, the rising Hædi are wont to stir up winds, bring violent rains, and raise storms at sea. Whence Germanicus sings the star hostile to sailors. HELIACAL rising and setting among astronomers signifies the emergence of a star from the rays of the Sun, so that it becomes visible, or when it sinks into them and can no longer be seen, whether this happens because of the Sun’s approach to or recession from it, or the star’s own movement toward the Sun, which occurs only in the planets. This takes place at a distance of more or less 17 degrees in the Moon, but in the others about one sign. Ovid describes the heliacal rising of Aquarius, in book 2 of the Fasti, when he sang: Now light Aquarius had fallen back at the turning of the year: Next the Fish, driving the bronze-hued horses. For in the month of February the Sun is in Aquarius, and therefore hides it with its brightness; but when at the end of February it enters Pisces, Aquarius begins gradually to emerge from the Sun’s rays, and so in the morning before sunrise becomes visible. On the other hand, Virgil in book 1 of the Georgics understood the heliacal setting of the Dog-star when he said: When bright Taurus opens the year with golden horns, and the Dog, yielding to the opposite star, sets. For when the Greater Dog formerly stood in Gemini, as the Sun drew near to it in Taurus, it set heliacally; for since it had previously been visible, from that point it began to be hidden and to sink into the Sun’s rays, so that it could no longer be seen. HELIAC, by a Greek name, as also Callisto and Megisto, is called the Greater Bear, a constellation in the sky near the Arctic Pole opposite Cassiopeia, so named from its circular motion, because in the space of day and night it revolves around the pole in a small circle. Ptolemy gives it altogether 35 stars, that is, 27 enclosed within the figure, and eight wandering outside it and unformed, although Bayer counts only 32 in it. Since Kepler has observed that he di-
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MATHEMATICVM. 221 medietate Epicycli. Vide Cicero de natura Deorum lib. 2. de ea loquens infima est, inquit, quinque errantium, terraque proximæ stella Veneris, qua Latinè Lucifer dicitur cum antegraditur Solem; cum subsequitur autem, Hesperus. Portò Venus Occidentalis à Sole fortior est quam Orientalis, sicut & Mercurius, & Luna, quia aucti lumine, ad differentiam superiorum, qui augentur lumine, cum sunt Orientales, minuuntur, cum fiunt Occidentales. HETEROSC. 1 apud Astronomos scriptores passim atque < 22.> Cosmographos appellantur populi habitantes in Regionibus, sed Zonis temperatis ab Tropicis ad Circulos Arcticum & Antarcticum; quo nomine & nos venimus, eoquia experi- mur vmbram vnam tantum ad Septentrionem vergentem, vel econtrà qui vltrà Tropicum Capricorni degunt, ad Au- strum, licet retineant semper Orientalem, atque Occidenta- lem: & qui immediatè sub Tropicis habitant, vel propè ipsos semel in anno nullam habeant in metidie, cum Sol illis fiat ver- ticalis. HEXAGONVM. Vide Exagonum. H 1 HINNICVLVS, Equi sectio, Rostrum Equi, &c. dicitur si- < 23.> dus in cælo repræsentans caput equi mutilatum, quod habet stellas quatuor obscuras de natura Saturni, Martis, & Mercurij. Vide in V. Equiculus. HIBESIM Arab. dicitur constellatio Cygni, quasi rosa, vel < 24.> lilium redolens. Habet stellas 17. cum duabus informibus, de qua in V. Cygni. HICCVS, Capella Arab. Alaios fidus, seù potius vnica stella < 25.> ptimæ magnitudinis, de natura Martis, & Mercurij existens in sinistro humero Aurigæ, ac repræsentans Capellam lactantem duos hædos in eiusdem manu sinistra hærentes. Est fidus tem- pestuosum procellosum, & Nautis inimicum, vt vocat Ger- manicus, ventos impetuosos producens, & Mare concutiens. De eo horoscopante in alicuius natuitate, hæc habet Firmi- cus. Nati erunt nimia mentis trepidatione solliciti, & quo- rum corpus assiduus tremor semper impugnet. Hi leuibus com- motionibus opptimentur, & leuibus etiam nuncijs graui timo- ris incursione quassabuntur. Erunt tamem omnium rerum cu- riosi, & qui quodcumque nouum dictum fuerit, id impatien- ti cupiditate desiderent; vt semper noua quæque curiosa desi- derij cupiditate sectentur, eaque intelligere studeant. Si verò in occasu fverit, ex pradijs habebunt substantiæ facultatem: sed si propter læsas religiones graui pulsabuntur inuidia. Ha- bebunt etiam substantiam, aut ex naufragijs collectam, aut ex
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MATHEMATICVM. 221 at half the epicycle. See Cicero, De Natura Deorum , book 2, speaking of it: “it is the lowest,” he says, “of the five wandering stars, and next to the earth is the star of Venus, which in Latin is called Lucifer when it goes before the Sun; but when it follows after, Hesperus. Moreover, Venus in the West is stronger than in the East, as is Mercury and the Moon, because, having increased light, unlike the superior planets, which are increased in light when they are in the East and diminished when they become Western.” HETEROSC. 1. Among astronomical writers and cosmographers, peoples dwelling in regions, but in the temperate zones from the tropics to the Arctic and Antarctic circles, are so called; by which name we too are included, because we experience only one shadow tending toward the north, or conversely those who live beyond the Tropic of Capricorn, toward the south, although they always retain the Eastern and Western; and those who dwell immediately under the tropics, or near them, once a year have no shadow at midday, when the Sun becomes vertical to them. HEXAGONVM. See Exagonum. H 1 HINNICVLVS, the Horse’s part, the Horse’s snout, etc., is called a constellation in the sky representing the mutilated head of a horse, which has four faint stars of the nature of Saturn, Mars, and Mercury. See under V. Equiculus. HIBESIM, in Arabic, is called the constellation of Cygnus, as it were a rose or a sweet-smelling lily. It has 17 stars with two unformed ones; see under V. Cygni. HICCVS, Capella in Arabic, Alaios fidus, or rather a single star of the first magnitude, of the nature of Mars and Mercury, situated on the left shoulder of Auriga, and representing a nursing goat with two kids clinging to its left hand. It is a stormy, tempestuous star, and hostile to sailors, as Germanicus calls it, producing violent winds and shaking the sea. Of it, when it is horoscopic in someone’s nativity, Firmicus says this: “Those born will be anxious with excessive trembling of the mind, and their body will always be assailed by a continual tremor. They will be oppressed by slight disturbances, and they will be shaken by slight announcements with the onset of great fear. Yet they will be curious about all things, and whatever new thing is said, they will desire it with impatient eagerness; so that they always pursue all new and curious things with the craving of desire, and strive to understand them. But if it is in the setting, they will obtain wealth from plunder; but if because of injured religions they are gravely struck by envy. They will also have substance, either collected from shipwrecks, or from
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124 LEXICON quas complectitur quota pars Zodiaci coascendens aut condescendens: quorum ope perficiuntur directiones ad mentem Ptolomæi, ac singularum domorum cælestium, tam supra quam infra terram existentium sit distributio. Nam bina horaria tempora diurna, seu tertia pars arcus semidiurni constituit sparium singularum domorum supra terram existentium: geminata item horatia tempora nocturna, seu tertia pars arcus seminocturni constituit quantitatem singularem domorum infra terram existentium. Tabulam horariorum temporum ad singulas Eclipticæ partes habent ferè omnes scriptores in introductorijs ad Ephemeridas. Si planeta habeat latitudinem, & vera eius horaria tempora venari volueris, acceptam eius declinationem ad rationem latitudinis quam habet reuoca ad eclipticam, ac postea cum gradu illo < 14.> eclipticæ accipe horaria tempora, quæ illi respondent in tabula, & sies voti compos. Quod si tanta sit declinatio planetæ, vt excedat illam eclipticæ, vel fixarum maximam latitudinem habentium horaria tempora velis extrahere, diuide eius arcum semidiurnum, vel seminocturnum acceptum in gradibus & minutis, in sex partes, & singulæ erunt horaria tempora diurna, vel nocturna Arcus autem semidiurnus, vel seminocturnus cujuscumque sideris quacunque latitudine præditi, habetur per additionem differentiæ ascensionalis competentis declinationi sideris ad gr. 90. si quidem declinatio fuerit Borealis, vel per diminutionem ab gr. 90, si declinatio fuerit australis: & econtrâ arcus seminocturnus habetur per additionem differentiæ ascensionalis ad gr. 90. si declinatio stellæ fuerit australis, per subtractionem, si fuerit Borealis, & residuum, vel summa erit arcus semidiurnus, vel seminocturnus diuidendus, vt dixi in sex partes æquales, ad hoc vt habeantur horaria tempora diurna, vel nocturna; nec non horæ inæquales, seu planetariæ, si gradus & minuta æquatoris conuertantur in horas, < 15.> & minuta temporis, tribuendo, vt supra, quindecim gradus singulis horis æquinoctialibus, & singulis minutis æquatoris singula minuta temporis. HORINÆVM vocat Ptolemæus lib. 3 cop. 14. Quadrip. motum directionis conuersum, quo significator motu primi mobilis raptus fertur in locum promissoris à consequentibus ad præcedentia signa: docetque motu dirigendum esse vitæ moderatorem existentem in quarta Occidentali supraterranea, à < 17.> medio videlicet cæli ad occasum, ad ipsum occiduum sinitorem, quem solum in eo casu agnoscit habere vim Anæreticam, eo quia inquit Dominum vita abscondit Hoc motu dirigi possunt omnes moderatores qui mouentur in Zodiaco, & rapiuntur.
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124 LEXICON which includes what part of the Zodiac is ascending or descending: by means of these are worked out directions according to the method of Ptolemy, and the division of the several celestial houses, both those existing above and below the earth. For two diurnal horary times, that is, the third part of the semidiurnal arc, constitute the extent of the individual houses existing above the earth; likewise, doubled nocturnal horary times, that is, the third part of the seminocturnal arc, constitute the individual quantity of the houses existing below the earth. A table of horary times for the several parts of the Ecliptic is found in almost all writers in introductions to Ephemerides. If a planet has latitude, and you wish to find its true horary times, reduce the declination you have taken to the ratio of the latitude it has to the ecliptic; and afterward, with that degree < 14.> of the ecliptic, take the horary times that correspond to it in the table, and you will achieve your desire. But if the declination of the planet be so great that it exceeds that of the ecliptic, or if you wish to extract the horary times of fixed stars having the greatest latitude, divide its semidiurnal, or seminocturnal, arc, taken in degrees and minutes, into six parts, and each will be a diurnal or nocturnal horary time. Now the semidiurnal, or seminocturnal, arc of any star whatsoever, endowed with any latitude whatever, is obtained by adding the ascensional difference appropriate to the star’s declination to 90 degrees, if the declination is Boreal, or by subtracting from 90 degrees if the declination is southern: and conversely the seminocturnal arc is obtained by adding the ascensional difference to 90 degrees if the star’s declination is southern, by subtraction if it is Boreal, and the remainder, or the sum, will be the semidiurnal or seminocturnal arc to be divided, as I said, into six equal parts, in order that diurnal or nocturnal horary times may be had; as well as unequal hours, or planetary hours, if the degrees and minutes of the equator are converted into hours, < 15.> and minutes of time, assigning, as above, fifteen degrees to each equinoctial hour, and to each minute of the equator a minute of time. HORINÆVM Ptolemy calls, book 3, chapter 14 of the Quadripartite, the reversed motion of direction, by which the significator, carried along by the motion of the first mover, is borne into the place of the promissor from following to preceding signs: and he teaches that the ruler of life existing in the western supraterrene fourth part is to be directed, namely from the midheaven to the west, to the very setting point itself, which alone in that case he acknowledges to have Anaretic force, because, he says, the Lord has hidden life. By this motion all rulers which move in the Zodiac and are carried along can be directed.
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MATHEMATICVM. 229 Æquinoctio autumnali vsque ad Venum, & contactum Solis ad primum punctum Arietis. Nunc verò facta anni diuisione in quatore tempora, dicitur ea pars, quæ mediat inter Autum- num, & Ver, omnium frigidissima; atque amplectitur tempus quo Sol tria signa perlustrat Capricornum, Aquarium, & Pis- ces. Accipitur etiam hyems pro maxima elongatione Solis à vertice, vnde dicitur sub polis perpetuò hyemare: & sub æqua- tore duas esse hyemes, eoquia bis Sol elongatur à vertice in sua maxima declinatione, quando reperitur in Tropicis. Hoc tempore notat Plinius lib. 2. cap. 50. rara esse fulmina, nisi in vrbe, & in toto tractu campaniæ; atque scithiam aliasque fi- nitimas regiones ob summum frigus immunem esse à fulmine: Quoniam, inquit, hyeme densatus aer nubium crassiore corso spis- fatur: omnisque exhalatio rigens, ac gelida quicquid accipit ignei vaporis extinguis. Hæc Plinius explicans subinde cæteras hyemis qualitates, à quibus nos recensendis breuitatis studio absti- nemus. HYLEG, seù Hylech Arab. Latinè dimissor: estque apud Astro- < 51.> logos Planeta, vel locus in cælo, qui in hominum natiuitate vitæ moderationem sortitur. Græcis apheta dicitur: Apud nos communiter Vitæ dator. Vide ibi. Hinc HYLEGIALIA loca dicuntur ea, in quibus repertus Planeta, < 52.> vel pars fortunæ sortiri potest vitæ moderationem; suntque horoscopus à quinque gradibus suprà cuspidem vsque ad 25. infrà: (licet in spatio crepusculorum in quibus nouissimè docet Titus dirigendum esse Solem cum sit vitæ moderator, possit etiam vltra 25. gradus protendi, vt nos docuimus in V. Cre- pusculum.) Medium cæli quod de quadrato respicit horosco- pum; Cardo Occidentis, qui de opposito: nona, quæ de tri- no: & vndecima, quæ de sextili. Solum tamen aduertit Titus in primo mobile canone 29. in vndecima non euadere prorogato- < 53.> rem planetam in omni ejus spatio consistentem, sed tantum in prima medietate (secundam ipse vocat procedendo ordine anuerso ad rationem motus primi mobibilis) eoquia citra illam medietatem versus duodecimam incurrit in semiquadrarum ad horoscopum; vnde ratione istius radij imperfecti & contra- < 54.> rij ad rationem sextilis non potest sortiri vitæ prorogatiouem. HYPAVGVS, teste Valla dicitur Planera compræhensus sub < 55.> Solis radijs hinc inde ad distantiam graduum 17. quæ quidem est maxima planetæ debilitas: nam omnis eius virtus à poten- tia Solis absorbetur; & quò maior fuerit cum Sole vicinitas, eò maior erit debilitas, & eneruatio. Vide quæ diximus in V. Combustus, & in V. Cæzini. HYPOGÆVM Græcè propriè dicitur aliquid subterraneum: < 54.> Piij
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MATHEMATICVM. 229 From the autumnal equinox up to Venus, and the conjunction of the Sun with the first point of Aries. Now, however, the year having been divided into four seasons, that part which lies between Autumn and Spring is said to be the coldest of all; and it includes the time in which the Sun traverses the three signs Capricorn, Aquarius, and Pisces. Winter is also taken for the Sun’s greatest elongation from the zenith, whence it is said that beneath the poles it is perpetually winter; and beneath the equator there are said to be two winters, because the Sun is twice at its greatest declination, when it is found in the Tropics. At this time Pliny notes, book 2, chap. 50, that thunderbolts are rare, except in the city and in the whole territory of Campania; and that Scythia and other neighboring regions are exempt from lightning on account of the intense cold: “For,” he says, “in winter the air, being thickened by the denser course of the clouds, is condensed; and every exhalation, being stiffened and frozen, extinguishes whatever fiery vapor it receives.” Pliny, explaining these and other qualities of winter in due course, from which we abstain from listing here in the interest of brevity. HYLEG, or Hylech, Arab.; in Latin dimissor: and among Astrologers it is a planet, or a place in the heavens, which in men’s nativities receives the governance of life. Among the Greeks it is called apheta: among us commonly the giver of life. See there. Hence HYLEGIAL places are called those in which the found planet, or part of fortune, may receive the governance of life; and they are the horoscopes from five degrees above the cusp to 25 degrees below it; (though in the space of the crepuscules, in which Titus most recently teaches that the Sun must be directed, since it is the moderator of life, it may also be extended beyond 25 degrees, as we have taught in V. Crepusculum.) The Medium Coeli, which from the square regards the horoscope; the Western Angle, which does so from opposition; the ninth, which does so by trine; and the eleventh, which does so by sextile. Yet Titus observes, in the first mobile canon 29, that in the eleventh the prorogator planet does not succeed in every part of its span remaining there, but only in the first half (the second he himself calls, proceeding in reverse order according to the motion of the first mobile), because short of that half toward the twelfth it falls into the semiquadrature of the horoscope; whence, by reason of this imperfect and contrary ray to the reason of the sextile, it cannot obtain prolongation of life. HYPAVGVS, according to Valla, is said of a planet enclosed beneath the rays of the Sun on both sides at a distance of 17 degrees, which indeed is the planet’s greatest weakness: for all its power is absorbed by the Sun’s power; and the greater its proximity to the Sun, the greater will be its weakness and enervation. See what we have said in V. Combustus, and in V. Cæzini. HYPOGÆVM, in Greek, properly means something subterranean: Piij
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14. LEXICON Tabula Signorum inconiunctorum. Aries habet inconiunctum Taurum, & Scorpium. Taurus Arierem, Geminos, Libram, & Sagittarium. Gemini Taurum, & Scorpium. Cancer Leonem, & Aquarium. Leo Cancrum, Virginem, Capricornum, & Pisces. Virgo Leonem, & Aquarium. Libra Scorpium, & Taurum. Scorpio Sagittarium, Libram, Arietem, & Geminos. Sagittarius Scorpium, & Taurum. Capricornus Leonem, & Aquarium. Aquarius Capricornum Pisces, Cancrum, & Virginem. Pisces tandem, Leonem, & Aquarium. 12. Porrò horum signorum, quæ, vt modo diximus, ideò coniuncta vocantur, quia nullo inter se ordine, ac familiaritate sunt nexa, nemo ferè est, qui rationem habeat, atque obseruet quænam in inferioribus hisce, seù bona, seù mala importent: cum tamen, meo iudicio, ea maximè seruari debeant; atque vt bonus ordo rerum ex ordine, colligatione, & consonantia cælestium corporum, quibuscum aliquam essendi habent necessitudinem, pendet, ita & perturbatio, discordia, & discrasia ab eorundem affectionibus, mutuo dissidio, ac disiunctione, seù disparitate naturæ, trahit originem. Etenim partium nexus, & amor, vt volebat Plato mundi anima est: hunc ordinem, hanc harmoniam si minimum turbes, & ipsum orbem turbari, confundi, infirmarique videbis, perinde ac in humano corpore ex humorum bono ordine perturbato, partiumque diuisione, dolores, moibos, viræ discrimina prodire passim videmus. Igitur, vt in loco fusè dicemus, omnis in inferioribus hisce discordiæ, auersionis, atque antipathiæ ratio, huic vni signorum nulli colligantiæ & ordini accepta ferenda est: vti econtrà omnis ratio sympathiæ, amoris, concordiæ, animi propensionis, ad signorum, siderumque familiaritates, quibuscum ordinem causaliraris habent (vt habet etiam Ptolemæus in Quadrip. lib. 4. cap. 7) reducenda. 13. Hac etiam ratione, ni fallor, anni climacterici, seu schalares, in quibus semper aliqua corporum nostrorum discraria expectanda est, prodeunt, & inconiuncta hac inconiunctorum signorum serie ordinantur. Siquidem singulis sepienarijs, ac nouenarijs recurrentibus, quoniam omnis bona siderum ad radicem Natalis configuratio expleta est, & non sequi-
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14. LEXICON Table of disjoined signs. Aries has disjoined Taurus, and Scorpio. Taurus has Aries, Gemini, Libra, and Sagittarius. Gemini, Taurus, and Scorpio. Cancer, Leo, and Aquarius. Leo, Cancer, Virgo, Capricorn, and Pisces. Virgo, Leo, and Aquarius. Libra, Scorpio, and Taurus. Scorpio, Sagittarius, Libra, Aries, and Gemini. Sagittarius, Scorpio, and Taurus. Capricorn, Leo, and Aquarius. Aquarius, Capricorn, Pisces, Cancer, and Virgo. Pisces, finally, Leo, and Aquarius. 12. Moreover, of these signs, which, as we have just said, are therefore called disjoined, because they are linked by no order or familiarity among themselves, there is hardly anyone who takes care to observe what in these lower things they bring about, whether good or bad: yet, in my judgment, these things ought especially to be observed; and just as a good order of things depends on the order, connection, and consonance of the celestial bodies, with which they have some necessity of being, so too confusion, discord, and disharmony derive their origin from the affections of the same, mutual disagreement, and disjunction, or difference of nature. For the connection, and love, of parts, as Plato wanted, is the soul of the world: if you disturb this order, this harmony even in the least, you will see the very globe disturbed, confounded, and weakened, just as in the human body, from the disturbance of the good order of the humors, and the division of the parts, pain, disease, and the hazards of life are seen to arise everywhere. Therefore, as we shall explain more fully in the place, all the reason for discord, aversion, and antipathy in these lower things is to be attributed to this one lack of connection and order among the signs: whereas, on the contrary, all the reason for sympathy, love, concord, and inclination of mind must be referred to the familiarities of the signs and stars, with which they have a causal order (as Ptolemy also has in Quadrip., book 4, chapter 7). 13. For this same reason also, unless I am mistaken, the climacteric, or scalar, years, in which some change in our bodies is always to be expected, arise, and are arranged by this series of disjoined signs. For in each recurrent septenary and nonary, since every good configuration of the stars to the radix of the Nativity has been completed, and not follo-
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MATHEMATICVM. 249 Arequipa in Peruano regno: Hecla mons in Islandia: Pittacia in Petside: alijque quos referunt Plinius, Maiolus & alij. Quod tum ratio naturalis suadet, tum frequentissimæ historiæ; ac plurium Philosophorum auctoritas. Ratio, inquam, quia ignis quicunque naturaliter euaporare petit, & quoddam spiraculum, vnde exhalare queat, & fumum traiscere, ergò id etiam infernali competet, qui sanè per huiusmodi terræ hiatus exhalat. Accedunt historiæ. Refert enim Henricus Kermanus in lib. de miræ. mortuor in Tutingia apud montem Ferrariam extare quandam voraginem, seu terræ hiatum, qui horrisonus est, & communitet reputatur esse ostium quoddam Inferni; eoquod sæpissimè ex eo audiuntur clamotes, & vlulatus animarum, & circa ipsum ignes quosdam apparere. Simile quid refet, Sutius de Hecla Islandiæ monte, Pompilius Azzelus de rebus natural. lib. 5. cap. 16. Olaus magnus Saxo Grammaticus. Brocardus, & alij multi. Claudianus etiam Poëta in Rufin. lib. 10. meminit cuiusdam loci in Hybernia, qui nunc creditur esse Vorago illa, quam idcircò vulgo appellant Puseum S. Patricij, vnde auditur frequens luctus, & eiulatus animarum. Sic enim ait. Est locus extremum, qua pandit Gallialistus, Oceani prætextus aquis, quo sertur Vlysses, Sanguine libato populum mouisse silentum. Illuc vmbrarum tenui stridore volantum, Fiebilis auditur quasius simulachra coloni, Pallida, defunctasque vident migrare figuras. Huius rei ampliorem historiam, & quomodo precibus S. Patricij Hybernorum Apostoli ad aliquam infernalium tormentorum cognitionem populis ingerendam, vt à malis pattandis auocarentur, fuetit ei à Christo Domino sibi visibilitet apparente monstrata quædam spelunca rotunda, & obscura, quam qui ingrederentur referrent, ibi se immania tormenta perpessos, & vidisse foueas quasdam, & ostia inferni, per quæ damnati proijciebantur: qui, inquam, huius rei vberiorem notitiam volet pluraque testimonia, videat Franciscum Restam de Meteores lib. 1. Tract. 4. cap. 4. Denique in hanc sententiam inclinant, vel certè apertè veniunt multi ex SS. Patribus, Augustinus, Gregorius, Bernardus, Isidorus, Tertullianus, Bonauentura, Petrus Damianus, Bernardinus Senensis, & alij. Vt iam modò nonnihil temeritatis habeat affitmare huiusmodi igniuomos montes, & antra non esse Inferni ostia, & ignis ibi existentis euaporamenta si non ad aliud, certè ad hoc vnum ab Authore Naturæ in varijs terreni orbis locis aperta, vt homines inde ediscerent, leo est
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MATHEMATICVM. 249 Arequipa in the kingdom of Peru; Mount Hecla in Iceland; Pittacia in Petside; and others also, as Pliny, Maiolus, and others relate. This is supported both by natural reason and by very frequent histories; and by the authority of many philosophers. The reason, I say, is that whatever fire naturally seeks to exhale, and some outlet, through which it may breathe out and send forth smoke, therefore this also will be fitting for infernal fire, which indeed exhales through such-like gaps in the earth. Histories are added. For Henry Kermanus relates in the book de miræ. mortuor that in Turingia, near Mount Ferraria, there exists a certain abyss, or fissure in the earth, which is most dreadful in sound, and is commonly held to be a certain door of Hell; because from it are very often heard cries and howlings of souls, and around it certain fires appear. Something similar is reported by Sutius concerning Mount Hecla of Iceland, by Pompilius Azzelus in de rebus natural. book 5, chapter 16, by Olaus Magnus, Saxo Grammaticus, Brocardus, and many others. The poet Claudian also, in Rufin. book 10, mentions a certain place in Ireland, which is now believed to be that same abyss, which for that reason the common people call the Cave of St. Patrick, from which is heard a frequent lamentation and wailing of souls. For thus he says: There is a place, where the farthest edge opens, bordered by the waters of the Ocean, to which Ulysses is borne, having poured out blood, to stir the silent people. There, with a thin whistling of flying shadows, the mournful likeness of the peasant is heard; pale forms are seen, and the departed shapes pass away. A fuller history of this matter, and how, through the prayers of St. Patrick, apostle of the Irish, for the purpose of instilling into the people some knowledge of infernal torments, so that they might be turned away from pursuing evil, it was shown to him by Christ the Lord visibly appearing to him, that a certain round and dark cave should be entered, and that those who entered it would report that they had suffered there immense torments, and had seen certain pits and the gates of hell, through which the damned were cast down: whoever, I say, desires a fuller knowledge of this matter and more testimonies, let him consult Francisco Resta, de Meteores book 1, Treatise 4, chapter 4. Finally, many of the Holy Fathers incline toward this opinion, or certainly come openly to it: Augustine, Gregory, Bernard, Isidore, Tertullian, Bonaventure, Peter Damian, Bernardinus Senensis, and others. So that now it has something of rashness to affirm that such fire-breathing mountains and caves are not the doors of Hell, and the vapors of the fire existing there, if not for any other purpose, certainly for this one, opened by the Author of Nature in various places of the earthly globe, so that men might learn from them, it is a lion
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MATHEMATICVM. 251 < 47.> INTERROGATIONES, seu Quæstiones Astrologicæ dicuntur quæ ex naturali, vt aiunt impulsu de re aliqua, fiunt Astrologo coniectori, vt inde is ex figura cæli ad momentum quæstionis erecta prædicat, quid de tali re futurum sit. De ijs multa vanè scripserunt Arabes, & Iudæi, quos inter ex professo Hali Aben-Ragel, & Guido Bonatus. Non nulla etiam verba ad hanc rem habet Centiloquij Author, vt vel inde euidentet appareat, non esse id Ptolemæi opus, qui in nullo suorum operum eas vnam admisit, aut admisisse viderat. Et quidem si si qua est in rebus Astrologicis vanitas, & dementia, hæc summum apicem tenet. Neque enim naturalis ratio elucet, quomodo cum fortuito interrogantis occursu connexionem vllam habeat cæli positus; quomodo hic & rem futuram indicet, & interrogantem ad sciscitandum impellat; vt benè discurtit Titus in cælesti Philosophia lib. 1. cap. 6. Namque, ait ipse, res futuræ habent naturales suas causas dependentes à radice Natalis, vel à diurnis lationibus, quæ non cohærent cum præsenti siderum habitudine, quæ mouet nosita phantasmaræ opus est enim, vt inter signa, & res significatas sit aliqua connexio. Denique explicati non potest quomodo ex eadem cæli figura ad momentum factæ interrogationis erecta prædici vni ex præliantibus, aut dimicantibus mors, alteri victoria; si profectò eodem tempore, & in ijsdem circumstantijs ab ambobus fiat interrogatio. Sed hanc vanitatem fusè imbrobar Cardanus non vno in loco suorum operum. Maius sanè fundamentum habent Electiones s tum in certo siderum positu factæ, quippe quæ nec ratione, neque experimentis carent. Sed & hæ quoque cum radice natuitatis conferendæ sunt, & inde, vt feliciter exant aggrediendæ. < 48.> INVERSARIF apud Arabes est oppositum Mutatil, cum videlicet Planera existens in corde alterius, & agglutinatus ei vsque ad minutum separatur ab eo vel ad gradum vnum. Ptolemæus in versione Arabica Hali Rodoan. IR < 49.> IRIS Græcè denotat arcum illum cælestem, qui aduerso sole formatur in nube roscida, vel in minutissimis aquæ cadentis guttulis, in quibus tanquam in speculo excipianius solares radij, in orbem diffusi, ac miram illam repræsentent colorum varietatem sua specie mentes hominum præstringentem, atque in Dei laudem trahentem. Vnde Eccl. 4t. dicitur Vide arcum & benedic Deum qui fecit illum: valde spectosus est in splendore suo. Hinc etiam antiquis Thaumantias, hoc est admi-
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MATHEMATICVM. 251 <47.> INTERROGATIONS, or what are called Astrological Questions, are those which, from a natural, as they say, impulse about some matter, are put to the astrologer-conjecturer, so that from the figure of the heavens erected for the moment of the question he may foretell what will happen concerning such a matter. The Arabs and Jews wrote many foolish things about these, among whom especially Hali Aben-Ragel and Guido Bonatus. The author of the Centiloquium also has some words relating to this matter, so that it may even from that be plainly seen that this is not the work of Ptolemy, who in none of his works admitted any one of them, nor was seen to have admitted them. And indeed, if there is any vanity and madness in astrological matters, this holds the highest place. For no natural reason is apparent, how the position of the heavens, upon the chance encounter of the questioner, should have any connection; how it should both indicate the future thing and impel the questioner to inquire; as Titus discourses well in Celestial Philosophy, book 1, chapter 6. For, he says, future things have their natural causes, depending either on the root of nativity, or on daily motions, which do not cohere with the present disposition of the stars, which moves us; the work of imagination is needed, for there must be some connection between the signs and the things signified. Finally, it cannot be explained how, from the same figure of the heavens erected at the moment the question is asked, death may be predicted to one of two combatants, or victory to the other, if indeed the inquiry is made by both at the same time and under the same circumstances. But this vanity Cardanus thoroughly disproved in more than one place in his works. A greater foundation surely belong to Elections made at a certain position of the stars, since these are not without reason or without experience. Yet these too must be compared with the root of nativity, and from that, if successful, undertaken. <48.> INVERSARIF among the Arabs is the opposite of Mutatil, when, namely, a planet being in the heart of another, and bound to it, is separated from it even to the extent of a minute or by one degree. Ptolemy in the Arabic version of Hali Rodoan. IR <49.> IRIS in Greek denotes that celestial bow which is formed opposite the sun in a dewy cloud, or in the very smallest drops of falling water, in which, as in a mirror, the sun’s rays are received, spread in a circle, and represent that wonderful variety of colors, striking the minds of men by their appearance and drawing them to praise God. Hence in Ecclesiasticus 4: it is said, “See the rainbow and bless God who made it: it is very beautiful in its splendor.” Hence also among the ancients it was called Thaumantias, that is, admis-
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142 LEXICON Tabula Signorum inconiunctorum. Aries habet inconiunctum Taurum, & Scorpium. Taurus Arietem, Geminos, Libram, & Sagittarium. Gemini Taurum, & Scorpium. Cancer Leonem, & Aquarium. Leo Cancrum, Virginem, Capricornum, & Pisces. Virgo Leonem, & Aquarium. Libra Scorpium, & Taurum. Scorpio Sagittarium, Libram, Arietem, & Geminos. Sagittarius Scorpium, & Taurum. Capricornus Leonem, & Aquarium. Aquarius Capricornum Pisces, Cancrum, & Virginem. Pisces tandem, Leonem, & Aquarium. 12. Porto horum signorum, quæ, vt modo diximus, ideò coniuncta vocantur, quia nullo inter se ordine, ac familiaritate sunt nexa, nemo ferè est, qui rationem habeat, atque obseruet quænam in inferioribus hisce, seù bona, seù mala importent: cum tamen, meo iudicio, ea maximè seruari debeant; atque vt bonus ordo rerum ex ordine, colligatione, & consonantia cælestium corporum, quibuscum aliquam essendi habent necessitudinem, pendet, ita & perturbatio, discordia, & discrasia ab eorundem affectionibus, mutuo dissidio, ac disiunctione, seù disparitate naturæ, trahit originem. Etenim partium nexus, & amor, vt volebat Plato mundi anima est: hunc ordinem, hanc harmoniam si minimum turbes, & ipsum orbem turbari, confuudi, infirmarique videbis, petinde ac in humano corpore ex humorum bono ordine perturbato, partiumque diuisione, dolores, morbos, vitæ discrimina prodire passim videmus. Igitur, vt in loco fusè dicemus, omnis in inferioribus hisce discordiæ, auersionis, atque antipathiæ ratio, huic vni signorum nulli colligantiæ & ordini accepta ferenda est: vti econtra omnis ratio sympathiæ, amoris, concordiæ, animi propensionis, ad signorum, siderumque familiaritates, quibuscum ordinem causalitatis habent (vt habet etiam Ptolemæus in Quadrip. lib. 4. cap. 7) reducenda. 13. Hac etiam ratione, ni fallor, anni climacterici, seu schalares, in quibus semper aliqua corporum nostrorum discrata expectanda est, prodeunt, & inconiuncta hac inconiunctorum signorum serie ordinantur. Siquidem singulis septenarijs, ac nouenarijs recurrentibus, quoniam omnis bona siderum ad radicem Natalis configuratio expleta est, & non sequi-
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142 LEXICON Table of Inconjunct Signs. Aries has Taurus and Scorpio as inconjunct. Taurus, Aries, Gemini, Libra, and Sagittarius. Gemini, Taurus, and Scorpio. Cancer, Leo, and Aquarius. Leo, Cancer, Virgo, Capricorn, and Pisces. Virgo, Leo, and Aquarius. Libra, Scorpio, and Taurus. Scorpio, Sagittarius, Libra, Aries, and Gemini. Sagittarius, Scorpio, and Taurus. Capricorn, Leo, and Aquarius. Aquarius, Capricorn, Pisces, Cancer, and Virgo. Pisces, lastly, Leo, and Aquarius. 12. Therefore, of these signs, which, as we have just said, are called conjunct because they are bound together by no order or familiarity with one another, there is scarcely anyone who takes care to observe what, in these lower things, they import, whether good or bad: and yet, in my judgment, they ought especially to be considered; and just as the good order of things depends on the order, conjunction, and harmony of the heavenly bodies, with which they have some relation of being, so also disorder, discord, and dyscrasia draw their origin from their affections, mutual disagreement, and separation, or disparity of nature. For the bond and love of the parts, as Plato wished, is the soul of the world: if you disturb this order, this harmony ever so little, you will see the whole sphere itself disturbed, confused, and weakened, just as in the human body we plainly see pains, diseases, and dangers to life arise from the disturbance of the good order of the humors and the division of the parts. Therefore, as we shall discuss at length in its place, all the reason for discord, aversion, and antipathy in these lower things is to be attributed to this lack of conjunction and order among the signs: whereas, on the contrary, all the reason for sympathy, love, concord, and inclination of mind must be referred to the familiarities of the signs and stars, with which they have an order of causality (as Ptolemy also has in Quadrip., book 4, chapter 7). 13. For this same reason, if I am not mistaken, the climacteric years, or “schalar” years, in which some dyscrasia of our bodies must always be expected, arise, and are arranged by this series of inconjunct signs. For with each recurring seven and nine years, since every good configuration of the stars to the radix of the Nativity has been completed, and not fol-
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MATHEMATICVM. 245 qui vitam regendam, substentandamque suscepit, occupabar. Siquidem, quia quarto, sexto, octauo mense succedit in re- gimen signum, quod nulla familiaritate signo horoscopo conceptionis præsidenti conuinctum est, ideò nulla vitæ pro- rogatio expectanda, bene verò cum signa contingunt, quæ cum radicali aliquo ordine, ac familiaritate nectuntur, qualia sunt, quæ quinto, septimo, nono, & reliquis mensibus, ex necessitate subintrant. Denique hæc eadem ratio arrisisse vi- deretur Plutarcho lib. 5. de placitis Philosophorum cap. 18. vbi hæc hithet. Mathematici, inquit, octo menses ad quemuis partum in- sociabiles aiunt, septem sociabiles, quæ incidunt in stellas demibus calestibus dominantes, & sub se natis vitam infælicem, ac non longauam portendunt. Sunt autem insociabilis, quorum vnum cum altero octauum numeratur, vt Aries ad Scorpium, Taurus ad Sagittarium, &c. Hinc fieri, vt septimo, vel decimo mense in lu- cem edita vitalia sint; octauo nati, ob dissidium mundi pereant. Hæc Plutarchus, cui astipulari videtur etiam Fracastorius de Sympathia cap. 1. asserens omnem huius rei rationem refun- dendam esse in sympathiam mensium, adeoque signorum, at- que antipathiam. <37.> INDICTIO est certus quidam annorum numerus & computus describi solitus in Principum Diplomatibus, & scripturis publicis ad dignoscenda recurrentia tempora, sicut Olympia- des, Lustra, & similia: amplectitur enim revolutionem quin- decim annorum, qua expleta, iterum reditur ad vnitatem. Ortum habuit, & nomen sortita est ab indictione Vestigalium, ac tributorum, quam Romani Principes olim vniuerso o[mn]ibi imperitantes populis publicè faciebant. Cum enim comperis- sent, difficile admodum esse ab remotissimis mundi plagis ve- nire singulis annis Romam subiectarum prouinciatum legatos ad soluenda tributa, statuerunt, vt singulis quinquennijs sin- gula soluerentur, & in quindecim totis annis, compleretur tota indicti vestigalis solutio: itaut in primo quinquennio apporta- rent pro tributo ferrum, pro fabricandis a: mis: in secundo ar- gentum pro stipendijs militaribus copijs erogandis: in tertio aurum pro Deorum simulachris fabricandis: & sic semper post aurum, quod in quintodecimo quoque anno ferebatur, inci- piebat quinquennium deputatum ad apportandum ferrum; sicque noua indictio, quasi nouus quidam temporis circuitus incipiebat, vnde nomen huic spatio datum est, quod in publi- cis annalibus describebatur, ac successiuè postea in scripturis pu- blicis registrari semper consueuit, & etiam num eius vsus ei- get, licet alioqui eius ratio cum Romani Imperij sceptro iam exciderit. Prædictum autem spatium quiuque annorum voca- (11)
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MATHEMATICIAN. 245 who was occupied with the matter of governing and sustaining life. For since, in the fourth, sixth, and eighth month, a sign succeeds into rule which is bound by no familiarity to the sign horoscopicly presiding at conception, therefore no prolongation of life is to be expected; but where the signs happen to be such as are joined by some radical order and familiarity, as are those which necessarily come in in the fifth, seventh, ninth, and the remaining months. Finally, this same reasoning would seem to have pleased Plutarch, book 5, De placitis Philosophorum , chapter 18, where he has it thus: “The Mathematici,” he says, “say that eight months are unfavorable to any birth, seven favorable, which fall under stars ruling in the heavenly regions, and portend an unhappy and not long life for those born under them. Those are unfavorable whose one is reckoned eighth from the other, as Aries to Scorpio, Taurus to Sagittarius, etc. Hence it comes that those born in the seventh or tenth month come forth into life vigorous; those born in the eighth perish on account of the discord of the world.” This is Plutarch, to whom Fracastorius also seems to assent in De Sympathia , chapter 1, affirming that the whole reason for this matter must be referred to the sympathy of months, and consequently of signs, and the antipathy of them. <37.> INDICTION is a certain number and reckoning of years, commonly set down in the diplomas of princes and public writings for recognizing recurring times, such as Olympiads, Lustrums, and the like: for it embraces a revolution of fifteen years, when completed, one returns again to unity. It had its origin and took its name from the imposition of taxes and tributes, which the Roman princes, once they had gained dominion over all peoples, used publicly to make. For when they discovered that it was very difficult for the envoys of the subject provinces to come from the remotest parts of the world to Rome every year to pay the taxes, they decreed that each installment should be paid every five years, and that in the whole fifteen years the entire payment of the tax impost should be completed; so that in the first five-year period they would bring iron as tribute, for making weapons; in the second, silver, to be expended on military pay for the troops; in the third, gold, for making statues of the gods; and thus always after the gold, which was carried in the fifteenth year as well, the five-year period assigned for bringing iron would begin again. And so a new indiction, as it were a new circuit of time, began; from this the name was given to this period, which was set down in public annals, and afterward has always been customarily registered successively in public writings, and even now its use remains, although otherwise its basis has already fallen away with the scepter of the Roman Empire. The aforesaid span of five years...
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LEXICON 246 rum est Lustrum, quia eo tempore venientes nuncij prouinciarum ad ferendum triburum cum magna pompa, & comitatu vrbem lustrabant. Olim hic cyclus annorum numerari iucipiebat à die 24. Septembris. Nunc autem post correctionem Gregorianam incipit à Ianuario. Quod si quis quolibet anno currente indictionem venari voluerit, sic facili iure p[er]tæstabit. Annis à Nariuitate Domini excusis adjiciat tres: deinde productum diuidat per quinque, & quod residuum fuerit ex quoriente erit indictio illius anni. Quod si nihil super sit, signum erit, quod eo anno indictio est 15. & complementum cycli. Sic exempli gratia: Anno currenti 1660. addo 3. & fient 1663. summam diuido per 15 & provenient in quoriente 108. & adhuc residuum erit 13. hæc igitur erit indictio præsentis anni. Quod memoriæ ergo non nemo his versibus expressit. Si tribus adiunctis Domini diuiseris annos, Per ter quinque datur indicto certificata. Et hæc quidem de indictione, eiusque instituendæ ratione. INDVS sidus in Cælo ad polum Antarcticum, nobis inconspicuum à recensioribus vnà cum alijs vndecim detectum non ira pridem, atque in hominis indi formam, manu renentis jaculum, figurarum: stellas habet 13. quintæ & sextæ magnitudinis sub signo Capricorni. 39. INFERNVS: & hic nostræ molitionis subiectum. Est enim Vniuersi istius centrum, (unde Hydoro dictus tanquam insus furnus, id est niger.) Locus omnium insimus, obscurus, & abjectissimus, in quem perinde arque in humano corpore viscera, & vmbilicus, omnes mundi sordes, & retrimenta, tanquam in propriam sedem abijcienda sunt peracto finali judicio, vt ex Basilio aduertit D. Thomas in 4. Sentent. distinct. 47. qu. 2. art. 5. Ea propter condignus dæmonum, & damnarorum carcer vbi perperuò morabuntur æternis ignibus addicti. Ex eo verus locus siderum procul quacumque parallaxis deuiatione, obseruari exquisissimè posset, si telluris densitas, obuiret. Lessius existimar eius diametrum non excedere vnius milliarj belgici mensuram: quippe, ait circumferentia eius tantæ amplitudinis erit, vt optimè capax esse possit tot millium corporum, quot planè vero similiter coniectari possumus, futuros esse damnatos. Putat enim eos ibi locandos post acceptam Iudicis senteniam illam Ite maledicti in ignem æternum, tanquam muriaricos pisces in dolio, ita vt aliter alterum premat, nec vllum aliud spatium sit, quod non corporibus repleatur. Franciscus Ribeta in Apocalyps. cap. 14 probabiliter coniectæ infernæ diametrum esse longam ducentis italicis milliarj,
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LEXICON 246 It is called a lustrum because at that time the envoys of the provinces, coming to bring the tribute with great pomp and escort, made the city ritually clean. Formerly this cycle of years began to be reckoned from the 24th day of September. Now, however, after the Gregorian correction, it begins from January. If anyone wishes, in any current year, to determine the indiction, he will do so by this easy rule. Let him add three to the years counted from the Nativity of the Lord; then divide the product by five, and whatever remains from the quotient will be the indiction of that year. But if nothing remains, it will be a sign that in that year the indiction is 15, and the completion of the cycle. Thus, for example: in the current year 1660, I add 3, and it becomes 1663. I divide the total by 15, and there will result in the quotient 108, and there will still remain 13; therefore this will be the indiction of the present year. For the sake of memory, someone has expressed this in these verses. If you have divided the years of the Lord by three added together, By three times five is given, the indiction certified. And this indeed concerns the indiction and the method of establishing it. INDUS, a star in the sky near the Antarctic pole, invisible to us, recently discovered together with eleven others, and figured in the form of a man of India holding a dart in his hand; it has 13 stars of the fifth and sixth magnitude under the sign of Capricorn. 39. INFERNUS: and this too is a subject of our inquiry. For it is the center of this universe, (whence it is called by Hydoro, as if an insus furnace, that is, black.) The lowest, darkest, and most abject place of all, into which, just as in the human body the entrails and the navel, so all the filth and refuse of the world are to be cast, as into their proper seat, after the final judgment has been completed, as St. Thomas notes from Basil in 4 Sentent. dist. 47, q. 2, art. 5. Therefore it is the fitting prison of the demons and the damned, where they will dwell forever, bound to eternal fires. From it, the true position of the stars could be observed most accurately, far from any deviation of parallax, if the thickness of the earth did not obstruct it. Lessius thinks its diameter does not exceed the measure of one Belgian mile: for, he says, its circumference will be of such size that it can very well be capable of so many thousands of bodies as we can truly and similarly conjecture the damned will be. For he thinks they are to be placed there after receiving the Judge’s sentence, “Depart, cursed ones, into eternal fire,” like salted fish in a barrel, so that one presses upon another, and there is no other space that is not filled with bodies. Francisco Ribera in Apocalyps. cap. 14 conjectures probably that the diameter of hell is two hundred Italian miles long,
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MATHEMATICVM. 253 sequitur. Vnde ab ipsomet Conditore Deo post diluuum po- sita est in signum serenitatis, & foederis, inter ipsum & homines, ne deinceps aquis diluuij perderet omnem carnem. Quod quidem mysticè explicat de Christi humanitate Iacobus Episcopus Christopolitanus in expositione Cantici Habacue in illa verba suscitans suscitabis arcum suum, iuramenta tribubus, quæ loquutus es. < 52.> Dices, qualiter Deus Pater sit instar Solis fontis, & principij omnis lucis diuinitatis, qui debebat imprimere imaginem suam in nube humanitatis, id est mittere filium suum, qui est imago Patris in carnem; qui debebat lasere in nube humanitatis: in qua persona sunt tres substantia, scilices Verbum, anima, & Caro, ex quibus constituitur vnica persona sub vnico esse personali, & diuino. Qui quidem arcus diuinus debebat fugare omnem tempestatem, & totum diluuium peccatorum, & sedare omnes tenbras veteris pacti, & inducere lucem, & serenitatem grata. Ad quem arcum sapiens pater non amplius debebat recordari veteris pacti: immò Deus respiciens illum arcum qui est filius incarnatus, illicò recordatur foederis promissi inter ipsum, & genus humanum. Et sic Pater respiciens illum arcum in cruce recordatus foederis promissi remisit pactum toti generi humano. Hucusque Episcopus Christopolitanus piè quidem, & eruditè nimis. Sed longè à nostro instituto aberrauimus. Hæc sufficiant. IRINA Virgarum species apud Arist. ab Inde dicta pluuix certum præsagium: de qua vide in V. Virga. < 53.> I S ISARITHMI Græcè significant prima numerorum elementa quæ in decem figuris continentur, quas nos in V. Abaculi < 54.> explicauimus ab Isag, quod initium, & rythmos qui numerum denotat, deriuarum. Porro Isorythma numero paria significat, ab Iso, quod est æquale. Hiue Isomaros dicitur quod æquales continet partes. Sic ISAGONIVS est figura Geometrica æqualibus angulis con- < 55.> stans. ISOPERIMETRAE figuræ, quæ æqualem habent circumferentiam, & his similia pari ratione. < 56.> ISOMÆRINOS sæpissimè apud scriptores Græcanicos dicitur < 57.> Æquator, & Circulus æquinoctialis, eoquod æquet diebus noctes, & æquales diuidatur in partes. Iis etiam Græcè præcipuè apud Hermetem dicitur stella < 58.> fixa in Canis aure sinistra. At Auieno audit Virginis sidus. ISOSCELES est figura Geometrica triangularis, quæ duo tan- < 59.> tum latera habeat æqualia, tertium vetò neutro æquale, sed aut
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MATHEMATICVM. 253 follows. Hence, after the Flood, by God himself the Creator, it was placed as a sign of serenity and of the covenant between himself and men, lest thereafter he should destroy all flesh with the waters of the Flood. This indeed is mystically explained concerning Christ’s humanity by Bishop Jacob of Christopolis in his exposition of the Song of Habakkuk, in those words, “raising, thou shalt raise his bow, the oaths to the tribes which thou hast spoken.” <52.> You will say how God the Father is like the fountain of the Sun, and the principle of all light of divinity, who ought to imprint his image in the cloud of humanity, that is, send his Son, who is the image of the Father, into flesh; who ought to shine in the cloud of humanity: in which person there are three substances, namely the Word, the soul, and the flesh, from which one person is constituted under one personal and divine being. This divine bow indeed ought to drive away every storm, and the whole flood of sins, and to calm all the darkness of the old covenant, and to bring in light and a welcome serenity. At this bow the wise Father ought no longer to remember the old covenant: rather, God, regarding that bow which is the incarnate Son, immediately remembers the promised covenant between himself and the human race. And so the Father, looking upon that bow on the cross, remembered the promised covenant and remitted the pact to the whole human race. Thus far Bishop Christopolitanus, piously indeed, and too learnedly. But we have wandered far from our purpose. Let these things suffice. IRINA is a kind of rod, according to Aristotle, said to be a certain omen of rain: see under V. Virga. <53.> I S ISARITHMI in Greek signify the first elements of numbers, which are contained in the ten figures, which we explained under V. Abaculi <54.>, deriving it from Isag, meaning beginning, and rhythmos, which denotes number. Moreover, Isorythma signifies equal in number, from Iso, which means equal. Hence Isomaros is said, because it contains equal parts. Thus ISAGONIVS is a geometric figure consisting of equal angles. <55.> ISOPERIMETRAE are figures which have equal circumference, and the like by a similar relation. <56.> ISOMÆRINOS is very often called by Greek writers <57.> the Equator, and the equinoctial circle, because it makes nights equal to days, and is divided into equal parts. It is also called in Greek, especially by Hermes, the fixed star in the left ear of Canis. But by Avienus it is called the Virgin’s star. ISOSCELES is a triangular geometric figure, which has only two equal sides, but the third equal to neither, but either
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LEXICON K. 1. KABAR, seu Elkabar Elscheer Chaldaice Latinè Canis maior sidus, ira Kircherus in Oedipo. 2. KACHITICHI Græcè Latinè interpretatur Mala fortuna. Apud Astronomos hac notione signarut sexra domus ab Horoscopo cadens ab angulo Imi Cæli, locus infælix, & omnium iocorum cæli abiectissimus: quippequi, & cadens, & suberraneus, & nulla familiaritate cum horoscopo copularur. Ideò ex ea sumuntur significationes de nari valetudine, infirmitate, sururis morbis, ac vitijs corporis, alijsque malis bonam corporis constitutionem, ac temperiem infestantibus. Significar eriam seruos, ancillas, animalia minora, & commoda, vel incommoda, quæ inde perceptrurus sit natus. Habet debilitatis quatuor parres: colorem sibi vendicat nigrum, & gaudet in ea Mars. KALB. Arabicè idem sonat, ac meditullium, penetralia, 3. Cor. Vnde Kalb Alarrab idem valet, ac Cor scorpij. Kalb Alpharad, ac Latinè cor hydræ. Kalb Eleced, Cor Leonis, & sic discurre. Quorum omnium naturam & qualitates si s quæris vide sub propijs nominibus. KAYTOS vel cum articulo Elkaytos Arab. idem sonat ac Latinè Cetus, balena, &c. sidus in australi plaga continens apud Ptolemæum stellas 22 apud Keplerum 21. & apud Bayerum 27. in eo præcipuà Natis, quæ etiam Mandibula dicitur, Arab. Menchar: Tum Lucidior, & australior in cauda dicta Deneb Kaytos: tandem media in Ventrè, Baten siue Bara-Kaytos omnes de natura Saturni. KALVROPS, scu Alkalutops. Arab. dicitur hostile Bootis 5. stella fixa de qua in V. Ceginus. 6. KENEN SATVRNI dicitur in sphæra barbarica, tertius Decanus Sagittarij maneris sub dominatu Saturni, habensque significare obstinacionem in proposito contradicendi, dexteritatem in malis rixis, & factis abominabilibus. 7. KERTHO Chaldaicè dicitur signum, & constellatio Sagittarij apud Hebræos aurem Keschesh. Testis est Kircherus in Oedipo Ægyptriaco. 8. KESIL scu Kesil Hebraicè dicitur sidus Orionis, de quo vide in V. lugula. Item 9. KETPHOLT SVMMAN corrupto nomine Garaclos Chaldaicè dicitur Hercules sen fixa secundæ magnitudinis in capite alterius Geminorum existens: dicitur etiam Abrachalens de qua vide ibi. KIMACH
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LEXICON K. 1. KABAR, or Elkabar Elscheer, in Chaldaic, in Latin, the greater Dog Star, by Kircher in Oedipus. 2. KACHITICHI in Greek, in Latin, signifies bad fortune. Among astronomers this name denotes the sixth house falling from the Horoscope, from the angle of the lower heaven, an unlucky place, and the lowest of all the places of the heavens: since it is both falling and subterranean, and joined to the horoscope by no familiarity. Therefore from it are taken significations of bodily health, weakness, surfeit, diseases, and defects of the body, and other evils that assail a good bodily constitution and temperament. It also signifies servants, maidservants, smaller animals, and the goods or inconveniences that the native shall derive from it. It has four parts of debility: it claims the color black, and Mars delights in it. KALB. In Arabic it means the same as center, inward parts, 3. heart. Hence Kalb Alarrab has the same meaning as the heart of Scorpius. Kalb Alpharad, as in Latin, the heart of Hydra. Kalb Eleced, the Heart of Leo, and so on. If you seek the nature and qualities of all these, see under their proper names. KAYTOS, or with the article Elkaytos, in Arabic, means the same as in Latin, Cetus, whale, etc.; a constellation in the southern region, containing 22 stars according to Ptolemy, 21 according to Kepler, and 27 according to Bayer; in it, the chief star is Natis, which is also called the Jaw, Arabic Menchar. Then the brighter and more southern one in the tail, called Deneb Kaytos; finally the middle one in the Belly, Baten or Bara-Kaytos; all of the nature of Saturn. KALVROPS, or Alkalutops. In Arabic, it is said to be the hostile fixed star of Bootes, 5. of which in V. Ceginus. 6. KENEN SATVRTNI is called, in the barbarous sphere, the third decan of Sagittarius, under the dominion of Saturn, and it is said to signify stubbornness in a chosen purpose, skill in evil quarrels, and abominable deeds. 7. KERTHO in Chaldaic is said to be the sign and constellation of Sagittarius among the Hebrews, the ear of Keschesh. Kircher is witness in Oedipus Aegyptiacus. 8. KESIL, or Kesil, in Hebrew is called the constellation of Orion, concerning which see in V. lugula. Likewise 9. KETPHOLT SVMMAN, by a corrupted name Garaclos, in Chaldaic is called Hercules, or the fixed star of the second magnitude, standing in the head of the other Gemini: it is also called Abrachalens, see there. KIMACH
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MATHEMATICVM. 263 LINEA autem veri motus, vel apparentis est linea recta ducta à centro terræ per centrum sideris vsque ad Eclipticam, vel sane à superficie terræ. Qua de re vide Ricciol. in Almagesto lib. 10. sect. 6. cap. 2. LO LOGARYTHMICA est pars Arithmeticæ, quæ per loga- rythmos hoc est per numeros absolutos tradit facilem metho- dum soluendi triangula præsertim sphærica, & ex solutione docet condere tabulas astronomicas: siquidem ope illius regu- la illa celebris aurea dicta per quam facile absoluitur sola ad- ditione facta numerorum artificialium, & muliò citiùs res ex- peditur, quam per tabulas sinuum tangentium & secantium. De qua re vide etiam ipsum Ricciol. 10. 2. Almagesti lib. 1. trigonometrico. Hinc LOGARITHMI sunt numeri artificiales ab Arithmeticis eo studio excogitati, vt substituti loco numerorum naturalium, apti sint in ijs manifestare quancumque differentiam progres- sivam. Seruant enim easdem differentias numerales, seù mavis dicam, seruant in seipsis semper, & constantissimè eandem pro- gressionem arithmaticam, quandiu illi, quorum loco sunt con- stituti seruat progressionem geometricam. Hinc est, vt quando 4 numeri habent proportionem ad inuicem, summa logarithmorum primi, & vltimi numeri sit æqualis summæ mediorum. vt si v. g. statuantur duo numeri 4. & 8. quorum alter est altero duplo maior, inde sit, vt eadem proportio sit inter om- nes numeros duplo maiores ad inuicem: sicque inter 5. & 10. inter 12. & 24. inter 24. & 48 inter 50. & 100. & sic deinceps eadem proportio semper seruetur: Quapropter logarithmi num. 4. & 10. 4. & 24. 4. & 48. 4. & 100. &c. simul iuncti æquales inueniuntur aggregato logarithmorum 8 & 5. 8. & 12. 8. & 24. 8. & 50. &c. eoquia, vt dictum est, eadem proportio arithmatica seruatur in logarithmis, quæ geometricè inueni- tur in numeris naturalibus, quorum loco illi substituuntur. Ex quo sit, vt magna vtilitas eorum ope arithmeticis cedat, ma- gnumque temporis lucrum: Quod enim per regulam auream fastidioso calculo, ac longo nimis circuitu per multiplicationem, ac diuisionem sit, vt tandem inueniatur quartus nume- rus ignorus ex tribus notis; id per logarithmos vna & simplici operatione perficitur. Nam si duo numeri multiplicandi sint, acceptis eorum logarithmis, habetur intentum sola additione. Si alter il alterum diuidendus; id per logarithmos sit sola sub- tractione. Quinimò si adhibetur residuum logarithmi, quod complementum arithmaticum vocant, exhibebunt nuluplica- R iii)
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MATHEMATICVM. 263 The line of true motion, or apparent motion, is a straight line drawn from the center of the earth through the center of the star to the Ecliptic, or indeed from the surface of the earth. On this matter see Ricciol., in the Almagest, book 10, sect. 6, chap. 2. LO LOGARITHMICA is a part of Arithmetic, which, by means of loga- rithms, that is, by absolute numbers, teaches an easy method of solving tri- angles, especially spherical ones, and from the solution teaches how to construct astronomical tables: since by its aid that famous rule called the golden rule is easily performed, by which, with only the addition of artificial numbers, the result is obtained much more quickly than by tables of sines, tangents, and secants. On this matter see also Ricciol. 10. 2. of the Almagest, book 1, trigonometric. Hence LOGARITHMS are artificial numbers devised by mathematicians with this purpose, that, when substituted in the place of natural numbers, they may be fit to show in them whatever progressive difference. For they preserve the same numerical differences, or, if you prefer, they always preserve in themselves the same and most constant arithmetic progression, as long as those in whose place they are set preserve a geometric progression. Hence it is that, when 4 numbers are in proportion to one another, the sum of the logarithms of the first and last number is equal to the sum of the middles. For example, if two numbers, 4 and 8, are set down, of which one is twice as large as the other, it follows that the same proportion exists among all numbers that are twice as large in relation to one another: thus between 5 and 10, between 12 and 24, between 24 and 48, between 50 and 100, and so on, the same proportion is always preserved. Wherefore the logarithms of 4 and 10, 4 and 24, 4 and 48, 4 and 100, and so forth, taken together, are found equal to the aggregate of the logarithms of 8 and 5, 8 and 12, 8 and 24, 8 and 50, and so forth, because, as has been said, the same arithmetic proportion is preserved in logarithms as is found geometrically in the natural numbers, in whose place they are substituted. From this it follows that by their aid there is great usefulness for mathematicians, and a great saving of time: for what by the golden rule, with tedious calculation and an excessively long circuit through multiplication and division, would be needed so that the fourth unknown number may at last be found from three known ones; that is accomplished by logarithms in one single and simple operation. For if two numbers are to be multiplied, taking their logarithms, the desired result is obtained by addition alone. If one is to be divided by the other, this is done by logarithms by subtraction alone. Indeed, if the residue of the logarithm is used, which they call the arithmetic complement, they will display nuluplica- R iii)
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Lexicon tionem, ac diuisionem iam factam sola expunctione primæ si- guræ: quod sanè ingens operæ compendium est, magnum la- boris leuamen, dignumque magnæ illius aureæ regulæ operam frustrare laudem assequi, palmam pioripere. Ideicò ad maiorem commoditatem, quò numerorum natu- ralium fractiones penè insensibiles fiant, logarithmus nume- ri 1. ab inuentoribus artis statutus est 0. logarithmus 10. 10000000. logarithm. 100. 20000000 logarithm. 1000. 30000000. & sic de reliquis progrediendo in infinitum, ob- seruando semper quod prima figura logarithmi, quæ ideò ap- pellatur Characteristica, sit in numero vno minor figuris, qui- bus numerus naturalis consistit, vt si numerus propositus sit sex figurarum, prima figura logarithmi sit 7. si constet ille decem figuris prima logarithmi sit 9. & c. eoquia numerum eius implei numerus figurarum logarithmi sic constitui. Porrò logarithmi alij constituti sunt pro numeris naturali- bus absolutè sumpiis, alij pro numeris aruum circuli, seu angulorum, quos arcus ipsi mesuntur, vicemque gerunt ac sibi officium feliciùs assumunt, quod est proprium tabulæ si- num, tangentium, & secantium. Quandoquidem accipiuntur logarithmi duorum mediorum sinuum, seu tangentium, aut secantium, quibus simul iunctis, si ex summa subtrahatur lo- garithmus primi numeri, reliquum erit logarithmus quarti quem querimus, è regione cuius in tabulis sinuum, tangen- tium, & secantium habetur numerus quartus quæsitus. Extant tabulæ absolutissimæ logarithmorum iam numerorum natura- lum ab vnitare ad 10000. quam sinuum, & tangentium è re- gione ipsarum tabularum, magno cum laboris foenore editæ nuper ab Adriano Vlacq. Hagæ comitum anno 1661. vbi vni- co ictu oculi habentur, & gradus, & minuta aruum; & sinus, tangentes atque secantes, & regione ipsarum eorum logarith- mi, vt iam nil desu studioso Trignomerriæ, quin omnem triangulorum resolutionem facili iure assequi possit, nec fasti- dioso labore teneri. Qui plura hac de re volei adeat Arithme- ticam logarithmicam Henrici Briggi, vbi tota natura, fun- damentum, & excellentissimus vsus logarithmorum in omni- bus quæstionibus Arithmeticis, & Geometricis luculentissimè demonstratur. Logistica item pars est Arithmeticæ, quæ regulas suppu- tandi, multiplicandi, & partiendi applicar gradibus signorum, circulorum, & angulorum: nec non & diebus horisque atque ipsorum graduum, horarumque munitis, seu sexagenis, & se- xagenarum sexagenis vsque ad decima. Longitudo apud Astronomos atteuditur in Zodiaco à pri-
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Lexicon tionem, and division already made by the sole removal of the first sign; which surely is a very great saving of labor, a great relief of work, and worthy of attaining the praise of frustrating the work of that great golden rule, of carrying off the prize. Therefore, for greater convenience, so that the fractions of natural numbers may become almost imperceptible, the logarithm of the number 1 was established by the inventors of the art as 0; the logarithm of 10, 10000000. logarithm. 100, 20000000 logarithm. 1000. 30000000. and so on for the rest, proceeding to infinity, always observing that the first figure of the logarithm, which is therefore called the Characteristic, is in one number less than the figures by which the natural number consists, so that if the proposed number be of six figures, the first figure of the logarithm be 7; if that one consist of ten figures, the first of the logarithm be 9, and so on, because the number of figures of the logarithm is thus constituted to fill its number. Moreover, some logarithms have been established for natural numbers taken absolutely, others for the numbers of arcs of the circle, or of angles, which arcs themselves are measured by them and perform their office in place of them more happily, which is proper to the tables of sines, tangents, and secants. Since the logarithms of two mean sines, or tangents, or secants are taken, which when joined together, if the logarithm of the first number be subtracted from the sum, the remainder will be the logarithm of the fourth which we seek; opposite which in the tables of sines, tangents, and secants is found the fourth sought number. There are extant most complete tables of logarithms now of natural numbers from 1 to 10000, as well as of sines and tangents opposite the tables themselves, recently published with great labor’s profit by Adrianus Vlacq, at The Hague of the Counts, in the year 1661, where at a single glance are found both degrees and minutes of arcs; and sines, tangents, and secants, and opposite these their logarithms, so that nothing is now lacking to the student of Trignomerry, and he may be able to attain every solution of triangles by easy right, nor be held back by tiresome labor. Whoever wishes more on this matter should consult the Logarithmic Arithmetic of Henry Briggs, where the whole nature, foundation, and most excellent use of logarithms in all Arithmetic and Geometric questions is most clearly demonstrated. Logistic also is a part of Arithmetic, which applies the rules of calculating, multiplying, and dividing to the degrees of signs, circles, and angles; and also to days and hours and to the minutes of the same degrees and hours, or sixties, and sixties of sixties, up to the decimal. Length among astronomers is considered in the zodiac from the first
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268 LEXICON significatores ac largitores omnium bonorum vnde nil mirum, si impedita in deliquijs eorum luce, impediatur etiam aliquatenus actio, & influxus, ex quo demum eueniant morbi aëris corruptela, sterilitas terræ, caloris innati defectus, humidi radicalis extinctio, & alia id genus, quæ deficientibus causis primarijs arguunt etiam effectuum consequentiam. Quapropter iure, & consequenter arguens magnus ille Areopagita in magno illo, ac præternaturali Luminarium defectu in passione Domini exclamasse fertur: Aus Deus natura patitur, aus mundi machina dissoluetur, quia vide- licet fine peculiari Dei assistentia, & miraculo mundi machina diu consistere non potuisset, quandiu à luminaribus, ac Sole præsertim tanto tempore obscurato, lucem adeoque vitam, haurire non ei foret permissum Sed de hac re satis: Plura cum de ipsis luminaribus singillatim redibit sermo. <43.> In suo lumine dici solet esse Planeta cum est in loco suæ naturæ conformi, hoc est, vt diurnus sit de die suprà terram, & de nocte sub terra: sicut econtrà nocturnus de nocte sit supra terram, & de die sub terra: & insuper sit in loco apto ad rem quæ per ipsum naturaliter significetur. <44.> LVNA luminare minus sic dicta quasi contracti à lucuna eo quod cum Sole aliquando luceat, vel vt placet Isidoro à Lucina, abiecta media sillaba, vna ex septem erraticis proximior terræ, planeta foemininus, ac nocturnus, quippequi (vt paulò ante dictum est) cum habeat lumen à Sole mutuatum, & extensum magis, quam intensum vincit in qualitatibus passiuis, atque in humiditate: & ideò, vt Sol præest cordi, spiritibus, sanguini, &c. ita & Luna præest cerebro, visceribus, pituitæ, & quemadmodum Sol potentiæ vitalis scaturigo est, ita Luna potentiæ naturalis. Quantam verò in terris actiuitatem habeat Luna, nemo est, qui non videat: vnde meritò à D. Ambrosio in Hexamer. Maseroris, decor noctis, ministra humoris, maris dominatrix, mensura temporis, motrix aëris Solis, denique æmula appellatur. Idque oritur tum ex eius propinquitate ad terram, tum etiam ex maiori consistentia: plus enim quam reliqui planetæ suprà terram consistit, motu suo resistens motui primi mobilis, atque vna ferè integra hora plus alijs nostrum hemisphærium perlustrans. Perficit enim cursum suum in Zodiaco spatio dierum 27. hor. 7. min. 41. cum alias quousque ad Solem iterum feratur, requirantur dies 29. hor. 12. min. 44. Hinc triplex mensis, & Lunarium vicissitudinum momenta tria à scriptoribus communiter assignantur. Periodicus, seu peragrationis, in quo Luna complet integram revolutionem in Zodiaco, & reuertitur ad idem
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268 LEXICON signifiers and bestowers of all good things; whence it is no wonder if, through the light hindered in their faults, action and influence are also in some measure hindered, from which at last arise diseases, corruption of the air, barrenness of the earth, defect of innate heat, extinction of the radical moisture, and other things of that kind, which, causes being deficient, also argue the consequence of effects. Wherefore, rightly and consequently arguing, that great Areopagite is said to have cried out in that great and preternatural defect of the Luminaries at the Passion of the Lord: Aus God suffers in nature, or the machine of the world will be dissolved, because, namely, without the special assistance of God and a miracle, the machine of the world could not have long stood, so long as from the luminaries, and especially the Sun darkened for so long a time, it was not permitted to it to draw light and therefore life. But enough on this matter: more will be said later when we come in detail to the luminaries themselves. <43.> In suo lumine a planet is said to be when it is in a place conformable to its nature, that is, when it is diurnal by day above the earth, and by night beneath the earth: just as, conversely, a nocturnal planet is by night above the earth and by day beneath the earth: and in addition it must be in a place fit for the thing which is naturally signified through it. <44.> LVNA, the lesser luminary, is so called as if contracted from lucuna because, when it sometimes shines together with the Sun, or, as Isidore prefers, from Lucina, with the middle syllable removed, one of the seven wandering stars, nearest the earth, a feminine and nocturnal planet, since indeed (as was said a little before) because it has its light borrowed from the Sun, and is more extended than intense, it prevails in passive qualities and in moisture: and therefore, as the Sun presides over the heart, spirits, blood, etc., so also the Moon presides over the brain, the viscera, phlegm; and just as the Sun is the source of vital power, so the Moon is of natural power. But how much activity the Moon has on earth, there is no one who does not see: wherefore deservedly by St. Ambrose in Hexameron, Maseroris, adornment of night, minister of moisture, ruler of the sea, measure of time, mover of the air, rival of the Sun, and finally emulation, she is called. And this arises both from her proximity to the earth and also from her greater consistency: for she stands above the earth more than the other planets, resisting by her motion the motion of the first mobile, and traversing our hemisphere by almost a whole hour more than the others. For she completes her course in the Zodiac in the space of 27 days, 7 hours, 41 minutes. Whereas otherwise, until she is again brought back to the Sun, there are required 29 days, 12 hours, 44 minutes. Hence three kinds of month, and three moments of lunar vicissitudes, are commonly assigned by writers. Periodic, or of traversal, in which the Moon completes an entire revolution in the Zodiac and returns to the same
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MATHEMATICVM. 169 punctum, vnde discesserat; synodicus, seu coniunctionalis, & est quem modò explicaui, in quo à Sole discedens, iterum ad ipsum reueritur, vt ei corpore iungatur; ac terius, quem dicunt apparitionis, seu illuminationis in quo Luna viuibilis est, & lumen suum exerit, quod sit spatio dierum 26. hor. 12. reliquis tribus diebus silens . quæ causa omnis motionis in hisce inferioribus, vt præ cæteris obseruat Plinius lib. 2. cap. 45. 99. Cæterum Lunare corpus sphæricum est, densum, opacumque, nulla præditum luce, sed tota quam habet à Sole mutuata: Hinc pro diverso, ac multiplici ad Solem positu, aspectus, ac figuræ diuersitas, quas Phases dixere. Nam quamuis perpetuò eius medietas illustretur à Sole, & eò magis quò Sol vicinior; (vt enim habetur ex opticis, sphæra maior luminosa intensiùs, & ampliùs lumen suum commuicat sphæræ minori è proximo illi obiectæ, quam è longinquo,) nihilominus non eodem modo semper à nobis conspicitur, sed pro diuersa ad terram habitudine, modò tota obscura (quod in Solari defectione, maximè obseruari potest, vbi conspicitur quidem Lunare corpus Soli aduersum, sed prorsus obscurum, cum ea medietas nobis obuersa à solaribus radijs minimè attingatur, sed ea rantum, quæ nobis inconspicua est,) modò corniculata, modò dichotoma, modò demum in Solis oppositione, plena, & eâ parie totà, quæ nobis offertur, tota etiam illuminata conspicitur. Quod autem etiam in plenilunio aliquæ maculæ, seù eius particulæ minùs illustratæ videantur, existimauit Plinius lib. 2. cap. 9. eas aliud non esse, quam terra raptas cum humore fordes. Arcesila verò partes adustas, & nigras. Tales econìrà partes humidiores, quibus igneus orbis attemperatur; sicut inquit etiam Diodorus in Cælena: Luna semperat ignis astum, ne orbem consummas, & perdas: Philolaus, eas montes, ac sylvas autumar: alij demum purant id oriri ex telluris effigie imbutæ aliqua luce à Sole illi communicata (quod ego sanè non item inficias) quam postea Luna tanquam speculum in se recipêret, ac referret. Verum ex hoc necessariò sequeretur, in varijs horizontis paribus, & pro diuersa telluris ad Lunam habitudine variandas fore huiusmodi maculas; quod tamen experientia falsitatis euincit; cum semper, & vbique locorum ipsa eandem formam retineat. Quare concludendum est, eas nil aliud esse, quam partes densiores, pressiores, & rudiores ipsius corporis Lunaris, quæ Solis lumen excipere æquè non possunt, ac quæ magis planæ ac lauigatæ: Quod etiam in tellure à Solis radijs illustrata fieri credendum est. Hinc diuersitas illa aspectuum; maria, montes, valles, fluiuos, campos
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MATHEMATICVM. 169 the point from which it had departed; synodic, or conjunctional, and this is the one I have just explained, in which, departing from the Sun, it returns again to it, so as to be joined to it in body; and a third, which they call the apparition, or illumination, in which the Moon is visible, and displays its light, which lasts for 26 days, 12 hours; for the remaining three days it is silent. This is the cause of all motion in these lower regions, as Pliny observes above all others, book 2, chap. 45. 99. Moreover, the lunar body is spherical, dense, and opaque, endowed with no light of its own, but wholly borrowed from the Sun. Hence, according to its different and multiple positions relative to the Sun, comes the diversity of aspect and figure, which they called phases. For although its half is perpetually illuminated by the Sun, and the more so the closer the Sun is; (for, as is found from optics, a larger luminous sphere more intensely and more broadly communicates its light to a smaller sphere placed near it than from a distance,) nevertheless it is not always seen by us in the same way, but according to its different relation to the earth, sometimes wholly dark (which can especially be observed in a solar eclipse, where the lunar body is seen opposite the Sun indeed, but entirely dark, since that hemisphere turned toward us is by no means reached by the solar rays, but only the one that is invisible to us), sometimes horned, sometimes dichotomous, and finally, at the opposition of the Sun, full, and with that whole part which is presented to us also seen as wholly illuminated. But that even in the full moon certain spots, or parts of it less brightly illuminated, appear, Pliny, book 2, chap. 9, thought these to be nothing other than dirt dragged from the earth together with moisture. Arcesilas, however, said they were burnt and black parts. Others said they were more humid parts, by which the fiery orb is moderated; as Diodorus also says in Celena: “The Moon always [feeds] the heat of fire, lest it consume the orb and destroy it.” Philolaus supposes them to be mountains and forests; others finally think that this arises from the figure of the earth, imbued with some light communicated to it by the Sun (which I certainly do not deny in that way), which the Moon would later receive in itself and reflect, like a mirror. But from this it would necessarily follow that, in different horizons and according to the different relation of the earth to the Moon, such spots would have to vary; yet experience proves this false, since it retains the same form always and everywhere. Therefore it must be concluded that they are nothing other than the denser, more compact, and rougher parts of the lunar body itself, which cannot receive the Sun’s light equally as the more flat and smooth parts. The same must be believed to happen also in the earth, when it is illuminated by the Sun’s rays. Hence that diversity of aspects: seas, mountains, valleys, rivers, fields
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MATHEMATICVM: 271 litatibus, quibus proinde affectam, obseruauit antiquitas, varios diuersosque influendi modos induere in isthæc inferio- ra. Earum origo vti ab initio bona, innocens, naturalis, ta- zioni atque experientiæ conformis fuit; sic post modum Ægyptiorum vanitatibus deprauata, nullum est in tota Astro- logia commentum, cui in vanitate cedat. Copi eas suo gentili vocabulo quasi Lunæ diuersoria, seu habitacula nominant, alij Deorum stationes, rectius cum Kirchero dixeris, Dæ- moniorum stabula, cum tot tantisque superstitionibus sint referta. Et quoniam Luna cursum suum perficit diebus ferè 28. ideò singulis diebus singulas mansiones constituerunt, singulis proprias notiones, ac certa rerum significata attribuentes, & quod magis mireris, singulis suos genios, seu dæmones ad- ministros præficientes. Placet hic ad lectorum curiosirem leuandam ex Kircheri Oedipo, prout in eorum monumentis iacent, transcribere: inde eas nitori suo redditas, atque ab Argolo ad isthuc tempus diligenrissimè supputatas ex ponere, quoniam, vt dixi, omni superstitione abiecta ad solum natu- raliter consideratæ ex diuerso Lunæ cum stellis fixis congressu, experientia duce plurimum valent in rerum electionibus. Ergò Prima Lunæ mansio, quam Ægyptij stationem piscis dixerunt à ventre Ceti stella videlicet fixa dènatura Saturni, quæ incidebat in eam, proindeque infestationis inimicorum appellabant, cuique genium præficiebant nemine Kiacel, com- butabatur olim ab initio Arietis vsque ad 12. gradum eiusdem. Hanc modò Argolus temperatam vocat, ac figit in gr. 22. Arietis; dicitque esse idoneam ad medicinam laxatiuam su- mendam, atque iter quodcumque arripiendum. < II.> Statio, quam antiqui reconciliationis Principum appellabant, dantes ei pro genio Hiaiel computabatur à 12. gradu Arietis, vsque ad 25. ob fixam in capite eiusdem Arietis. Moderni autem eam constituunt in gr. 4. Tauri, quam dicunt aptam ad ferendum plantandum, atque iter faciendum per aquam, verum purgationibus inopportunam. < III.> Statio, quam Ægyptij vocabant prosperitatis, & bona fortuna præfecto ei genio Ginchiael, erat olim à gr. 25. Arietis, vbi incidebat triangulum propè ventrem Ceti. Nunc autem est in gr. 17. Tauri, & eam vice versa vocat Argolus humidam, affetentem mala in itineribus. < IV.> Statio est in Pleiadibus, estque apud Arabes statio inimicitæ, & vindictæ dicta suo gentili vocabulo Altarich, cuius genius dicebatur Delhaicel. Hanc recensiores vocant tempe- ratè humidam, proindeque bonam ad ferendum, plantandum, iterque faciendu per aquas, & eam constituunt, in gr. 30. Tauri.
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MATHEMATICVM: 271 The ancients observed that these lunar stations, affected as they are by such qualities, therefore assume various and different modes of influencing these lower regions. Their origin, while at first good, innocent, natural, and in accordance with reason and experience, was later corrupted by Egyptian vanities; and in the whole of Astrology there is no fiction that yields to it in absurdity. The Copi call them, in their native term, as it were the Moon’s resorts or dwellings; others, the stations of the gods; more correctly, as you may say with Kircher, the stalls of demons, since they are filled with so many and such superstitions. And since the Moon completes her course in about 28 days, they therefore established as many mansions, assigning to each day its own mansion, to each its own meanings and fixed significance of things; and, what is more surprising, appointing over each its own spirits, or ministering demons. For the curiosity of readers, I think it proper here to transcribe from Kircher’s Oedipus, as they lie in his records; and then to present them restored to their proper form, and as carefully computed up to the present time by Argolus, since, as I have said, when all superstition is cast aside, and they are considered only in a natural way from the varied conjunction of the Moon with the fixed stars, they are of great value, under the guidance of experience, in choosing things. Therefore the First mansion of the Moon, which the Egyptians called the station of the fish, from the star fixed in the belly of the Whale, of the nature of Saturn, which fell in it, and which they therefore called the affliction of enemies, and over which they assigned the spirit Kiacel, was formerly reckoned from the beginning of Aries to the 12th degree of the same sign. Argolus now calls this tempered, and places it at the 22nd degree of Aries; and says that it is suitable for taking a laxative medicine and for undertaking any journey. < II.> The station which the ancients called that of the reconciliation of princes, assigning to it as spirit Hiaiel, was reckoned from the 12th degree of Aries to the 25th, because of the fixed star in the head of Aries. Modern writers, however, place it at the 4th degree of Taurus, which they say is suitable for transplanting, planting, and for traveling by water, but unsuitable for purgations. < III.> The station which the Egyptians called that of prosperity and good fortune, with the spirit Ginchiael appointed over it, was formerly at the 25th degree of Aries, where the triangle fell near the belly of the Whale. Now, however, it is at the 17th degree of Taurus, and Argolus, on the other hand, calls it humid, and conducive to ill fortune in journeys. < IV.> This station is in the Pleiades, and among the Arabs is called the station of enmity and revenge, by its native name Altarich; its spirit was said to be Delhaicel. More recent writers call it moderately humid, and therefore good for transplanting, planting, and traveling by water, and they place it at the 30th degree of Taurus.
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MATHEMATICVM. 275 ex[em]lo ad australem plagam sub signo Libræ constans stellis 29. de natura Malesicarum. Vide fusius in verbo Bestia Cansauri. Lxv est qualitas quædam corporis lucidi ei propria ab 50. eoque intrinsecè emanans: vnde differt à lumine, quod est quid posterius ab ipsa luce productum per effluxum radiorum ab ipsa luce ad alia corpora luminis receptiua quale est quod in sære, seù alio quouis diaphano producitur per reflexionem ra- diorum ab ipsa luce emanantium, vel quod etiam videmus in corporibus opacis, sed leuigatis, in quibus recipitur lumen à luce primigenia derivatum, ac præcipuè in sideribus lumen suum à Sole mutuantibus. Quare lux propriè dicitur Soli com- petere omnis luminis fonti, lumen verò sideribus. Radius verò est instrumentum proximum, quo ipsa lux se communi- cat, & lumen gignit, licet sæpissimè etiam lux cum lumine conuertatur. De qua re vide quæ erudite habet Kircherus in libro Artis magnæ lucis, & vmbræ. Lux etiam quandoque accipitur pro ipsis stellis: sic Cicero in Arati Phænom. Illæ, quæ fulgent luces ex hore corusco, Sunt inter partes gelidas Aquilone locatas, Atque inter spatium, & lati vestigia Solis. LY LYBICVS ventus, idem, qui Africus, vnsus ex ventis Occi- <51.> dentalibus, lateralis Fauonio, oppositus directè Cæciæ, spirans ab occasu bruniali, sic dictus, à Lybia per quam spirando transit. Est de natura sua frigidus, & humidus, pluuiosus, ac tempestatis indez, de eoscribir Plinius, vt alibi obseruatum est, quod statu suo facit pecudes foemineam prolem concipere. Vide in V. Africus. LYBANOTVS ventus item Lateralis, sed adiacens Austro <52.> dictas etiam Austro-Africus, directè oppositus Aquiloni. Est de natura sua calidus, sed magis humidus, pluuiosus; noxius, & morbificus, habet sibi collaterales Y polybanorum adiacentem Notolibico ad occasum, Mesolybanorum verò ad Austrum ipsi vento Cardinali immediatum. LYRA Vultur cadens, Fidicula Græcis Chelys Arab. verò <53.> Vvega, &c. sidus in octaua sphæra ad borealem plagam, ha- bens stellas decem de natura Veneris, & Mercurij, quarum potissima est, quæ Arabicè dicitur Brinek primæ magnitudi- nis, existens nunc in gr. 11. Capricorni cum latitudine bor. ferè gr. 62 Hæc oritur Romæ circà Kalendas Nouembris cum gr. 10. Scorpij. occidit verò cum ultimo gradu Aquarij; S ij
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MATHEMATICVM. 275 extending from Aries to the southern region beneath the sign of Libra, consisting of 29 stars. On the nature of the Malesic stars. See more fully under the word Bestia Cansauri. Light is a certain quality of a luminous body, proper to it and flowing intrinsically from it; whence it differs from lumination, which is something later produced by light itself through the efflux of rays from the light itself to other receptive bodies of light, such as that which is produced in the air, or in any other diaphanous body, by the reflection of rays emanating from the light itself, or that which we also see in opaque but polished bodies, in which illumination derived from primordial light is received, and especially in the stars, which borrow their light from the Sun. Therefore light is properly said to belong to the Sun, the source of all light, but lumination to the stars. A ray, however, is the nearest instrument by which light itself communicates itself and generates lumination, although very often light is also used interchangeably with lumination. On this matter see what Kircher has learnedly written in the book Artis magnae lucis, & vmbræ. Light is also sometimes taken for the stars themselves: thus Cicero in the Arati Phænom. Those lights that shine with a gleaming flame Are among the cold regions placed under the North Wind, And between the space and the broad tracks of the Sun. LY LYBICUS wind, the same as Africus, one of the western winds, lateral to Favonius, directly opposite Cæcias, blowing from the western quarter, so called from Libya through which it passes while blowing. By nature it is cold and humid, rainy, and a sign of storm; as Pliny writes, and as has elsewhere been observed, in this condition it causes cattle to conceive female offspring. See under Africus. LYBANOTVS wind likewise lateral, but adjacent to the South, also called Austro-Africus, directly opposite Aquilo. It is by nature warm, but more humid and rainy; harmful and disease-causing. It has as its collateral winds the one adjacent to the west, Notolibicus, and toward the south Mesolybanus, immediately next to the cardinal wind itself. LYRA, the falling Vulture, Fidicula of the Greeks, Chelys of the Arabs, Vega, etc., a constellation in the eighth sphere in the northern part, having ten stars of the nature of Venus and Mercury; the principal one is that which in Arabic is called Brinek, of first magnitude, now at 11 degrees of Capricorn with northern latitude of almost 62 degrees. It rises at Rome about the Kalends of November with 10 degrees of Scorpio; and it sets with the last degree of Aquarius. S ij
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282 LEXICON vincunt in qualitatibus actiuis, ac proinde masculina signa dicenda sunt, Taurus, Virgo, Scorpio, & Pisces habent habitudinem, & familiaritatem cum Cancto, & Capricorno: igitur vincunt in qualitatibus passiuis, atque adeò foeminina sunt. Vide quæ fusiùs haber Titus loco citato. 25. MASVROTH Chaldaicè dicitur Zodiacus apud Cerdam, apud Kircherum vetò in Oedipo Ægyptiaco Aedronitho demalnsche hoc est orbis signorum. Vide in V. Zodiacus. 26. MATER dicitur à Latinis facies interior Astrolabij seù caua pats, quæ limbo exttinscus definita, intrinsecus amplectitur timpana, seù tabulas, & voluellum respondens ad singulas partes in planitie limbi descriptas: dicta est quasi mater quæ tabulas intrà se perinde ac foetus in vtero gerat. MATHEMATICA, seù Mathesis scientiarum omnium nobilissima, & quæ iute optimo mater omnium dici potest, quippe quæ in summo certitudinis apice sita vniuersa, quæ quanta sunt amplitudine sua complectitur, & scrutatur à Græco verbo quod disciplinam sonat, originem duxit. solæ enim mathematicæ facultates ad inserendam animo disciplinam idoneæ sunt, solæ scientiæ nomen merentur: quia solæ procedunt per demonstrationes, ac principia nota solæ ex principijs per se notis procedût ad cognitionem eorum quæ miius nota sunt, vt & ipsa fiant nota, & manifesta, eaque cognitione parta procedunt vlterius ad inuestionem aliorum quæ adhuc minus nota etant, vt ea quoque manifesta reddantur, donec tandem admirabilem, ac certam rerum intelligentiam consequamur: quod profectò aliæ facultates non præstant, vt Philosophia, Logica, Metaphysica, &c. quæ non per principia nota, sed per argumentationes & syllogismos procedunt, suaque obiecta probant, non supponunt probata. Eius obiectum, circà quod versatur est quantum sub ratione extensi, & vt aptum est mensurate alia quanta, & ipsum vicissim per alia mensuretur per proportionalem comparationem ad inuicem. Et quoniam quantum considerati potest præcisè prout habet rationem mensutæ proportionisque vt sic sine vllo respectu ad materiam quantam, & vt tale est obiectum Geometriæ, quæ præscindit à ratione quantorum, & solum considerat illa quatenus extensa sunt, vel considerari potest cum respectu ad materiam quantam, & sic vel sistit incontemplatione, & mensuratione partium orbis terrarum, & vocatur Geographia vel mensurat & maria dicitur Hydrographia, vel materialium rerum aceruos vt fru-
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282 LEXICON they prevail in active qualities, and therefore are to be called masculine signs. Taurus, Virgo, Scorpio, and Pisces have a relationship and familiarity with Cancer and Capricorn; therefore they prevail in passive qualities, and are thus feminine. See more fully what Titus has in the cited passage. 25. MASVROTH is called the Zodiac in Chaldaic by Cerda; but in Kircher’s Oedipus Aegyptiacus , Aedronitho demalnsche, that is, the circle of the signs. See under V. Zodiacus. 26. MATER, by the Latins, means the inner face of the Astrolabe, or hollow part, which, bounded on the outside by the limb, internally receives the tympans, or plates, and the volvelle, corresponding to the individual parts described on the surface of the limb: it is called mother, as though it carried the plates within itself, just as a womb carries the fetus. MATHEMATICA, or Mathesis, the noblest of all the sciences, and one which by right may be called the mother of them all, since it is set at the highest summit of certainty and embraces and investigates universal things, takes its origin from the Greek word meaning discipline. For only the mathematical sciences are fit to instill discipline in the mind; only they deserve the name of science: because only they proceed by demonstrations and known principles; only they advance from principles known in themselves to the knowledge of things less known, so that these too may become known and manifest, and, once that knowledge has been gained, they proceed further to the investigation of other things that are still less known, so that these also may be made manifest, until at last we attain an admirable and certain understanding of things. Other branches do not provide this, such as Philosophy, Logic, Metaphysics, etc., which proceed not by known principles but by arguments and syllogisms, and prove their objects; they do not assume them proven. Its object, around which it is concerned, is quantity considered under the aspect of extension, and as suited to be measured by another quantity, and in turn itself measured by others through proportional comparison with one another. And since quantity can be considered precisely as having the character of measure and proportion, thus without any regard to matter as quantity, and as such is the object of Geometry, which abstracts from the notion of quantities and considers them only insofar as they are extended; or it can be considered with respect to matter as quantity, and thus either it deals with the contemplation and measurement of the parts of the globe of the earth, and is called Geography; or it measures the seas and is called Hydrography; or the heaps of material things, as fru-
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MATHEMATHICVM. 189 resultant inde Mineralia, & fossilia, vt Autum, Argen- tum, lapides pretiosi, &c. humanæ cupiditatis, atque aua- ritiæ subiectum, reuerà tamen longè viliora, quam cæte- ra mixta perfecta, plantæ, animalia, homo. Ex his liquet in quo differant vapor, & exhalatio: Ambo < 53.> enim vi siderum, præcipuè verò solis è terra prosiliunt, at- que in sublime trahuntur; sed enim hæc, vtpote calida & sicca sursum euehirur, atque in ignem vt plurimum trans- mutatur, vel in aëtem, vnde venti exsurgunt: ille verò ha- bet calorem mixtum humiditati, quæ tamen paulatim ca- lorem debilitat, itavit vapore ille nequeat sursum in supre- mam aëris regionem ascendere, sed in media tantum con- sistat, ibique tandem calore exincto, vel sanè extenuato conuertatur in imbes, niues, nebulas, aliaque superius enumerata. Hæc omnia ex Arist. 1. Meteor. cap 4. Metonicus Annuus. Vide Annus. Micromega est instrumentum geometricum representans < 54.> sextam partem quadrantis hoc est gr. 15. descriptos in lim- bo, cuius ope rerum stantiæ, & altitudines meriuntur. Eius vsum abunde tracta peculiari libro Lucius Scaranus in- uentor. Micros Contaratos. teste Kirchero, dicitur spica Vir- < 55.> ginis ad differentiam Arctari, qui dicitur Magnus Conta- ratus. MILES apud Astronomos, seù potiùs Meteorologicos est < 56.> species quædam Cometæ criniti, & caudati de natura Ve- neris, magnitudine sua, aeducis fulgore ferè Lunam exæ- quans, qui quando apparet diu conspicuus est, & solet quan- doque peragare totum Zodiacum. Habet significare se- ctas, contentiones, fæminum sexum, & adolescentes. Item magnas ariditates, aëris corruptelam, humorum tur- bationem, & quæ inde proueniunt mala: Idque maximè portendit in locis, ad qua terenderit eius cauda. Talem ap- paruisse ferunt, cum Xerces Persarum Rex in Græciam traiecit. MINUTVM, ET SCRIPVLVM apud Astronomos dicitur mi- < 57.> nima, & sexagesima quæque pars fractionis inregri gradus, aut horæ: itavit quælibet hora, vel gradus æquatoris, aut Zodiaci diuidatur in sexaginta minuta: quodlibet minutum in sexaginta secunda, vt vocant: Secunda adhuuc in toti- dem Tertia: & sic deinceps vsque ad Decima, & si quis volet vsque in infinitum. Vide quæ diximus in V. Græ- dus. MIRACHarab. dicitur Cingulus, seu Vmbilicus Andro. < 58.> T
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MATHEMATHICVM. 189 resulting from it are minerals and fossils, such as gold, silver, precious stones, etc., subject to human greed and avarice, though in truth far more base than the other perfect mixtures, plants, animals, man. From these things it is clear in what vapor and exhalation differ: for both arise from the earth by the power of the stars, especially of the sun, and are drawn upward; but this, since it is hot and dry, is carried aloft and is for the most part transformed into fire, or into air, from which winds arise: that other, however, has heat mixed with humidity, which nevertheless gradually weakens the heat, so that vapor cannot ascend upward into the highest region of the air, but remains only in the middle, and there at length, when the heat has been extinguished, or indeed greatly diminished, it is converted into rains, snows, mists, and the other things enumerated above. All this from Aristotle, Meteor. 1, cap. 4. Metonicus Annuus. See Annus. Micromega is a geometrical instrument representing the sixth part of a quadrant, that is, 15 degrees, marked on the limb, by means of which distances and heights of things are measured. Its use Lucius Scaranus, the inventor, discusses fully in a special book. Micros Contaratos. According to Kircher, this is what the spike of Virgo is called, as distinct from Arcturus, which is called the Great Contaratus. MILES among astronomers, or rather meteorologists, is a certain kind of hairy and tailed comet, of the nature of Venus, in size and brilliant glow almost equaling the moon, which when it appears is long visible, and sometimes is accustomed to traverse the whole Zodiac. It is said to signify sects, contentions, the female sex, and young men. Likewise great dry spells, corruption of the air, disturbance of humors, and the evils arising therefrom: and this especially portends in places toward which its tail is directed. They say that such a one appeared when Xerxes, king of the Persians, crossed into Greece. MINUTVM, ET SCRIPVLVM among astronomers is called the smallest, and every sixtieth part of a whole degree or hour; that is, each hour or degree of the equator or Zodiac is divided into sixty minutes: each minute into sixty seconds, as they are called: the seconds again into as many thirds, and so on, up to tenths, and if one wishes, even to infinity. See what we said under V. Gradus. MIRACHarab. is called the Girdle, or Navel, of Andro.
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LEXICON men falsum esse videmus. Demum quia regiones aëris superiores frigidiores sunt, quam insima, & terræ vicinior, cum tamen si verum esset, quod cælorum motus calorem in sublunaribus hisce produceret, maiorem vtique atque intentiorem ibi quam isthic deberet efficere: quò enim passum proximius est agenti, eô validius patitur; ac virtus illius intenditur. Quod cum reipsa minimè experiamur, concludendum est, cælorum motus nil aliud efficere in hæc sublunaria, quam applicare, ac diffundere lumen siderum, pro cuius diuersa applicatione diuersi etiam producuntur effectus. Itaque motus est præcipuum instrumentum luminis astrorum, quo mediante lumen ipsum diffunditur, euaditque aptum ad tot genera effectum producenda. <74.> Porrò duplicem motum cælestium corporum communiter asserunt omnes tam Philosophi, quam Astronomi, alterum raptus, & vniuersalem, quo simul omnia rapiuntur à Nona, siue quæcumque tandem ea sit, postrema omnium infrà Empyreum, sphæra, concitatissimo motu ab Oriente in Occidentem, spatio ferè 24. horarum: alterum proprium cuiusque orbis, qui sit modò explicato contrarius, & eo ferantur in partes orientaliores, quo quisque orbis, aut planeta statuto tempore periodum suam perficit in Zodiaco. Hinc duo mobilium geneta: Alterum quod autonomasticè dicitur. <75.> Primum Mobile, quod est supradicta nona sphæra, vel decima, aut etiam vndecima, quæ in quam reliquas omnes complectitur, & simul trahit ab ortu ad occasum super polos mundi revolutionem suam perficiens spatio integræ diei naturalis, & hoc cælum solo motu dignoscitur, quippe nullæ in eo stellæ, nullæ imagines, nullæ lineationes aut characteres (vt aliqui sóniantes volebant, quos non ita pridè cùm de Monomeriis egimus deridentes reiecimus) sed signa, & circuli, quos in eo imaginamur, fictitij sunt, & vel ab Firmamento, & octaua sphæra, quam olim ob motus tarditatem cum nona sphæra confundebant, vel ab effectibus illi tributi. Cæterum insensibile est, vnde & ignoratur, quanta sit eius crassities, & conuexi amplitudo. Aliqui verò Astronomi, inter quos videretur esse Tycho, vt apparet ex eiusdem Epistolis existimant, nullum esse cælum Anastron, atque ad solum motum quempiam efficiendum addictum. Quapropter probabiliter putant, diurnam mundi conuersionem à nullo primo mobili provt ab aliis distincto sieri sed à tota cælesti regione, hoc est totum ætherem simul
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We see that this is false. Finally, because the upper regions of the air are colder than the lower ones, and nearer the earth, whereas if it were true that the motion of the heavens produced heat in these sublunary things, it ought certainly to produce it greater and more intense there than here; for the closer the patient is to the agent, the more strongly it is affected, and its power is intensified. Since in fact we experience nothing of the sort, we must conclude that the motion of the heavens effects nothing else in these sublunary regions than the application and diffusion of the light of the stars, according to whose different application different effects are also produced. Therefore motion is the chief instrument of the light of the stars, through which the light itself is diffused and becomes fit to produce so many kinds of effects. <74.> Moreover, all both philosophers and astronomers commonly assert a twofold motion of the heavenly bodies: one, the carrying movement and universal motion, by which all things are borne together from the Ninth, or whatever the last sphere beneath the Empyrean may be, with the most rapid motion from east to west, in the space of about 24 hours; the other, the proper motion of each sphere, which is contrary to the one just explained, and by which they are carried toward the eastern parts, as each sphere or planet completes its period in the zodiac at a fixed time. Hence two kinds of moving bodies: one which is called by a proper name. <75.> The Primum Mobile, which is the aforementioned ninth sphere, or tenth, or even eleventh, which encompasses all the rest and at the same time carries them along from east to west, performing its revolution about the poles of the world in the space of a whole natural day; and this heaven is known solely by its motion, since there are in it no stars, no images, no lines or characters (as certain dreamers wanted, whom not so long ago, when we were discussing Monomeriis, we mocked and rejected), but the signs and circles that we imagine in it are fictitious, and derived either from the Firmament and the eighth sphere, which in former times they confused with the ninth sphere because of the slowness of its motion, or from the effects attributed to it. Otherwise it is imperceptible, and therefore the thickness and breadth of its convexity are unknown. However, some astronomers, among whom Tycho seems to be, as appears from his Letters, think that there is no heaven Anastron at all, and that it is devoted solely to producing some motion. Wherefore they probably think that the daily turning of the world is not caused by any first mobile, distinct from the others, but by the entire heavenly region, that is, by the whole ether at once
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MATHEMATICVM. 299 moueri in polis mundi propria virute ab Oriente in Occidentem: in quo interim sidera omnia, & Planetæ propriis motibus ab occasu in orum super polos Zodiaci ferantur, quasi contrà primum mobile, vel sanè, vt ego aliàs explicaui, lentius ob sui resistentiam ab ipso primo mobili rapiantur qui idecirco. < 76.> Secundi Mobiles, appellantur ad differentiam primi motus, suntque siue orbis singularum planetarum, necnon octaua sphæra fixarum, siue ipsa siderum corpora, quæ nitantur contrà motum primi mobilis in consequentia signa ab Occidente in Orientem super polos Zodiaci statis temporibus singulis integrum Zodiacum permeantibus. Et Firmamentum quidem id præstat in annis 36000. seu, vt volunt recensiores spatio annorum 49000. singulis 70. annis vnum tantum gradum assequendo: Saturnus totam suam circulationem complet in annis triginta: Iupiter in duodecim: Mars in duobus: Sol, Venus, Mercurius ferè in vno: Luna tandem spatio dierum 27. hor. 7. min. 41. sunt tamen qui asserunt cælum ipsum non moueri, sed Astra in ipso, tanquam aues in aëre; quippe vnum tantum cælum admittunt, illudque fluidum, & vagum instar aëris habens magnam crassitiem, in cuius determinatis spatiis sidera constituantur: quæ postea per eius ambitum moueantur, causentque hanc appareniarum varietatem: in qua opinione est Aretius de Generat. disp. 2. quost. 27. Sett. 7. aitque in ea etiam fuisse antiquos Patres Chrysostomum, Origenem, Eusebium, Emisenum, Diodorum Tarsensem, & alios. Verum ego etsi certo certius haheam cælum esse fluidum idque omninò vnum; non tamen in hoc conuenire possum; vt illud absoluè immobile astruant, sed existimo ipsum, seu potius omne æthereæ regionis expansum, quod complectitur totum id, quod inter nos, & cælum Empyreum intercipitur, vnito moru ab Oriente in Occidentem moueri, secumque trahere sidera in eius crassitie in determinatis quæq; spatiis constituta, quo pacto mouetur etiam aër, & noua Phenomena, seu Cometæ in eo geniti; ita tamen, vt hæc ex se minimè moueantur, sed partes cæli, & aëris in quibus reperiuntur, quæ secum postea sidera inibi constituta sua violentia rapiant, & circumducunt. Et partes quidem superiores velocius, inferiores verò lentiùs, & lentius in infinitum quò magis ad terram approximantur, ac longè fiunt à primo motore semper magis, ac magis huius impulsi resistentes. Neque etim aliter saluari possunt & fixarum motus semper æqua-
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MATHEMATICVM. 299 to move in the poles of the world by its own power from East to West: in which meantime all the stars, and the Planets, by their proper motions from the setting to the rising, over the poles of the Zodiac are carried, as though contrary to the first mobile, or indeed, as I have elsewhere explained, more slowly, because of their resistance, they are drawn by the first mobile itself, whence it follows. < 76.> The Second Mobiles are so called in distinction from the first motion, and are either the orbs of the individual planets, as well as the eighth sphere of the fixed stars, or the very bodies of the stars, which strive against the motion of the first mobile in the successive signs from West to East over the poles of the Zodiac, at fixed times, each of them traversing the whole Zodiac. And the Firmament indeed accomplishes this in 36,000 years, or, as more recent writers wish, in a span of 49,000 years, reaching only one degree every 70 years: Saturn completes the whole of its circuit in thirty years: Jupiter in twelve: Mars in two: the Sun, Venus, Mercury almost in one: the Moon finally in the space of 27 days, 7 hours, 41 minutes. There are, however, some who assert that heaven itself does not move, but the stars in it, like birds in the air; for they admit only one heaven, and that fluid and wandering, with the nature of air and of great thickness, in whose determined spaces the stars are placed: and that afterward they are moved through its circuit, and cause this variety of appearances: in which opinion Aretius is, de Generat. disp. 2. quest. 27. Sett. 7. and he says that in this also were the ancient Fathers, Chrysostom, Origen, Eusebius, Emisenus, Diodorus of Tarsus, and others. But I, although I hold with certainty that heaven is fluid and altogether one; nevertheless I cannot agree in this: that they should maintain it to be absolutely immovable, but I judge that it, or rather the whole expanse of the ethereal region, which embraces all that is intercepted between us and the Empyrean heaven, is moved by a united motion from East to West, and draws with itself the stars placed in its thickness in their determined spaces; in which way the air also is moved, and the new Phenomena, or Comets, generated in it; yet so that these are moved by no power of their own, but the parts of heaven and air in which they are found, and which afterward by their force carry along and whirl around the stars placed there. And the upper parts indeed are swifter, the lower however slower, and slower to infinity the more they approach the earth, and they are ever more and more distant from the first mover, always resisting this impulse more and more. Nor otherwise can the motion of the fixed stars be preserved always equal-
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301 LEXICON Motus quotidianus respectiuus ad loca Natalis sive inceptionis rerum, quem similiter transitum vocat; de quibus omnibus suo loco. 79. MòTLATVM seù MTLATVM, teste Kirchero Arabice dicitur Triangulum sidus in cælo constans stellis 4. vel vt placet Baiero 5. de natura Mercurij, cuius in horoscopo est afferte sublime ingenium. Hebraicè dicitur Humoschlusch. id est, tri partitus. 80. MOZNAIM, seù MOZNAIM, apud Hebræos idem sonat ac Bilanxe, denotatque Libræ sidus, seù signum in cælo septimum ab Ariete, illique directè oppositum, vnde incipit australis semicirculus signorum. 81. MVNOVS, appellatur Vniuersum hoc constans ex regione elementari & ætherea complectens quidquid in rerum natura existit, suoque loco disponitur: Vnde Cicero lib. 2. de Natura Deorum. Mundus, inquit, est quasi communis Deorum, atque hominum Domus, atque vtrorumque Vrbs. Et author lib. de Mundo ad Alex. Est compages inquit, è cælo, terraque coagmentata, & ex iis naturis, qua inter ea continentur. Græci Cosmon appellant, ab ornatu; est enim hæc Mundi machina perfecta, & absoluta rerum omnium dispositio, & ornamentum. Hinc etiam à Latinis abortu, & mundo muliebri dictus est, eoquod nil sit eo mundius, & ornatius; vt aduertit Plin. lib. 2. cap. 4. Quandoquidem secundum omnes sui partes tam perfectus est, tam suis omnibus numeris absolutus, vt, neque eo perfectiorem fieri posse; asserat D. Th. prima parte quast. 25. art 6. neque minimum quid addi possit, quod non eius ordinem, & proportionem corrumpat; vt in Cythara corrumpitur melos, si vel vna chorda plus debito intendatur. In eo enim videre est rerum omnium genera suis quæque locis aptè disposita, & ordinata: Cælos ob materiæ nobilitatem, ob luminis claritatem, molis immensitatem super omnia constitutos: Terram vtpote elementum omnium grauius, & vilius in centro sitam: mox aquam, mox aërem, inde ignem. In eo omne genus viuentium: Corporea, Incorrea, Mixta. In eo inanimata; in eo tertij ordinis entia, quæ sensu prædita sint, necne, iure ambigeres. Videmus in eo entia per se stantia, quæ idcircò vocitamus substantias; in eo substantiæ inhærentia accidentia. Habet insuper ad gignendum nunquam deficientem materiam, elementa: in iis ipsis, quæ generantur admirabilem connexionem, varietatem, vt vel ipsa cuiuis Atheo faris sit ad Conditoris sui notitiam ingerendam, cum nullo pacto credendum
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301 LEXICON Daily motion, or the movement with respect to the places of birth or beginning of things, which he likewise calls a transit; of all these, in their proper place. 79. MÒTLATVM or MTLATVM, according to Kircher, in Arabic is called the triangular star in the heavens, consisting of 4 stars, or, as Bayer prefers, 5, of the nature of Mercury, whose presence in the horoscope gives lofty genius. In Hebrew it is called Humoschlusch, that is, tripartite. 80. MOZNAIM, or MOZNAIM, among the Hebrews has the same meaning as Librae, and denotes the constellation or sign of Libra in the heavens, the seventh from Aries, and directly opposite it, from which the southern semicircle of the signs begins. 81. MVNOVS is called the universe itself, consisting of the elemental and ethereal region, embracing whatever exists in the nature of things, and disposed in its proper place: whence Cicero, book 2 of On the Nature of the Gods : “The world,” he says, “is as it were the common house of gods and men, and the city of both.” And the author of the book On the World to Alexander says: “It is,” he says, “a structure composed and joined together from heaven and earth, and from those natures which are contained between them.” The Greeks call it Cosmos , from adornment; for this machine of the world is a perfect and complete ordering and ornament of all things. Hence also among the Latins it is called from cleanliness and the feminine world, because nothing is cleaner or more elegant than it; as Pliny notes, book 2, chapter 4. Indeed, according to all its parts it is so perfect, so complete in all its numbers, that D. Thomas, in the first part, question 25, article 6, says that neither can anything more perfect be made; nor can the least thing be added that would not corrupt its order and proportion; as in a cithara the melody is spoiled if even a single string is tightened more than is due. For in it may be seen all kinds of things suitably disposed and ordered in their proper places: the heavens, because of the nobility of their matter, the clarity of their light, and the immensity of their bulk, established above all things; the earth, as the heaviest and most base of all elements, set in the center; then water, then air, then fire. In it is every kind of living thing: corporeal, incorporeal, mixed. In it are inanimate things; in it beings of a third order, which you would rightly wonder whether they are endowed with sense or not. We see in it entities standing by themselves, which for that reason we call substances; in it, accidental properties adhering to substances. It also has, for generating, an inexhaustible matter, the elements; in those same things that are generated, a marvelous connection and variety, so that even to any atheist the...
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LEXICON cui dubio intellectualis est, hoc est ab intellectu. Hæc Caie- tanus. < 87.> Verum, etsi id non ineptè, falsò tamen assertum, con- stat modò ex Concilio Constantinopolitano V. vbi anathemate feriuntur quotquot dixerint, Calum, & Solem, & Lunam, & Stellas animatas quasdam esse, & mobiles virtutes. An autem ibi Anima in vniuersum remoueatur à cælis, atque sideribus, an verò solum rationalis, dubium magnum est. Certè D. Thomas, etsi hanc materiam ex instituto pertractans in pag. 1. quæst. 70 art. 1. dicat paruam, vel nullam differentiam inueniri in re, sed in voce tantum in hac controuersia, concludatque corpora cælestia non nisi æquiuocè animata dici ab iis inferioribus, quibus conjungitur anima, vt forma, illis verò, vt motor tantum, nihilo- minus in 1. contra Gentes cap. 71. vult ex Arist. necessariò ponendam esse in cælis aliquam animam, quæ illis intrinsecè vniatur vt forma; aitque parum spectare ad Catholica veritatem disquirere num cæli animati sint, an non. Ad auctoritatem verò Concilij supra allatam respondet, eam vel non esse authenticam, vel sanè intelligendam esse de Anima rationali, secùs autem de alia specie omninò diuersa. Et quidem aliquam mundi formam substantialem, quæ < 88.> hanc rerum compagem intrinsecùs nectat, diffiteri non possimus, ni velimus Vniuersum hoc aggregatum per accidens nominare, quo nihil ineptius: ipse ordo, & consensus partium clarè indicat esse aliquid interiùs, quod omnia vniat, & substantialiter compleat: Ipsa Macrocosmi ad Microcosmum analogia id apertè suadet: quandoquidem, vt aduertit Picus in Epsaplo ipse Mundus à Moïse magnus homo appellatur; Nam si homo, inquit, est paruus Mundus; vtique Mundus est magnus homo. Prætereà cælos ab intrinseca forma moueri, absque vlla temeritatis nota doceri posse, asserit Raynaudus in Theologia naturali, disput. 1. quæst. 1. art. 1 id olim plures Philosophi atque insignes Astronomi docuerunt; & ex recentionibus Longomontanus, Keplerus, Bulliardus, Tycho, Nierembergensis, Baranzanus, & alij: ex quibus Tycho, Keplerus, & Baranzanus adhuc illis vitam attribuunt, sed longè ab aliis viuenribus differentem, homine quidem inferiorem, cum in hoc Anima à Deo immediatè veniat, & creetur, reliquis autem absoluè perfectiorem, & in superiori ordine. Si ergò cælis vitam concedunt isti, cur non potiùs eandem nos toti Mundo impertiamur? Si illis animam quamdam specie ab rationali, ac sensitiva diuersam, quam iure dixe-
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LEXICON whose intellectual doubt is, that is, from the intellect. This is Cajetan. <87.> But although this is not ineptly stated, it is nevertheless falsely asserted, as is clear now from the Fifth Council of Constantinople, where they are struck with anathema, as many as shall have said that the Heaven, the Sun, and the Moon, and the Stars are certain animated and mobile virtues. Whether in that place the Soul is removed from the heavens and the stars in general, or only the rational soul, is a great question. Certainly St. Thomas, although treating this matter in detail in p. 1, q. 70, art. 1, says that little or no difference is found in the thing, but only in the word in this controversy, and concludes that the heavenly bodies are called animated only equivocally by those lower things with which the soul is joined as form, but in those as mover only; nevertheless in 1 Contra Gentiles, ch. 71, he holds that according to Aristotle some soul must necessarily be posited in the heavens, which is intrinsically united to them as form; and he says that it matters little for Catholic truth to inquire whether the heavens are animated or not. But regarding the authority of the council cited above, he replies that it is either not authentic, or certainly is to be understood of the rational soul, but not of another altogether different kind. And indeed we cannot deny some substantial form of the world, which <88.> inwardly binds this fabric of things together, unless we wish to call this whole aggregate accidental, than which nothing is more inept: the order itself and the agreement of the parts clearly indicate that there is something within that unites all things and substantially completes them. The very analogy of the Macrocosm to the Microcosm plainly suggests this: since, as Picus notes in the Epsaplon, the world itself is called by Moses a great man; for if man, he says, is a little world, then surely the world is a great man. Moreover, that the heavens can be moved by an intrinsic form, without any mark of temerity, may be taught, as Raynaud says in the Theologia naturalis, disput. 1, q. 1, art. 1; this was once taught by many philosophers and notable astronomers, and among the more recent by Longomontanus, Kepler, Bulliardus, Tycho, Nierembergensis, Baranzanus, and others: among whom Tycho, Kepler, and Baranzanus still attribute life to them, but very different from living beings, indeed inferior to man, since in man the soul comes immediately from God and is created, but in the others absolutely more perfect, and in a higher order. If, then, those men grant life to the heavens, why should we not rather bestow the same upon the whole world? If they grant them some soul different in kind from the rational and the sensitive, which with good reason I would have said...
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MATHEMATICVM. 107 xis locomotricem, assignant, cur non eadem prorsùs anima totum mundum debeat informare; proindeque habeat cælis conferre motum, brutis animantibus vitam, cæteris partibus connexionem, atque consensum, quando vide- mus, hæc omnia vnam animam rationalem in homine, hoc est in mundo parvo præstare? Et mirum est quam acriter Recensiores fere omnes in hanc Mundi formam conspitent: & quando nouis formis effectis, nouorumque entium varietate Mundum istum exornant, hunc ipsum propria forma exutum planè audeant deformare. Enimuerò quæ maior deformitas, quam in tam grandi corpore incomplexio? quid absurdius, quam Vniuersum hoc aggregatum per accidens dicere? Etenim si ex consensu, & connexione, quam habent inter se partes vnius corporis, arguimus illud corpus naturale esse sua forma substantiali præditum; quæ verò si- bi accidentaliter tantum adhærent, hanc consensus societatem minimè admittere; si ex vnitate per se, perfectionem alicuius enitis colligimus, qua ratione debeamus affirmare mundum, exetetoqui adeò perfectum vt dicatur in se genere perfectiorem fieri non potuisse, hæc præcipua & maxima perfectione eatere, vt non sit quid per se existens, sed aggregatum per accidens, cuius partes sine forma substantiali intrinsecus inhærente, temanerent naruraliter incompactæ perindè ac parres domus, cui non habet artifex tribuere vnitatem, nisi tantum incomplexam, atque accidentalem; & alias maiorem consensum, & sympathiam videmus inter cælum, & tertam, quam inter partes vnius corporis naturalis? Si autem stante tali consensu & sympathia inter partes istius vasti corporis dicimus eas non habere vnam formam communem, non est ratio cur non dicamus lapides, plantas, cætera omnia esse vnam quid aggregatum per accidens. Quis autem hæc cogitans sibi persuadeat Auctorem Naturæ, qui perfectissimè omnia operatur, quique singulis rebus peculiarem indidit formam, Naturam ipsam, hoc est rerum omnium congeriem, & suum opus maximum effecisse eum accidentali tantum vnione inter partes, casque reliquisse substantialiter inconnexas? Ex his igitur, aliisque permultis, quæ abundè congerit Resta, lib. 2. tract 2. cap. 5 de Meseoris, concludendum est, aliquam mundi formam necessariò admittendam esse: An autem ea adhuc vitalis sit, id ipse affirmare non audet; sed tamen ex iis, quæ huc vsque diximus, tum etiam ex mox infra dicendis manifestè conuincitur. Equidem Vita, ex communi omnium Philosophorum V ij
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MATHEMATICVM. 107 …they assign a locomotory soul; why then should not the same soul altogether inform the whole world, and therefore have the power to impart motion to the heavens, life to brute animals, and connection and harmony to the other parts, when we see that all these things one rational soul accomplishes in man, that is, in the little world? And it is astonishing how sharply almost all the moderns spit upon this form of the world; and when, by inventing new forms and adorning this world with the variety of new beings, they strip this same world of its proper form, they dare plainly to deform it. Indeed, what greater deformity than lack of composition in so great a body? What is more absurd than to say that this universe is a mere accidental aggregate? For if from the agreement and connection which the parts of one body have among themselves we infer that that body is natural and endowed with its substantial form; but those things which adhere to it only accidentally do not at all admit this society of agreement; if from unity in itself we infer the perfection of some being, by what reasoning ought we to affirm that the world, since it is so perfect that it may be said that in its own kind no more perfect thing could have been made, lacks this chief and greatest perfection, namely that it is not something existing in itself, but an accidental aggregate, whose parts, without an intrinsically inhering substantial form, would remain naturally unconnected, just as the parts of a house, to which the craftsman cannot bestow unity except merely in a composite and accidental way; and elsewhere do we see greater agreement and sympathy between heaven and earth than between the parts of one natural body? But if, with such agreement and sympathy standing between the parts of this vast body, we say that they do not have one common form, there is no reason why we should not say that stones, plants, and all other things are one kind of accidental aggregate. And who, thinking these things, would persuade himself that the Author of Nature, who works all things most perfectly and who has assigned a peculiar form to each thing, has made Nature itself, that is, the aggregate of all things, and his greatest work, by only an accidental union among the parts, and has left them substantially unconnected? From these things, therefore, and from many others which Resta abundantly heaps together, book 2, tract 2, chapter 5, De Meseoris, it must be concluded that some form of the world must necessarily be admitted: whether, however, it is still a vital one, he himself does not dare to affirm; but nevertheless from what we have said thus far, and also from what will be said immediately below, it is clearly proved. Indeed, life, from the common opinion of all philosophers V ij
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MATHEMATICVM. < 93.> Animal foret: Sol, Luna, sideraque omnia Animantia fo- rent sensu, & vegetatione prædita, quando ipsa ad animalium vegetabilium, ac sensitiuorum productionem, tanquam causæ immediatæ, ac principales concurrerent, quod nemo vnguam dixerit, & manifestè reiicitur à Concilio Constantinopolitano supra relato: & insuper nullum gradum sensationis, aut vegetationis in ipsis videmus. < 94.> Fateor, hoc maximum, ac difficillimum in tota hac contouersia argumentum. At non tanti apud me est, vt præponderet aliis; cæteroqui euidentibus demonstrationibus modò allatis, euincentibus Mundi vitam. Scio equidem Thomam Campanellam lib. de sensu, & Magia rerum, totum in eo esse, vt contendat, Mundum esse viuam Dei statuam, omnesque illius partes sensu, alias clariore, alias obtusiore præditas: Et in Epilogo Operis in fine, post uam elementa, lapides, plantas, suo modo sentire dixit, in hæc verba coucludit. Mundus ergò totus est sensus, vita, anima, corpus, statua, et altissimi ad ipsui condita gloriam. Verum, etsi ego Mundum viuere vita propriè dicta, quæ sit omni vita, (excepta intellectuali, quæ est per intellectum, ac voluntatem, qua viuit etiam homo per animam rationalem à Deo immediat infusam) superior, detque omnibus viuentibus, etiam homini quoad vitam animalem, qua nutritur, & sentit, viuere, & moueri, constanti animo affirmem; tamen non per hoc, ipsum vastum aliquod animal dicere audeo, nec si adhuc ausim, concessero. Etenim, Animal, propriè denotat viuens sensu, & cognitione præditum: iuxta quam acceptionem Arist. lib. de Vita, & Mortem, ait, Plantam viuere quidem, sed non esse Animal. Plante enim, inquit, viuunt quidem, non habent autem sensum: per sentire autem, animal à non animali determinamus. Sic igitur, viuit cælum, viuunt sidera, viuit vniuersus Orbis, sed animantia non sunt, quia sensu, & ratione carent. Nec, quia hos gradus viuendi non habent, dicenda sunt cæteris viuentibus imperfectiora: Quandoquidem vegetatio, & sensatio sunt imperfectiones quædam viuentium, sine quibus melius quidem in suo genere vita fruerentur: at enim vegetatio in inferioribus hisce necessaria est ad speciei, atque indiuidui conservationem; sensus autem in animalibus ad sibi conducentia prosequenda, & incommoda sugienda. Vnde ex hoc tantum rationem animalitatis excludere videtur D. Thomas à cælis, atque ab vniuerso Mundo, ait enim loco cit. art. 3. ad 3. Vita in istis inferioribus re- cipitur in natura corruptibili, qua indiget & generatione V iiiij
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MATHEMATICVM. < 93.> An animal would exist: the Sun, Moon, and all the stars would be living beings, endowed with sensation and vegetation, since they themselves would concur in the production of animal, vegetable, and sentient beings as immediate and principal causes, which no one ever said, and it is manifestly rejected by the Constantinopolitan Council cited above; and moreover we see in them no degree of sensation or vegetation. < 94.> I confess that this is the greatest and most difficult argument in the whole controversy. But with me it is not so weighty as to outweigh the others; otherwise, with the evident demonstrations just now brought forward, which prove the life of the World. I certainly know that Thomas Campanella, in his book De sensu et Magia rerum, is wholly intent on maintaining that the World is the living statue of God, and that all its parts are endowed with sense, some with a clearer, others with a duller one: and in the Epilogue of the work at the end, after saying that the elements, stones, and plants in their own way sense, he concludes in these words: “Therefore the whole world is sense, life, soul, body, statue, and created by the Most High for his glory.” But although I firmly affirm that the World lives with a life properly so called, which is above every life, except the intellectual, which is through intellect and will, by which man also lives through the rational soul immediately infused by God, and which gives to all living things, even to man as regards the animal life by which he is nourished and feels, to live and move; nevertheless, for this reason I do not dare to call it some vast animal, nor, if I should still dare, would I grant it. For “animal” properly denotes a being living and endowed with sensation and cognition: according to which meaning Aristotle, in book De Vita et Morte, says that a plant does indeed live, but is not an animal. For, he says, plants do indeed live, but they do not have sensation: by perceiving, however, we distinguish an animal from a non-animal. Thus, therefore, heaven lives, the stars live, the whole universe lives, but they are not living creatures, because they lack sensation and reason. Nor, because they do not have these degrees of life, must they be said to be more imperfect than the other living things. For vegetation and sensation are certain imperfections of living things, without which they would indeed enjoy life better in their own kind; but vegetation in these lower things is necessary for the preservation of the species and of the individual; sensation, however, in animals is for pursuing what is conducive to them and fleeing what is harmful. Hence D. Thomas seems from this alone to exclude the reason of animality from the heavens and from the whole world, for he says in the cited place, art. 3, ad 3: Life in these lower things is received in corruptible nature, which has need both of generation and of... V iiiij
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MATHEMATICVM. 111 MVTA SIGNA sunt quæ præseferunt figuram Animalium voce carentium, qualia sunt Cancer, Scorpio, & Pisces: sicut econtrà vocem habentia perhibentur esse tum humana, Gemini, Virgo, Libra, Sagittarius, & Aquarius, tum ferina, quæ etiam raucâ dicuntur, brutorum videlicet vocalium formam habentia, vt Aries, Taurus, Leo, Capricornus. Horum maxima consideratio habetur in Gene- thliacis, quoad vitia, & impedimenta linguæ, de qua re Ptolemæus lib. 3. Quadrip. cap. 17. MVTATIT arab. idem sonat ac latinè agglutinatus; cum vi- delicet Planetaria est alteri iunctus, vt nec in minuto qui- dem aberrer. Hoc vocabulo frequenter vtilur Ptolemæus in Quadrip. ex versione arabica, & Hali eius commen- tator. MVTATLVM arab. Vide in V. Motlatum. 104 MVTELATA SIGN. sunt quæ membrum aliquod seu etiam corpus mutilum repræsentant, vt Taurus, Equi sectio, Caput Medusæ, quæ quidem, vt benè obseruat Titus in Cælesti Philosophia lib. 2. cap. 3. hanc habent naturam & in- fluendi vim, vt ferè semper inducant membrorum incisio- nem, si Vitæ moderatoribus infeliciter se habentibus in Natali, per directionem postea misceantur. Hinc Ptole- mæus in Quadrip. lib. 4. cap. 10 vbi de genere mortis agir, In signis mutilis, inquit, aut quorum figurà sunt imperfe- cta, aut circà caput Medusa Mars significat capite truncan- dos, aut membris mutilandos. Quod D. Thomas obseruauit opusc. 28. art 3. dicens, quod stella illa funerea sunt, & mon- struosam indicant vita terminationem. Vide quæ diximus in V. Gorgonis caput. N. NABLON SCHALIAF seu etiam Nescussackat teste schie- chardo Chaldaicè dicitur Lyra sidus in Cælo, de quo sæ- pius dictum est. NAASCH LAAZAR hoc est Feretrum Lazari dicitur apud Christianos arabes Plaustrum, vt testatur Kircherus in Oc- dipo, eo quod non minus plaustrum, quam Feretrum re- præsentare videantur stellæ quatuor magis conspicuæ in Ve- sa, quæ quatuor plaustri totas effingunt. Schillerus autem, qui ex hoc occasionem sumpsit omnes coelestes imagines transmutandi, atque ex Diuorum nominibus appellandi, hoc ipsum Astrum vocat Petri Nauiculam. NADIR apud Arabes significat punctum Cæli sub terra oppositum diametraliter vertici capitis nostri, quod ipsi pari- ter gentili suo vocabulo Zenith appellant: itavt ambo sint
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MATHEMATICVM. 111 MUTE SIGNS are those which present the figure of animals lacking voice, such as Cancer, Scorpio, and Pisces: while, conversely, those that have voice are said to be both human, Gemini, Virgo, Libra, Sagittarius, and Aquarius, and beastly, which are also called hoarse, namely those having the form of vocal brutes, as Aries, Taurus, Leo, Capricorn. The greatest consideration of these is had in Genethliacs, as regards defects and impediments of speech, concerning which matter Ptolemy, lib. 3. Quadrip. cap. 17. MVTATIT arab. means the same as, in Latin, glued together; namely when a planetary body is joined to another, so that it does not differ even by a minute. Ptolemy frequently uses this word in the Quadrip. from the Arabic version, and also Hali, his commentator. MVTATLVM arab. See under V. Motlatum. 104 MVTELATA SIGN. are those which represent some limb or even a mutilated body, as Taurus, the cutting of the Horse, the Head of Medusa, which indeed, as Titus rightly observes in Cælesti Philosophia lib. 2. cap. 3, have this nature and power of influencing, that they almost always bring about the cutting off of limbs, if, with the governors of Life unfortunately situated in the Nativity, they are later mixed by direction. Hence Ptolemy, in Quadrip. lib. 4. cap. 10, where he speaks of the kind of death, “In mutilated signs,” he says, “or those whose figure is imper- fect, or around the Head of Medusa, Mars signifies that they are to be beheaded, or mutilated in their members.” Which St. Thomas observed opusc. 28. art. 3, saying that that star is funereal, and indicates a monstrous end of life. See what we said under V. Gorgon's head. N. NABLON SCHALIAF, or also Nescussackat, according to Schie- chard, is the Chaldaic name for the constellation Lyra in the heaven, concerning which much has been said. NAASCH LAAZAR, that is, the Bier of Lazarus, is called among the Arab Christians the Wain, as Kircher testifies in Oc- dipus, because the four more conspicuous stars in the Vesa seem to represent not less the Wain than the Bier, and they fashion the whole of the Wain. Schiller, however, who took occasion from this to transform all the celestial images, and to name them from the names of the Saints, calls this same star the Little Ship of Peter. NADIR among the Arabs signifies the point of heaven beneath the earth diametrically opposite the zenith of our head, which they likewise call by their native word Zenith: so that both are
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LEXICON 316 veluti poli horizontis, & distent ab eodem hinc inde gr. 90. ac proinde necessario incidant in ipsum meridianum, Zenith quidem supra terram, Nadir autem sub terra. Et quam propositionem vnvem eorum habeat ad æquatorem & alterum polorum Mundi, eandem vice versa habeat alterum ad oppositum polum, & aduersam æquatoris partem. 4. NAHAR, ALCHARNER teste Kirchero in Oedipo arabice dicitur Fluuius Eridanus sidus ad australem plagam constans stellis triginta tribus, de quo plura diximus suo loco. 5. NARIS CETI teù etiam Mandibula Ceti vulgò dicitur steila sira secundæ magnitudinis valdè præsignis, de naturæ Saturni, existens in rictu Ceti, atque in longitudine sub gr. 10. Tauri arab. dicta Menchar. 6. NATIVITAS, Natalitium thema, seù etiam Natiuitatis figura dicitur vulgò apud Astrologos constitutio Cæli erecta ad punctum Natiuitatis alicuius hominis, aut etiam initium alicuius rei. Quale autem dicendum sit verum punctum Natiuitatis, disputatum est luculenter in V. Genesis. 7. NATURA, eisi secundum varias acceptiones plura significet, quæ ad nostrum institutum non pertinem, primo tamen loco, & ex sui notione appellat generationem viuentium ex insita sibi à Creatore vi naturaliter, hoc est nullatenus alterata, constituto sibi primitùs ordine prodeuntium: vnde dicta est Natura quasi Nascitura, græcis autem expressiore vocabulo Physis & naturale dicitur quidquid non violentè, non casu, non artificiosè, non denique præter naturæ cursum emanat. Adeo vt iam Naturæ nomine proprie, & vniuersalissimè veniat congeries illa causarum secundarum, ex indita sibi à Creatore virute necessatio operantium, quæ sui varietate pulcherrimum hunc rerum ordinem constituunt, atque à Deo ita præordinatæ sunt, vt nulla vi, nullo planè artificio, nullo humanæ voluntatis adminiculo ex se suos effectus promant, ac naturali ordine progrediantur: cuius admirabilem cursum demirans D. August. lib. 8. in Genesim. Quod enim, inquit mains, mirabiliusque spectaculum est, aut ubi magis cum rerum natura humana ratio quodammodo loqui potest, quam cum positis seminibus, plantatis surculis, translatis arbustulis, insitis malleolis, tanquam interrogatur quæque v[erò] radicis & germinis, quid possit, quidve non possit; vnde possit, vnde non possit? quid in ea valeat numerorum inuisibilis, interiorque potentia, quid extrinsecùs adhibita diligentia, inque ipsa consideratione perspicere, quia neque qui plantat est aliquid, neque qui rigat, sed qui incrementum dat Deus: quia & illud
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LEXICON 316 like the poles of the horizon, and they are distant from the same on either side by 90 degrees. and therefore they necessarily fall upon the meridian itself, the Zenith indeed above the earth, but the Nadir beneath the earth. And as one of them has that proposition with respect to the equator and the other to one of the poles of the world, the other vice versa has the opposite one with to the opposite pole, and to the contrary part of the equator. 4. NAHAR, ALCHARNER, according to Kircher in Oedipus, is called in Arabic the River Eridanus, a star set on the southern side, consisting of thirty-three stars, concerning which we have spoken more in its place. 5. NARIS CETI, or also the Jaw of Cetus, is commonly called a very conspicuous star of the second magnitude, of the nature of Saturn, standing in the mouth of Cetus, and in longitude under 10 degrees of Taurus, called in Arabic Menchar. 6. NATIVITY, the natal theme, or also the figure of the Nativity, is commonly called among astrologers the constitution of the heavens erected for the point of the nativity of some man, or also the beginning of some thing. But what should be said to be the true point of Nativity has been clearly discussed in V. Genesis. 7. NATURE, although according to various meanings it signifies many things, which do not belong to our purpose, in the first place, and by its own notion, it denotes the generation of living things proceeding by a natural force, implanted in them by the Creator, that is, in no way altered, and moving forth according to the order first established for it: whence it is called Nature as though Nascitura, and in Greek by a more expressive term Physis; and natural is called whatever does not arise violently, not by chance, not artificially, nor finally beyond the course of nature. So that now under the name of Nature, properly and most universally, there comes that whole assemblage of secondary causes, operating necessarily by a virtue implanted in them by the Creator, which by their variety constitute this most beautiful order of things, and are so preordained by God that by no force, by no art at all, by no aid of human will do they bring forth their effects of themselves, but proceed in natural order: at the contemplation of whose admirable course St. August. lib. 8. in Genesis. For what, he says, is a more wonderful spectacle, or where can human reason speak, as it were, more in accord with the nature of things, than when seeds have been placed, cuttings planted, small shrubs transplanted, grafts inserted, as though each one were being asked concerning the root and the shoot, what it can do, and what it cannot; whence it can do, whence it cannot? what in it the invisible number and inward power avail, what the diligence applied from without, and in that very consideration to discern, because neither he who plants is anything, nor he who waters, but God who gives the increase: because also that
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318 LEXICON conseruant, immutant, alterant, perdunt: neque eorum actiuitas tolli vel impediri potest ab humana voluntate, aut ab vllis causis inferioribus, sed tantum à Causa prima Deo, atque adeò vel ob id cæteris omnibus præstant. Benè verò potest homo eorum naturam, qualitates, effectus, inalterabilem agendi vim callens excolere in ipsis inferioribus, applicare, præuertere, declinare, sicut dixit Ptolemæus in Centiloquio Verbo 8, Sapiens anima, inquit, confert calesti operationi, quemadmodum optimus Agrico a arando, expurgandoque confert Natura. Igitur non potest homo facere, vt Astra suos naturales virtutes non exerant, effectus sibi proprios non producant, qualitates maleficas, aut beneficas, quibus intrinsecus potiuntur exuant, & contrarias induant, potest verò aliquatenus in causis inferioribus eas alterando, impediendo, aut etiam destruendo, sicque totaliter eorum effectus præuertere. 9. Sic non potest homo vllò modo Eclipsim futuram impediire, neque effectus, inde naturaliter emanaturos: non potest, exempli gratia, æstum nimium ex congressu solis, & Martis sequuturum præuertere, nives, pluuias, ventos, aëris infectiones, &c. potest autem in naturis inferioribus, vt ædificando super solum, ne herbas getminet, exsiccando stagna, ne aërem corrumpant; recidendo arbores ne fructus proferant. Sic etiam astris subfamulando eorum operationi conferre, vt subministrare materiam, vel remouere, sese contrà prauas siderum influentias præmunire, bonis substernere, disponere, & passibilem applicare tempore præuisæ sterilitatis (vt fecit Ioseph Patriarcha) magnam frumenti vim in hortea comportare, in bonis siderum configurationibus terram excolere, maria exsulcare; in malis domi consistere, atque à labore inutili abstinere, &c. Concludam igitur cum iis quæ appositè ad hanc rem habet Kircherus in Arte Magna Lucis & Vmbra lib. 6. part. 3. cap. 2. Natura, inquit, duobus principiis regitur, natura, & voluntate: Natura subiecta est sideribus, voluntas libera, & ideò effectus, & operationes purè naturales sideribus planè obediunt tanquam causis necessariis, vt sanitas, vel infirmitas; longa, vel breuis hominum vita, &c. alia qua purè voluntaria, vt speculari, docere, actus virtutum aut vitiorum: alia mixta, vt facere iter, comedere, &c. Vtrum autem iter commodum futurum sit, necne, à sideribus pendet, aërisque constitutione. Si quis igitur perfectè cognosceret influxus siderum corpori nostro congruum, vel incongruum, haud dubiè de fortunato, vel infortunato itineris statu certò
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318 LEXICON preserve, change, alter, destroy: nor can their activity be taken away or impeded by human will, or by any lower causes, but only by the First Cause, God, and indeed for that very reason they surpass all other things. Truly, man can improve their nature, qualities, effects, and immutable power of acting in the lower things by skill, applying, preventing, or turning aside their action, as Ptolemy said in the Centiloquium, Word 8: The wise soul, he says, contributes to the celestial operation, just as the best farmer contributes by plowing and clearing the land. Therefore man cannot cause the stars not to exercise their natural powers, not to produce their proper effects, or to put off the harmful or beneficial qualities by which they are intrinsically possessed, and to assume contrary ones; but he can, to some extent, in lower causes, by altering, impeding, or even destroying them, and thus entirely turn aside their effects. 9. Thus man cannot in any way prevent a future eclipse, nor the effects that would naturally flow from it: he cannot, for example, avert the excessive heat that will follow from the conjunction of the sun and Mars, nor snow, rains, winds, corruption of the air, etc. But he can, in lower natures, as by building on the ground so that herbs do not sprout, by drying out pools so that they do not corrupt the air; by cutting down trees so that they do not bear fruit. In this way, also, by cooperating with the stars he can contribute to their operation, as by supplying matter or removing it, by guarding himself against harmful stellar influences, by laying a good foundation, preparing, and adapting the susceptible matter at a time of foreseen sterility (as the Patriarch Joseph did), by bringing a large supply of grain into the barns, by cultivating the land in good configurations of the stars, by sailing the seas; in bad ones by staying at home and abstaining from useless labor, etc. I shall conclude, therefore, with what Kircher pertinently has on this subject in his Ars Magna Lucis & Umbra , book 6, part 3, chapter 2. Nature, he says, is governed by two principles, nature and will: nature is subject to the stars, will is free, and therefore effects and operations that are purely natural obey the stars entirely as necessary causes, such as health or sickness; the long or short life of men, etc. Other things are purely voluntary, such as observing, teaching, acts of virtues or vices; others are mixed, such as making a journey, eating, etc. Whether the journey will be convenient or not depends on the stars and on the state of the air. If anyone therefore perfectly knew the influences of the stars as suited or unsuited to our body, he would no doubt be certain of the fortunate or unfortunate state of the journey
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MATHEMATICVM. 327 non item, sed ad singulos ferè minutum vnum, quinimò nodi Lunares ad sua ferè minuta, vt patet in Ephemeridibus, ac tabulis secundorum mobilium. Habent in Genethliacis nodi maximam significationem quoad formam corporis, quam plerumque deturpant, si cum Luminaribus, vel infortunis fuerint reperti, præsertim in Angulis, & in signis detruncatis; vel euruis; qualia sunt Aries, Taurus, Cancer, Scorpio, & Capricornus. Vnde Nati euadent gibbi, strabi, claudi, contorti, vel quouis modo debilitati, vt habet Ptolemæus lib. 3. cap. 17. NUNA SPHÆRA communiter dicitur Primum Mobile, quod constituitur supra octauam sphæram, seu Cælum stellarum, quod secum trahit omnes inferiores sphæras ab oriente in occidentem eursu concitatissimo revolutionem suam perficiens spatio ferè 24. horarum. Alij autem hanc nonam sphæram admittunt distinctam à Primo mobili, quin, & Decimam, quas vocant librationis; seu trepidationis, quam in vident in Firmamento; obseruarunt enim ipsum præter motum vniuersalitatis, & proprium, moueri irregulariter ab septentrione in Austrum, & ab Austro ad Septentrionem sub coluro solstitiorum primi mobilis, vltrò eitróque: rursus moueri ab ortu in occasum, & ab occasu in ortum sub Ecliptica, & super polos eiusdem: Quare cum tot motus comperiantur in firmamento; atque in planetis, nec duos modò explicatos posse haberi dicant ex se, aut à primo mobili, ex vulgato illo axiomate corpus vnum simplex natura sua vno tantum simplici motu moueri posse intrinsecè, ab extrinseco verò pluribus, consequenter, & hanc nonam sphæram admittunt, quæ dat moueri ab ortu in occasum, & ab occasu in ortum super polos Zodiaci per minuta 14. annorum 1716. vt dicunt spatio, & rursus Decimam; quæ det moueri à septentrione in Austrum sub coluro solstitiorum per minuta 24. spatio annorum 3432. Quæ de re vide Clauium, & Blancanum in sphæra mundi lib 18. c.7. Ego vero hos motus distinctos, proindeque distinctas sphæras admittere nullatenus possum, quoniâ repugnat vnum & idem mobile duobus motibus contrariis moueri, quo pacto essent huiusmodi motus trepidationis, qui prorsus fictitij sunt, & optimè saluantur apparentiæ siderum, irregularitates, &c. in sola cæli fluxibilitate, & vnco tantum motu ab oriente in occidentem regulariter tamen irregulari secundum omnes cæli partes remotiores, & remotiores à prima virtute motrice. Vide quæ fusè diximus in V. Motus. NOTA PELIOTES ventus est vnsus ex quatuor intermediis 28. X
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MATHEMATICVM. 327 not so, but for each individual almost a single minute, indeed the lunar nodes to their own minutes, as is evident in the Ephemerides, and tables of the second motions. In genethliacs the nodes have the greatest significance with regard to the form of the body, which they usually disfigure, if they are found with the luminaries or the unfortunate planets, especially in the angles, and in the mutilated signs; or the broad ones; such as Aries, Taurus, Cancer, Scorpio, and Capricorn. Whence those born will turn out hunchbacked, cross-eyed, lame, twisted, or weakened in any way, as Ptolemy has in book 3, chapter 17. THE NINTH SPHERE is commonly called the Primum Mobile, which is placed above the eighth sphere, or the heaven of the stars, which drags along with itself all the lower spheres from east to west, accomplishing its revolution in the space of almost 24 hours. Others, however, admit this ninth sphere as distinct from the Primum Mobile, and even a Tenth, which they call of libration or trepidation, which they see in the Firmament; for they have observed that it, besides the motion of universality and its proper motion, is moved irregularly from north to south and from south to north under the solstitial colure of the first mobile, back and forth; also to move from east to west and from west to east under the Ecliptic, and over its poles: wherefore, since so many motions are found in the firmament, and in the planets, and since they say that the two motions just explained cannot be had from themselves or from the first mobile, from that common axiom that a body simple by its nature can be moved inwardly by only one simple motion, but from without by several, consequently they admit also this ninth sphere, which causes movement from east to west, and from west to east over the poles of the Zodiac by 14 minutes over the space of 1716 years, as they say, and again a Tenth, which causes movement from north to south under the colure of the solstices by 24 minutes over the space of 3432 years. On this matter see Clavius and Blancanus in Sphaera Mundi , book 18, ch. 7. But I for my part cannot in any way admit these distinct motions, and therefore distinct spheres, because it is repugnant that one and the same mobile should be moved by two contrary motions, by which reckoning motions of this sort would be motions of trepidation, which are wholly fictitious, and the appearances of the stars, their irregularities, etc. are excellently preserved in the sole fluxibility of the heavens, and by a single motion only from east to west, though regular in an irregular way according to all the more distant and more distant parts of the heaven from the first moving power. See what we have discussed at length in V. Motus. NOTE. Peliotes is a wind, one of the four intermediate ones. 28. X
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MATHEMATICVM. 311 MVTA SIGNA sunt quæ præseferunt figuram Animalium 102 voce carentium, qualia sunt Cancer, Scorpio, & Pisces: sicut econtrà vocem habentia perhibentur esse tum humana, Gemini, Virgo, Libra, Sagittarius, & Aquarius, tum ferina, quæ etiam raucâ dicuntur, brutorum videlicet vocalium formam habentia, vt Aries, Taurus, Leo, Capricornus. Horum maxima consideratio habetur in Gene- thliacis, quoad vitia, & impedimenta linguæ, de qua re Ptolemæus lib. 3. Quadrip. cap. 17. MVTATIT arab. idem sonat ac latinè agglutinatus; cum vi- 103 delicet Planeta ita est alteri iunctus, vt nec in minuto qui- dem aberret. Hoc vocabulo frequenter vtilur Ptolemæus in Quadrip. ex versione arabica, & Hali eius commen- tator. MVTLATVM arab. Vide in V. Motlatum. 104 MVTLATA SIGN. sunt quæ membrum aliquod seu etiam 105 corpus mutilum repræsentant, vt Taurus, Equi sectio, Caput Medusæ, quæ quidem, vt benè obseruat Titus in Cælesti Philosophia lib. 2. cap. 3. hanc habent naturam & in- fluendi vim, vt ferè semper inducant membrorum incisio- nem, si Vitæ moderatoribus infeliciter se habentibus in Natali, per directionem posteà misceantur. Hinc Ptole- mæus in Quadrip. lib. 4. cap. 10 vbi de genere mortis agit, in signis mutilis, inquit, aut quorum figurà sunt imperfe- tta, aut circà caput Medusa Mars significat capite truncan- dos, aut membris mutilandos. Quod D. Thomas obseruauit opus. 28. art 3. dicens, quod stella illa funerea sunt, & mon- struosam indicant vita terminationem. Vide quæ diximus in V. Gorgonis caput. N. NABLON SCHALIAF seù etiam Nescussackat teste schie- 1. chardo Chaldaicè dicitur Lyra sidus in Cælo, de quo sæ- pius dictum est. NAASCH LAAZAR hoc est Feretrum Lazari dicitur apud 2. Christianos arabes Plaustrum, vt testatur Kircherus in Oe- dipo, eo quod non minus plaustrum, quam Feretrum re- præsentare videantur stellæ quatuor magis conspicuæ in Vr- sa, quæ quatuor plaustri rotas effingunt. Schillerus autem, qui ex hoc occasionem sumpsit omnes coelestes imagines transmutandi, atque ex Diuorum nominibus appellandi, hoc ipsum Astrum vocat Petri Nauiculam. NADIR apud Arabes significat punctum Cæli sub terra 3. oppositum diametraliter vertici capitis nostri, quod ipsi pari- ter gentili suo vocabulo Zenith appellant: itavt ambo sint
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MATHEMATICVM. 311 MUTA SIGNA are those which present the figure of animals 102 lacking voice, such as Cancer, Scorpio, and Pisces: just as, on the contrary, those said to have a voice are both human, Gemini, Virgo, Libra, Sagittarius, and Aquarius, and bestial, which are also called hoarse, that is, having the form of vocal brutes, such as Aries, Taurus, Leo, Capricorn. The chief consideration of these is found in Gene- thliacs, as regards defects and impediments of speech, concerning which Ptolemy, lib. 3. Quadrip. cap. 17. MVTATIT, in Arabic, signifies the same as in Latin agglutinated; namely when a planet is so joined to another that it does not depart even by a minute. Ptolemy frequently uses this term in the Quadrip. from the Arabic version, and Hali his com- mentator. MVTLATVM, Arabic. See under V. Motlatum. 104 MVTLATA SIGN. are those which represent some limb or even 105 a mutilated body, as Taurus, the Cut of the Horses, the Head of Medusa, which, as Titus rightly observes in Cælesti Philosophia lib. 2. cap. 3, have this nature and in- fluencing power, that they almost always bring about the cutting off of limbs, if, with the rulers of life being ill-disposed in the Nativity, they are later mixed by direction. Hence Ptole- my in Quadrip. lib. 4. cap. 10, where he treats of the kind of death, says that in mutilated signs, or those whose figure is imper- fect, or around the head of Medusa, Mars signifies those to be beheaded, or mutilated in their limbs. This St. Thomas observed in opus. 28. art 3, saying that that star is funereal and indicates a monstrous termination of life. See what we said under V. Gorgonis caput. N. NABLON SCHALIAF, or also Nescussackat, according to Schie- chard, is in Chaldean the name given to the constellation Lyra in the heavens, concerning which fre- quent mention has been made. NAASCH LAAZAR, that is, the Bier of Lazarus, is called among Arab Christians the Wagon, as Kircher testifies in Oe- dipus, because the four more conspicuous stars in the Bear seem to represent no less a wagon than a bier, since they depict the four wheels of the wagon. Schiller, however, who took from this occasion to transform all the heavenly images, and to name them from the names of saints, calls this very star Peter’s Little Ship. NADIR among the Arabs signifies the point of the sky beneath the earth, diametrically opposite to the zenith of our head, which they likewise, by their gentile word, call Zenith: so that both are
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318 LEXICON conseruant, immutant, alterant, perdunt: neque eorum activitas tolli vel impediri potest ab humana voluntate, aut ab vllis causis inferioribus, sed tantum à Causa prima Deo, atque adeò vel ob id cæteris omnibus præstant. Benè verò potest homo eorum naturam, qualitates, effectus, inalterabilem agendi vim callens excolere in ipsis inferioribus, applicare, præuertere, declinare, sicut dixit Ptolemæus in Centiloquio Verbo 8, Sapiens anima, inquit, confert cælesti operations, quemadmodum optimus Agrico'a arando, expurgandoque confert Natura. Igitur non potest homo facere, vt Astras suos naturales virtutes non exerant, effectus sibi proprios non producant, qualitates maleficas, aut beneficas, quibus intrinsecus potiuntur exuant, & contrarias induant, potest verò aliquatenus in causis inferioribus eas alterando, impediendo, aut etiam destruendo, sicque totaliter eorum effectus præuertere. 9. Sic non potest homo vllò modo Eclipsum futuram impediire, neque effectus, inde naturaliter emanaturos: non potest, exempli gratia, æstum nimium ex congressu solis, & Martis sequuturum præuertere, nives, pluuias, ventos, aëris infectiones, &c. potest autem in naturis inferioribus, vt ædificando super solum, ne herbas getminet, exsiccando stagna, ne aërem corrumpant; recidendo arbores ne fructus proferant. Sic etiam astris subfamulando eorum operationi conferre, vt subministrare materiam, vel remouere, sese contrà prauas siderum influentias præmunire, bonis substernere, disponere, & passibilem applicare tempore præuisæ sterilitatis (vt fecit Ioseph Patriarcha) magnam frumenti vim in horrea comportare, in bonis siderum configurationibus terram excolere, matia exsulcare; in malis domi consistere, atque à labore inutili abstinere, &c. Concludam igitur cum iis quæ appositè ad hanc rem habet Kircherus in Arte Magna Lucis & Vmbra lib. 6. part. 3. cap. 2. Natura, inquit, duobus principiis regitur, natura, & voluntate: Natura subiecta est sideribus, voluntas libera, & ideò effectus, & operationes purè naturales sideribus planè obediunt tanquam causis necessariis, vt sanitas, vel infirmitas; longa, vel breuis hominum vita, &c. alia qua purè voluntaria, vt speculari, docere, actus virtutum aut vitiorum: alia mixta, vt facere iter, comedere, &c. Vtrum autem iter commodum futurum sit, necne, à sideribus pendet, aërisque constitutione. Si quis igitur perfectè cognosceret influxus siderum corpori nostro congruum, vel incongruum, haud dubiè de fortunato, vel infortunato itineris statu seriò
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318 LEXICON preserving, changing, altering, destroying: nor can their activity be taken away or impeded by human will, or by any lower causes, but only by the First Cause, God, and therefore on that account they surpass all others. But man can indeed, knowing their nature, qualities, effects, and unchangeable power of acting, cultivate them in lower things, apply, prevent, or turn aside, as Ptolemy said in the Centiloquium, Word 8: “The wise soul,” he says, “contributes to celestial operations, just as the best farmer does by plowing and clearing.” Therefore man cannot make his stars not exercise their natural virtues, not produce their proper effects, or divest themselves of the harmful or beneficial qualities with which they are intrinsically endowed and put on contrary ones; but he can to some extent, in lower causes, alter them, hinder them, or even destroy them, and thus entirely avert their effects. 9. Thus man cannot in any way prevent a future eclipse, nor the effects naturally flowing from it: he cannot, for example, avert the excessive heat that will follow from the conjunction of the sun and Mars, nor snow, rains, winds, infections of the air, etc. But he can, in lower natures, do so by building over the ground so that herbs do not sprout, by draining ponds lest they corrupt the air, by cutting down trees lest they bear fruit. In this way, too, by serving the stars, he can contribute to their operation, as by supplying matter or removing it, guarding himself against the evil influences of the stars, preparing for good ones, arranging things, and making himself receptive at the time of foreseen scarcity (as the Patriarch Joseph did) by bringing a great quantity of grain into the granaries; in favorable configurations of the stars, by cultivating the land, by digging channels; in unfavorable ones, by staying at home and abstaining from useless labor, etc. I shall therefore conclude with what Kircher aptly has on this subject in the Ars Magna Lucis & Umbra, book 6, part 3, chapter 2: “Nature,” he says, “is governed by two principles: nature and will. Nature is subject to the stars; will is free, and therefore effects and purely natural operations obey the stars completely as necessary causes, such as health or illness; the long or short life of men, etc. Other things are purely voluntary, such as to look on, to teach, acts of virtues or vices; others are mixed, such as to make a journey, to eat, etc. Whether a journey will be convenient or not depends on the stars and on the constitution of the air. If someone therefore perfectly knew the influences of the stars fitting or not fitting to our body, he would undoubtedly think seriously about the fortunate or unfortunate condition of the journey”
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MATHEMATICVM. 127 non item, sed ad singulos ferè minutum vnum, quinimò nodi Lunares ad sua ferè minuta, vt patet in Ephemeridibus, ac tabulis secundorum mobilium. Habent in Genethliæis nodi maximam significationem quoad formam corporis, quam plerumque deturpant, si cum Luminaribus, vel infortunis fuerint reperti, præsertim in Angulis, & in signis detruncatis, vel curuis; qualia sunt Aries, Taurus, Cancer, Scorpio, & Capricornus. Vnde Nati euadent gibbi, strabi, claudi, consorti, vel quouis modo debilitati, vt habet Ptolemæus lib. 3. cap. 17. N NASPHÆRA communiter dicitur Primum Mobile, quod constituitur supra octauam sphæram, seu Cælum stellarum, quod secum trahit omnes inferiores sphæras ab oriente in occidentem cursu concitatissimo revolutionem suam perficiens spatio ferè 24. horarum. Alij autem hanc nonam sphæram admittunt distinctam à Primo mobili, quin, & Decimam, quas vocant librationis; seu trepidationis, quam in vident in Firmamento; obseruarunt enim ipsum præter motum vniuersalitatis, & proprium, moueri irregulariter ab septentrione in Austrum, & ab Austro ad Septentrionem sub coluro solstitiorum primi mobilis, vltró citróque: rursus moueri ab ortu in occasum, & ab occasu in ortum sub Ecliptica, & super polos eiusdem: Quare cum tot motus comperiantur in firmamento; atque in planetis, nec duos modò explicatos posse haberi dicant ex se, aut à primo mobili, ex vulgare illo axiomate corpus vnum simplex natura sua vno tantum simplici motu moueri posse intrinsecè, ab extrinseco verò pluribus, consequenter, & hanc nonam sphæram admittunt, quæ dat moueri ab ortu in occasum, & ab occasu in ortum super polos Zodiaci per minuta 14. annorum 1716. vt dicunt spatio, & rursus Decimam; quæ det moueri à septentrione in Austrum sub coluro solstitiorum per minuta 24. spatio annorum 3432. Quæ de re vide Clauium, & Blancanum in sphara mundi lib 18. c.7. Ego vero hos motus distinctos, proindeque distinctas sphæras admittere nullatenus possum, quoniâ repugnat vnum & idem mobile duobus motibus contrariis moueri, quo pacto essent huiusmodi motus trepidationis, qui prorsus fictitij sunt, & optimè saluantur apparentiæ siderum, irregularitates, &c. in sola cæli fluxibilitate, & vnico tantum motu ab oriente in occidentem regulariter tamen irregulari secundum omnes cæli partes remotiores, & remotiores à prima virtute motrice. Vide quæ fusè diximus in V. Motus. NOTA PELIOTES ventus est vnsus ex quatuor intermediis 13. X
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MATHEMATICVM. 127 not so, but to each one almost a minute, indeed even the Lunar Nodes to their own minutes, as is evident in the Ephemerides, and tables of secondary motions. In Genethliacs the nodes have the greatest significance as regards the form of the body, which they usually mar if they are found with the luminaries or with the malefics, especially in the angles, and in truncated or curved signs; such as Aries, Taurus, Cancer, Scorpio, and Capricorn. Whence those born will turn out humpbacked, cross-eyed, lame, deformed, or weakened in some way, as Ptolemy has in book 3, chap. 17. In the sphere is commonly called the Primum Mobile, which is situated above the eighth sphere, or the heaven of the fixed stars, and which carries along with it all the lower spheres from east to west, accomplishing its revolution at the swiftest speed in the space of almost 24 hours. Others however admit this ninth sphere distinct from the Primum Mobile, indeed also a Tenth, which they call of libration, or trepidation, which they see in the Firmament; for they have observed that it, besides the motion of the whole, and its proper motion, moves irregularly from north to south, and from south to north under the colure of the solstices of the Primum Mobile, back and forth: again to move from east to west, and from west to east under the ecliptic, and over its poles: wherefore since so many motions are found in the firmament, and in the planets, and since they say that not even the two motions just explained can be had by themselves, or from the Primum Mobile, from that common axiom that one simple body by its own nature can be moved intrinsically by only one simple motion, but extrinsically by several, consequently they also admit this ninth sphere, which causes motion from east to west, and from west to east over the poles of the Zodiac by 14 minutes in the space of 1716 years, as they say; and again the Tenth, which causes motion from north to south under the colure of the solstices by 24 minutes in the space of 3432 years. On this matter see Clavius and Blancanus in Sphaera Mundi book 18, ch. 7. But I myself can by no means admit these distinct motions, and therefore distinct spheres, because it is repugnant for one and the same mobile to be moved by two contrary motions, by which account such motions of trepidation would exist, which are utterly fictitious, and the appearances of the stars, irregularities, etc. are excellently preserved in the mere fluxibility of the heavens, and in the single motion alone from east to west, though regular yet irregular according to all the parts of the heavens farther and farther removed from the first motive power. See what we have said at length in V. Motus. NOTE: Peliotes is a wind, one of the four intermediate ones. 13. X
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MATHEMATICVM. 313 subsistens, sua vniuersali forma præditum, eâque substan- tiali, & perfectissimâ, quæ det quidem toti, cunctisque eius partibus, atque animantibus vitam, non tamen ipsum nun- dum, aut præcipuas eius partes, nempe cælum, sidera, ele- menta, animantes denominet: & quia sensu, & vegera- tione carent, proindeque, vt ait Conc. Constantinop. om- ninò animantes non sunt, Non tamen ex hoc sequitur vi- tam Mundi præcipuarumque eius partium non esse cæteris viuenibus, etiam ipso homine secundum gradus vegeta- tionis, nurriationis, & sensationis, superiorem, atque vni- uersaliorem; non autem secundum gradum intellectui, in quo homo spiritualis est; ac minimè à cælorum Influxibus pender. Viuit ergo Mundus, cælum, sidera, gradu quodam vivæ superiore, cui profectò parem, aut similem in inferio- ribus hisce non sit inuenire: sed omnis ipsorum vivæ ratio, & gradus eminenter in vita mundi est, & ab ipsa tanquam vniuersali, & æquiuoca causa deriuat; vnde est etiam vir- tus ad causandam hanc rerum varietatem. Et hoc, vt benè habet D. Th. 1. part. 9. 105. art. 3 inquantum hac (seilicet cælestia corpora) vniuersali virtute cōtinet in se quidquid in inferioribus generatur & quia (vt paulo ante dixerat) quid- quid in istis inferioribus generat & mouet ad speciem, est in- strumentu[m] cælestis corporis. I girur cælestia corpora sunt causæ superiores, ac principales vivæ, omnisque motionis infe- riorum ad certas species: & quà talia in se ipsis eodem, sed longè nobiliore gradu vivæ prædita sint, necesse est. MVNIR, seù, vt alij legunt, MUMIR, Arabicè dicitur quasi pu- <96.> pilla lueida Coronæ Gnostiæ, Stella fixa secundæ magnitudi- nis de natura veneris, & Mercurij, quâ ob sui pulchritudine[m] verisque apperitionem quam ortu suo facit cæli pupillam, serum aperitionem que dixerunt. Vide fusiùs in V. Corona. MVSATUR, dicitur à Cicerone sagitta sidus apud Aquilam <97.> constans stellis quinque de quibus vide in V. Sagitta. MVSCA, seù, Apis sidus in cælo ad polum Antarcticum no- <98.> bis inuisum, & nuper à nouis Astronomis ad Australes pla- gas appulsis cum aliis vndecim obseruarum, continens qua- tuor stellas infimæ notæ: Est nunc in longirudine sub signo Scorpij incidens in ipsum Antarcticum circulum: Apud In- dos Muia. MVSIDA EQVR, Arabicè Alpheratz, vulgò dicitur stella <99.> fixa ictiæ magnitudinis in dictu Pegasi existens, de natura mixta Marris, Iouis, & Veneris de qua vide iam dicta in V. Alpheratz. MVSICA, vna est ex quatuor præcipuis Mathesis diuisio- <100>
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MATHEMATICVM. 313 subsisting, furnished with its universal form, and with that substantial and most perfect one, which indeed gives life to the whole and to all its parts, and to living beings, yet does not thereby denominate the whole itself, nor its principal parts, namely the heavens, the stars, the elements, and living beings: and because they lack sense and vegetation, and therefore, as the Council of Constantinople says, are not living beings at all. Nevertheless, it does not follow from this that the life of the World, and of its principal parts, is not superior and more universal than that of other living things, even than man himself according to the degrees of vegetation, nourishment, and sensation; but not according to the degree of intellect, in which man is spiritual; and least of all dependent on the influences of the heavens. Therefore the World, the heavens, and the stars live by a certain higher degree of life, to which, indeed, no equal or like thing is found in these lower things: but all their life and degree of life eminently exist in the life of the world, and derive from it as from a universal and equivocal cause; whence also comes the power of causing this diversity of things. And this, as St. Thomas well has it, 1. part. 9. 105. art. 3, insofar as it (namely these celestial bodies) contains in itself by universal virtue whatever is generated in the lower things; and because, as he said a little before, whatever in these lower things generates and moves toward a species is an instrument of the celestial body. Therefore the celestial bodies are higher and principal living causes of every motion of the lower things toward certain species; and as such, they must in themselves be endowed with the same kind of life, but in a far nobler degree. MVNIR, or, as some read, MUMIR, is called in Arabic, as it were, the lucid pupil of the Gnostic Crown, a fixed star of the second magnitude, of the nature of Venus and Mercury, because of its beauty and the appearance of the true openings which it makes with its rising, the opening of the sky they called the late opening. See more fully under V. Corona. MVSATUR, is called by Cicero the arrow-star near Aquila, consisting of five stars, concerning which see under V. Sagitta. MVSCA, or Apis, a star in the sky near the Antarctic pole, invisible to us, and recently observed by the new astronomers who came to the southern regions along with eleven others, containing four stars of the lowest magnitude: it is now in longitude under the sign of Scorpio, falling upon the Antarctic circle itself. Among the Indians, Muia. MVSIDA EQVR, in Arabic Alpheratz, is commonly called a fixed star of the second magnitude, situated in the said Pegasus, of mixed nature of Mars, Jupiter, and Venus; concerning which see what has already been said under V. Alpheratz. MVSICA, is one of the four chief divisions of Mathematics. 100
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MATHEMATICVM. 317 operis, quod accedit extrinsecus, per illum accedit, quem nihilominus creauis, & quem regit atque ordinat inuisibiliter Deus? Hinc iam in ipsum mundum velut in quamdam magnam arborem rerum oculus cogitationis attollitur, atque in ipso quoque gemina operatio prouidentia reperitur partim Naturalis, partim Voluntaria. Naturalis quidem per occultam Dei administrationem, quæ etiam lignis, & herbis dat incrementum, voluntaria verò per angelorum opera, & hominum. Secu[n]dum illam primam cælestia superiùs ordinari, inferiùsque terrestria, luminaria, sideraque fulgere, diei, noctisque vices agitari, aquis terram fundatâ interlui, atque circumlui, aërem altius superfundi, arbusta, & animalia concipi, & nasci, crescere, & senescere, occidere, & quidquid aliud in rebus interiori, naturalique motu geritur: In hac autem altera signa dari, doceri, & discere, agros coli, societates administrari, artes exerceri, & quoque alia, sive in superna societate aguntur, sive in hac terrena atque mortali, ita- vt bonis consulatur, & per nescientes malos: inque ipso homine eandem geminam prouidentia vigere potentiam: primò erga corpus naturale scilicet eo motu quo fit, quo crescit, quo senoscit; voluntarium vero quoad victum, tegumentum, curationemque consulitur. Hucusque D. August. Ex quibus liquet, duo esse rerum principia; naturam, & voluntatem; eaque ambo à Diuina prouidentia regi, promoueri, disponi, atque etiam superiori potentia impediri posse: Verum in suo cursu relicta Naturam necessariò operari, Voluntatem liberè, ac naturæ cursum disponere posse, coadiuare, & aliquatenus impedire hinc quæ à natura pure & absque voluntatis adminiculo prodeunt, naturalia; quæ à sola voluntate nihil subfamulante Natura, purè voluntaria: quæ verò à voluntate provt applicat actiua passuis, impedimenta remouet, naturam ipsam ad operandum disponit artificialia dicuntur Quod, & obseruauit ipsemet Augustinus paulò post subdens: Sicut autem in arbore id quod agit agricultura forinsecus, ut illud proficiat, quod geritur (à natura) intrinsecus; sic in homine secundum corpus, ei quod intrinsecus agit natura, seruit extrinsecus medicina: quod autem ad arborem colendi negligentia, hoc ad corpus medendi incuria, hoc ad animam discendi seenitia. Et quod ad arborem humor inutilis, hoc ad corpus victus exitiabilis, hoc ad animam persuasio iniquitatis. Porrò inter naturales causas principem sibilocum vendicant corpora cælestia, quæ sua vniuersali potentia in omnia isthæc sublunaria agunt, suis influxibus producunt, 8.
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MATHEMATICVM. 317 of a work which comes in from outside, by that comes in which nevertheless you create, and which God invisibly governs and orders? From this the mind is now lifted up to the world itself, as to some great tree of things, and in the world itself also a twofold operation of providence is found, partly natural, partly voluntary. Natural indeed through the hidden administration of God, which even gives increase to trees and herbs; voluntary truly through the works of angels and of men. According to that first kind, the heavenly things are ordered above, and the earthly things below; lights and stars shine; the alternations of day and night are carried on; the waters flow over and around the earth, with a firm spreading out; the air is poured above; shrubs and animals are conceived and born, grow and grow old, die, and whatever else is done in things by an inward and natural movement. But in this other kind signs are given, teaching is given, and learning, fields are cultivated, communities are governed, arts are exercised, and also other things, whether they are carried on in the society above or in this earthly and mortal one, so that provision is made for the good, and through the ignorant for the evil; and in man himself the same twofold power of providence is active: first with regard to the body, namely in the natural motion by which it is made, by which it grows, by which it grows old; but voluntarily, as to food, clothing, and care, provision is made. Thus far St. August. From these things it is clear that there are two principles of things: nature and will; and that both are ruled, promoted, ordered, and even can be hindered by a higher power by Divine providence. But in its own course, nature, being left to itself, necessarily acts; will can freely dispose the course of nature, assist it, and to some extent hinder it. Hence those things that from nature purely and without the aid of will proceed are called natural; those that come from will alone, nature not at all participating, are purely voluntary; but those that come from will insofar as it applies active things to passive ones, removes impediments, and disposes nature itself to act, are called artificial. This, too, Augustine himself observed, a little later, adding: “As in a tree, that which agriculture does from outside, so that that may profit which is worked out by nature from within; so in man, as regards the body, to that which nature works within, medicine serves from without: and what neglect in cultivating is to a tree, this to the body is negligence in healing, and this to the soul is sloth in learning. And what unwholesome moisture is to a tree, this a harmful diet is to the body, and this persuasion of wickedness is to the soul.” Moreover, among natural causes the chief place is claimed by the heavenly bodies, which with their universal power act upon all these sublunary things, produce them by their influences, 8.
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MATHEMATICVM. 519 iudicare posset: item desanitare, de morbo, &c. Item de successu negotij cum principe. Verum cum hæc difficulter fieri possint, & scire, hinc electionum harum notitia, nisi experientiis fulciatur, vt plurimum fallax est. Hæc Kircherus. Ex quibus patet quid ars, seu humanum ingenium, quid Natura possit, quidve homo ex rerum natura probè cognita aggredi possit, quid demum frustrà, quid etiam temerè ag- grediatur. NAVBARACH, siue Nambahàr arab. idem sonat, ac No-10; uenariæ Dominus. Vide in V. Anaubarach. NAVIS vulgò audit sidus ad australem plagam constans 11. stellis 65. vt liquet ex accuratissimis nouorum Astronomorum obseruationibus, omnibus ferè de natura Saturni, & Louis, quorum præcipua est Canopus in temone consistens primi honoris arab. Rubail, cui proximè accedit dicta Marcheb in medio scuti posita. Hoc sidus à schillero immutatum fuit in Arcam Noe. Hebraicè autem dicitur sephina. NEBOLASSID apud Fetzanos, Maroccenses, cærerosque 12. Nubianos astrologos appellatur Cauda Leonis, stella fixa primæ magnitudinis, de qua satis dictum est suo loco. NEBVLOSÆ STELLÆ sunt fixæ quædam obtuso lumine, 13. pallenti, & suboseuro micantes: eò dictæ vel quia nebulas quasdam specie sua præseferunt, (quales præcipuè sunt dux magnæ & satis conspicuæ ad polum Antarcticum) vel sanè, quia nebulas generant, & cum sole occidentes aerem nebulosum reddunt, vt obseruarunt Ptolemæus & Plinius, in Presepi, existente in pectore Cancri, in ea, quæ est in oculo Sagittarij, sed præsertim videre est in ea, quæ sequitur aculeum scorpij. Idque, vt obseruat Titus lib.1. cap.12. quia earum nebulositas parem, & consimilem effectum parit in hisce inferioribus. Hinc etiam experientia compertum est, vt quandocumque cum Luminaribus in alicuius genesi congredientur, semper excitatem, nebulas, aut aliud vitium in oculis importent; quod ipsa naturalis ratio suadet, Nam earum lux valdè exilis, ac debilis est, ac proinde non mirum, si oculorum lucem adimant, aut obtundant, quando ipsis luminaribus, à quibus lumen in oculos derivatur congressu fiant infensæ. NEMER hoc est Pardus hæbreorum lingua dicitur Lupus 14. sidus de quo alibi dictum. NEOMENIVM græcè idem valet, ac Nouilunium, de quo 15. mox infrà. NEPA Cicetoni, & aliis idem est, ac Scorpij ludus fortè à 16.
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MATHEMATICVM. 519 could judge: likewise to heal from illness, etc. Also concerning the success of a business with a prince. But since these things can be done with difficulty, and be known, hence the knowledge of these choices, unless supported by experience, is for the most part deceptive. Thus Kircher. From which it is clear what art, or human ingenuity, can do, what Nature can do, what man, having rightly known the nature of things, can undertake, and finally what he undertakes in vain, and what even rashly he undertakes. NAVBARACH, or Nambahàr, in Arabic, means the same as No-10; venariæ Dominus. See in V. Anaubarach. NAVIS, commonly called a constellation on the southern side, consisting of 11. stars 65. as is evident from the most exact observations of the new Astronomers, all almost concerning the nature of Saturn and Louis, whose principal star is Canopus, standing in the rudder of the first rank, arab. Rubail, to which closely follows the said Marcheb placed in the middle of the shield. This constellation was changed by Schiller into Noah’s Ark. In Hebrew it is called sephina. NEBOLASSID, among the Fetzans, the Moroccans, and the other 12. Nubian astrologers, is called the Lion’s Tail, a fixed star of the first magnitude, of which enough has been said in its place. NEBVLOSÆ STELLÆ are certain fixed stars with a dull light, 13. pale, and dimly shining: so called either because they present certain nebulae in their appearance, such as especially are the two great and quite conspicuous ones near the Antarctic pole) or indeed, because they generate nebulae, and, when setting with the sun, make the air cloudy, as Ptolemy and Pliny observed, in the Crib, located in the breast of Cancer, in that which is in the eye of Sagittarius, but especially one may see it in that which follows the sting of Scorpio. And this, as Titus observes, lib. 1. cap. 12. because their nebulosity produces an equal, and similar effect in these lower regions. Hence experience has also established that whenever they come together with the Luminaries in someone’s nativity, they always bring blight, clouds, or some other defect in the eyes; which natural reason itself suggests, For their light is very slender and weak, and therefore it is not surprising if they take away or dull the light of the eyes, when they are made hostile by conjunction with those luminaries, from which light is conveyed into the eyes. NEMER, that is, Pardus in the Hebrew language, is called a Wolf 14. a constellation, of which elsewhere something has been said. NEOMENIVM in Greek means the same as New Moon, of which 15. soon below. NEPA, for Cicetoni and others, is the same as the Scorpion’s game, perhaps 16.
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320 LEXICON Chelis dictum; eandem etiam ob rationem. 18. NEPA, Afrorum linguâ dicitur Cancer aliud sidus, quod in nominibus sæpe cum Scorpione confunditur. 19. NESCHER, Hebraicè dicitur Aquila. 20. NIGEAR, (teste Iunctino in Sphætam Io: de Sacrobosco) apud Arabes scriptores dicitur axis Mundi, qui ad eiusdem polos terminatur, & concipitur transire per centrum terræ, Vide in V. Axis. 21. NIGRA, seù Niger, appellatur species quædam Cometæ nigri coloris, seù potiùs plumbei, & suboscuri de natura, & conditione Saturni, ac proinde vt in colore, ita & in qualitatibus ei omninò persimilis. Significat enim cum apparuerit anni inopiam, diuturnas locustas, & alia id genus animalia perniciosa, pestilentiam, febres chronicas, &c. Adducit etiam nebulas, nimbos, glacies, niues, & in hominibus Saturninis solitudinis, austeritatis, inurdiæ, obstinationis, auaritiæ incitamentum, & incrementum. NITACH, Arab. seù potius Chaldaicè significat Zodiacum, & circulum signorum. Vnde Alchabitius ita incipit librum suum, Nitach; id est circulus signorum diuiditur in duodecim partes æquales, &c. Vide quæ fusius dicenda sunt in V. Zodiacus. 23. NITVRA, pro Genitura, seù Natalitio Themate per Apocopen sæpissimè ab aliquibus vsurpatur. Vide Isidorum. 24. NOCTRNVM signum, vel etiam Planeta denominatur in quo præponderant qualitates passiuæ, quales sunt humiditas, & siccitas: sicut è contrà Diurna dicuntur signa & planetae in quibus abundant qualitates actiuæ: qua de re vide quæ diximus in V. Diurnus. 25. NODI vocantur ab Astronomis intersectiones orbitarum solis, & singulorum planetarum latitudinem habentium, vbi videlicet orbitæ planetarum incidunt in Eclypticam in duobus punctis opposiris, & Nodus quidem boreus dicitur punctum in quo Planeta è latitudine australi transit in borealem; Austrinus verò vbi à borea descendit ad Austrum. Qvi etiam ex forma quam referunt caput, & cauda Draconis dicuntur; Item Attollens, seu euehens; atque deprimens. Vbi autem Planetæ maximam latitudinem habent appellatur venter Draconis, quia & hic in ventre latior est, quam in extremitatibus. Porro Nodi isti permutant locum in Zodiaco, quemadmodum ipsi Planetæ sed gradiuntur contrà successionem signorum. Et trium quidem superiorum Nodi insensibiliter mouentur; inferiorum verò non
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320 LEXICON Chelis dictum; for the same reason also. 18. NEPA, in the language of the Africans, Cancer is said to denote another star, which is often confused in names with Scorpio. 19. NESCHER, in Hebrew, means Eagle. 20. NIGEAR, (according to Iunctinus in the Sphere of Io: de Sacrobosco) among Arabic writers means the axis of the World, which terminates at its poles, and is conceived to pass through the center of the earth. See under V. Axis. 21. NIGRA, or Niger, is the name of a certain species of comet of a black color, or rather leaden and somewhat dark, of the nature and condition of Saturn, and therefore, as in color, so also in qualities altogether very like him. For it signifies, when it has appeared, scarcity of the year, long-lasting locusts, and other harmful animals of that kind, pestilence, chronic fevers, etc. It also brings clouds, storms, ice, snow, and in Saturnine men an incitement and increase of solitude, austerity, insensibility, obstinacy, and greed. NITACH, in Arabic, or rather in Chaldaic, signifies the Zodiac and the circle of the signs. Hence Alchabitius begins his book thus, Nitach; that is, the circle of the signs is divided into twelve equal parts, etc. See what is to be said more fully under V. Zodiacus. 23. NITVRA is very often used by some, by apocope, for Genitura, or the natal figure. See Isidore. 24. NOCTURN sign, or also planet, is called that in which passive qualities prevail, such as humidity and dryness: just as, on the contrary, signs and planets in which active qualities abound are called Diurnal: concerning which see what we said under V. Diurnus. 25. NODI are called by astronomers the intersections of the orbits of the sun and of individual planets having latitude, namely where the orbits of the planets cut the ecliptic at two opposite points; and the northern node is indeed called the point at which the planet passes from southern latitude into northern; the southern, however, where it descends from north to south. They are also so called from the form which they present, namely the head and tail of the Dragon; likewise the ascending, or raising, and the descending. But where the planets have their greatest latitude, it is called the belly of the Dragon, because here too it is broader in the belly than at the extremities. Moreover, these nodes change their place in the Zodiac, just as the planets themselves do, but they move contrary to the succession of the signs. And indeed the nodes of the three superior planets move imperceptibly; but those of the inferior not
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320 LEXICON Chelis dictum; eandem etiam ob rationem. 18. NEPA, Afrorum linguâ dicitur Cancer aliud sidus, quod in nominibus sæpe cum Scorpione confunditur. 19. NESCHER, Hebraïcè dicitur Aquila. 20. NIGEAR, (teste lunctino in Sphætam Io: de Sacrobosco) apud Arabes scriptores dicitur axis Mundi, qui ad eiusdem polos terminatur, & concipitur transire per centrum terræ, Vide in V. Axis. 21. NIGRA, seù Niger, appellatur species quædam Cometæ nigri coloris, seù potiùs plumbei, & suboscuri de natura, & conditione Saturni, ac proinde vt in colore, ita & in qualitatibus ei omninò persimilis. Significat enim cum apparuerit anni inopiam, diuturnas locustas, & alia id genus animalia perniciosa, pestilentiam, febres chronicas, &c. Adducit etiam nebulas, nimbos, glacies, niues, & in hominibus Saturninis solitudinis, austeritatis, inurdiæ, obstinationis, auaritiæ incitamentum, & incrementum. NITACH, Arab. seù potius Chaldaicè significat Zodiacum, & circulum signorum. Vnde Alchabitius ita incipit librum suum, Nitach; id est circulus signorum diuiditur in duodecim partes aquales, &c. Vide quæ fusius dicenda sunt in V. Zodiacus 23. NITVRA, pro Genitura, seù Natalitio Themate per Apocopen sæpissimè ab aliquibus vsurpatur. Vide Isidorum. 24. NOCTURNVM signum, vel etiam Planeta denominatur in quo præponderant qualitates passiuæ, quales sunt humiditas, & siccitas: sicut è contrà Diurna dicuntur signa & planetae in quibus abundant qualitates actiuæ: qua de re vide quæ diximus in V. Diurnus. 25. NODI vocantur ab Astronomis intersectiones orbitarum solis, & singulorum planetarum latitudinem habentium, vbi videlicet orbitæ planetarum incidunt in Eclypticam in duobus punctis oppositis, & Nodus quidem boreus dicitur punctum in quo Planeta è latitudine australi transit in borealem; Austrinus verò vbi à borea descendit ad Austrum. Qvi etiam ex forma quam referunt caput, & cauda Draconis dicuntur; Item Attollens, seu euehens; atque deprimens. Vbi autem Planetæ maximam latitudinem habent appellatur venter Draconis, quia & hic in ventre latior est, quam in extremitatibus. Porrò Nodi isti permutant locum in Zodiaco, quemadmodum ipsi Planetæ sed gradiuntur contrà successionem signorum. Et trium quidem superiorum Nodi insensibiliter mouentur; inferiorum verò non
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320 LEXICON Chelis dictum; for the same reason also. 18. NEPA, in the African language, means Cancer; another constellation, which in names is often confused with Scorpio. 19. NESCHER, in Hebrew, means Eagle. 20. NIGEAR, (as testified by Iunctinus in his commentary on the Sphere of Ioannes de Sacrobosco) is said by Arab writers to be the axis of the world, which terminates at its poles, and is conceived to pass through the center of the earth. See under V. Axis. 21. NIGRA, or Niger, is the name of a certain kind of Comet, of black color, or rather leaden and somewhat dark, by nature and condition of Saturn, and therefore, as in color, so also in qualities entirely like him. For it signifies, when it appears, shortage of the year, long-lasting locusts, and other such harmful animals, pestilence, chronic fevers, etc. It also brings fogs, heavy rains, ice, snows, and in Saturnine men an incitement and increase of solitude, austerity, rudeness, stubbornness, and greed. NITACH, in Arabic, or rather in Chaldean, signifies the Zodiac and the circle of the signs. Hence Alchabitius begins his book thus: Nitach; that is, the circle of the signs is divided into twelve equal parts, etc. See what is to be said more fully under V. Zodiacus. 23. NITVRA is very often used by some, by apocope, for Genitura, or the natal figure. See Isidorus. 24. A NOCTURNAL sign, or even planet, is one in which passive qualities predominate, such as humidity and dryness; just as, on the contrary, signs and planets in which active qualities abound are called Diurnal: on this matter see what we said under V. Diurnus. 25. NODI are called by astronomers the intersections of the orbits of the sun and of the individual planets that have latitude, namely where the orbits of the planets meet the Ecliptic at two opposite points; and the northern Node is the point at which a planet passes from southern latitude into northern; the southern, however, where it descends from the north to the south. They are also called from the shape they bear, the head and tail of the Dragon; also the Ascending, or lifting; and the descending. But where the planets have the greatest latitude it is called the belly of the Dragon, because this also is broader in the belly than at the extremities. Moreover, these Nodes change their place in the Zodiac, just as the planets themselves do, but they proceed contrary to the succession of the signs. And indeed the Nodes of the three superior planets move imperceptibly; but those of the inferior do not.
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LEXICON ad conseruationem species. & alimento ad conseruationem indiuidui: & propter hoc in istis inferioribus non inuenitur vita sine anima vegetabili, sed hoc non habet locum in in- corruptibilibus: & art. 1. in responsione ad primum argu- mentum, quo inferebatur omnium rerum naturalium pro- prium esse viuere; vltrò fatetur, quod si totum uniuersum corporale esset unum animal, ita quod iste motus esset amo- uente intrinseco, vt quidam posuerunt, sequeretur, quod motus esset vita omnium naturalium corporum. Similiter ratio sensus impertinens est ad vitam, & potius passio & imperfectio, quam perfectio. Ait enim Philosophus, in lib. de Somno, & Vigilia, quod iis conuenit sensus, in qui- bus est tristari, & gaudere, contupiscere, & odisse: plantis autem nihil horum inesse, vnde conuenienter iis à Natura inditus non est sensus: supra quod D. Thomas in commen- to. Complexio, inquit, plantarum in nutrimento, & aug- mento, & his similia melius fiunt sine sensu, quam cum sensu: ergo planta non habent sensum, cum naturæ semper faciat quod melius est. Cum igitur isti gradus vitæ potius sint imperfectiones, & defectus naturæ, quam perfectiones, & Sol, Astra, & mundus non indigeant generatione, & nutritione ad conseruationem speciei vel indiuidui, & adhuc non habeant aliquod ad sui esse conducens, vel ad sui esse contrarium, quod amore prosequi debeant, aut odio; iure illis à Natura neque sensu, neque vegetatione prouisum, sed solum vitâ quadam superiore, quæ omnem vitam inferiorum eminenter contineat, & colligitur ex motu perfectissimo, qui est circularis, & ab intrinseco, po- tens naturaliter in æuum protrahi, & motum cæteris viuen- tibus participare. Alloquin si gradus huiusmodi vitæ, vege- tatio inquam & sensatio absolutè, & simpliciter dicerent rationem vitæ perfectiorem, quæ non in aliquo eminentet conrineretur, posset etiam dici, quod vita hominis est per- fectior vita Angeli, quia viuit, nedum intellectualiter, vt ille, sed adhuc vita sensitua, & vegetabili. Sicut igitur vita Angeli est perfectior vita hominis, etiamsi non sit ve- getabilis, & sensibilis, ita etiam vita Muudi est perfectior omnibus viuentibus inferioribus; atque adeo plantis, & animalibus, etiamsi sensum, & vegetationem non habeat. Qui quidem gradus vitæ in talibus viuentibus dicunt per- fectionem, at non in superiotibus, quæ tali modo viuendi non indigent. Igitur pro coronide huius nobilissimæ Controversiæ, concludendum est, vniuersum hoc unum quid esse, per se
Transcription: Translated (English)
LEXICON for the preservation of the species, and food for the preservation of the individual: and for this reason in these lower things there is not found life without a vegetative soul; but this has no place in incorruptible beings: and art. 1 in the response to the first argu- ment, by which it was inferred that it belongs to all natural things to live; he freely admits that if the whole corporeal universe were one animal, so that this motion were from an intrinsic mover, as some have held, it would follow that motion would be the life of all natural bodies. Likewise the notion of sense is irrelevant to life, and rather a passion and imperfection than a perfection. For the Philosopher says, in book De Somno et Vigilia, that sense belongs to those in whom there is sadness and joy, desire and hate: in plants however none of these are found, wherefore sense was not suitably bestowed on them by Nature: on this D. Thomas in the comment adds, The constitution, he says, of plants in nourishment and growth, and things like these are better brought about without sense than with sense: therefore plants do not have sense, since nature always does what is better. Since therefore these grades of life are rather imperfections and defects of nature than perfections, and the Sun, Stars, and world do not need generation and nourishment for the preservation of the species or the individual, and still do not have anything conducive to their own being, or contrary to their own being, which they ought to pursue with love, or hate; by right Nature has provided them with neither sense nor vegetation, but only with a certain higher life, which eminently contains every life of lower things, and is gathered from the most perfect motion, which is circular, and from within, naturally able to be extended into eternity, and to share motion with other living things. Otherwise, if the grades of this kind of life, namely vegetation and sensation absolutely and simply, were said to constitute a more perfect notion of life, which is not contained eminently in anything, it could also be said that the life of man is more perfect than the life of an Angel, because he lives not only intellectually, as that one does, but still a life of sense and vegetation. Just as therefore the life of an Angel is more perfect than the life of man, although it is not vegetative and sensible, so also the life of the World is more perfect than all lower living things; and indeed than plants and animals, even if it does not have sense and vegetation. Those grades of life in such living things indeed denote perfection, but not in higher beings, which do not need to live in such a way. Therefore, as the crown of this most noble Controversy, it must be concluded that this universe is one thing, by itself
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MATHEMATICVM. 313 subsistens, sua vniuersali forma præditum, eâque substan- tiali, & perfectissimâ, quæ det quidem toti, cunctisque eius partibus, atque animantibus vitam, non tamen ipsum mun- dum, aut præcipuas eius partes, nempe cælum, sidera, ele- menta, animantes denominet: & quia sensu, & vegeta- tione carent, proindeque, vt ait Conc. Constantinop. om- ninò animantes non sunt, Non tamen ex hoc sequitur vi- tam Mundi præcipuarumque eius partium non esse cæteris viuensibus, etiam ipso homine secundum gradus vegeta- tionis, nutricationis, & sensationis, superiorem, atque vni- uersaliorem; non autem secundum gradum intellectiui, in quo homo spiritualis est; ac minimè à cælorum Influxibus pendet. Viuit ergo Mundus, cælum, sidera, gradu quodam vitæ superiore, cui profectò parem, aut similem in inferio- ribus hisce non sit inuenire: sed omnis ipsorum vitæ ratio, & gradus eminenter in vita mundi est, & ab ipsa tanquam vniuersali, & æquiuoca causa deriuat; vnde est etiam vir- tus ad causandam hanc rerum varietatem. Et hoc, vt benè habet D. Th. 1. part. q. 105. art. 3 inquantum hac ( scilicet cælestia corpora) vniuersali virtute cōtinet in se quidquid in inferioribus generatur & quia (vt paulo antedixerat) quid- quid in istis inferioribus generat. & mouet ad speciem, est in- strumentu[m] cælestis corporis. Igitur cælestia corpora sunt causæ superiores, ac principales vitæ, omnisque motionis infe- riorum ad certas species: & quà talia in se ipsis eodem, sed longè nobiliore gradu vitæ prædita sint, necesse est. MVNIR, seù, vt alij legunt, Mumir, Arabicè dicitur quasi pu- <96.> pilla lucida Coronæ Gnostiæ, Stella fixa secundæ magnitudi- nis de natura veneris, & Mercurij, quâ ob sui pulchritudine[m] verisque apperitionem quam orru suo facit cæli pupillam, sertum aperitionem que dixerunt. Vide fusiùs in V. Corona. MVSATOR, dicitur à Cicerone sagitta sidus apud Aquilam <97.> constans stellis quinque de quibus vide in V. Sagitta. MVSCA, seù, A pis sidus in cælo ad polum Antarcticum no- <98.> bis inuisum, & nuper à nouis Astronomis ad Australes pla- gas appulsis cum aliis vndecim obseruatum, continens qua- tuor stellas infimæ novæ: Est nunc in longitudine sub signo Scorpij incidens in ipsum Antarcticum circulum: Apud In- dos Muia. MVSIDA Eqvi, Arabicè Alpheratz, vulgò dicitur stella <99.> fixa tertiæ magnitudinis in rictu Pegasi existens, de natura mixta Martis, Iouis, & Veneris de qua vide iam dicta in V. Alpheratz. MVSICA, vna est ex quatuor præcipuis Mathesis diuisio- <100>
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MATHEMATICVM. 313 subsisting, endowed with its universal form, and with that substantial and most perfect form which indeed gives life to the whole and to all its parts and living beings, yet does not designate the world itself, or its principal parts, namely heaven, the stars, the elements, and living beings: and because they lack sense and vegetation, and therefore, as the Council of Constantinople says, are not living beings at all, nevertheless it does not follow from this that the life of the World and of its principal parts is not, even above all other living things, and even above man himself according to the degrees of vegetation, nutrition, and sensation, superior and more universal; though not according to the degree of intellect, in which man is spiritual; and he depends least of all on the influences of the heavens. Therefore the World lives, heaven and the stars live by a certain higher degree of life, to which indeed no equal or similar one is to be found in these lower things: but all the account and degree of their life exists eminently in the life of the world, and derives from it as from a universal and equivocal cause; whence also comes the power for causing this variety of things. And this, as St. Thomas rightly has it, 1st part, q. 105, art. 3, insofar as these (namely celestial bodies) contain in themselves by universal power whatever is generated in lower things; and because (as he had said a little before) whatever in these lower things generates and moves toward species is the instrument of the celestial body. Therefore celestial bodies are the higher and principal causes of life and of all motion in lower things toward certain species: and as such it is necessary that they themselves, in their own way, be endowed with the same, but far nobler, degree of life. MVNIR, or, as others read, Mumir, in Arabic is called, as it were, the bright pupil of the Crown of Gnostia, a fixed star of the second magnitude, of the nature of Venus and Mercury, which, because of its beauty and the true openings which it makes through its rising, they called the pupil of the sky, and also a garland opening. See more fully in V. Corona. MVSATOR, is called by Cicero the arrow, a star in the Eagle, consisting of five stars; see in V. Sagitta. MVSCA, or, the Bee, a constellation in the sky near the Antarctic pole, invisible to us, and recently observed by the new astronomers who had arrived at the southern regions together with eleven others, containing four stars of the lowest magnitude. It is now in longitude under the sign of Scorpio, falling upon the Antarctic circle itself. Among the Indians, Muia. MVSIDA Eqvi, in Arabic Alpheratz, is commonly called a fixed star of the third magnitude, situated in the mouth of Pegasus, of mixed nature from Mars, Jupiter, and Venus; see what has already been said under V. Alpheratz. MVSICA, is one of the four principal divisions of Mathematics. <100>
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MATHEMATICVM. 51. iudicare posset: item desanitate, de morbo, &c. Item de successu negotij cum principe. Verum cum hæc difficulter fieri possint, & scire, hinc electionum harum notitia, nisi experientiis fulciatur, vt plurimum fallax est. Hæc Kircherus. Ex quibus patet quid ars, seu humanum ingenium, quid Natura possit, quidve homo ex rerum natura probè cognita aggredi possit, quid demum frustrà, quid etiam temerè ag- grediatur. NAVBARACH, siue Naubahar arab. idem sonat, ac No-10. uenariæ Dominus. Vide in V. Anaubarach. NAVIS vulgò audit sidus ad australem plagam constans 11. stellis 65. vt liquet ex accuratissimis nouorum Astronomorum obseruationibus, omnibus ferè de natura Saturni, & Louis, quorum præcipua est Canopus in temone consistens primi honoris arab. Rubail, cui proximè accedit dicta Mar- cheb in medio scuti posita. Hoc sidus à schillero immu- tatum fuit in Arcam Noe. Hebraicè autem dicitur Se- phina. NEBOLASSID apud Fetzanos, Maroccenses, cærerosque 12. Nubianos astrologos appellatur Cauda Leonis, stella fixa primæ magnitudinis, de qua satis dictum est suo loco. NEBVLOSÆ STELLÆ sunt fixæ quædam obtuso lumine, 13. pallenti, & suboscuro micantes: eô dictæ vel quia nebulas quasdam specie sua præseferunt, (quales præcipuè sunt dux magnæ & satis conspicuæ ad polum Antarcticum) vel sanè, quia nebulas generant, & cum sole occidentes aerem nebu- losum reddunt, vt obseruarunt Ptolemæus & Plinius, in Presepi, existente in pectore Cancri, in ea, quæ est in oculo Sagittarij, sed præsertim videre est in ea, quæ sequi- tur aculeum scorpij. Idque, vt obseruat Titus lib. 1. cap. 12. quia earum nebulositas parem, & consimilem effectum parit in hisce inferioribus. Hinc etiam experientia compertum est, vt quandocumque cum Luminaribus in alicuius genesi congredientur, semper excitatem, nebulas, aut aliud vi- tium in oculis importent; quod ipsa naturalis ratio suadet, Nam earum lux valdè exilis, ac debilis est, ac proinde non mirum, si oculorum Incem adimant, aut obtundant, quando ipsis luminaribus, à quibus lumen in oculos deri- uatur congressu siant infensæ. NEMER hoc est Pardus hæbreorum lingua dicitur Lupus 14. sidus de quo alibi dictum. NEOMENIVM græcè idem valet, ac Nouilunium, de quo 15. mox infrà. NEPA Ciceroni, & aliis idem est, ac Scorpij fidus fortè à 16.
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MATHEMATICVM. 51. could judge: likewise about health, about disease, etc. Likewise concerning the success of business with a prince. But since these things can scarcely be done, and to know them, hence the knowledge of these elections, unless supported by experience, is for the most part deceptive. Thus Kircher. From these things it is clear what art, or human ingenuity, can do, what Nature can do, what a man, having properly known the nature of things, can undertake, and finally what he undertakes in vain, and what also rashly he undertakes. NAVBARACH, or Naubahar in Arabic, sounds the same as the Lord of No- venaria. See in V. Anaubarach. NAVIS, commonly called a constellation on the southern side, consisting of 11. stars, 65, as is clear from the most accurate observations of the newer Astronomers, all almost of the nature of Saturn and Louis, of which the chief is Canopus, standing in the prow, of the first honor in Arabic, Rubail, to which closely follows the said Mar- cheb placed in the middle of the shield. This constellation was im- proved by Schiller into the Ark of Noah. In Hebrew, however, it is called Se- phina. NEBOLASSID, among the Fetzans, the Moors, and the others, 12. is called by Nubian astrologers the Tail of the Lion, a fixed star of first magnitude, concerning which enough has been said in its place. NEBULOUS STARS are certain fixed stars shining with a dull, pale, and dim light: they are so called either because they present certain clouds by their appearance, (such especially are the two great and quite conspicuous ones near the Antarctic pole) or indeed because they generate clouds, and when setting with the sun make the air cloudy, as Ptolemy and Pliny observed, in the Beehive, existing in the breast of Cancer, in the one which is in the eye of Sagittarius, but especially it is seen in the one which follows the sting of Scorpio. And this, as Titus observes, lib. 1. cap. 12. because their nebulosity produces a similar and comparable effect in these lower things. Hence also experience has shown that whenever they conjoin with the Luminaries in anyone’s nativity, they always bring excitation, clouds, or some other defect in the eyes; which natural reason itself suggests. For their light is very slight and weak, and therefore it is not surprising if they take away or dull the sight of the eyes, when they become hostile through conjunction with the very luminaries, from which light is derived into the eyes. NEMER, that is, Pardus in the Hebrew tongue, is called the Lupus 14. a constellation, concerning which something has been said elsewhere. NEOMENIVM in Greek means the same as New Moon, about which 15. soon below. NEPA, for Cicero and others, is the same as the constellation of Scorpio, perhaps from 16.
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LEXICON Nascuntur prono, descendunt tramite rectio. 7. OBLIQV TO PLANETA, teste Abraham Auenarre, & insimitas, & defectio virium illi accidens in situ Mundi, cum videlicet repertus fuerit in domibus cadentibus, Nona, Tertia Sexta, & Duodecima; sed in his postremis longè grauiùs debilitatur: quod quidem in Infortunis bonum est, minus quippe noxiæ sunt; Et inde forte euasit, vt Saturnus dicatur gaudere in Duodecima, Mars in Sexta, ibi siquidem benè quoad nos locaniur. 8. OBSC RÆ STELLAe audjunt, quæ lumine obtuso, & sub- oscuro prædiæ sunt; quales in Sectione equi quatuor, toti- dem circa Helicon, & vna antecedens caput Medulæ. Ha- rum esse & us, vt diximus cum de Nebulosis, suis causis assi- milantur; atque adeò prodibunt obscuri, tenebrosi, &c. Cum enim Astra agant per lumen, qualis erit huius affectio, tale etiam esse dabunt effectibus. 9. OBSESSIO est passio contingens Planetæ quando à duobus præsertim contrariæ naturæ, Medius intercipitur, & val- latur, absque aliorum aspectu, & fulcimenio Quæ qui- dem passio, si bonis planetis ab infortunis obuenerit, pessima est, si à fortunis optima: si demum malefico à fortu- nis contigerit, eius vires funditus infringuntur, absque tamen, vel saltem leui beneficarum repassione, ac ia- ctura. 10. OBTVSVS ANGULVS. Vide in V. Angulus. 11. OCCIDENS apud Astronomos dicitur ea horizontis pars, vbi cadit æquator, aut stella in æquatore consistens in in- ferius hemisphærium, vnde spirat Zephyrus ventus: im- propriè verò complectitur totum illum horizontis arcum, qui stellarum occiduam amplitudinem definit. Quemadmo- dum oriens locus illi directè oppositus nominatur, vnde spi- rat subsolanus, & emergunt sidera ex horizonte. Hinc septi- ma Domus ab horoscopo Occidens, & Cardo occiduus ap- pellari consueui. Apud Geographos verò, quoniam Oriens, & Occidens variantur secundum varietatem Regionum, & horisonnis, computari solet verum occidens ab Insulis for- tunatis æquarori subiectis, à quibus Ptolemæus, vtpore ab extremis finibus terræ habitabilis incipit computare lon- gitudines Ciuitarum versus Orientem, qui consequenter conciplendus est in parte terræ habitabilis, quæ distat ab In- sulis fortunatis medietate Circuli, hoc est gr. 180. Vnde sunt qui ponunt verù Orientè in Ciuitate Arym quàm dicut esse sub Æquatore. Verum id falsum esse vel ex eo liquet, quod neque a Ptolomæo neq[ue] ab alio insigni Comosgrapho
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LEXICON They are born with a downward course, they descend by a straight path. 7. OBLIQUE TO A PLANET, as Abraham Avenarre testifies, and weakness, and a defect of powers occurring to it in the situation of the World, when, namely, it is found in falling houses, the Ninth, Third, Sixth, and Twelfth; but in these latter it is weakened much more severely: which indeed is good in the Infortunes, for they are less harmful; and from this perhaps it has come about that Saturn is said to rejoice in the Twelfth, Mars in the Sixth, since there they are well placed in relation to us. 8. OBSCURE STARS are called those which are endowed with dim and sub-obscure light; such as in the section of the four horses, two alike around Helicon, and one preceding the head of Medusa. Their nature, and also their use, as we said when speaking of the Nebulous, is assimilated to their causes; and thus they will appear obscure, dark, etc. For since the stars act through light, whatever the quality of this affection may be, such also will it give in the effects. 9. OBSESSION is a passion affecting a planet when, especially by two of contrary nature, it is intercepted in the middle and surrounded, without the aspect and support of the others. This passion, indeed, if it happens to good planets from the infortunes, is the worst; if from the fortunes, the best: if finally it befall a malefic from the fortunes, its powers are utterly broken, though without, or at least with a slight rebound and loss from the benefics. 10. OBTUSE ANGLE. See in V. Angle. 11. OCCIDENT is called by astronomers that part of the horizon where the equator falls, or a star standing in the equator, into the lower hemisphere, whence the west wind Zephyrus blows: more improperly, however, it includes the whole of that arc of the horizon which defines the setting amplitude of the stars. Just as the opposite place is called the orient, whence the east wind blows and the stars rise from the horizon. Hence the seventh house from the horoscope is customarily called the Occident, and the western angle. Among geographers, however, since the Orient and Occident vary according to the diversity of regions and horizons, the true west is usually reckoned from the Fortunate Islands under the equator, from which Ptolemy, as it were, begins to compute longitudes of cities toward the East from the extreme boundaries of the habitable earth, which consequently must be conceived in that part of the habitable earth which is distant from the Fortunate Islands by half a circle, that is, 180 degrees. Hence there are those who place the true East in the city of Arym, which they say is under the Equator. But that this is false is clear even from the fact that neither by Ptolemy nor by any other distinguished cosmographer
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LEXICON 338 nologiæ certitudine elogium protulerunt. Ante Olympiades, inquiuat, nihil in Græcorum Historia explorarum inueniri, sed esse omnia confusis scripsa temporibus: post Olympiades autem quoniam quadriennio diligentissimè omnia notabantur, nullam temporum confusionem excitisse. Nomen, Originem, authoritatem, & famam compararunt ex Ludis illis Olympicis toto Orbe celeberrimis, quinto quoque anno in Elide fieri solitis; quos ob Solis quadriennalem cursum, in quo dies vns adijciur, ob sex illas horas singulis annis ad 365. die residuas, institutos esse docet D. Cyrillus Episcopus Hierosolimitanus Catechisi 12. atque ab Hercule primùm inuentos testantur Strabo, Clemens Alexandrinus, Eusebius aliique sequuti Plutarchum, Plinium, Solinum, Pausaniam, Diodrorumque Siculum. Incipiebant autem numerari ab solstitio Æstuiali, quo tempore, Ludi illi celebrabantur: Vnde & initium anni, & primi mensis quem Hecatonbæon vocabant ab eo die fiebat, vt refert Simplicius in explanatione, lib. 5. Physic. text. 25. & fusè probat Theodorus Gaza in libro, quem de Mensibus, Atticis scripsit. Quamquam Io: Lucidus Samotheus in emendatione temporum cap. 8. & in lib. cui titulus de vero die Passionis Domini, Hyppohesi 7 & 8. contentiosè velit, initium Ludorum Olympicorum, & Olypiadum fuisse circà æquinoctium Autumnale. Sed quidquid sit de hac re, certum est, quod, licet Olympiades ab Ludis Olympicis fuerint denominatæ, non tamen cum illis & ab eorum initio computari cæperunt, sed multo post tempore, Etenim Ludos Olympicos, etiam ante bellum Troianum fieri solitos apud omnes ferè Græcarum rerum scriptores inuenimus: Olympiadum autem vsum, non nisi post quadringentos annos ab excidio Troix legimus introductum, vt pax cæteris aduertit Pererius. De communibus rerum omnium Principiis lib. 4. 3ap. 3 Nisi fortè vellimus dicere, eos, qui vsum, idemque viriusque rei initium excitisse opinati sunt, loquutos fuisse de Ludorum illorum, qui iam diù intermissi fuerant, restauratione facta ab Iphito Elio, qui certamen Olympicum longè celebriùs renouauit, in quo certamine victor cuasit Coræbus Elæus, & ab eo tempore prima Olympias numerari cæpit. Igitur Olympiadum ratio haberi cæpit annis anre Christum natum 774. & consequenter ab origine Mundi, anno 4425. iuxta sæpuaaginta interpretum supputationem, quam sequitur, & amplexa est Romana Ecclesia in Martyrologia Romano. Cæterum, quia vera ætatis Mundi notitia haberi
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LEXICON 338 They have produced a statement with certainty of chronology. Before the Olympiads, he says, nothing trustworthy is to be found in Greek history, but everything is written in confused times; after the Olympiads, however, since everything was carefully recorded every four years, no confusion of times arose. They gained their name, origin, authority, and fame from those Olympic Games, celebrated throughout the world, customarily held in Elis every fifth year; and that they were instituted because of the sun’s four-year cycle, in which one day is added, on account of those six hours left over each year beyond 365 days, is taught by St. Cyril, Bishop of Jerusalem, in Catechesis 12. Strabo, Clement of Alexandria, Eusebius, and others following Plutarch, Pliny, Solinus, Pausanias, and Diodorus Siculus testify that they were first invented by Hercules. Now they began to be reckoned from the summer solstice, at which time those Games were celebrated; hence the beginning of the year, and of the first month which they called Hecatombaeon, was from that day, as Simplicius reports in his explanation of book 5 of the Physics, text 25, and Theodorus Gaza proves at length in the book he wrote on the Attic Months. Although Io. Lucidus Samotheus, in Emendation of Times, chap. 8, and in the book entitled On the True Day of the Passion of the Lord, hypotheses 7 and 8, contends obstinately that the beginning of the Olympic Games and of the Olympiads was around the autumnal equinox. But whatever the case may be, it is certain that, although the Olympiads were named from the Olympic Games, they were not computed together with them and from their beginning, but much later. For we find that the Olympic Games were customarily held even before the Trojan War, in almost all the writers on Greek affairs; but the use of Olympiads we read was introduced only after four hundred years from the destruction of Troy, as Pererius notes. On the Common Beginnings of All Things, book 4, chap. 3. Unless perhaps we wish to say that those who thought the use, and likewise the beginning of both matters, had arisen, were speaking of the restoration of those Games, which had already long been discontinued, made by Iphitus of Elis, who renewed the Olympic contest, far more celebrated, in which contest Coroebus of Elis was victor, and from that time the first Olympiad began to be numbered. Therefore the reckoning of the Olympiads began in the year 774 before Christ was born, and consequently from the origin of the world in the year 4425, according to the computation of the seventy interpreters, which the Roman Church follows and has embraced in the Roman Martyrology. However, because a true knowledge of the age of the world cannot be had
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MATHEMATICVM. 341 < 35.> OPTICA scientia est, quæ per radios visuales, vmbrasque radiis terminatas rerum distanias, magnitudines, corpo- rumque cælestium, adhuc parallaxes, refractiones, & vm- bras accipit, ac dimesitur: idque siue directè, siue reflexè radij ipsi ab obiecto ad oculum transmittantur: ita tamen, vt si directè id fiat per foramina aut rimas alicuius instru- menti excipiendo siderum radios, appelleretur Dioptrica: si verò reflexè ex superficie aliqua partim opaca partim Dia- phana, dicatur Catoptrica, vel Anacamptica: si autem per lineas refractas in medio diuersæ densitatis Anaclastica audiat, de quibus omnibus suo loco. < 34.> ORBIS propriè dicitur de deferentibus singulorum plane- tarum quæ vulgò Sphæræ appellantur. Differt verò Orbis à sphæra, quod hæc propriè globum significer vnica superficie contentum, aique vsque ad centrum cousque solidum; Or- bis autem dicit corpus sphæricum duabus superficiebus fini- rum, vna exteriore conuexa, altera interiore concaua: & ideo, quot cæli tot orbes inuicem contigui, & immediati, itavt superior includat inferiorem, & quanta est superficies concaua superioris, tanta etiara sit conuexa inferioris, non secus ac vnius cæpæ tunicæ. Quia autem vnusquisque orbis, seu cælum intrà se alios etiam orbes continet, vt, pro exem- plo, orbis solis habet tres alios orbes à se inuicem diuisos, ac sibi contiguos, quorum duo sunt excentrici secundum quid; tertius simpliciter excentricus; ideo ad euitandam vo- cabulorum confusionem vsus obtinuit, vt ipsi cæli iam non orbes sed spæræ appellitentur: & sic sphæra omnium maxi- ma sit primum mobile quod omnes alias suo ambitu com- plectitur, & secum rapit: Post (si dantur) decima, & nona sphæra trepidationis dictæ. Inde octaua, seu Firmamen- tum: mox cælum Saturni, posteà Iouis, & sic deinceps vs- que ad Lunam, itavt sphæra Lunæ sit omnium minima tam circuitu, quam crassitie, & ambitus quidem concaui ipsius su millariorum 758250. crassuies verò, hoc est intercapedo inter concauum & conuexum illius sit milliar. 109056. am- bitus autem conuexi, qui vt dixi est idem cum concauo su- perioris, & sic Mercurij est milliar. 1443750. Crassuies orbis Mercurij lara est milliar. 370480. Ambitus superficii eius conuexæ est milliar. 3772500. Crassities Orbis Veneris est milliar. 3413756. ambitus ve- rò conuexi 25230375. Crassities deferentiis solis, est milliar. 339102. ambitus verò extiunæ superficii conuexæ est milliar. 27361875. Crassities Orbis Martis est lara milliar. 27339375. ambitus V
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MATHEMATICAL. 341 < 35.> OPTICS is the science which, by means of visual rays and shadows bounded by rays, receives and measures the distances, magnitudes, and bodies of things celestial, as well as parallaxes, refractions, and shadows; and this whether the rays themselves are conveyed directly or reflected from the object to the eye: yet so that if this is done directly, by admitting the rays of the stars through the holes or slits of some instrument, it is called Dioptrics; if, however, by reflection from some surface partly opaque and partly diaphanous, it is called Catoptrics, or Anacamptics; but if through refracted lines in a medium of different density, it is termed Anaclastic science, of all which in their proper place. < 34.> An ORB is properly said of the deferents of each of the planets, which are commonly called spheres. An orb, however, differs from a sphere, because the latter properly signifies a globe contained by a single surface, and solid all the way to the center; but an orb means a spherical body bounded by two surfaces, one outer convex, the other inner concave. And therefore, as many heavens, so many orbs contiguous to one another and immediately adjacent, so that the superior encloses the inferior, and as great as is the concave surface of the superior, so great also is the convex surface of the inferior, just as with the tunics of an onion. But since each orb, or heaven, contains within itself other orbs also, as, for example, the orb of the sun has three other orbs separated from one another and contiguous to itself, of which two are in a certain respect eccentric; the third is simply eccentric; therefore, to avoid confusion of terms, usage has prevailed that the heavens themselves are now called not orbs but spheres. And thus the greatest sphere is the Primum Mobile, which embraces all the others in its circuit and carries them along with itself. After it, if there are such, the tenth and ninth spheres, called those of trepidation. Then the eighth, or Firmament: next the heaven of Saturn, then of Jupiter, and so on down to the Moon, so that the sphere of the Moon is the smallest of all both in circumference and in thickness; and the circumference of its concave surface is indeed 758250 miles, its thickness, that is, the interval between its concave and convex, 109056 miles, while the circumference of the convex surface, which, as I said, is the same as the concave surface of the sphere above, is 1443750 miles for Mercury. The thickness of the sphere of Mercury is 370480 miles. The circumference of its convex surface is 3772500 miles. The thickness of the sphere of Venus is 3413756 miles; the circumference of the convex surface, 25230375. The thickness of the deferent of the sun is 339102 miles; the circumference of the outer convex surface is 27361875 miles. The thickness of the sphere of Mars is also 27339375 miles. The circumference of
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MATHEMATICVM. 343 tuor partes æquales, Septentrionalem, Orientalem, Meridianam, & Occidentalem, à quarum initiis spirant quatuor Venti cardinales, Septentrio, qui & Boreas, Subsolanus, Auster, & Fauonius, de quibus suo loco. Porrò Oriens apud Geographos dicitur illa pars orbis terrarum ad dexteram sita, quam sol primò lustrat in nostrum Hemisphærium se attollens, & vniuersaliter ea loca, quæ solem priùs Orientem vident dicuntur Orientaliora, quam, quibus Sol seriùs oritur; quæ proptereà respectu illorum vocantur Occidentiora. Verum autem Oriens, (vt diximus eum de Occidente sermo incidit) computari debet in eo tractu terræ habitabilis, quæ diametraliter opponitur vero Occidenti, quod non iam est in insulis fortunatis, sed in insulis Azorum, vbi acus magnetica se vertit recti ad polos mundi, diuidens æquatorem ad angulos rectos, vnde consequenter erit in Sarapa, Asiæ Ciuitate, provt latè in loco probauimus. ORIENTALES DOMVS, & Quadrantes. Vide in V: Occidentales. 40. ORIENTALIS PLANETA. Vide item in V. Occidentalis 41. Planeta. ORION, qui & Iugula, sidus est in octaua sphæra ad australem plagam hinc inde ad æquatorem, (in quem incidit eius cingulus habens stellas 38. conspicuas sub signo Geminorum, omnes serè de natura Iouis & Saturni, præter duas de natura Martis, & Mercurij, quarum altera primæ magnitudinis, in dextro humero, altera adhuc rubore, & actiuitate præsignior, licet corpore minor, & secundæ magnitudinis est in sinistro humero, & vocatur bellatrix à bello ad quod mirè animos incitat, & impellit. Est item in sinistro pede altera insignis stella nomine Rigel communis fluuo, nec non aliæ tres in ciugulo supra memorato valde lucidæ, & secundæ magnitudinis stantes ad rectam, & aliæ multæ præsertim in ense, & in scuto: quippe non est in cælo sidus tam latum, tam conspicuum, tam multiplici stellarum varietate ornatum, & in eo quidem Galilæus tot stellas minutiores suo Telescopio obseruauit, vt pænè in numerando defeererit, vt refert in Nuncio sidereo. Porrò Orion sidus maximè tempestuosum est, quod & Virgilius obseruauit 7. Æneid. Quam multi Lybico voluntur marmore fluctus, Sauus vbi Orion Hybernis conditus vndis! Cum sole enim congrediens, siue in ortu, siue occasu ventos ciet, turbat aërem, mare tempestatibus quatit, imbræs Y. ij
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four equal parts, Northern, Eastern, Southern, and Western, from whose beginnings blow the four cardinal Winds, Septentrio, who is also Boreas, Subsolanus, Auster, and Fauonius, of which in their place. Moreover, the East among Geographers is called that part of the world situated on the right hand, which the sun first illuminates as it rises toward our Hemisphere, and universally those places that first see the rising sun are called more Eastern, than those to which the Sun rises later; which for that reason, in relation to the former, are called more Western. But the true East, as we said when speaking of the West, must be reckoned in that tract of habitable land which is diametrically opposed to the true West, which is no longer in the Fortunate Islands, but in the Azores, where the magnetic needle turns directly to the poles of the world, dividing the equator at right angles, whence consequently it will be in Sarapa, a city of Asia, as we have shown at length in the place. ORIENTAL HOUSES, and Quadrants. See under V: Occidental. 40. ORIENTAL PLANET. See also under V. Occidental 41. Planet. ORION, also called Iugula, is a star in the eighth sphere on the southern side, extending on both sides to the equator, (into which its belt falls, having 38 visible stars under the sign of Gemini, almost all of the nature of Jupiter and Saturn, except two of the nature of Mars and Mercury, of which one, of first magnitude, is in the right shoulder, the other still more distinguished by redness and activity, though smaller in body, and of second magnitude, is in the left shoulder, and is called Bellatrix from the battle to which it wonderfully stirs up and impels the spirits. There is also in the left foot another notable star by the name of Rigel, common in the flood, as well as three others in the aforesaid belt, very bright, and of second magnitude, standing at right angles, and many others especially in the sword, and in the shield: for there is no star in the sky so broad, so conspicuous, so adorned with such a manifold variety of stars, and indeed Galileo observed so many smaller stars in it with his Telescope that he nearly failed in counting them, as he relates in the Sidereal Messenger. Moreover, Orion is a most stormy star, as Virgil also observed, 7. Aeneid. How many waves roll on the Libyan marble, when fierce Orion is shut up in the winter waves! For when it comes into conjunction with the sun, whether at rising or setting, it stirs up winds, disturbs the air, shakes the sea with storms, rains Y. ij
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LEXICON 344 facit, fulgura & tonitrua: quod & cum Saturno, & cum Mercurio facit, & eò maximè si omnes vnà conueniant. At si eo exoriente Iupiter soli, aut Mars permisceatur, eius sideris vehementia longè lateque dignoscitur: quippe tempestatem sub ortu Sirij producit, & Aquilo magnis flatibus aërem quauis corruptione purgabit: Inde exurgent Etesiæ, & Autumnus salubris erit. In Genethliacis etiam, inquit Maternus: Si Orin in horoscopo partilicer fuerit, faciet homines velocis corporis mobilitate conspicuos, & quorum animus variis solicitudinibus implicatus peruigili cogitatione semper exastuet. Hi enim variabuntur, sæpè domicilia & domos, sedesque mutabunt, ac per omnium limina matutinis semper salutationibus discurrant. Si verò in occasu fuerit, subdit: Tales nascentur homines, quorum animos varia solicitudo semper exagitet. Hi quoque à ciuibus suis in legationem missi, ac in ipso munere constituti peregrè morientur, leue quoddam solatium ad inferos afferentes quod illis à ciuibus suis darum fuerit. Iis quoque honores perpetui, imagines, tituli, & honorabilium statuarum cernuntur insignia. Hucusque Firmicus. Vide in V. Ingula. 43. ORIZON. Vide Horizon. 44. ORNITHIAS ventus est ex genere Ethesiarum, nomen ex Græco ab auium aduentu sortitus, quod potissimum Vèris tempore quando illæ ad nos aduentant exsufflare soleat circà vespertinum Arcturi exortum. Fertur humilis circà terræ latera: vnde & omnium commodissimus est: qui vt plurimùm vertitur in Fanonium, ob idque à Plin. Zephrus appellatur. 45. OROASER in sphæra Barbarica, ditur primus Decanus Aquarij manens sub dominatu Veneris: significator ærumnarum pro lucro, inquietudinis, laboris, pauperratis, &c. 46. ORTHOGONIVS Græcè idem sonat, ac rectus angulus: significat enim apud Geometras figuram, quæ rectis angulis constet, & omnium partium æqualitatem habeat. Vnde & Columella, lib.5. Orthogonium agrum appellauit. 47. ORTHOGRAPHIA est descriptio frontis, erectæque magnitudinis, quam ædificium construendum habiturum est, facta ex regulis Geometricis, ad cuius postea idæam tota moles consurgit. Quapropter est ars Architecturæ ministra, illique subseruiens. Vide Vitruuium lib.1.cap.2. 48. ORTVS, & occasus siderum, Achronicus, Cosmicus, Heliacus, Matutinus, Vespertinus, &c. Vide in propriis cu-
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LEXICON 344 produces lightning and thunder; and it does this both with Saturn and with Mercury, and especially if all come together at once. But if, at its rising, Jupiter alone or Mars is mixed with it, the violence of that star is recognized far and wide: for it brings storms at the rising of Sirius, and the north wind, with its great blasts, will cleanse the air of any corruption. Then the Etesian winds will arise, and autumn will be wholesome. In Genethliacals also, says Maternus: If Orion shall be exactly in the horoscope, it will make men remarkable for the mobility of a swift body, and whose mind, entangled in various cares, is always heated by wakeful thought. For these men will be changeable, often changing lodgings, houses, and dwellings, and will run from all doorways with morning salutations. But if it shall be in the setting, he adds: Such men will be born, whose minds some varying care will always disturb. These men too, sent by their fellow citizens on an embassy, and established in that office, will die abroad, bringing to the underworld a certain slight consolation because it was granted to them by their fellow citizens. To these also are seen perpetual honors, images, titles, and the insignia of honorable statues. Thus far Firmicus. See under V. Ingula. 43. ORIZON. See Horizon. 44. ORNITHIAS is a wind of the class of the Etesian winds, taking its name from the Greek from the coming of the birds, because it is accustomed to blow chiefly in the springtime when they come to us, around the evening rising of Arcturus. It blows low near the surface of the earth; whence it is also the most agreeable of all winds: it usually turns into Favonius, and for that reason Pliny calls it Zephyrus. 45. OROASER in the Barbaric sphere is said to be the first Decan of Aquarius, remaining under the dominion of Venus: a significator of troubles for gain, restlessness, labor, poverty, etc. 46. ORTHOGONIVS in Greek sounds the same as a right angle: for among geometers it signifies a figure that consists of right angles and has equality of all its parts. Hence Columella, book 5, called a field orthogonium. 47. ORTHOGRAPHIA is the delineation of the front and upright height which a building to be constructed will have, made according to geometric rules, from which later the whole mass rises according to the idea. For this reason it is a ministering art of Architecture, serving it. See Vitruvius, book 1, chapter 2. 48. ORTVS, and the setting of the stars, Acronic, Cosmic, Heliacal, Morning, Evening, etc. See in the proper cu-
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LEXICON etumest; ideò nullam possunt recipere malam influentiam à planetis; immò resistunt malitia eorum; instancum quod nullum possunt facere nocumentum in toto hemisphario ultrà Capricornum, propter virtutes illarum stellarum prohibentium maliam planetarum. Et ita est dicendum de radiis solaribus, quia non possunt causare intensum, & inordinatum calorem, & astum cum illis astris, sicut cum nostris, per eandem rationem, propter nobilitatem, & temperantiam illorum. Et sic planeta nullum possunt causare nocumentum, nec disproportionem in illis partibus propter benignitatem, & fauorem, & virtutem illorum astrorum resistentium malitia planetarum. Tandem concludit Sic patet, quod nullum inconueniens sequitur ex ista positione, sed multa, & plura inconuenientia sequerentur, si Paradisus deliciarum collocaretur sub linea aquinoctiali inter tropicos, prout quidam dicunt, aut circa tropicos in parte orientali, sicut alij autumant: quia vtraque istarum partium est subiecta multis miseris vt patet Verum, vtcumque sit de ista assertione, in qua multa gratis assumuntur, multa effinguntur profus veritati, & experientiæ Hispanorum contraria; illud vnum ei maximè officit, quod Paradisus ille dicitur omninò inaccessibilis, atque à cognitione hominum remotissimus. Ita autem terra australis (excepta forsitam ea parte, quam diximus ab igne denominari) non modò est permeabilis, sed adhuc tota inhabitata, atque à nostris magna ex parte detecta. Ex quo etiam manifestè conuincitur, neque in partibus orientalibus, præsertim circa Mesopotamiam, & Armeniam, vt multi pro certo autumnant, posse constitui; vel ex eo id approbantes, quod illa quatuor sumina, quæ dicuntur ex fonte in medio Paradis[us] collocato exire, præsertim Tigris, & Euphrates in Asia ortum habent: & hi quidem in Armenia; vnde postea per Mesopotamiam & Assyriam transeuntes in sinum Persicum exonerantur. Ganges autem ex Caucaso Indiæ Monte prosilit, vt author est strabo: & Nilus ex quodam Monte Mauritianæ infertoris non longè ab Oceano, stagnante ibi lacu, quem vocant Nolidem: deinde se condit itinere plurium dieru[m]; rursumque erumpit alio matore lacu in Mauritania Cæsariensi, iterumque arenis receptus per desertum, viginti dierum spatio fertur ad proximos Æthiopas, & denuò prostlit fonte qui Nigris dicitur: Mox Africam ab Æthiopia disterminans, mediosque Æthiopas secans, in Ægyptum venit; ac tandem septem ostiis in Mare Ægyptium se exonerat. Ex quo eludere conantur obiectionem illam, quod heiusmodi fontes non ab eodem loco originem
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LEXICON and so they cannot receive any evil influence from the planets; indeed, they resist their malice, inasmuch as they can do no harm in the whole hemisphere beyond Capricorn, because of the virtues of those stars that restrain the malice of the planets. And the same must be said of the solar rays, because they cannot cause intense and disorderly heat and burning with those stars, as with ours, for the same reason, because of their nobility and moderation. And so the planets can cause no harm, nor any disproportion in those parts, because of the benignity and favor and power of those stars resisting the malice of the planets. Finally he concludes: Thus it is clear that no inconvenience follows from this position, but many, and even more inconveniences would follow if the Paradise of delights were placed under the equinoctial line between the tropics, as some say, or around the tropics in the eastern part, as others suppose; because both of those parts are subject to many miseries, as is clear. But however it may be with this assertion, in which many things are assumed without basis, many things are fabricated contrary to the truth and to the experience of the Spaniards; the one thing that especially counts against it is that that Paradise is said to be wholly inaccessible and most remote from human knowledge. But in this way the southern land, except perhaps that part which we said is named from fire, is not only passable, but is still entirely uninhabited and for the most part discovered by our people. From this it is also clearly proved that it cannot be established in the eastern parts, especially around Mesopotamia and Armenia, as many confidently suppose; or approving it for that reason, because those four great rivers, which are said to flow out from the fountain placed in the middle of Paradise, especially the Tigris and Euphrates, have their source in Asia, and indeed in Armenia; whence later, passing through Mesopotamia and Assyria, they discharge into the Persian Gulf. The Ganges, however, springs from Mount Caucasus of India, as Strabo is author: and the Nile from a certain mountain of inland Mauritania, not far from the ocean, with a stagnant lake there, which they call Nolidem: then it disappears in a journey of several days, and again bursts forth from another larger lake in Mauretania Caesariensis, and again, taken up by the sands through the desert, it is carried for a span of twenty days to the nearby Ethiopians, and once more springs up from a fountain called Nigris: soon separating Africa from Ethiopia and cutting through the middle Ethiopians, it comes into Egypt; and finally it discharges into the Egyptian Sea through seven mouths. From this they try to evade that objection, that sources of this kind do not originate from the same place.
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LEXICON author est Beda in explanat. cap. 2. Genes. quem sequuti sunt strabo, Isidorus Rabbanus, Magister, Alensis, Caiet. & a ij, quos refert Maluenda cap. 11. Hoc, inquam, nequit subsistere: tum quia id planè officeret terræ globositati, & figuræ sphæricæ, quam Mathematici omnes mille obseruationibus adacti admittere compulsi sunt: & licet montium, & vallium inæqualitates huic globositati aliquatenus videantur obstare; tamen ob terreni orbis amplitudinem, vt aliàs dictum est, hæc perinde se habent, ac in aurantij pomo tuberculi: quod de tam sublimi monte, qui vsque ad Lunæ orbem pertingeret autumari nequaquam posset. Tum quia si vllibi terrarum daretur tam altus mons, sanè foret omnibus notus, ac celebris propter summam altitudinem, solis radios exorientis diutissimè impediret, facileque posset & oculis cerni, & pedibus inuestigari: cum tamen hoc vnum memoria proditum sit, solum Olympum esse cæteris omnibus altiorem, quippe qui, seù verè, seù hyperbolicè dicitur nubes ipsas excedere. D Thomas, id alia ratione confutat. Quia inquit, ea Regio neque commoda esset habitationi hominum, neque salubritati. Verum ea ratio non conuincit: quia possent ibi homines assuescere, fierique aër ille tenuissimus iugiter, & ab incunabilis habitantibus oppidò opportunus, atque connaturalis, eo planè modo, quo Lusitanis primo ad Indias orientales appulsis aër ille longè diuersus euadebat incongruus; itavt ob climatis nouitatem mox extinguerentur: at postmodum eò destinatis adolescentulis, qui paulatim aëri assuescerent factus tandem sui connaturalis, & proprius. Sic igitur dici posset de hac editissima regione, quæ ad Lunæ orbem pertingeret. Sed, vt diximus, obstat experientia, quod neutiquam talis regio comperta sit, nunquam talis mons oculis tentus, qui vertice suo aliquando Lunam attingeret, aut eius cursum impediret, faciemve saltem seù sui corporis densitate opposita, seù vmbra suæ proiectione aliquatenus obuelaret: Cum tamen ad nostra tempora vniuersus penè Orbis sit penitissimè inuestigatus, cælestium corporum affectiones, Lunæque, vel minimæ quæuis defectiones exquisitissimè obseruatæ. 9. Constituto itaque dari verè Paradisum terrestrem, arque etiam nùm extare in rerum natura; ibique asseruari sanctos illos Heroas Henoch, & Eliam, ( & vt aliqui volunt etiam S. Ioannem Euangelistam) vbi, loco depositi sistant, quoadvsque finis Mundi aduenerit, quando ex Dei ordinatione inde huc remeare debent, & finem suum prædicatio-
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LEXICON The author is Bede in his explanation of chapter 2 of Genesis, whom Strabo, Isidore, Rabbanus, the Master, Alensis, Caiet. and some others followed, as Maluenda relates in chapter 11. This, I say, cannot stand: both because it would plainly offend against the globosity of the earth and the spherical figure, which all the Mathematicians, driven by a thousand observations, were compelled to admit; and although the inequalities of mountains and valleys seem to obstruct this globosity to some extent, yet on account of the vastness of the terrestrial globe, as was said elsewhere, these are in the same way as the little knobs on an orange: which could by no means be supposed of so lofty a mountain that it would extend even to the orbit of the Moon. Then because, if anywhere on earth there were such a high mountain, it would surely be known to all and famous because of its extreme height; it would very long impede the rays of the rising sun, and could easily be seen by the eyes and traced by foot; yet this one thing has been handed down by memory, that Olympus alone is higher than all the rest, inasmuch as, whether truly or hyperbolically, it is said to exceed even the clouds. D. Thomas refutes this by another argument. Because, he says, that region would be neither suitable for human habitation nor for health. But that reason does not prove the point, because men could become accustomed there, and that exceedingly thin air would become continually, and from childhood for those living there, altogether suitable and natural, in precisely the same way as, when the Portuguese first arrived in the East Indies, that air, very different from theirs, became unsuitable; so that, because of the novelty of the climate, they would soon perish: but later, when young people were sent there who would gradually become accustomed to the air, it finally became natural and proper to them. Thus, then, one might say the same of that very elevated region which would reach to the orbit of the Moon. But, as we have said, experience stands in the way, because no such region has ever been found, nor has any such mountain ever been seen by the eyes, which would at some point with its summit touch the Moon, or hinder its course, or at least obscure its face somewhat, whether by the density of its body set in opposition, or by the shadow of its projection. Yet up to our time the whole earth has been very thoroughly explored, and the conditions of the heavenly bodies, and the Moon’s even the slightest phases, have been most carefully observed. 9. Therefore, it being established that there truly is a terrestrial Paradise, and also whether it exists in the nature of things; and that those holy heroes Enoch and Elijah are preserved there, (and as some wish, also St. John the Evangelist) where, in the place of deposit, they remain, until the end of the world shall come, when, by God’s ordinance, they are to return from there here, and their end by preaching-
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LEXICON 356 radisus terrestris, hoc est in liquidissimo illo Lunaris regionis æthere, quod ipsissimum aerem, seù eiusdem substantiæ, licet purioris alibi satis aperte monstrauimus. Et vt iam, detecto velo, elariùs & sidentiùs loquar, in ipsa superficie Lunæ (quam Beatarum mentium sedem Veteres non omninò extra aleam, alteram terram Plato, Pythagoreique omnes apud Tullium, stobeamque dixere quamque habitabilem, arboribus consitam, vitæque hominum opportunam nedum ex veteribus, sed ex neothericis multi, variis obseruationibus edocti probabiliter astruunt) in ipsa inquam superficie lunaris globi Paradisus ille est constitutus; quam & olim primi parentes nostri incoluerunt, & nunc sancti illi secundi saluatoris aduentus prodromi diuinitùs translati, illi finem mundi expectantes, loco depositi detinentur. 10. Fateor, id nouum, singulare, & hactenus inauditum: at non per hoc temerarium, arque intolerabile dixeris; quia & id Antiquiores dixissent, si eam rerum notitiam habuissent, quam nos longo vsu, experientiateste, nouis obseruationibus, & eorum qui nos præcesserunt, detectis, reuulsisque erroribus comparauiimus. Equidem olim temporibus Augustini, Antipodas affirmare, non absimili ratione; vt alias dictum est, hæreticum habebatur. Verùm posteà Orbis peragrarione, & ipsâ experientiâ, ita res firmata fuit, vt iam modò eosdem non admittere erroneum, ac ridiculum foret. Ita planè: olim Paradisum terrestrem extrà terreni Orbis ambitum sistere, error intolerabilis, ac censurâ dignus meritò habebatur, præsertim eum nomen ipsum oppositum videatur euincere: at modò partâ tanta rerum noviâ, Lunæ facie Telescopio penitissimè obseruata, veterum dictis expensis, locis inuestigatis, Paradisum in Lunæ superficie collocare, ratio ipsa compellit. Siquidem, vt dixi, nouis obseruationibus compertum est Lunæ globum esse alteram veluti terram, Montibus; vallibus, syluis, arque aliis id genus præditam, adeo vt eam terram cælestem; ac terram hanc nostram Lunam terrestrem, cælesti lumine afflatus appellarit Diuinus Plato: vt David fabritius apud Argolum: nec nostris temporibus absfuerunt, qui ausi sint affirmare, Lunam esse habitatoribus culram, se jue inibi homines & iumenta discurrere Telescopio obseruasse, vt nos in V. Luna litteris consignauimus, (quod tamen nimis audenter, minùs verè dictum existimauerim, fideique prorsus contrarium, cum exinde planè deduceretur, homines esse non à primo homine naturali propagine deriuetos, proindeque
Transcription: Translated (English)
LEXICON 356 radisus terrestris, that is, in that most liquid ether of the lunar region, which I have elsewhere clearly shown to be the very same air, or of the same substance, though purer. And so now, with the veil removed, to speak more clearly and plainly, on the very surface of the Moon (which the ancients did not altogether exclude as the dwelling-place of blessed minds; Plato called it another earth, as did all the Pythagoreans in Tully and Stobaeus; and which many, both from the ancients and from more recent writers, instructed by various observations, plausibly maintain to be habitable, planted with trees, and fit for human life) — on the very surface, I say, of the lunar globe that Paradise is situated; the same Paradise which our first parents once inhabited, and now those holy forerunners of the second coming of the Saviour, translated there by divine means, are kept in a place set apart, awaiting the end of the world. 10. I confess, this is new, singular, and until now unheard of; but on that account you should not call it rash and intolerable, because the ancients too would have said it, if they had possessed that knowledge of things which we have acquired by long use, by the testimony of experience, by new observations, and by the discoveries and refutations of those who went before us. Indeed, in the time of Augustine, to affirm the Antipodes, by no dissimilar reasoning, as has elsewhere been said, was held to be heretical. But afterward, through world-travel and experience itself, the matter was so firmly established that now not to admit the same would be erroneous and ridiculous. Thus it was altogether: once, to place the earthly Paradise outside the bounds of the terrestrial globe was rightly considered an intolerable error and worthy of censure, especially since the name itself seems to prove the opposite; but now, since so much new knowledge has been gained, with the face of the Moon examined most carefully by telescope, with the sayings of the ancients weighed, and with places investigated, reason itself compels us to place Paradise on the surface of the Moon. For, as I have said, by new observations it has been found that the lunar globe is as it were another earth, furnished with mountains, valleys, woods, and other things of that kind, so that the divine Plato called it a heavenly earth, and our earth a terrestrial moon, inspired by heavenly light, as David Fabricius says in Argolus; nor have there been lacking in our own times those who have dared to affirm that the Moon is inhabited, and that they observed with a telescope men and beasts moving about there, as we recorded in Book V concerning the Moon, which nevertheless I would judge to have been said too boldly and less truly, and altogether contrary to the faith, since from that it would plainly follow that men are not derived from the first man by natural propagation, and consequently...
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MATHEMATICVM. 317. deque non à Christo redemptos.) At verò locum illum esse habitationi hominum congruum, ibique tantùm vitam suam agere sanctos illos Hæroas miraculosè illuc translatos, non ità incredibile est, non multum à plurimorum Patrum dictis aberrans, nec demùm Fidei dogmatibus repugnans, Consonant sacræ Paginæ attestantes Eliam sublimè elatum, & curru igneo raptum in cælum, non vtique Empyreum, neque in aëra, vt constat, sed in Paradisum voluptatis, vt omnes Patres affirmant, in Cælo, hoc est in Lunæ globo situm. Et de Henoch dicitur Gen. 5. quod tulit, eum Deus, & amplius non apparuit; translatus vtique in Paradisum: vti Ecclesiast. 44. apertè dicitur. Consonant SS. Patres id, etsi non clarè affirmantes, tamen aliqualiter innuentes, atque ad metam propè collineantes. Etenim Iustinus martyr in responso. ad orthodoxor. quæst. pluribus in locis præsertim quæst. 75. 76. & 85. clarè docet, Paradisum illum etiamnùm extare, & permansurum vsque ad diem Iudicij, in'eoque loco versari Henoch, & Eliam, & D. Ioannem Euangelistam. Ambrosius lib. de Paradiso, cum testatur in terra non esse, sed in tertio Cælo. Irenæus lib. 5. aduersus Hareses, addit, hunc Paradisum esse illum, ad quem raptus est Paulus; eiusdemque sententiæ suffragatores laudat Asiæ Presbyteros Apostolorum discipulos. Cæterùm Paradisum ab hacterra non quidem discontinuum, ac disiunctum, sed ex ipsa insurgere, atque ad orbem vsque Lunæ pertingere Rupertus Abbas lib. 1. de Trin. cap. 37. Damasc. lib. 2. de fide cap. II. Basil. Orat. de Paradiso, Glossa in cap. 14. Gen. aliique Patres, quos supra retulimus, docuerere: quibus indubitantes subscribit etiam Augustinus ad Orofium scribens in hæc verba. Paradisus in Oriente situs est, interiecto Oceano, & à nostro Orbe longe remotus in altissimo loco constitutus, pertingens vsque ad lunarem circulum: unde illuc aqua diluuij minimè peruenisse dicuntur. Quin & eiusdem sententiæ primus author fuisse dicitur Thomas Apostolus, vt proinde eam ob causam ei contradicere non audent Albertus Magnus 2 part. Summa Theolog. tr. 13. q. 19. ac Dionys. Carthus. in 2. sentent. dist. 17. quæst. 5. qui de hac sententia, hæc reuerenter habent. Hoc tamen dico sine praiulicio sententia melioris; quoniam in quibusdam libris antiquissimis inuenitur, quod gloriosus Thomas Apostolus fuit illius sententia author, qua Beda & strabo in ascribitur, quod scilicet Paradisus sua altitudine tendat vsque ad sphæram Luna. Quis igitur damnare audebit sententiam, quam tantus Apostolus primus docuit, quamque experimenta Z
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MATHEMATICVM. 317. and of those not redeemed by Christ.) But that that place is indeed suited to the habitation of men, and that those holy heroes, miraculously transported there, live their life only there, is not so incredible, not straying much from the sayings of most of the Fathers, nor finally repugnant to the dogmas of the Faith. The sacred pages agree, testifying that Elijah was exalted on high and snatched up in a fiery chariot into heaven, not indeed into the Empyrean, nor into the air, as is clear, but into the Paradise of delight, as all the Fathers affirm, in heaven, that is, situated in the globe of the Moon. And of Enoch it is said in Gen. 5 that God took him away, and he appeared no more; certainly translated into Paradise: as is clearly said in Ecclesiasticus 44. The holy Fathers agree with this, though not clearly affirming it, yet hinting at it in some measure, and drawing very near to the mark. For Justin the martyr in the response to the questions of the orthodox, in many places, especially questions 75, 76, and 85, clearly teaches that that Paradise still exists, and will remain until the day of Judgment, and that in that place Enoch, and Elijah, and St. John the Evangelist dwell. Ambrose, in book On Paradise, testifies that it is not on earth, but in the third heaven. Irenaeus, book 5, Against Heresies, adds that this Paradise is the one to which Paul was caught up; and he praises as supporters of the same opinion the Presbyters of Asia, disciples of the Apostles. Moreover, that Paradise is not indeed discontinuous and separated from this earth, but rises from it and extends as far as the orbit of the Moon, Rupert the Abbot taught in book 1 On the Trinity, chap. 37; Damasc. book 2, On the Faith, chap. II; Basil, Oration On Paradise; the Gloss on Gen. chap. 14; and other Fathers, whom we have mentioned above. To these, without doubting, Augustine also subscribes, writing to Orosius in these words: Paradise is situated in the East, with the Ocean interposed, and far removed from our world, established in a very high place, reaching even to the lunar circle; whence it is said that the waters of the Flood in no way came there. Indeed, it is said that Thomas the Apostle was the first author of this same opinion, so that for that reason Albertus Magnus does not dare contradict him, in the 2nd part of the Summa Theologica, tract. 13, q. 19, and Dionysius the Carthusian in the 2nd Sentences, dist. 17, question 5, who on this opinion speak thus reverently: Yet I say this without prejudice to a better opinion; because in certain very ancient books it is found that the glorious Apostle Thomas was the author of that opinion, to which Bede and Strabo are assigned, namely, that Paradise in its height extends as far as the sphere of the Moon. Who then will dare to condemn an opinion, which so great an Apostle first taught, and which experiments Z
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MATHEMATICVM. 355 quit, terrestris ascendit vsque ad globum Lunarem, vnde aqua diluuij aluc minimè peruenerunt: ex quo patet, quod erat altior media regione aëris, & nulla erat nox in illo Pa- radiso. Sed quaritur, cur à sphæra ignis non consumebatur attingensconcauum Luna? Respondetur, quod priuilegio spe- ciali fuit locus isto conditus; vnde circumquaque erat sphæra ignis, non tamen intrans eum, dono Dei: & hoc innuitur Gen 1. vbi gladius igneus, & versatilis sphæra ignis intelli- genda est. Hucusque prædictus auctor: & quidem valdè ad rem, nam non nisi de sphæra ignis verificari magis propriè possunt quæ de flammea illa romphæa à Scripturis, & Pa- tribus dicuntur. Benè autem versatilis dicitur quia, vt ali- bi dictum est, & ipsa cum cæteris sphæris, ac regione aëris pro sua quæque à primo motore distantia, alia citiùs alia lentius circà terrarum orbem motu vniuersitatis rotatur. Constat igitur in hac celeberrima, ac difficili admodum quæstione non esse adeò intolerabile, nec rationi, aut Sacris Saginis repugnans, affirmare Paradisum Terrestrem, in quo primi parentes fuerunt, & nunc temporis vitam suam degunt Henoch, & Elias esse in Lunari globo situm, romphæa ignea, hoc est sphæra ignis vndique circum- feptum. Cæterùm hæc disputandi gratia dicta sint, non vt noui < 154> quicquam hactenùs inauditum è meo capite audeam affirmare. Cùm aliàs Quæstio hæc ex earum genere sit, quas Augustinus lib. 2. contrà Pelagium, & Celestium cap. 23. præter fidem esse ostendit. In quibus, inquit, salua fide Christianismus, aut ignoratur quid verum sit, & senten- tia definitiua suspenditur, aut aliter, quam est, humanâ, & infirma suspicione coniicitur. Veluticum quaritur QV A- LIS, VEL VBI SIT PARADISVS, vbi con- stituit Deus hominem quem formauerat ex puluere, cum tamen ESSE ILLVM PARADISVM, Fides Christiana nou dubitet. Vel cùm quaritur, vbi sint nunc Elias, & He- noch, an ibi, an alicubi; quos tamen non dubitamus in qui- bus nati sunt corporibus, viuere, &c. & post pauca. Quis enim non sentiat, subdit, in his, atque huiusmodi variis, & innumerabilibus quæstionibus, siue ad obscurissima opera Dei, siue ad Scripturarum abditissimas latebras pertinentibus, quas certo aliquo genere complecti, ac definire difficile est, & multa ignorari, salua Christiana fide, & alicubi errari, si- ne aliquo hæresico dogmatis crimine? Hæc Augustinus. Cui consonat Theodorus quæst. 45. in Genes. cap. 23 Cyprianus Lib. de montibus Sina, & Sion, & alij vltrò affirmantes, Z ij
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MATHEMATICVM. 355 it ceases, the terrestrial [world] rises as far as the lunar globe, from which the waters of the Flood hardly reached: from which it is clear that it was higher than the middle region of the air, and there was no night in that Pa- radise. But it is asked why it was not consumed by the sphere of fire, since it touched the concavity of the Moon? It is answered that, by a spe- cial privilege, that place was established there; hence it was surrounded on every side by the sphere of fire, yet not entering it, by the gift of God: and this is implied in Gen. 1, where the fiery sword, and the revolving sphere of fire, are to be understood. Thus far the aforesaid author: and indeed very much to the point, for only of the sphere of fire can there be a more proper verification of those things which are said by the Scriptures and the Fa- thers about that flaming rhomphaea. It is rightly called revolving, because, as has been said elsewhere, together with the other spheres and the region of the air, according to each one’s distance from the first mover, some more quickly, others more slowly, it revolves around the globe of the earth with the motion of the universe. It is therefore established in this most celebrated and very difficult question that it is not so intolerable, nor contrary to reason, or the Sacred Writings, to affirm that the Terrestrial Paradise, in which our first parents were, and where at the present time Enoch and Elijah spend their life, is situated in the lunar globe, and is surrounded on every side by the fiery rhomphaea, that is, the sphere of fire. Moreover, let these things have been said for the sake of discussion, not that I should dare to affirm anything new or hitherto unheard of from my own head. Since otherwise this question belongs to the class of those which Augustine, book 2 against Pelagius and Celestius, chapter 23, shows to be beyond the faith. In such matters, he says, while Christian faith is preserved, either what is true is unknown, and the definitive judgment is suspended, or otherwise it is conjectured by human and weak suspicion, not as it is in fact. For example, when it is asked what KIND OF PLACE, OR WHERE PARADISE IS, where God placed the man whom He had formed from the dust, although the Christian Faith does not doubt that THAT PARADISE EXISTS. Or when it is asked where Elijah and Enoch are now, whether there or elsewhere; whom nevertheless we do not doubt to be alive in the bodies in which they were born, etc. And after a few lines. For who, he adds, would not feel that in these and similar various and innumerable questions, whether they pertain to the most hidden works of God or to the most hidden recesses of the Scriptures, which it is difficult to include and define under any certain kind, and that many things may be unknown, while Christian faith is preserved, and one may err somewhere, with- out any charge of heretical doctrine? These are Augustine’s words. To him Theodorus agrees, question 45 in Genesis, chapter 23; Cyprian in the book On Mounts Sinai and Zion, and others freely affirming, Z ij
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LEXICON in eadem distantia à cardinibus Mundi, eam tamen acqui- rant directione, & motu primi mobilis, quod duplici modo fieri concipi potest: altero, vt significator existens immo- bilis in suo circulo positionis expectes, vt Promissor motu primi mobilis feratur ad situm æquè distantrem à cardini- bus Mundi, ac erat significator in radice constitutus; & tunc emanat effectus huius directionis: altero, vt ambo motu primi mobilis rapiantur, tam Promissor, quam si- gnificator (ab vtroque enim imprimitur virtus in Primo mobili seù in gradibus Zodiaci in quibus tempore radicis reperiebantur) & tunc quando ambo motu primi mobilis sapri ponuntur in proportionali distantia hinc inde ad ali- quem cardinem, iunc intelligitur compleri directio, & emanat profecto idem, vel sanè consimilis effectus, ac in parallelis modo explicatis; & sicut illi Paralleli Cosmici simpliciter appellantur; ita isti ad differentiam illorum Pa- alleli Ascensionales iure appellari poterunt; quoniam am- bo tam significator, quam Promissor pariter supponuntur ascendere, & suum suum mutando æquidistantiam istam à cardine acquirere. Quorum omnium dirigendi methodum docet Titus in Primo Mobili Canoné 35. PARALLELI etiam, vt supra tactum est, vocantur apud Geographos circuli in superficie terræ descripti æquè distan- tes à circulo immediatè æquatori subiecto, de quibus suprà in V. Climæ pertractauimus. Qui profecto infiniti concipi possunt: de facto tamen tot concipiuntur, quor satis sunt ad faciendam notabilem diei maximi varietatem. At- que hac ratione Antiqui cum Ptolemæo septem climata constituebant, quorum singula tribus parallelis definie- bant, singulis parallelis singulos horæ æquinoctialis quadrantes assignando Quoniam vero experientia comper- tum est, non solum partem aliquam vnius, vel etiam cu- jussiber quadrantis habitabilem esse, sed toram ferè terræ molem; vbique enim Insulæ sunt, vel etiam terræ conti- nentes, quocunque versus navigari instituatur, nec vlla planè regio est tam calida, aut frigida, in qua degere non possint homines; quin immò vbique ferè terrarum tam ho- mines, quam bruta animania reperta sunt: idcircò Re- centiores multo plura Climata adeoque plures etiam paral- lelos numerant, quam Antiqui, totum sparium quod est ab æquatore ad polos in tot parallelos dividendes, quor horæ quadrantes accresionis diei maximæ ab locis æquareti sub- iectis ad ea quæ immediatè polo subsunt. Adeoque insi- stentes nihilominus Ptolemæi præceptis viginti-tria Clima-
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LEXICON in the same distance from the cardinal points of the world, they may nevertheless acquire it by the direction and motion of the first mobile, which can be conceived as being done in two ways: one, when the significator, remaining immobile in its circle of position, you expect the Promissor to be carried by the motion of the first mobile to a place equally distant from the cardinal points of the world as the significator was when placed in the radix; and then the effect of this direction arises. The other, when both are carried along by the motion of the first mobile, both the Promissor and the significator (for from each of them a force is impressed upon the first mobile, or upon the degrees of the Zodiac in which they were found at the time of the radix), and then when both, by the motion of the first mobile, are set in a proportional distance on either side of some cardinal point, then the direction is understood to be completed, and the same, or certainly a similar, effect arises as in the parallels explained above; and just as those are simply called Cosmic Parallels, so these, in distinction from them, may rightly be called Ascensional Parallels; since both the significator and the Promissor are likewise supposed to ascend, and by changing their distance from the cardinal point acquire this condition. Titus teaches the method of directing all of these in the Canon on the First Mobile, Canon 35. PARALLELS are also called, as noted above, by geographers circles described on the surface of the earth that are equally distant from the circle immediately subject to the equator, concerning which we treated above in Book V on the Climates. Indeed, they can be conceived as infinite; but in fact only so many are conceived as suffice to produce a notable variation in the longest day. And for this reason the Ancients, with Ptolemy, established seven climates, each of which they defined by three parallels, assigning a single equinoctial hour quadrant to each parallel. But since experience has shown that not only some part of one quadrant, or even of any quadrant whatsoever, is habitable, but almost the whole mass of the earth; for everywhere there are islands, or even continuous lands, whichever way one sets out to sail, and there is absolutely no region so hot or so cold in which men cannot dwell; indeed, almost everywhere on earth both men and brute animals have been found: therefore the more recent authors count many more climates, and consequently also more parallels, than the Ancients, dividing the whole space from the equator to the poles into as many parallels as there are hour quadrants of the increase of the longest day from the places under the equator to those which lie immediately beneath the pole. Therefore, nevertheless adhering to Ptolemy’s precepts, twenty-three climata...
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LEXICON 366 lateris constans, quorum quodlibet æquale est, & paralle- lum opposito. Cuius ea conditio est, vt super æquales ba- ses constitutæ plures huiuscemodi figuræ, & in eadem altitudine, æquales etiam sint inter se. Differt à Parallelogrammo, quod hoc dicit vnum tantum planum quadrilaterum, constans quatuor tantum angulis: illud autem inuoluit plura plana, nempè sex in superficie, & consequenter octo angulos ex aduerso sibi inuicem respondentes, ita- vt non vnam figuram superficialem, sed vnum corpus solidum omnis dimensionis capax præseferat: huiusmodi sunt taxilli, quibus in alveolo luditur. Cæterum Parallelopipedum, habet omnes conditiones parallelogrammi, cum aliud non sit, quam multa parallelogramma in vnum conuenientia. Vnde etiam est, vt non nisi in quatuor differentias parallelogrammo etiam communes diuidi possit. Si enim continet sex parallelogramma æquilatera, & rectangula, correspondet quadrato in planis figuris, & dicitur Cubus, qualis est, vt modò dixi, taxillus. Si sex illa parallelogramma fuerint quidem rectangula, sed non omnia æquilatera sed duobus æqualibus, & minoribus existentibus, reliqua sint longiora, vocabitur parallelopipedum altera parte longius. Si fuerit quidem omni ex parte æquilaterum, sed non æqualibus angulis respondentibus, & omnibus rectis, cor- respondebit Rhombo. Si demum neque omnia parallelogramma æquilatera, neque omnes anguli recti erunt, quam- uis duo ex iis rectangula fuerint, & æquilatera; vel re- tangula tantum, vel æquilatera tantum; fuerint nihilo- minus verè parallelogramma; ita vt tam plana, seu latera, quam anguli ex aduerso æqualia sint, correspondet Rhomboidi. Porrò quodcumque parallelopipedum vocari etiam poterit Prisma; sed non omne Prisma, parallelopipedum: vt ex definitione Prismatis, quam infra trademus, constabit. 24. PARELIA sunt reflexiones solarium radiorum in nube rotida, sed benè compacta; quæ quasi speculum in se recipiat, & referat imaginem solis, ita vt quasi sol alrer appareat, & ferè nescias quisnam sit verus, & quis fictitius. Di- cuntur autem Parelia, quasi pares Elio, hoc est Soli, vocabulo ex duplici idiomate Græco, & Latino compacto: & quandoque duo, quandoque etiam tres soles apparere solent, vt videre accidit Romæ anno 1621. die 11. Februarij ferè in meridie, & durauit per duas circiter horas, vt refert Raphaël Auersa quest. 42. sect. 5. & ante Salvatoris orium tres item soles apparuisse omnes pænè illius temporis scri- ptores testantur: quod olim pro ostento habitura, postea
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LEXICON 366 sides are constant, each of which is equal, and parallel to the opposite. Its condition is that, above equal bases, several figures of this kind, and at the same height, are also equal among themselves. It differs from the Parallelogram, because the latter denotes only one plane quadrilateral, consisting of only four angles; the former, however, involves several planes, namely six on the surface, and consequently eight angles corresponding opposite one another, so that it presents not one superficial figure, but one solid body capable of every dimension: such are dice, with which one plays in a dice-box. Moreover, a Parallelopiped has all the conditions of a parallelogram, since it is nothing other than many parallelograms brought together into one. Hence also it follows that it can be divided into no more than four differences, common also to the parallelogram. For if it contains six equal-sided and right-angled parallelograms, it corresponds to the square among plane figures, and is called a Cube, such as, as I just said, a die. If those six parallelograms are indeed right-angled, but not all equal-sided, but with two equal and smaller sides, and the rest longer, it will be called a parallelopiped longer in one direction. If it is indeed equal-sided on every side, but not with equal corresponding angles, and not all right angles, it will correspond to a Rhombus. Finally, if neither are all the parallelograms equal-sided nor all the angles right, although two of them may be right-angled and equal-sided; or if they are right-angled only, or equal-sided only; yet if they are nevertheless truly parallelograms, so that both the planes, or sides, and the opposite angles are equal, it corresponds to a Rhomboid. Furthermore, whatever parallelopiped may also be called a Prism; but not every Prism is a parallelopiped, as will be clear from the definition of Prism, which we shall give below. 24. PARELIA are reflections of the sun’s rays in a round cloud, but well compacted; which receives and reflects the image of the sun in itself as if it were a mirror, so that another sun seems to appear, and you can scarcely tell which is the true one and which the fictitious. They are called Parelia, as if pares Elio, that is, equal to the Sun, a term formed from a double idiom, Greek and Latin: and sometimes two, sometimes even three suns are seen to appear, as happened to be observed at Rome in the year 1621, on the 11th of February, at about midday, and it lasted for about two hours, as Raphael Aversa reports in question 42, section 5; and before the rising of the Saviour three suns also appeared, as nearly all the writers of that time testify: which was once regarded as a portent, afterward
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MATHEMATICVM. 373 Si Manors solo infelix rutilante lacessat, Quo sol, aut quo Luna loco, Dominumque locorum, Nec felix stella occurset, calove cadenti Sese agat occasum versus regione secunda. Huic caput auulsum collo violenta bipennis Auferet, & media truncus spectatur arena. Hucusque Pontanus. Quæ omnia in funeream Gorgonis stellam recidunt; quam alibi authoritate etiam D. Thomæ, violentæ nimis, ac luctuosæ naturæ fuisse semper, aduer- timus. PERSONA Astronomis idem valet, quod Facies: Vnde < 49.> Planetæ dicuntur personas suas gerere, quandocumque se facie ad faciem intuentur; præsertim verò cum luminatibus, hoc est, vt eo modo configurentur cum Sole, aut Luna (ita tamen vt sint Orientales ab illo, Occidentales ab ista) quo eorum domicilia cum domibus luminarium. Hanc familiaritatis, scù dignitatis speciem Arabes Almugeam vocant: de qua vide quæ fusiùs diximus suo loco. PERSPECTIVA vna est, ex Mathematicis disciplinis, quam < 50.> Geometriæ filiam vocant: Facultas est, quæ iuxta princi- pia Geometrica per radios visuales, tamquam lineis, & an- gulis res longè ab oculis dissitas specularur, siue ea cælestia corpora sint, siue quæcumque colorata; (inquo latiùs paret quam Optica) atque ad rationem emissarum specierum in modum Pyramidis dimetitur. Est in triplici differentia: Alia enim est, quæ absolutè, & anthonomasticè dicitur Perspe- ctiua, & in eo consistit, vt rationem reddat earum appa- rentiarum, quæ aliter, ac res sunt, nostris obtutibus sese offerre solent, ob diuersam rerum situationem, atque di- stantiam; qua ratione videmus circulos rectos tamquam li- neas, quadrata tamquam circulos, &c. Alia est, quæ ver- satur circa varias, ac multiplices refractiones; quæ profe- cto ab speculis, ex quibus eas potissimum exquirit, specula- ria, siue specularia appellatur. Alia demum, quæ circa vmbras versatur; atque ostendit qua ratione fieri queat, vt ea, quæ in picturis apparent confusa & inordinata, ex di- versitate situs concinna & ordinata, & è contrà quæ aliàs benè disposita, è longinquo, aur è latere deformia, & incon- cinna videantur; Et hæc dicitur Sciacoptrica, de quibus om- nibus eruditè admodum scripsit Alaazel in sua Perspecti- ua, Vitellion, Guidobaldus è Marchionibus Montis, ac nouissimè Kircherus in Arte Magna lucis, & vm- bræ. A a
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MATHEMATICUM. 373 If Manors, with the ground only, should assail the unhappy one with its gleaming splendor, where the sun is, or where the Moon, and the Lord of places, and no fortunate star should meet him, nor should he move himself toward the setting heaven, falling toward the west in a second region. This violent two-edged axe shall take away his head, torn from the neck, and the trunk is seen in the middle of the arena. Thus far Pontanus. All these things fall back upon the funeral star of Gorgon; which elsewhere, even by the authority of St. Thomas, we note to have always been of too violent and sorrowful a nature. PERSONA means the same to astronomers as Facies: hence <49.> the planets are said to bear their own persons whenever they look face to face; especially indeed when with the luminaries, that is, when they are configured with the Sun or with the Moon in such a way (so, however, that they are Oriental from the former and Occidental from the latter) as are their domiciles with the houses of the luminaries. This kind of familiarity, or dignity, the Arabs call Almugeam: see what we have more fully said elsewhere about it. PERSPECTIVE is one of the mathematical disciplines, which <50.> they call the daughter of Geometry: it is a faculty which, according to geometrical principles, by visual rays, as by lines and angles, examines things far distant from the eyes, whether they are heavenly bodies or any colored objects; (in which it differs more broadly from Optics) and measures them according to the proportions of emitted species in the manner of a pyramid. It is of three kinds: one, namely, is absolutely and in the strict sense called Perspective, and consists in giving an account of those appearances which, otherwise than things are in themselves, are accustomed to present themselves to our sight, because of the different position and distance of things; by which means we see straight circles as lines, squares as circles, etc. Another is that which deals with various and multiple refractions; and indeed, from mirrors, from which it chiefly seeks them out, it is called specularia, or specularia. A third, finally, is that which deals with shadows; and it shows by what means it can happen that those things which appear in paintings confused and disordered, because of the difference of position, may be neat and ordered, and on the other hand those which are otherwise well arranged may, from a distance or from the side, seem deformed and ill-composed; and this is called Sciacoptrica, about all of which Alaazel wrote very learnedly in his Perspectiva, Vitellio, Guidobaldus of the Marchesi of Monte, and most recently Kircher in the Great Art of Light and Shadow. A a
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LEXICON hoc quod dicit Deo rem improbam fore annumerate nouas stellas, atque ad formam expandere, quod ausum esse di- cit Hipparchum, non satis intelligo. 60. Cæterum de istis stellis varia fuit tum antiquorum, tum recensiorum Astronomorum opinio. Democritus, cuius sen- tentiam amplecti videtur Bodinus lib. 2. Theatri, somnia- uit, eas esse illustrium virorum mentes, quæ postquam in- numerabilibus seculis viguerunt in terris, tandem obituræ extremos peragunt triumphos, aut in cælum stellarum, quasi splendida sidera reuocanrur, ac proptereà sequuntur fames, morbi populares, ac ciuilia bella, quasi Ciuitates & populi ducibus illis optimis, & gubernatoribus, qui di- uisos furores placabant, desererentur. Aristoteles minus absurdè dixit eas omnes gigni ex materia elementari, ferri- que aliquando ad ipsam regionem ætheream: Sequuntur eum non pauci recensiores, eo maximè, quod posita cæloru[m] fluxibilitate, iam nil obstare videtur, quin ijsdem Cometæ, qui in regione aërea generantur, si subtilioris materiæ sint, possint orbes planetarum transcendere, atque etiam ad ipsum Firmamentum peruenite, vbi postea perinde ac astra refulgeant, quoadusque eorum materia penitùs absumatur. Quod, præcæteris, actiter sustinet Christophorus Roth- mannus. 61. Verum etsi fortè huic rei non obstet ipsa cælorum sub- stantia, quæ sit fluxibilis, & per consequens facillimè etiam attrahi à sideribus possint huiusmodi ignitæ exhalationes; attamen non videtur credibile, eas tanto tempore durare posse, cum Stella Cassiopææ duos integros durarit annos, & de ea quæ apparuit anno 1600. in pectore Cygni testatur Blancanus adusq[ue] suum tempus hoc est anno 1616. fuisse vi- sibilem, quando Cometæ in aëre apparentes vix ad mensem durare solent. Deinde vnde emanat tanta exhalationum co- pia, quæ ad cælum vsque fixarum possit ascendere, ibique accensa, sint probè visibilis? non certè è rerra, quæ si tota ad sidera euolaret è loco vbi modo consistit, videri ob sui tenuitatem minimè posset cum ipsa terra ad Firmamentum relata se habeat vt punctum, & minima Stella visibilis Fir- mamenti, bis nouies sit rerra maior. Non ergo noua phæno- mena suprà orbem Saturni visa esse possunt ex mareria ele- mentari coagmentata, sed necessario debent esse ex ipsa re- gone ætherea. Melius philosophatur Pythoras putans eas non esse de nouo genitas, sed ex perpetuo recurso terris approximari, fierique visibiles, cuius opinionem minimè absurdam existimat Blancanus, dicens ideo eas nouiter, ac
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LEXICON I do not sufficiently understand what he says there, namely that it is an impious thing to count new stars among the objects of worship, and to extend them into a shape, as Hipparchus, he says, dared to do. 60. In any case, there was among both the ancients and the more recent astronomers a variety of opinions about these stars. Democritus, whose opinion Bodin seems to embrace in Book 2 of the Theatrum, dreamed that they are the minds of illustrious men, which, after flourishing for innumerable ages on earth, at last, when about to die, perform their final triumphs, or are recalled into the sky of the stars like brilliant constellations; and that therefore famines, pestilences, and civil wars follow, as though cities and peoples were abandoned by those best leaders and governors who restrained divided madness. Aristotle said, less absurdly, that they are all generated from elemental matter and are sometimes carried up to the very etherial region. Not a few of the more recent writers follow him, especially because, once the fluidity of the heavens is posited, nothing now seems to stand in the way of those same comets, which are generated in the air region, if they are of a subtler matter, from passing beyond the spheres of the planets and even reaching the very Firmament, where afterward they shine like stars, until their matter is entirely consumed. This, above all, Christophorus Rothmann vigorously maintains. 61. Yet although perhaps the very substance of the heavens, which is fluid, does not hinder this matter, and consequently such fiery exhalations can very easily also be drawn up by the stars, nevertheless it does not seem credible that they could last for so long a time, since the Star of Cassiopeia endured two full years, and Blancanus testifies of the one that appeared in the breast of Cygnus in the year 1600 that it was visible up to his own time, that is, until the year 1616, whereas comets appearing in the air usually scarcely last a month. Then whence comes such a quantity of exhalations as could ascend all the way to the fixed stars, and there, once ignited, be made clearly visible? Certainly not from the earth, which, if the whole of it were to fly up to the stars from the place where it now stands, could by no means be seen on account of its tenuity; for the earth itself, if carried to the Firmament, would be as a point, and the smallest visible star of the Firmament is twenty-nine times greater than the earth. Therefore the new phenomena seen above the sphere of Saturn cannot be from elemental matter brought together, but must necessarily be from the etherial region itself. Pythagoras reasons better, thinking that they are not newly generated, but are drawn near to the earth from a perpetual return and made visible, whose opinion Blancanus considers by no means absurd, saying that for this reason they are newly, and
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MATHEMATICVM. 379 PINNA vulgò Astronomorum dicuntur duo spicilla in extremis Dioptræ partibus constituta ad excipiendos stella- rum radios, aliaque speculanda per quadrantem, Astrola- bium, & alia similia instrumenta PINACIM KOELASMENON in tabulis persicis dicitur Lucida Coronæ Gnostiæ, hoc est discus paruus contractus. PIOTHANATOS. Vide Biothanatos 75. PISCES duodecimum, ac postremum Zodiaci signum in australi semicirculo, sed conterminum Arii, adeoque commune, aqueum, frigidum, & humidum, domicilium Iouis, & Exaltatio Veneris, sic dictum eoquod Sole il- lud intrante omnia in aquis natare videntur. Arabicè vero Haut, & cum articulo Elhaut, & quoniam signum Bicor- poreum est, piscis, qui ad boream inflectit dicitur Haut Elschemali, qui verò ad austrum Haut Elgenubi. Qui sub hoc signo nascuntur, inquit Ptolemæus erunt colore albo, capite paruo, maxillis amplis, pectore ma- gno, membris omnibus inæqualiter, & malè dispositis, & vt plurimum cum aliquo vitio inseparabili, qualis esset claudicatio, & gibbositas. Piscium sidus in octaua sphæra habet stellas 34. secundum Ptolemæum, sed iuxta Keplerum 59. sed non admodum nobiles, quippequæ non excedunt[ur] quartam vel quintam magnitudinem præter vnam tertij ho- moris de natura Iouis, & Mercurij quæ est in nodo lini vtrosque pisces nectentis. Eius initium nunc est in gr. 15. Piscium primi mobilis, & proctenditur vsque ad gr. 27. Arietis. Pars prior frigida est, media humiditate abundans; vl- tima ob communicationem cum stellis in capite Arietis con- fidentibus caliditate. Quæ ad boream flectit, ventosa; quę. ad Austrum, humida, & aquosa. PISCIS NOTIVS. Vide in V. Notius Piscis. 78. PISCIS VOLANS. Vide Passer. 79. PISTRIX, Cætus, Balena sidus in octaua sphæra, de quo 80. alibi dictum. Hoc vocabulo sæpè vtitur Cicero in Atati Phoenom. PITHETIS Cometæ genus ad formam Dolij vnde & Do- 81. liaris dicitur, habens in concauo fumidæ lucis obscuros quosdam radios, de quo Plin. lib. 2. cap. 25. ad hunc etiam reducitur Tenaculum, PLANETÆ dicuntur ex Græco stellæ non in Firmamento, 82. vt fixæ, sed in proptiis cuiusque orbibus fixæ, atque erran- tes singularibus motibus in Zodiaco contra motum primi mobilis ab Occidente in Orientem secundum successionem signorum; vnde & ab errando sunt dicti, nedum apud Græ- A a iiiij
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MATHEMATICVM. 379 PINNA, in common usage among astronomers, are called the two little points set at the extremities of the Dioptra, for receiving the rays of the stars and observing other things through the quadrant, Astrolabe, and similar instruments. PINACIM KOELASMENON, in Persian tables, is called the Lucida Coronæ Gnostiæ, that is, a small contracted disc. PIOTHANATOS. See Biothanatos 75. PISCES, the twelfth and last sign of the Zodiac, in the southern semicircle, but adjoining Aries, and therefore common, watery, cold, and moist; the domicile of Jupiter, and the exaltation of Venus, so called because when the Sun enters it, all things seem to swim in the waters. In Arabic, however, Haut, and with the article Elhaut; and since it is a bicorporeal sign, the fish which bends toward the north is called Haut Elschemali, and that which bends toward the south Haut Elgenubi. Those born under this sign, says Ptolemy, will be of white complexion, with a small head, broad jaws, a large chest, and all their limbs unevenly and ill-formed, and for the most part with some inseparable defect, such as lameness and hunchbackedness. The constellation of Pisces in the eighth sphere has 34 stars according to Ptolemy, but according to Kepler 59; yet not very noble, since none exceed the fourth or fifth magnitude, except one of the third magnitude, of the nature of Jupiter and Mercury, which is in the knot of the line joining both fishes. Its beginning is now at 15 degrees of Pisces in the first movable sphere, and it extends as far as 27 degrees of Aries. The first part is cold, the middle abounds in moisture; the last, through communication with the stars in the head of Aries, has warmth. That which bends toward the north is windy; that which bends toward the south is moist and watery. PISCIS NOTIVS. See under V. Notius Piscis. 78. PISCIS VOLANS. See Passer. 79. PISTRIX, Cetus, the Whale constellation in the eighth sphere, concerning which 80. is spoken elsewhere. Cicero often uses this word in Atati Phoenom. PITHETIS, a kind of comet in the shape of a cask, whence it is also called Doliaris, having in the concavity of its smoky light certain dark rays, concerning which Pliny, book 2, chapter 25. To this also is referred Tenaculum, PLANETÆ are called, from the Greek, stars not in the Firmament, as are the fixed stars, but fixed in their proper orbits, and wandering with singular motions in the Zodiac against the motion of the first movable heaven, from West to East, according to the succession of the signs; whence they are also called wandering stars, not only among the Greeks, A a iiij
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MATHEMATICVM. 381 æquatorem non per ellipses, sed per lineas rectas designantur. Tertium tandem, quod vulgò dicitur Astrolabium, in quo centrum refert polum Arcticum, diameter horizontem rectum, linea secans Meridianum; Retè primum mobile, ac cælum stellatum, cum principalioribus fixis in ea longitudine, & latitudine, in qua nunc temporis sunt: tandem tabulæ ad singulas poli eleuationes constructæ situm mundi, & singula horizonta obliqua, cum suis circulis parallelis, seu altitudinum quos vocant almicantarath, nec non circulis verticalibus parallelis ad meridianum dictis Azimuth, quorum ope cuiusque stellæ positus in situ mundi facillimè nosci poterit. De huius fabrica & vsu scripsit Io: Stophlerinus Latinè, & Ignatius Dantes italicè: de illis Auctores, à quibus denominantur. PLANVM apud Geometras dicitur superficies recta, seu corpus habens superficiem rectam hoc est vt definit Euclides lib. 1. prop. 7. quæ ex æquo suas intetiacet lineas: per quod opponitur corpori sphærico, & circulo, quæ linea, aut supersicie curua circumscribuntur. Vnde vulgatum illud Axioma, quod corpus sphæricum non tangit planum, nisi in puncto. PLATICVS ASPICTVS dicitur ad differentiam Partilis. Est enim radius proiectus à planeta non quidem ad corpus altetius planetæ, cum non sit in exquisita distantia, sed ad orbem sphæræ lucis illius: vt ad Saturnum intrà spatium decem graduum ante, & rectò; ad Iouem 12. ad Martem gr. 7. min. 30. ad Solem gr. 17. ad Venerem gr. 8. ad Mercurium gr. 12. ad Lunam gr. 12. min. 30. tanta est enim quantitas Orbis ipsorum, ad quam lux, & actiuitas lateraliter se extendit. Quemadmodum etiam fixæ primæ magnitudinis habent Orbem hinc inde latum ad gr. 7. min. 30. Secundæ magnitudinis gr. 5. min. 30 Tertiæ gr. 3. m. 40. Quartæ gr. 1. min. 30. Portò vel iste aspectus plaricus proijcitur citrà, vel vltrà corpus Planetæ; si citrà, dicitur Applicatio, applicat enim planeta aspiciens, ac se disponit ad habendum cum altero familiaritatem, & aspectum partitem: Vel iam fuit in partili, & inde per motum suum ab eo separatur, ita tamen, vt adhuc sit intrà fines orbis illius, & hæc dicitur Separatio, seu Defluxus, vt dictum est suo loco. Quæ quidem in Luna maximè attenditur: & quo aspectus erit partili vicinior, eo efficacior: sicut etiam potentior qui ad partilem se disponit, quam qui à partili recedit. Vide quæ ibi diximus, similiter ad aspectum platicum applicanda. PLAVSTRVM fidus in cælo ad borealem plagam intra He- 87.
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MATHEMATICVM. 381 the equator is shown not by ellipses, but by straight lines. Thirdly, finally, what is commonly called the Astrolabe, in which the center refers to the Arctic pole, the diameter the horizon, the line cutting the Meridian; the Retè, the first mobile, and the starry heaven, with the principal fixed stars in that longitude and latitude in which they are at the present time: finally the tables constructed for each elevation of the pole show the position of the world, and each oblique horizon, with its parallel circles, or altitude circles, which they call almicantarath, as well as the circles parallel to the meridian called Azimuths, by whose aid the position of any star in the state of the world may be most easily known. On the construction and use of this, Io: Stophlerinus wrote in Latin, and Ignatius Dantes in Italian: on the others, the authors from whom they are named. PLANE, among geometers, is called a straight surface, or a body having a straight surface, that is, as Euclid defines it Book 1, prop. 7, which contains its lines equally within itself: by which it is opposed to a spherical body, and to a circle, which are bounded by a line or curved surface. Hence the common axiom that a spherical body does not touch a plane except at a point. PLATIC ASPECT is so called to distinguish it from Partile. For it is a ray projected from a planet not indeed to the body of another planet, since it is not at an exact distance, but to the orb of the sphere of that light: thus to Saturn within a space of ten degrees before and directly; to Jupiter 12; to Mars 7 degrees 30 minutes; to the Sun 17 degrees; to Venus 8 degrees; to Mercury 12 degrees; to the Moon 12 degrees 30 minutes. For so great is the quantity of their orb, to which light and activity extend themselves laterally. In the same way also the fixed stars of first magnitude have an orb extending on either side to 7 degrees 30 minutes; those of second magnitude 5 degrees 30 minutes; of the third 3 degrees 40 minutes; of the fourth 1 degree 30 minutes. Moreover, this platic aspect is projected either this side of, or beyond, the body of the planet; if this side of it, it is called Application, for the planet that is regarding applies itself and disposes itself to have familiarity and a partile aspect with the other: or if it has already been in a partile aspect, and from there by its motion it separates from it, yet so that it is still within the bounds of that orb, and this is called Separation, or Defluxion, as was said in its place. This is especially to be observed in the Moon: and the nearer an aspect is to partility, the more effective it is; just as also more powerful is one who is disposing himself toward a partile aspect than one who is withdrawing from a partile aspect. See what we said there, likewise to be applied to the platic aspect. PLAVSTRVM, a constellation in the sky toward the northern region within the He- 87.
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386 LEXICON rij, & lentè nimis, imò etiam quandoque insensibiliter mo- uentur, dicantur leues, & illi Ponderosi, qui alioqui natura sua sunt leues. 101 PRÆSPE Stella est Nebulosa, in pectore Cancri de natura Martis, & Lunæ existens nunc temporis in gr. 3. Leonis cum vno ferè gradu latitudinis borealis: Stella, in- quam, infensa nimis, & pessimæ qualitatis; quippe cum So- le, aut Saturno repentinis motibus turbat aërem, ventos in- festissimos ciet, pluuias, & imbres impetuosos ex repenti- no affert, fulgura facit, & tonitrua, atque suo tempore ni- ues. In Genethliacis verò cum luminaribus affert cæcitatem aut debilitatem in oculis: in horoscopo autem reperta ho- minem violentum facit, seditiosum, vagum, inconstantem, & etiam oculorum affectionibus laborantem. In eo sidere ope Telescopij Galilæus obseruauit stellas omnino 36 eo ordine, quo ipse exponit in Nuncio sidereo. Oritur Romæ cum gr. 2. Leonis, occidit verò cum quatuor. De ea Plin. lib. 16, cap. ultim. Hæc, inquit, cum sereno calo appa- vere desserit, atrox hyems sequitur. 102 PRÆSTER. Græcè, Latine Turbo: ventus est impetuo- sissimus, ac vorticosus, ex eorum genere, qui de fundo at- que ex hiatibus terræ desiliunt, atque in superna elati irre- gulariter perflant, omnia sibi obuia violento nisu detur- bantes: quales sunt etiam Ecnephias Typhon, ac Vortex, necnon alij, (qui tamen in istos recidunt) de quibus lo- quitur Arist. in Meteoris. Ab Ecnephia autem eatenus diffe- re Præstera inquit Plin. lib. 1. cap. 48. quatenus eo fure ar- dentior, & contactu amburit pariter, ac prosternit. Et cap. 49. addit eum eodem modo à Typhone differre, quo flam- ma ab igne. Hic latè, inquit, funditur statu, illud con glo- batur impetu. 103 PRÆVENTIONALIS apud Astrologos vocatur ea Natiui- tas, Anni initium, aut aliud quodvis rerum exordium, quod proxime præuenit luminarium oppositio: sicut coniunctio- nalis dicitur Genesis, quæ subsequitur coniunctionem. A loci enim dispositore, in quo celebrata fuit alterutra, auspicari solent statum illius rei, & etiam in Natiuitatibus verum gradum horoscopantem, quem Arabes Annimodat dixere. Vide sub hoc verbo. 104 PRIMVM MOBILE. Vide in V. Motus. 105 PRINCIPATVS, teste Abraham Auenarre, in suo introdu- ctorio, idem est, ac Orientalitas à Sole respectu Superio- rum, & Occidentalitas respectu Inferiorum. Sic enim in- quit cap. 7. p[ro]topè finem. Principatus est, ut sint, tres Superio-
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386 LEXICON light, and those which, though by nature heavy, move very slowly, or even sometimes imperceptibly, are called light, and those ponderous, which otherwise by nature are light. 101 PRÆSPE. It is a nebulous star in the breast of Cancer, of the nature of Mars and the Moon, now at 3 degrees of Leo, with about one degree of northern latitude: a star, I say, exceedingly hostile and of the worst quality; for when joined with the Sun or Saturn, by its sudden motions it disturbs the air, stirs up the most violent winds, suddenly brings rain and heavy showers, causes lightning and thunder, and in its season snow. In nativities, however, with the luminaries it brings blindness or weakness of the eyes; but when found in the horoscope it makes a man violent, seditious, wandering, inconstant, and also suffering from eye afflictions. In this star Galileo observed, by means of the telescope, a total of 36 stars in the order in which he himself sets them out in the Starry Messenger. It rises at Rome with 2 degrees of Leo, and sets with 4. Of it Pliny, book 16, last chapter: “These, when they have appeared in a clear sky, leave it desolate; a harsh winter follows.” 102 PRÆSTER. In Greek, in Latin Turbo: it is a most violent and whirling wind, belonging to that class which spring from the depths and from the openings of the earth, and, rising aloft, blow irregularly above, violently driving down everything in their way: such also are Ecnephias, Typhon, and Vortex, and likewise others (which however are reduced to these), of which Aristotle speaks in the Meteorologica. Præstera differs from Ecnephias, says Pliny, book 1, chapter 48, in this respect: that it is more fiery in its fury, and by contact burns and at the same time throws down. And in chapter 49 he adds that it differs from Typhon in the same way that flame differs from fire: “The one,” he says, “is spread out broadly and steadily; the other is gathered into a ball by its force.” 103 PRÆVENTIONALIS. Among astrologers this term is applied to that nativity, the beginning of the year, or any other starting point of events, which immediately precedes the opposition of the luminaries: just as conjunctio-nalis is said of the genesis which follows the conjunction. For from the disposer of the place, in which either one was celebrated, they are accustomed to forecast the condition of that matter, and also in nativities the true degree of the horoscope, which the Arabs called Annimodat. See under that word. 104 PRIMVM MOBILE. See under the letter V, Motus. 105 PRINCIPATVS, according to Abraham Avenarre, in his Introductory Work, is the same as Orientality with respect to the superior planets, and Occidentality with respect to the inferior. For thus, he says, chapter 7, near the end: Principatus is that there may be three superio-
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MATHEMATICVM. 187 ves Orientales à Sole ab hora, qua visione incipiunt oculari videris, tunc que sunt in eius principatu sublimi, donec inter eos, & Solem interueniat aspectus sextilis, & ab inde vsque ad quadratam aspectum minuetur principatus eorum sublimitas: & deinde ad stationem secundam non est ipsorum principatus; etsi fuerint huiusmodi planeta à Sole Orientales, & Occidentales à Luna, non erit isto sublimior principatus. Trium verò inferiorum planetarum incipiet principatus ab hora visionis in Occidente post solis coniunctionem; & principatus elatio Veneris, & Mercurij permanet donec retrogradetur, & si fuerint Occidentales à Sole, à Lunaque Orientales, nullus isto sublimior principatu. Luna autem vsque ad mensis dimidium principatur. Huc vsque Abraham Quare autem Orientalitas in superioribus, & Occidentalitas in inferioribus faciat huiusmodi principarum, seu faciat planetas validiores dictum est in V. Occidentalis Planeta. PRISMA definitur ab Euclide lib 10. defin. 13. quo! sit si- 106 gura solida, quæ planis continetur, quorum aduersa duo sunt, & æqualia, & similia, & parallela; alia verò parallelogramma. Ex qua definitione apertè colligitur ipsum aliud planè non esse, quam columnam quamdam lateratam æqualis crastitudinis, cuius bases oppositæ æquales sunt, similes, & parallelae, siue sint triangulares, siue quadrangulares, siue pentagonæ, &c. Vnde tot parallelogramma continebit quodlibet Prisma, quot larera, vel etiam anguli in vnoquoque oppositorum planorum reperiuntur. Vide quæ diximus in verbo Parallelopipedum. PROCELLÆ nomine veniunt genericè omnes pseudouenti, qui videlicet è fundo, vel hiatibus terræ exiliunt, & < 107> cum magno impetu siue in mare proripiuntur, ac tempestates exsuscitant, siue ad superna conscendunt, & vt, inquit Apuleius in lib. de Mundo: Sursum tormentum illud ire pergit, densasque & tumidas nubes præ se agit, coactusque collidit, fit sonitus & intonat calum; non secus ac si commotum ventis mare cum ingenti fragore vndas littoribus impingat. Huiusmodi sunt Ecnephias, Turbo, Typhon, Vortex, & alij de quibus diximus suo loco. Græci Anaphysemata vocant. PRO YON Græcè, Arabicè Algomeysa, Canis minor, seù < 108> Anrecanis: fidus in octaua sphæra, duas tantummodo habens stellas; alteram in femore grandem, primi honoris, de natura Martis, & Mercurij; alteram quartæ magnitudinis de natura solum Mercurij. Oritur Romæ circa diem 24. Iulij
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MATHEMATICVM. 187 the Eastern ones from the Sun, from the hour at which they begin to be seen visually, then they are in their exalted dominion, until there intervenes between them and the Sun the sextile aspect, and from there up to the square aspect their sovereign power diminishes: and then at the second station there is no dominion of theirs; and although such a planet be Eastern from the Sun, and Western from the Moon, its dominion will not be higher than this. But for the three inferior planets, dominion begins from the hour of appearance in the West after conjunction with the Sun; and the exalted dominion of Venus and Mercury remains until they become retrograde, and if they are Western from the Sun, and Eastern from the Moon, there is no dominion higher than this. The Moon, however, rules up to the middle of the month. Thus far Abraham. Why, however, Easternness in the superior planets, and Westernness in the inferior ones, produces such dominion, or makes the planets stronger, has been stated in the entry V. Western Planet. PRISM is defined by Euclid, book 10, definition 13, as a solid figure contained by planes, two of whose opposite faces are equal, similar, and parallel, while the others are parallelograms. From this definition it is clearly gathered that it is nothing other than some sided column of equal thickness, whose opposite bases are equal, similar, and parallel, whether they be triangular, quadrangular, pentagonal, etc. Hence any Prism will contain as many parallelograms as there are sides, or even angles, found in each of the opposite planes. See what we said under the word Parallelopipedum. Under the name PROCELLÆ are included generically all pseudowinds, that is, those which leap out from the earth’s depths or caverns, and are driven with great force either into the sea, raising storms, or ascend to the upper regions, and, as Apuleius says in his book De Mundo: “That force strives to go upward, driving before it dense and swollen clouds, and, being pressed together, it produces a sound and the heavens thunder; not otherwise than when the sea, stirred by winds, with great crash beats its waves upon the shores.” Such are Ecnephias, Turbo, Typhon, Vortex, and others of which we spoke in their proper place. The Greeks call them Anaphysemata. PRO YON, in Greek; in Arabic, Algomeysa, the Lesser Dog, or Anrecanis: a fixed star in the eighth sphere, having only two stars; one, large, on the thigh, of the first magnitude, of the nature of Mars and Mercury; the other, of the fourth magnitude, of the nature of Mercury alone. It rises at Rome about the 24th day of July.
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MATHEMATHICVM. 389 buenda per totum annum, sic, vt singulis gradibus com- petant duodecim dies: & significator singulis mensibus proficiscatur in consequentiam signorum duos gradus, cum dimidio. In Profectione Menstrua singulis mensibus tri- buitur signum vnum, itavt singulis diebus competat gr. 1. min. 4. secund. 4. quomodo annus solaris integer dieum 365. diuiditur in tredecim partes æquales, & sic in toto an- no perficiatur integer circulus. In Profectione demum Diurna tribuitur signum vnum binis diebus, hor. 3. min. 52, itavt in hac profectione singulis diebus competant gr. 13. min. 51. sicque mensis profectionalis subdiuiditur etiam in 13. partes æquales; quo expleto significator regreditur ad idem signum, in quo erat initio mensis. Plura apud Aucto- res, & calculatores Ephemeridum in suis introductoriis, de hac regulari processione: De quarum singulis speciebus claritatis gratia afferunt tabulas expansas profectionum omnium locorum hÿlegialium, Annuarum videlicet, men- struarum, ac Diurnarum. Verum nouissimè Titus in cælesti Philosophia lib. 5 cap. 9. rem altiùs indagando, pluribus ingeniosè commonstrat, hanc æqualem significatorum processionem, provt modo explicatum est, naturalem non esse. Siquidem notat ipse, quod profectionum mensura constituitur per singulos Lunæ reditus ad eandem cum sole faciem, quam habebat in ra- dice Natalis. Nam quemadmodum per directionis motum præordinatur in potentia calor vitalis cum suis coeffectibus; sic per motum profectionis, inquit, præordinatur in poten- tia humidum radicale cum suis coeffectibus: ergò, sicut mo- tus directionis non instituitur vniformis, & æqualis in Zo- diaco, sed mensuratur ex motu solis successivo à die Natalis insequentis, vt alibi monstratum est; ita & motus progressionis instituendus est ex quotidianis lationibus Lunæ per signa Zodiaci suis assiduis circulationibus, ac rediribus ad eandem cum sole faciem, & illuminationem, seu distan- tiam, quam habebat initio anni: itavt singuli reditus, & circuitus Lunæ ad eandem cum Sole faciem referantur, ac respiciant tanquam causa, ad singulos annos subsequentes, & peragrario Lunæ per singula signa referant ad singulos ferè menses. Quandoquidem circuitus hic Lunæ erga So- lem ad viuum demonstrat anni circuitum: eo enim tempo- ris spatio, quo Luna post discessum à Sole ad ipsum redit, & Sol vice versa signum ferè vnum perambulat, ascendunt in singulis mundi cardinibus tot signa, quot sunt anni dies ad vnguem: quod sic euidenter ostenditur. Bb
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MATHEMATICVM. 389 in a year, thus twelve days correspond to each degree; and the significator each month proceeds in succession through the signs two degrees and a half. In Monthly Profection, one sign is assigned to each month, so that each day corresponds to 1 degree, 4 minutes, 4 seconds. Likewise the whole solar year of 365 days is divided into thirteen equal parts, and thus in the whole year the entire circle is completed. In the Daily Profection finally, one sign is assigned to two days, 3 hours, 52 minutes, so that in this profection each day corresponds to 13 degrees, 51 minutes; and thus the profectional month is also subdivided into 13 equal parts; when this is completed, the significator returns to the same sign in which it was at the beginning of the month. More may be found among the Authors and the calculators of Ephemerides in their introductions, on this regular progression: of whose several kinds, for the sake of clarity, they provide expanded tables of profections of all hylegial places, namely annual, monthly, and daily. But very recently Titus, in Celestial Philosophy , book 5, chapter 9, investigating the matter more deeply, ingeniously shows more fully that this equal progression of significators, as has now been explained, is not natural. For he notes that the measure of profections is constituted by each return of the Moon to the same aspect with the Sun that it had in the radix of the nativity. For just as by the motion of direction the vital heat with its coeffects is preordained in potency; so by the motion of profection, he says, the radical humidity with its coeffects is preordained in potency: therefore, just as the motion of direction is not established as uniform and equal in the Zodiac, but is measured from the successive motion of the Sun from the day following the nativity, as has elsewhere been shown; so also the motion of progression ought to be instituted from the daily motions of the Moon through the signs of the Zodiac, with its continual circuits and returns to the same aspect with the Sun, and illumination, or distance, which it had at the beginning of the year: so that each return and circuit of the Moon to the same aspect with the Sun is referred to, and looks back as cause, to each of the following years, and the passage of the Moon through each sign refers to each of the months. Since this circuit of the Moon with regard to the Sun vividly demonstrates the circuit of the year: for in that span of time in which the Moon, after departing from the Sun, returns to him, and the Sun in turn traverses nearly one sign, there rise in each of the angles of the world as many signs as there are days in the year, to a nicety: which is thus clearly shown. Bb
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LEXICON proportionis, mensuræque rationes, quatenus considerant quanrum, vt est extensum, proindeque vt mensura quædam est aptum per suam extensionem, vt per ipsum alia <116> quanta mensuremus, & ipsum vicissim per alia quanta mensuretur. Et quoniam duplex est quantum continuum, & discretum, ita & duplex proportio, Geometrica quæ attenditur in quantis continuis, & Arithmetica, quæ versatur in numeris conferendo vnum cum alio, & exinde aliorum ignotorum inducendo notitiam. Nihilomtnus vtraque per numeros expeditur & adhuc retento tuo nomine ad quantum alterius considerandum se exendir pro diuersa proportionum ratione, & habitudine vnius quanti ad alterum; applicando postea ad quantitatem continuam quod per discretam deductum est: & è contrà fingendo in numeris passiones omnes quætitatis continuæ, vt quod in quantitate continua perspicuum est, in discreta etiam fac clarum, per eandem habitudinis rationem. Sic in quantitate discreta perinde est assignare ac in continua, totum & partes, puncta indiuisibilia, quæ sunt vnitates componentes eandem quantitatem discretam, & ad quæ terminatur, Angulos, & latera. Sic datur numerus planus, & solidus; Quadratus, & cubus; simplex, & compositus: rationalis, & irrationalis, &c. Sicque suo modo, in quantitate discreta est assignare omnes figuras quantitatis continuæ, triangulares, quadrangulares, trilateras quadrilateras, pentagonas, exagonas, parallelogramma, trapezia, &c. vt latè explicat Claius in Elem. Euclid. lib. 7. <117> Igitur proportio Arithmetica est cum tres, vel plures numeri per eandem differenriam progrediunrur, vt 4. 7. 10. 13. 16. 22. & sic procedendo per reliqua, quorum quilibet numerus se proximè præcedenté ternario superat. Proportio Geometricà est cum tres, vel plures numeri eandem rationem habent: vt numeri 1. 6. 18. 54. 162. &c. quilibet enim ad suum antecedentem eandem proportionem habet, seù rationem triplam. Vnde porest, vt suprà dicebam eadem proportionalitas Arithmetica, atque Geomerrica, & continua esse, & discreta: Continua quidem, quando idem numerus, qui consequens est respectu numeri præcedentis est etiam antecedens respectu numeri subsequentis: vt proportionalitas, quæ est inter 1. 6. 28. 54. continua est, discreta autem, cum numerus, qui consequens est non est idem antecedens respectu alterius numeri consequentis, sed rursum assumitur alius numerus antecedens, & alius nume-
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LEXICON the relations of proportion and of measure, inasmuch as they consider quantity, as it is extended, and therefore as a certain measure fitted by its own extension, so that by it we may measure other <116> quantities, and in turn it itself may be measured by other quantities. And since continuous quantity is twofold, and discrete, so also proportion is twofold: Geometrical, which is observed in continuous quantities, and Arithmetical, which is concerned with numbers, comparing one with another, and thence inducing the knowledge of unknown others. Nevertheless both are dealt with by means of numbers, and while retaining still your name, it extends itself to consider the quantity of another according to the different ratio of proportions, and the relation of one quantity to another; afterward applying to continuous quantity what has been deduced from the discrete: and conversely, by imagining in numbers all the properties of continuous quantity, so that what is plain in continuous quantity, make clear also in discrete quantity, by the same relation of proportion. Thus in discrete quantity it is just the same to assign as in continuous, the whole and the parts, indivisible points, which are the units composing the same discrete quantity, and to which it is terminated, angles, and sides. Thus there is given plane and solid number; square and cube; simple and composite; rational and irrational, etc. And in its own way, in discrete quantity it is to assign all the figures of continuous quantity, triangular, quadrangular, trilateral, quadrilateral, pentagonal, hexagonal, parallelogram, trapezium, etc., as Clavius explains at length in Elem. Euclid. lib. 7. <117> Therefore Arithmetical proportion is when three or more numbers proceed by the same difference, as 4, 7, 10, 13. 16, 22, and so on through the rest, each number exceeding the one immediately preceding it by three. Geometrical proportion is when three or more numbers have the same ratio: as the numbers 1, 6, 18, 54, 162, etc.; for each has to its predecessor the same proportion, or triple ratio. Whence it is possible, as I was saying above, for the same proportionality, whether Arithmetical or Geometrical, to be both continuous and discrete. Continuous, indeed, when the same number, which is consequent with respect to the preceding number, is also antecedent with respect to the following number: as the proportionality which is between 1, 6, 28, 54 is continuous; but discrete, when the number which is consequent is not the same as the antecedent with respect to another following number, but again another antecedent is taken, and another nume-
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LEXICON 394 minor, qualis est proportio tripla 12 ad 4. quadrupla 16. ad 4. &c. Secunda est habitudo maioris quantitatis ad minorem, cum maior semel tantum minorem continet, sed adhuc eius aliquam partem aliquotam vt dimidiam, tertiam, quartam, &c. vt est proportio sesquialtera 3. ad 2. sesquitertia 11. ad 9. Tertia est habitudo talis maioris quantitatis ad minorem, vt maior minorem semel duntaxat contineat, & insuper aliquot eius partes aliquotas non efficientes vnam aliquotam, vt est 8. ad 5, Quarta constata ex multiplici, & superparticulari est cum maior quantitas minorem aliquoties continet, vt bis, ter; quater, & insuper vnam eius partem aliquotam, vt est proportio 9. ad 4. quæ numerum quaternarium bis continet, & prætereà vnitatem. Quinta demum composita ex multiplici, & superpartiente est habitudo maioris quantitatis ad minorem, quâ maior minorem complectitur aliquoties, & insuper aliquas eius partes aliquotas non valentes conficere vnam, vt est proportio 11. ad 3. vbi numerus 11. ter continet numerum ternarium, & adhuc duas vnitates non sufficientes conficere quartum ternarium. < 121> Tandem alia dicitur proportio ordinata, quæ in eo consistit; vt quemadmodum fuerit antecedens ad consequens, ita antecedens ad consequens, fuerit etiam vt consequens ad aliud quippiam, ita consequens ad aliud quippiam. Perturbata verò est cum positis tribus magnitudinibus, & aliis quæ sint his magnitudine pares, vt in primis quidem magnitudinibus se habet antecedens ad consequentem, ita in secundis magnitudinibus antecedens ad consequentem; vt autem in primis magnitudinibus consequens ad aliud quippiam, ita in secundis magnitudinibus aliud quippiam ad antecedentem. Plura qui volet videat Euclidem lib. 5. & lib. 7. vbi latè agit de proportionibus, quæ intercedunt tam inter duas magnitudines, seu quantitates continuas, quam inter duas quantitates discretas, seu numerorum quamlibet multitudinem. < 122> Propus dicitur Stella fixa quartæ magnitudinis de natura Veneris, & Mercurij in extremo pede sinistro præcedentis Geminorum consistens, sic dicta quasi propes, hoc est ante pedem, seu vt habet Proclus, quia ptesse est conversioni æstius, & initio Cancri: est enim in longitudine in gr. ferè 1. Cancri. Quæ tamen oritur Romæ cum gr. 25. eius-
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LEXICON 394 minor, such as is the triple proportion of 12 to 4, the quadruple of 16 to 4, etc. The second is the relation of a greater quantity to a lesser, when the greater contains the lesser only once, but still some part of it, such as a half, a third, a fourth, etc., as is the sesquialter proportion, 3 to 2, and the sesquitertian, 11 to 9. The third is the relation of such a greater quantity to a lesser, that the greater contains the lesser only once, and besides some of its aliquot parts which do not make up one aliquot whole, as is 8 to 5. The fourth, compounded of multiple and superparticular, is when the greater quantity contains the lesser several times, as twice, thrice, four times, and besides one aliquot part of it, as is the proportion 9 to 4, which contains the number four twice, and moreover unity. The fifth, finally, compounded of multiple and superpartient, is the relation of a greater quantity to a lesser, whereby the greater comprehends the lesser several times, and besides some of its aliquot parts not amounting to one whole, as is the proportion 11 to 3, where the number 11 contains the ternary number three times, and still two units not sufficient to make the fourth ternary. < 121> Lastly, another proportion is called ordered, which consists in this: that as the antecedent has been to the consequent, so the antecedent to the consequent shall also be as the consequent to something else, so the consequent to something else. But a perturbed proportion is when, three magnitudes being posited, and others equal in magnitude to these, as in the first magnitudes indeed the antecedent stands to the consequent, so in the second magnitudes the antecedent to the consequent; but as in the first magnitudes the consequent stands to something else, so in the second magnitudes something else stands to the antecedent. Whoever wishes for more, let him see Euclid, book 5 and book 7, where he treats at length of proportions, which intervene both between two magnitudes, or continuous quantities, and between two quantities discrete, or any multitude whatsoever of numbers. < 122> Propus is called a fixed star of the fourth magnitude, of the nature of Venus and Mercury, situated at the extreme left foot of the preceding Gemini; so called as it were propes, that is, before the foot, or, as Proclus has it, because ptesse is to the conversion of the heat, and at the beginning of Cancer: for it is in longitude at about 1 degree of Cancer. Yet it rises at Rome with 25 degrees of that-
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396 LEXICON seu adæquatio: estque pars illa Eclipticæ, quæ addenda est, vel minuenda à motu medio Planerarum, vt habeatur verus, aut à vetò, vt habeatur medius. Vide in V. Æquatio. < 127 > PROTHANATOS (alij Prothanatos) aq[ui]d Campanilam est Planeta vel locus in cælo mortis qualitatem decernens, qui videlicet in cælesti figura locum Anereticum aut præcedit, aut sequitur, aut etiam eidem applicat. Item Dominus termini, in quem incidit mortalis directio < 128 > PROTRIGETES item Græcè dicitur Vindemiator, stella fixa tertiæ magnirudinis de natura Saturni, & Mercurij, ab Arabibus dicta Alasaph existens in ala septentrionali Virginis, quæ tempore Vindemiæ oritur. Plinius lib.10.cap. cap. 31. eam vocat Astyriæ stellam. Vide in V. Vindemiator. < 129 > PSEUDOSTELLA communiter dicitur quicumque cometa, siue nouum Phænomenon de novo apparens in cælo, siue in regione elementari, siue in ætherea: pressus tamen accipitur pro iis qui in suprema aëris regione generantur, vnde pseudostellæ quasi falsæ, & veluti supposititiæ appellantur, ad differentiam earum quæ perpetuò in regione ætherea micant, & nullam mutationem subeunt. Nihilominus istæ sublunares, vii æthereas in luce, atque in coloribus imitanrur, ita & qualitatibus imbuuntur, & secundum naturam Planerarum, quibus assimilantur, & quos credendum est in ipsarum productione magis concurrere Fausta vel in fausta obnunciant; ita tamen, vt quia adulterina est earum activitas, atque ex cælorum partim, partim è tulluris prauis qualitatibus confarcinata, semper portemosa sit, ac timenda huiusmodi Phænomenon apariti. Et quidem, cum eorum materia sit exhalatio quædam spissa, pinguis, & crassa in vnum coiens, quæ siue ab ignis sphæra illis proxima, siue à sideribus; ex motu quo ignem concipit accenditur, & tantum durat quovsqve eius crassities absumatur, vt habet Arist. 1. Meteor. cap. 7. ideò eorum materia iam resoluta, consequens est, vt reliqua exhalatio, in ventos conueriatur, sicque maris tempestates, terræ motus, terræ sterilitatem, aëris intemperiem, aliaque id genus mala denunciei: Vnde Pontanus in Vrania: Ventorum quoque certa dabunt tibi signa Cometa. < 130 > Placet autem hic ex Iunctino in tractatu de Cometis particulares eorum significationes afferre siue ex natura Planetarum quos referunt, siue à qualitatibus signorum, in qui-
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396 LEXICON its aequation: and this is that part of the Ecliptic which must be added to, or subtracted from, the mean motion of the Planets, so that the true motion may be obtained, or from the true, so that the mean may be obtained. See under V. Equation. < 127 > PROTHANATOS (others, Prothanatos) aq[ui]d Campanilam is the Planet or place in the sky determining the quality of death, which, namely, in a celestial figure, occupies the Anaretic place, either before, after, or even applying to it. Likewise, the Lord of the term into which the mortal direction falls < 128 > PROTRIGETES is also called in Greek Vindemiator, a fixed star of the third magnitude, of the nature of Saturn and Mercury, called by the Arabs Alasaph, existing in the northern wing of Virgo, which rises at the time of the vintage. Pliny, book 10, chap. 31, calls it the Astyrian star. See under V. Vindemiator. < 129 > PSEUDOSTELLA is commonly called any comet, or new phenomenon appearing anew in the sky, whether in the elemental region or in the ethereal: strictly, however, it is taken for those which are generated in the highest region of the air, whence they are called pseudostellae, as it were false, and, as it were, spurious, in distinction from those which shine perpetually in the ethereal region and undergo no change. Nevertheless, these sublunary ones, like the ethereal, imitate in light and in colors, and are also imbued with qualities, and according to the nature of the Planets to which they are likened, and which it should be believed concur more in their production, they announce either favorable or unfavorable things; yet so that, since their activity is adulterine, and compounded partly from the heavens, partly from the corrupt qualities of the earth, it is always dangerous and fearful for such a Phenomenon to appear. Indeed, since their matter is a certain thick, fatty, and coarse exhalation coalescing into one, which either from the sphere of fire near it, or from the stars, is kindled by the motion with which it conceives fire, and lasts only so long as its thickness is consumed, as Aristotle says, Meteor. 1, chap. 7; therefore, when its matter has now been resolved, it follows that the remaining exhalation is turned into winds, and thus it announces sea storms, earthquakes, barrenness of the earth, unhealthy air, and other evils of that kind: whence Pontanus in Urania: Comets too will give you certain signs of winds. < 130 > It is pleasing here, moreover, from Junctinus in his treatise on Comets, to present their particular significations, whether from the nature of the Planets which they resemble, or from the qualities of the signs, in which-
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MATHEMATICVM. 197 bus apparuerint, quoniam eius rei notitia multum iuuare potest ad ea, quorum signa extiterint declinanda, nosque per contraria communiendos. itaque Cometæ, Pseudostellæ de natura Saturni, quales sunt quæ 131. referunt colorem plumbeum, liuidum, suboscurum, in quo genere veniunt Pithetes, Tenaculum, Hircus, &c. in Ho- roscopo mundi repertæ, obnunciant multorum perniciem, famem, pestem, exilia, inopiam, angustias, luctus, terrores; & brutis animantibus vsui hominum accommodatis detri- menta: Prætereà afferunt frigora suo tempore intensissima, glaciola, & nebulosa; niuium magnam vim, ventos vali- dissimos, tempestatas, naufragia, piscationis iacturam, frugum ab erueis, ac locustis deuastationem, inundationes, grandines, & similia. In hominibus insuper denotant varia accidentia, & pericula, quicque adhuc erunt plus solito tri- fles, inuidi, solitarij, laboriosi, &c. Phænomenon de natura Iouis, qualis est Argenteus, signi- 132. ficat anni fertilitatem, salutares pluvias suis temporibus con- gruentes, aëris serenitatem, præsertim si in signis aereis: Verum corporibus ad morbos dispositis, iis maximè qui Iouiam complexionem habent, pleuritides, aliasque ægri- tudines, quas Iouem facere diximus suo loco. Martius Cometes dictus Veru, seu Pertica indicat aridita- 133. tem fontium, & fluuiorum exsiccationem, Ventos morbi- ficos, fructuum, & satorum dissipationem: Ad hæc frequen- tissima sequentur tonitrua, coruscationes, & fulmina: Mare præter solitum agirabitur, & crebriora contingent naufragia. Et quia Mars naturaliter accendit bilem, ideo frequentes rixæ, contentiones, bella, seditiones, &c. ex- citabuntur. Ex morbis etiam grassabuntur disenteriæ, fe- bres ardentes; hæmorrhagia, & his similia. Cometa de natura Solis, qualis est qui communiter dici- 134 tur Rosa, si vitus fuerit in regionis alicuius horoscopo por- tendit Regis, aut alicuius viri præponentis mortem, aut se- ditiones, & tumultus eum rerum mutatione, sed qui- bus meliora forte succedent. Item bella, contentiones, æstus, & siceitates. Homines etiam solares, cuiusmodi sunt magnanimi, prudentes, hilares, generosi, graues, multis afflictabuntur incommodis. Veneris Pseudostella colore flauo, & valdè rutilans mina- 135. tur mala de ipsius natura, stomachi, renum, spermatico- rumque valorum affectiones, quibus potissimum laborabunt mulieres, sacræ Virgines, adolescentes delicatuli, vo- luptuosi & similes. Adducit etiam fructuum corruption-
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MATHEMATICVM. 197 because knowledge of this matter can greatly help in avoiding those things whose signs have appeared, and in fortifying ourselves against them by contraries. Thus: Comets, Pseudostars of the nature of Saturn, such as those which 131. have a leaden, livid, darkish color, among which sort are Pithetes, Tenaculum, Hircus, &c., found in the Horoscope of the world, foretell the ruin of many, famine, plague, exiles, want, distress, sorrows, terrors; and harm to brute animals adapted for human use. Moreover they bring at their proper season the most intense cold, hail and cloudy weather; great abundance of snow, very strong winds, storms, shipwrecks, loss of fishing, devastation of crops by locusts and beetles, inundations, hailstorms, and the like. In human beings they further denote various accidents and dangers, and those who are still alive will be more sad, envious, solitary, laborious, &c. than usual. A phenomenon of the nature of Jupiter, such as the Silver one, 132. signifies fertility of the year, healthful rains falling at their proper times, and serenity of the air, especially if it be in airy signs. But for bodies disposed to illness, especially those which have a Jovial complexion, it signifies pleurisy and other maladies, which we have said Jupiter causes in their proper place. The Martial Comet called the Spear, or Staff, 133. indicates dryness of springs and drying up of rivers, pestilential winds, dissipation of fruits and crops. To these will be added very frequent thunder, flashes, and lightning. The sea will be agitated more than usual, and shipwrecks will occur more frequently. And because Mars naturally kindles bile, frequent quarrels, disputes, wars, seditions, &c. will be stirred up. Among diseases there will also abound dysenteries, burning fevers, hemorrhage, and the like. A comet of the nature of the Sun, such as the one commonly called the Rose, if it be in the horoscope of some region, 134. portends the death of a king or of some ruling man, or else seditions and tumults with a change of affairs, though better things may perhaps follow. Likewise wars, disputes, heat, and droughts. Solar men also, such as the magnanimous, prudent, cheerful, generous, grave, will be afflicted by many inconveniences. A pseudostar of Venus, yellow in color and very red 135. threatens evils from its own nature: affections of the stomach, kidneys, and seminal vessels, with which women, sacred virgins, delicate adolescents, the voluptuous, and the like will chiefly labor. It also brings corruption of fruits-
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398 LEXICON nem, aquarum inundationes, rerum publicarum, legumque murationes. 136. Comeres Mercurialis colore ceruleus, dictus Dominus Ascone præter ventos plus solito ita uentes adducit fatem, bellum, & pestilentiam, cum magni viri alicuius morte, ac personis Mercurialibus præsertim ingeniosis phrænesim lethargum, epilepsiam, & similia. 137 Tandem lunaris muliebri statui, & popularibus aliquid mali semper obnunciat, iis præsertim qui sub Lunæ gubernaculo sunt, vt Phlegmatici, inconstantes, albi, mobiles, pusillanimes, meticulosi, &c. quibus ingerit morbos ex nimia humiditate, hidropem catarrhos, paralyses, epylepsias. In vniuersum autem significat sterilitates, legum, rituumque innouaiones, ac leuiabella. 138 Porrò si Cometa supra dictos planetas exaltabitur augebit supra modum significara: si super Saturnum infirmitates validas, ac diuturnas adducit: Si super Iouem, morientur homines eximij, nobiles, insignibus, ac laude conspiciui: Si suprà Martem homines litigabunt, & bella gerent: Si suprà solem, deprimentur Reges, ac potentes, & viles exaltabuntur: Si suprà Venerem, aquatum diminuiones cum siccitate denunciantur: Si suprà Mercurium, tixæ, & iuuenum morbi: Si suprà Lunam, in substantiis multorum derrimenta: Si suprà Draconis caput, interficientur nobiles, & qui in pretio erunt: Si suprà Caudam, denotar, quod in fructibus arborum erit iactura. 139 Addit prætereà Georgius Valla, quod si Crinita caudam ad Saturnum conuerterit, fructuum inopiam, & annonæ caritatem portendit; si ad Iouem, regias domos euertendas si ad Martem, ægritudines, interitus, & bella atrocia cum immutatione status rerum publicarum; si ad Venerem magnarum mulierum, Reginarumq[ue] mortem; si ad Mercurium multitudini suspendia, & infamiam. 140 Denique pro qualitate signorum, in quibus hæc Phoenomena apparuerint habent diversa significata. Nam si in Ariere fulserint, indicant futuros armorum strepitus, sanguinis effusionem, ac potentium virorum mortem: item siccitatem insignem, morbos vulgares, oculorum, & capitis affectiones, lucem pecudum, nobilium, summorumque virorum deiectionem, & ignobilium exaltationem, non sine magno æstu, & apprime noxio. Si in Tauro: significant messis, & fructuum corruptelam, terræmotus hotrendos, ventos validos; item & frigora suo tempore ingenia: Hinc erunt ægritudines vehementes, do-
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398 LEXICON nem, inundations of waters, changes of commonwealths and laws. 136. A Mercurial comet, colored blue, called Lord Ascone, besides winds more than usual, so brings on fate, war, and pestilence, with the death of some great man, and especially to Mercurial persons, particularly the ingenious, frenzy, lethargy, epilepsy, and the like. 137. Finally, the lunar pertains to the female state, and always foretells something evil for the common people, especially those who are under the governance of the Moon, such as phlegmatic, inconstant, pale, changeable, faint-hearted, fearful, etc., to whom it brings diseases from excessive humidity, dropsies, catarrhs, paralyses, epilepsies. In general, however, it signifies sterilities, innovations of laws and rites, and trifles. 138. Moreover, if a comet is exalted above the aforesaid planets, it will increase beyond measure the signification: if above Saturn, it brings strong and lasting illnesses; if above Jupiter, excellent men, nobles, and those distinguished by honors and praise will die: if above Mars, men will quarrel and wage wars: if above the Sun, kings and powerful men will be brought low, and the lowly will be exalted: if above Venus, a diminution of waters together with dryness is foretold: if above Mercury, strife, and diseases of youths: if above the Moon, losses in the property of many: if above the Dragon's Head, noble men and those held in esteem will be slain: and if above the Tail, it denotes that there will be loss in the fruits of trees. 139. Moreover, Georgius Valla adds that if the hairy star turns its tail toward Saturn, it portends scarcity of fruits and dear prices of grain; if toward Jupiter, the overthrow of royal houses; if toward Mars, illnesses, destruction, and savage wars, together with a change in the state of commonwealths; if toward Venus, the death of great women, and of queens; if toward Mercury, hangings and infamy for many. 140. Finally, according to the quality of the signs in which these phenomena appear, they have different meanings. For if they shine in Aries, they indicate future clamor of arms, spilling of blood, and the death of powerful men: likewise an outstanding drought, common diseases, afflictions of the eyes and head, the downfall of cattle, nobles, and supreme men, and the exaltation of the base, not without great heat, and exceedingly harmful. If in Taurus: they signify the corruption of the harvest and fruits, dreadful earthquakes, strong winds; likewise, and at their proper time, cold spells: hence there will be severe illnesses, do-
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MATHEMATICVM. 399 lores sicci, vt scabies, impetigines, pruritus, &c. Si in Geminis: significant rixas, belli seminaria, ægritudines & ex his mortes puerorum, & adolescentium, prægnantium aborsiones, auium interitum, famem, tonitrua, & corruscationes cum ventorum tanta vi, vt arbores eradicare valeant Item lasciviam, & fornicationis licentiam, pro- borumque hominum deiectionem. Si in Cancio; indicant multitudinem locustarum ingruentium, ac deuastantium messem, adeoque frumenti, & aliarum frugum paucitatem, vel ab iis corrosarum, vel sanè à vermibus in eis productis: Item præagiunt bella, discordias, submersiones, direptiones, famem, & quam plutima mala: Si in Leone denorant destructionem ædificiorum, infestationem luporum, & ex ipsis impedimenta multa in hominibus, productionem vermium in frugibus, canum rabiem, oculorum affectiones, & bella Si in Virgine: significant labores multos, dolores, ac febres, tremores, vlcera, & postulas, præsertim in foemineo sexu, in quo abortus valde erunt timendi. Item hominum proborum vexationes, ac malorum viuendi licentiam. Si in Libra: denotant pluviarum paucitatem, ventorum imperium, fluuiorum desiccationem, frugum inopiam, reræmotus horribiles. Item mortem Principum, cædes, proditiones, & alia huiusmodi. Si in Scortpone: portendunt multitudinem bellorum inter Principes viros, contentiones, & regnorum revolutiones. Insuper labores, & ægritudines in omni hominum genere: parturientium pericula dolores, & affectiones partium generazioni inseruientium, & fructuum terræ certissimam coruptelam. Si in Capricorno: præsignant magnam viuendi licentiam in hominibus ptauis, fornicationes, adulteria, bella, rixas, venena principibus propinata. Item hyemis asperitatem, grandines, niues; vnde fructuum caritas, & penuria. Si in Aquatio: afferunt infirmitates populares, bella longo tempore duratura; aëris obscuritatem cum ventorum, tonitudrum, & fu'minum imperiu. Insuper pestem luctuosam, & summorum præsertim virorum inopinatam mortem. Si denique in Piscibus apparuerint indicant plebis calamitosum statum, bella atrocia, rebelliones, ac proditiones.
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MATHEMATICVM. 399 dry disorders, such as scabies, impetigo, itching, &c. If in Gemini: they signify quarrels, the seedbeds of war, illnesses, and from these the deaths of boys and youths, miscarriages of pregnant women, the destruction of birds, famine, thunder, and lightning with such force of wind that they may uproot trees. Item: wantonness, and license for fornication, and the downfall of upright men. If in Cancer: they indicate a multitude of locusts descending and devastating the harvest, and thus a scarcity of grain and other crops, either eaten away by them, or indeed by worms produced in them: Item they foretell wars, discords, drownings, plunderings, famine, and very many other evils. If in Leo: they denote the destruction of buildings, the ravaging of wolves, and from these many hindrances among men, the production of worms in crops, madness in dogs, ailments of the eyes, and wars. If in Virgo: they signify many labors, pains, and fevers, tremors, ulcers, and pustules, especially in the female sex, in which miscarriages will be greatly to be feared. Item, the vexations of good men, and the license of the wicked to live as they please. If in Libra: they denote scarcity of rain, the rule of the winds, the drying up of rivers, scarcity of crops, and horrible earthquakes. Item the death of Princes, slaughter, betrayals, and other such things. If in Scorpio: they portend a multitude of wars among Princes and men, contentions, and revolutions of kingdoms. Moreover, labors and illnesses in every kind of men: dangers for those in labor, pains, and affections of the parts serving generation, and the sure corruption of the fruits of the earth. If in Capricorn: they foretell great license in living among depraved men, fornications, adulteries, wars, quarrels, poisons administered to princes. Item, the severity of winter, hail, snow; whence the dearness and scarcity of crops. If in Aquarius: they bring popular sicknesses, wars lasting a long time; darkness of the air with the rule of winds, thunder, and storms. Moreover, a mournful plague, and the unexpected death of the greatest men especially. If finally they have appeared in Pisces, they indicate the wretched condition of the people, wars of extreme cruelty, rebellions, and betrayals.
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400 LEXICON item periculosa erit nauigatio, & detrimentum patietur ars piscatoria. < 141> Ad hæc aduersendum, quod si in Oriente fuerit appari- tio, res indicata velocius accides, si verò in Occidente se- riùs. Loca autem quæ maximè his incommodis laborabunt sunt in quæ cauda hænomeni inclinabit, vel sanè subiecta signis, in quibus fieri conspicuum. Hæc ex Iunctino, cui est è cæteri scriptores de Comenis astipulantur. Vincentius tamen Guinitius è Societate IESV, in Oratione habita de Comenio anni 1648. viso in Romano hemisphærio conten- dit, eos non minus felicitatem quam infelicitatem afferre, cum tamen homines ob inditum à natura genium infor- tunia magis obseruent, quam prospera. Cæterum Ricciolus in Almagesto nouo lib. 8. sect. 1. cap 1. post longam huius rei ventilationem concludit, quod si Cometæ elementates sint, vniuersaliter, & ex natura sua habent obnunciare in- signem aliquam rerum mutationem in natura sublunari factam, cuius effectus nondum desierint, sed haud ita mul- tò post sint prodieri, iuxta dispositionem materiæ, & con- cursum aliarum causarum. Si verò cælestes sint, & ex ma- teria ætherea producti, à Deo ordinatos esse tum vt morta- les oculos ad cælum erigant; tum vt inde magnum aliquid expectent, vel in se, vel in suis regionibus quasi Dei lin- gua sint: maximè verò in tis quibus fuerint perpendicula- res, aut multum in horoscopo morabuntur. < 144> PVT SATIO apud Astronomos est commissio dispositionis suæ, quam facit Planeta alteri ad quem proijcit radium, aut in eius dignitatibus reperitur: tunc enim communicat esse suum, ac naturam ipsi, quem pulsat. Sicut econira Re- ceptio dicitur acceptatio, quam facit planeta pulsatus dispo- sitionis ab alio sibi commissæ. Ea autem est in triplici dif- ferentia, provt aduersis Abraham Auenarre in suo intro- ductorio; Virtutis, Potestatis, & Naturæ. Pulsatio virtutis est cum planeta fuerit in eius Domino, Exaltatione, Tripli- cite, aut Termino, & coniungatur alteri planetæ, aut il- lum respiciat: tunc enim suam virtutem dicetur alteri com- mittere. Pulsatio potestatis est cum planeta alium respi- cit radio perfectæ amicitiæ, qualis est Trinus, aut imper- fectæ, qualis est sextilis; tunc enim inter ipsos erit perfecta commixtio, & potestatis pulsatio. Pulsatio naturæ pluribus etiam modis sit. Primò cum planeta jungitur alteri planetæ existenti in suo domicilio, vel exaltatione. Secundò cum jungitur alteri de sua conditione, & natura, vt si masculus masculo, diurnus copuletur diutno, ac nocturnus noctu-
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400 LEXICON that item, navigation will be perilous, and the fishing trade will suffer loss. < 141> To this it must be added that, if the apparition be in the East, the indicated event will occur more quickly; if in the West, more slowly. The places that will suffer most from these inconveniences are those toward which the tail of the comet inclines, or indeed those lying beneath the signs in which it becomes visible. This is from Iunctinus, to whom, moreover, the other writers on comets agree. Vincentius Guinitius, however, of the Society of JESUS, in a discourse delivered on the comet seen in the Roman hemisphere in the year 1648, maintains that they bring not less happiness than misfortune; yet men, by a tendency implanted by nature, observe misfortunes more than prosperity. In any case, Ricciolus, in the New Almagest, book 8, section 1, chapter 1, after a long discussion of this matter, concludes that, if comets are elemental, they universally, and by their nature, have the function of foretelling some remarkable change in things brought about in the sublunary world, the effects of which have not yet ceased, but have appeared not long after, according to the disposition of the matter and the concurrence of other causes. But if they are celestial, and produced from ethereal matter, they were ordained by God, first, that mortals might lift their eyes to heaven; and secondly, that they might expect something great from it, either for themselves or in their regions, as though they were the language of God: especially, however, in those to which they are perpendicular, or where they will remain for a long time in the horoscope. < 144> PVT SATIO among astronomers is the transmission of its disposition, which one planet makes to another toward which it casts a ray, or in whose dignities it is found: for then it communicates its being and nature to the one it strikes. Likewise Reception is called the acceptance which the struck planet makes of the disposition entrusted to it by another. This, however, is of three kinds, as Abraham Auenarre states in his Introductory Work: of Virtue, Power, and Nature. The pulsation of virtue is when a planet is in its domicile, exaltation, triplicity, or term, and is conjoined with another planet, or regards it; for then it is said to entrust its virtue to the other. The pulsation of power is when a planet regards another by a ray of perfect friendship, such as a trine, or of imperfect friendship, such as a sextile; for then there will be among them a perfect blending, and a pulsation of power. The pulsation of nature also occurs in several ways. First, when a planet is joined to another planet existing in its own domicile or exaltation. Second, when it is joined to another of its own condition and nature, as if masculine be coupled with masculine, diurnal with diurnal, and nocturnal with noctur-
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LEXICON mus, tunc habebimus corpus solidum omnis dimensionis capax. Et hæc sunt tria genera quanti, secundum trinam dimensionem, circa quæ voluitur omnis Geometriæ labor, & speculatio. Porrò punctum, etsi quaptum non sit, nihilominus eius prima, & potissima est consideratio in Geometria: sine enim ipso quantitas vlla percipi haud posset, eo prorsus pacto, ac numerus sine vnitate, cum tamen vnitas numerum non constituat, sed tamen in numerosit eius initium, eius & finis. Vnde anguli omnes in figuris tam planis, quam solidis, quæ tamen angulos habeant, & circulares non sint in puncta necessariò terminari concipendi sunt. <144> PYTEVS ab aliquibus diciur in exlosidus, quod aliàs Ara, Lar, Thuribulum appellatur. Vide sub his dictionibus. <145> PYTEALE: GRADVS, vide in V. Gradus. <146> PYRAM s apud Geometras est figura solida, quæ definitur ab Euclide lib.11. propos. 2. esse eam, quæ sub p'uribus planis constata, ab uno plano, ad unum punctum constituitur. Ex qua definitione intelligimus figuram pyramidalem ex pluribus planis ad minus tribus in longum protractis constate; quæ enim uno vel duobus planis constituitur, non pyramis, sed superficies triangularis existat necesso est. Item omnia plana, quæ pyramidem constituunt, triangularia debere esse, excepta tamen basi, vel plano, à quo omnia plana pyramidem efformantia, incipiunt, & in idem punctum desinunt, quod vel triangulum, vel quadrangulum, vel pentagonum, vel exagonum, &c. potest esse: & quale est istud planum seu basis, talis tota pyramidalis figura denominabitur; tot enim triangulis quælibet pyramis construitur, & finitur, quod angulos, & latera planum dictum habet. <147> Porrò omne corpus seu opacum, seu luminosum, lumen suum, vel vmbram in aliud transmittit in formam pyramidalem, vt præ aliis notat Vitellio in Perspectiua lib.2. nisi quod corpus luminosum ita transmittit, vt vertex pyramidis efformatæ sit in puncto eiusdem corporis, vnde prosilit lumen, & basis cadat in superficiem corporis illuminati: corpus autem opacum ita vmbram suam transmittir, vt basis pyramidis efformatæ sit in superficie ipsius corporis vmbram suam diffundentis, & vertex in puncto corporis cuiuscumque ad quod vmbra protenditur. Plura apud ipsum Vitellionem, nec non apud Clauium, in Commentar. ad Elem. Euclidis.
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LEXICON mus, then we shall have a solid body of every dimension capable. And these are the three kinds of quantity, according to the threefold dimension, around which all the labor and speculation of Geometry revolves. Moreover, although a point is not a quantum, nevertheless its first and principal consideration is in Geometry: for without it no quantity at all could be perceived, in just the same way as number without unity, although unity does not constitute number, yet in number it is its beginning and its end. Wherefore all angles in figures, both plane and solid, which, however, have angles and are not circular, are to be conceived as necessarily terminating in points. <144> PYTEVS is said by some to be in exlosidus, which is otherwise called Ara, Lar, Thuribulum. See under these words. <145> PYTEALE: GRADVS, see in V. Gradus. <146> PYRAMS among geometers is a solid figure, which is defined by Euclid, Book XI, proposition 2, as that which is made up of several planes, and is constituted from one plane to one point. From this definition we understand that a pyramidal figure consists of several planes, at least three, drawn out in length; for that which is constituted by one or two planes must necessarily be not a pyramid, but a triangular surface. Likewise all planes which make up a pyramid ought to be triangular, except for the base, or plane from which all the planes forming the pyramid begin and end at the same point, which may be either a triangle, or quadrilateral, or pentagon, or hexagon, etc.: and such as that plane or base is, such the whole pyramidal figure will be named; for every pyramid is constructed and finished from so many triangles as the plane said to have angles and sides. <147> Moreover every body, whether opaque or luminous, transmits its light or shadow into another in a pyramidal form, as Vitellio especially notes in Perspectiva, Book 2; except that a luminous body transmits it in such a way that the apex of the formed pyramid is in the point of that same body from which the light springs, and the base falls upon the surface of the illuminated body: but an opaque body transmits its shadow in such a way that the base of the formed pyramid is on the surface of the body itself spreading its shadow, and the apex at the point of whatever body toward which the shadow is extended. More on this in Vitellio himself, as well as in Clavius, in the Commentaries on Euclid's Elements.
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MATHEMATICVM. 401 PYROIS Græcè dicitur Martis astrum ab ignea natura, eo- lore, & fulgore dictum. Vide in V. Mars. PYTHETES. Vide Pithetes. 149 PYTHON ab aliquibus dicitur serpens fidus in cælo ad 150 manus Ophiuci. Nomen à fabulis derivatum à Pythone quodam serpente ex putredine terræ producto, quem postea ab Apolline telis confossum, cælo inuexerunt, atque in eius figuram stellas quasdam veneficæ naturæ sapientes Astronomi colligarunt. Q QVADRA Græcè Plinthis, apud Geometras dicitur quodlibet instrumentum planum in quadratam figuram abiens: vnde ab aliis ex figura quam referebat Quadra appellabatur mensa illa parua, & portatilis, super qua carnes & cibaria in partes tribui consueuerunt: item &c panes olim in quadratam figuram efformatos, quadras dicebant: vnde est illud Virgilij 7. Æneid. Patulis, nec parcere quadris. Nune tamen pressius audit Quadra instrumentum Mathematicum rectangulum, quo quælibet figura plana in quatuor partes secatur, ex ea constituens quadratum, eubum vnde, & QVADRANTAL, & Cubus, & Quadrata figura dicitur quæ omni ex parte sit quadra, seu quæ sex planis quadrilateris, & rectangulis constat, & in quamcumque pariem incubuerit, semper æqualis in omni dimensione erit, & immotam seruans stabilitatem, quales sunt taxili, & resseræ, quibus in alueolo luditur. Quadrantal etiam dicitur mensuræ genus, de qua nihil ad nos. QVADRANGVLVS dicitur figura Geometria quatuor angulis constans, vr Parallelogrammum, Rhombus, Romboides, &c. de quibus omnibus suo loco. QVADRANS GEOMETRICVS est instrumentum Mathematicum, quod iure inter omnia Mathematica instrumenta principatum obtinet: siquidem eius ope omnia ferè Geometriæ, Astronomiæ, aliarumque Mathematicarum disciplinarum operationes, & complentur, & facilè percipiuntur: sed præcipuè deseruit ad inquirendam poli elevationem, Solis, aliorumque siderum, tam de die, quam de nocte altitudinem supra horizontem, declinatio- nem, ab inuicem distantiam, locum in Zodiaco, aliaque permulta, quibus tota Astronomia, ac Geometria ad praxim reducitur, & completur. Est igitur Quadrans Geome-
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MATHEMATICVM. 401 PYROIS is called in Greek the star of Mars, from its fiery nature, color, and brightness. See under V. Mars. PYTHETES. See Pithetes. 149 PYTHON is called by some the faithful serpent in the sky near the hands of Ophiuchus. The name is derived from the fables, from a certain serpent Python produced from the corruption of the earth, which later, having been pierced by Apollo with arrows, they placed in the heavens, and to its figure certain stars of a poisonous nature were skillfully joined by Astronomers. Q QVADRA in Greek, Plinthis, among Geometers, is called any flat instrument taking on a square figure: whence, by others, from the shape it bore, that little and portable table was called Quadra, upon which meats and provisions were wont to be divided into portions: also, etc., breads formerly shaped into a square figure were called quadras; whence is that line of Virgil, Aen. 7, “Patulis, nec parcere quadris.” Now, however, Quadra more strictly means a Mathematical instrument, rectangular, by which any plane figure is cut into four parts, thereby constituting from it a square, a cube, whence also QVADRANTAL, and Cube, and a square figure is said to be that which is square on every side, or which consists of six quadrilateral and rectangular planes, and in whatever direction it may lie, will always be equal in every dimension, and preserving unmoved stability, such as are dice and the tables used in games played in a small board. Quadrantal is also said of a certain kind of measure, concerning which nothing is for us. QVADRANGVLVS is said of a geometric figure consisting of four angles, as Parallelogram, Rhombus, Romboides, etc., of all which in their proper place. QVADRANS GEOMETRICVS is a Mathematical instrument, which by right holds the chief place among all Mathematical instruments: for by its aid nearly all the operations of Geometry, Astronomy, and the other Mathematical disciplines are both carried out and easily understood: but it especially serves to inquire into the elevation of the pole, the altitude of the Sun and other stars above the horizon, both by day and by night, their declination, their distance from one another, their place in the Zodiac, and many other things, by which the whole of Astronomy and Geometry are reduced to practice and completed. Therefore the Geometric Quadrant is
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tricus corpus solidum, & planum quartam partem circuli referens, atque in area sua descriptos continens per gyrum grad. 90. qui omnes per lineam rectam conveniunt in puncto, quod incidit in eius aangulum, & est centrum totius circuli, & quadrantis, & ex hoc centro dependet perpendiculum aliquod ex filo, quo mediante in limbo, gradus, eorumqueque fractiones metimur. Ad vnum autem laterum eius affixa sunt duo pinnacidia, seu spicillæ, cum foraminibus rese per lineam rectam respicientibus, non quidem amplis, sed taliter fabricatis, vi per ea res quidem mensurabilis probè conspici queat, & oculus nimio astri fulgore non præstringatur, sed rectà in ipsum, innoxieque possit intendere ipso quidem in ea quadrantis parte, quæ limbo sinitur constituto, astro verò, vel alia quauis remensurabili ex aduersa, iuavi ex centro quadrantis radium suum in oculum possit proicere. 5. Eius vsus hic est: Visa Solis de die, vel Lunæ aut alterius insignis stella de nocte altiudine supra terram; si vis præcisè indagare, quanta sit eius elevatio supra terram, declinatio ab æquatore, &c. vel etiam quota sit hora diei vel noctis, id per quadrantem duplici via assequi poteris. Primò per distantiam eius à vertice in cordis subiensis. Secundò per adminiculum sphæræ, quam præstat in hoc negotio eligere solidam. Nam posito, quod tantum eleuetur Sol, siue aliud Astrum supra horizontem, quantum abscindit in gradibus perpendiculi filum ex cento quadrantis pendens, computa gradus illos, & transfer ad sphæram collocatam ad elevationem poli suprà tuum horizonte, atque ibi in tali distantia graduum ex Meridiano computandorum constituere debes solem, aut aliud Astrum in sphæra, in quanta ipsum in cælo esse ex quadrante inuestigasti. At quorsum, inquies, metiri potero talem aliudinem, atque ab quadrante ad sphæram meam transferre? Sanè id facillimè poteris. Accipe igitur circinum, atque in sphæra tot gradus in æquatore enumera (ipse enim, vt alibi dictum est, totius sphæræ, totiusque motus regula est, & mensura tot inquam gradus enumera & circino comprehende, quot gradus siue ab horizonte, siue à vertice elongatur illa stella, quam per quadrantem vidisti: deinde circino inuariato pone pedem eius in contactu horizontis, & alio sursum è regione versicis elevato, tandiu sphæram voluas, quandiu locus solis eo die eadar subtus pedem alterum circini, & sic habebis elevationem Solis. Quo præstito revertere cum Sole, & constitue eum ad contactum horizontis, ac si tunc oriretur, & nota gradum
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A solid and flat quadrilateral body, representing the fourth part of a circle, and containing within its area around the circumference 90 degrees, all of which converge by a straight line to a point that falls upon its angle, and is the center of the whole circle and quadrant; and from this center hangs a certain plumb line by a thread, by means of which we measure on the limb the degrees and their fractions. To one of its sides are attached two little pinnacles, or sights, with holes looking through along a straight line, not indeed wide, but so made that the object to be measured may be clearly seen through them, and the eye may not be dazzled by the excessive brilliance of a star, but may safely look straight at it, the quadrant itself being in that part where the limb is fixed, while the star, or any other object to be measured, opposite it, may readily cast its rays from the center of the quadrant into the eye. 5. Its use is this: when the altitude of the Sun by day, or of the Moon or some other notable star by night, is observed above the earth; if you wish to determine precisely how great its elevation above the earth is, its declination from the equator, etc., or even what hour it is by day or by night, you can achieve this by the quadrant in two ways. First, by the distance from the zenith, measured in the suspended cord. Second, by the aid of the sphere, which in this matter it is best to choose as a solid one. For when it is given that the Sun, or another star, is elevated above the horizon by as many degrees as the plumb line hanging from the center of the quadrant cuts off on the degrees, count those degrees and transfer them to the sphere set according to the elevation of the pole above your horizon; and there, at that distance of degrees to be reckoned from the Meridian, you must place the Sun, or the other star, on the sphere, at the same distance at which you have found it to be in the heavens by means of the quadrant. But, you will ask, how shall I be able to measure such an altitude and transfer it from the quadrant to my sphere? Indeed, you can do this very easily. Take a compass, and on the sphere count as many degrees on the equator (for that, as has been said elsewhere, is the rule and measure of the whole sphere and of the whole motion), count, I say, and include with the compass as many degrees as the star you saw with the quadrant is distant either from the horizon or from the zenith; then, keeping the compass unchanged, place one foot in contact with the horizon, and with the other raised upward opposite the zenith, turn the sphere until the place of the Sun on that day comes beneath the other foot of the compass, and thus you will have the elevation of the Sun. When this has been done, return with the Sun, and place it at the contact of the horizon, as if it were then rising, and note the degree
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LEXICON hominis constituto, Fortè quia cum prius Apheta suum quadratum impunè transgredi poterat, saltem sine abscissione, & progredi illæsus vsque ad oppositionem, & eo amplius; vt euenit, & concessum fuit Patriarchis antiquis; postmodum Deus constituit vt prima occursatio Aphetæ ad Anaretam, nempe ad suum quadratum, vitam abscinderet. Sed de hæc re iterum redibit sermo in V. Trimorion. 9. QUADRATRA CIRCIT, quæ à Græcis dicitur Tetragonismus, nil aliud est, vt ipsum nominis eymon præsefert, quam circulum quadratum red lere; hoc est cuilibet circulo exhibêre quadratum æquale illi ex amussi respondens. Quod vti facile est intelligere, ità difficile admodum facto exequi, ac pethicere, & hactenus quod sciam à nullo est præstitum, licet quamplurimi, inque sapientissimi Mathematici, ac Principes ipsi pluribus annis in hoc negotio detenti, vsque ad defectionem spiritus desudarint. Etenim Circulum quadrare olim conati sunt apud Veteres, Antiphon, Bryso, & Hyppocrates Chius, quorum meminit Arist. 1. Physic. text. 11. & 1 Poster. text. 23. & 1. Elench cap. 10. Apud Recensiores verò Orontius Finçus, Campanus, & Nicolaus Cardinalis Cusanus, qui omnes Circuli Quadraturam inuenisse se iactant: & Cardinalis quidé Cusanus, scripto ad Georgium Peurbachium libro, duplicem à se inuentam profert: Prima autem in eo consistebat, vt, si ex semidiametro Circuli dati, & chorda quadrantis eiusdem, directè coniunctis, diameter alteri circulo constitueretur, triangulus æquilaterus posteriori circulo inscriptus, priori circulo Isoperimeter foret. Alia circuli quadrandi ratio ab Cusano excogitata, hæc erat. Si incirculo ductis duabus ad angulos rectos diametris una hinc inde producatur, & alteri ab uno extremo sic accommodetur sublensa trientis circuli, vt facto centro, qua in alia diametri parte desinit, circumducatur, & transsens per dictum extremum, secet hinc inde productam diametrum, recta intercepta his sectionibus erit circuli semicircumferentia æqualis. Verum hæc quadrandi circuli ratio, de qua controuertebatur, non erat. Nam circuli quadratura non consistit in eo quod conuerti debeant lineæ arcuales in rectas, aut econtrà: sed quod area circuli, seu superficies illa circularis, æqualis omninò sit, neque excedat neque excedatur ab area superficies quadratæ: iiavt Circulum quadrare aliud planè non sit, quàm reperire aream alicuius quadrati parem, & æqualem areæ cuiuspiam circuli, vt proinde areæ veriusque figuræ sint æque capaces. Non enim id sic intelligi debet, vt areæ istæ inter se congruant, & planè coaptent
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LEXICON of the human constitution, perhaps because formerly the Apheta could pass his square with impunity, at least without cutting off, and proceed unharmed as far as the opposition, and even beyond; as happened, and was granted to the ancient Patriarchs; later God ordained that the first encounter of the Apheta with the Anareta, namely with his square, should cut off life. But concerning this matter there will be further discussion again in V. Trimorion. 9. SQUARING THE CIRCLE, which among the Greeks is called Tetragonismus, is nothing else, as the very etymon of the name suggests, than to square the circle; that is, to provide any circle with a square equal to it, corresponding by exact measure. This, while easy to understand, is exceedingly difficult in practice to carry out and accomplish, and hitherto, so far as I know, it has not been achieved by anyone, although very many, and among them the wisest Mathematicians, and even Princes themselves, having been occupied for many years in this business, have labored until failure of spirit. For the squaring of the circle was once attempted among the Ancients by Antiphon, Bryson, and Hippocrates of Chios, whom Aristotle mentions in Phys. 1, text. 11, and 1 Poster. text. 23, and 1 Elench. cap. 10. Among the more recent authors, however, Orontius Finaeus, Campanus, and Nicolaus Cardinal Cusanus, all of whom boast that they found the Squaring of the Circle; and Cardinal Cusanus indeed, in a book written to Georg Peurbachius, presents two inventions by him: the first consisted in this, that if from the semidiameter of a given circle, and the chord of the quadrant of the same, directly joined, a diameter were constructed for another circle, then the triangle inscribed in the latter circle, equilateral, would be isoperimetric to the former circle. Another method of squaring the circle devised by Cusanus was this. If, in a circle, two diameters are drawn at right angles, and one of them is extended on either side, and to the other, from one end, is thus applied a raised arc of a third of a circle, so that, a center being made, from the point where the other diameter ends, it is carried around, and passing through the said end, cuts the extended diameter on either side, the straight line enclosed by these sections will be equal to the semicircumference of the circle. But this method of squaring the circle, about which there was controversy, was not the true one. For the squaring of the circle does not consist in this, that arcual lines must be turned into straight ones, or conversely: but that the area of the circle, or that circular surface, must be exactly equal, neither exceeding nor being exceeded by the area of a square surface: so that to square the circle is nothing else than to find the area of some square equal and equivalent to the area of some circle, so that accordingly the areas and more properly the figures may be equally capable. For it must not thus be understood, as though those areas were to coincide with one another and fit together exactly
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MATHEMATICVM. 411 mas qualitates vocant, caliditas, & frigiditas, humiditas & siccitas, quoniam primæ sunt, quæ per omnem substantiam materialem transcendunt, in omnibus vniuersaliter reperiuntur, & sunt veluti primi fontes, & radices, vnde cæteræ exsurgant, & quibus mediis operentur. Quandoquidem ex earum contrarietate, qua inuicem se expellunt, combinatione disparatarum, quase mutuò fouent, eiusdem quoad certos gradus intensione, ac remissione, mira hæc vniuersarum rerum consurgit varietas, conformitas, & differitas, passio, & resistentia, mixtio, & alterario, generatio, & corruptio, quæ alternantibus veluti modulis harmoniam quamdam efformantes, mundum istum exornant. Ex his, in primis rerum seminibus, hoc est elemenis, binæ, exque non contrariæ qualitates insunt, quarum vna actiua est, qua in reliqua possit vnumquodque agere, altera passiua, qua illis agentibus possit cedere, sicque, vt ait Arist. 2. de generat. text. 22. inter elementa sit concordia secundum vnam qualitatem, vt conseruenrur, & discordia secundum alteram, vt ex eorum elementorum pugna, & corruptione mixta omnia consurgant: Itaque igni conuenit calor, & siccitas, aëri humiditas & calor, Aq[ui]næ frigiditas & humiditas; Tetra siccitas, & frigiditas: itavt ex duabus qualitatibus, quæ in singulis elemenis reperiuntur illa dicatur vnicuique magis propria, quæ in eo vincit, & in certo illud genere constituit, illa minus propria, quæ priori subseruir, & in suo esse dat conseruari. Sic igni calor est propius, qui illum maximè facit actuum, siccitas autem in suo calore conseruat: Aëri maximè conuenit humor, cum sit passibilis, & in aliud facilè transmutabilis, cui præstò est calor, vt possit raresieri: frigiditas propria est aquæ; quæ per humorem sese magis insinuat: Tandem siccitas magis conuenit terræ quæ à frigore habet, quod sit difficile terminabilis, quatenus subiectum densat, ac facit difficile terminabile. Hinc quia calor & frigus, quatenus habent vim vniendi, & segregandi, seu reddendi subiectum faciè, vel difficile terminabile sunt qualitates actiæ, econtra siccitas, & humiditas dicuntur passiæ quia ipsis conuenit magis pati, quam agere itavt faciant, vt subiectum facile, vel difficile terminetur, cuiusmodi est in lapide cui ob siccitatem difficile est alienam formam recipere, & viceuersa in ceta, quæ ob humorem sit facilis ad quamcumque figuram recipiendam. Cæterum non ideò istæ passiæ dicuntur, quia nullam habeant activitatem, nam & ipsæ valent eiusdem generis qualitates in aliis subiectis producere, sed ideò dicun- C e iiij
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MATHEMATICVM. 411 those qualities they call calority and frigidity, humidity and dryness, since they are the first things that transcend through every material substance, are found universally in all things, and are as it were the first sources and roots from which the others arise, and by which means they operate. For from their contrariety, whereby they drive one another out, from the combination of dissimilar things, which mutually foster one another, from the same thing in certain degrees of tension and remission, there arises this marvelous variety, conformity, and difference of all things, passion and resistance, mixture and alteration, generation and corruption, which, as though alternating in modes, forming a kind of harmony, adorn this world. From these, in the first seeds of things, that is, in the elements, there are two non-contrary qualities, of which one is active, whereby each thing may act upon the other, the other passive, whereby it may yield to those acting upon it, and thus, as Aristotle says, 2 De Generatione, text. 22, there is agreement among the elements according to one quality, so that they may be preserved, and discord according to the other, so that from the struggle and corruption of those elements all mixed things may arise: thus fire is suited to heat and dryness, air to humidity and heat, water to frigidity and humidity; earth to dryness and frigidity: so that from the two qualities found in each element, that is called more proper to each one which prevails in it and constitutes it in a certain kind, the other less proper, which serves the former and preserves it in its being. Thus heat is more proper to fire, which makes it most active, while dryness preserves it in its heat: to air most of all belongs moisture, since it is passible and easily changed into another thing, to which heat is present, so that it may become rarefied: frigidity is proper to water, which by means of moisture insinuates itself more readily: lastly dryness more befits earth, which has from cold that it is difficult to be bounded, insofar as it densifies the subject and makes it difficult to be bounded. Hence, because heat and cold, insofar as they have the power of uniting and separating, or of making the subject easy or difficult to bound, are active qualities, conversely dryness and humidity are called passive because it befits them rather to undergo than to act, so that they make the subject easy or difficult to be bounded, such as is the case in stone, which because of its dryness is difficult to receive another form, and vice versa in wax, which because of its moisture is easy to receive any shape whatever. Moreover, they are not called passive for this reason because they have no activity at all, for they too are able to produce qualities of the same kind in other subjects, but they are called so C e iiij
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412 LEXICON tur, quia subiectum magis aptum faciunt ad recipiendum, quam ad agendum. Sic ignis magis actiùs est, quam aër, aqua magis, quam tellus; rursus magis passiuus aër, quam aqua, tellus, quam ignis, quia profecto in iis respectu aliorum vincunt qualitates actiuæ. 12. Porrò ex commixtione harum primarum qualitatum, oriuntur in mixtis alia quas secundas vocant, suntque præsertim illæ quindecim à Galeno enumeratæ. de vsu partium par. 9. & 1. de fac. natural. cap. 6. & sunt Mollities ac durities, lentor & friabilitas, raritas & densitas, lenitas &c asperitas, leuitas & grauitas, crassitudo & tenuitas, item diuersitates odorum, colorum, & saporum, quorum quilibet, vt notum est, continet varias qualitatum species, & gradus, ex quibus diuersitas illa conturgit: omnes tamen referuntur ad quauor illas primas tanquam ad prima mutationum initia, quæ in hoc mundo Elementari fiunt. 13. An autem qualitates elementares eiusdem rationis sint, ac cælestes, magnum dissidium est inter Philosophos, Astronomosque. Affirmant Conimbricenses 1. de Generat. cap. 3 quæst. eo quia experientia ipsa commonstrat eosdem prorsus effectus progigni ab Calore cælesti, elementari, ac vitali. Similiter vbi in planetis colores consimiles his nostris videmus, consimiles etiam effectus eosdem promere experimur. Negant alij communiter, & admittunt lolum eas habere aliqualem conuenientiam, ac sympathiam. Quinimò & Tius qualitates mixtorum non esse elementares, sed è cælo derivatas affirmat, vt nos fusè diximus in V. Mixta Fernelius, Argenterius, & alij admittunt in mixtis huiusmodi qualitates, quas vocant occultas, quæ quoniam supergrediuntur qualitates elementorum, existimant nullo modo esse ab illis participatas, nec posse ad illas referri, non tamen dicunt à cæcis derivatas, sed esse qualitates totius substantiæ quatenus ipsa per se immediatè & nullo interposito instrumento illam agendi seu operandi potentiam sortiatur, & ideò dicunt occultas, quia nullarum qualitatum auxilio quæ sensibus subiectæ sint manifestari possunt, quippe ea ratione qua substâcia ipsa sensibus, & intellectui est occulta, eadem has qualitates occultas, & reconditas dici putâr. 14. Et sanè, vt certa ab incertis segregemus, certum est mixta omnia, si puris qualitatibus elementaribus constarent, eas longè remissiores debere esse, quam in ipsis elementis, quippe eas & ab elementis derivatas haberent, & qualitatibus contrariis oppugnatas, vnde & infirmiores, quod non est in elementis puris, qua ratione Arist. de sensu
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they do so because they make the subject more fit for receiving than for acting. Thus fire is more active than air, water more than earth; and again air is more passive than water, earth than fire, because certainly in them, with respect to the others, active qualities prevail. 12. Moreover, from the mingling of these primary qualities there arise in mixed bodies other qualities, which are called secondary; and especially those fifteen enumerated by Galen, De usu partium , part 9, and De fac. natural. cap. 6, namely softness and hardness, stickiness and friability, rarity and density, smoothness, etc., and roughness, lightness and heaviness, thickness and thinness; likewise the differences of odors, colors, and tastes, each of which, as is well known, contains various species and degrees of qualities, from which that diversity arises. Yet all are referred back to those four primary qualities, as to the first beginnings of the changes that take place in this elemental world. 13. But whether elemental qualities are of the same nature as celestial qualities is a great point of disagreement among philosophers and astronomers. The Conimbricenses affirm it, 1. de Generat. cap. 3, because experience itself shows that exactly the same effects are produced by celestial, elemental, and vital heat. Likewise, where we see in the planets colors similar to our own, we likewise experience that they produce similar effects. Others commonly deny it, and admit only that they have some likeness and sympathy. Nay, Tius also affirms that the qualities of mixed bodies are not elemental, but derived from heaven, as we have explained at length in V. Mixta . Fernelius, Argenterius, and others admit in mixed bodies such qualities, which they call occult, and since these surpass the qualities of the elements, they think that they are in no way participated in from them, nor can they be referred to them. Yet they do not say that they are derived from the heavens, but that they are qualities of the whole substance, insofar as it immediately and by itself, and with no intermediary instrument, acquires the power of acting or operating; and therefore they call them occult, because they cannot be manifested with the aid of any qualities subject to the senses, since in the same way that substance itself is hidden from the senses and the intellect, they think these qualities are called hidden and concealed. 14. And indeed, to distinguish the certain from the uncertain, it is certain that if all mixed things consisted of pure elemental qualities, those qualities ought to be far more attenuated than in the elements themselves, since they would both derive from the elements and be opposed by contrary qualities, and thus be weaker, which is not the case in the pure elements; for which reason Aristotle, De sensu
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CAP. 4. docuit sola mixta perfecta cedere in viuentium alimentum, neque in hoc negotio quicquam posse pura elementa conferre, quorum qualitates, vipote intensores, non possunt à viuentium qualitatibus alterari, sieque vinci, &c tranire in substantiam aliti, vt nos etiam alibi adnotamus. Si igitur omnia mixta constarent ex qualitatibus elementorum, vel sanè iis solis, sequeretur, nullum esse mixtum potentius elementis: At enim videmus multa longè potentioribus qualitatibus pollere, multa longè diuersis, quæ non ad illas primas reduci possunt. Sic videmus herculeum lapidem attrahere ferrum, non equidem per vllam calidam; aut frigidam qualitatem, quia nunquam experientia visum fuit calida vel frigida tanta vi ferrum, aut aliud quid adeò ponderosum attrahere; sed nec per qualitates secundas, tum quia istæ ortum habent à primis, tum etiam quia nemo vidit vnquam rarum vel densum, gravé, vel leue, crassum tenue, durum vel molle simile quid præstare. Pari modo electrum allicere paleas, marinum leporem pulmonem, Cantharides vesicam exulcerare, non alias partes, præcipuè verò iccur mollius, & propinquius: Torpedinem manum piscatoris stupore afficere: Echeneidem pisciculum parum magnam nauem turgidis velis volantem firmare, &c. Quis igitur mentis compos existimet admirandas has operationes fieri à caliditate, frigiditate, siccitate, aut humiditate, vel à cæteris consequentibus qualitatibus? Igitur vel ab ipsa rerum substantia, quæ immediat habeat hos miros effectus progi- gnere, vel sanè à superiori, & occulta quadam qualitate, quæ non pateat sensibus prodeant necesse est admirandæ huiusmodi virtutes. Quod autem non ab substantia rerum immediatè prodeant; præter communem ferè omnium Philosophorum, Theologorumque consensum dicentium nullam substantiam immediatè agere, sed mediis suis potentiis tanquam proportionalibus instrumentis; vt præ cæteris evidentissimè probar D. Thomas 1. part. quæst. 77. art. 1. & in 1. sentent. dist. 3. quæst. 4. art 2 id manifestè suadet ratio & pluribus euincit experientia. Quandoquidem potentiæ operatrices à Philosopho collocantur in prædicamento qualitatis, quod genus differt natura & essentia à substantia: Idque ex eo quod actio ex natura sua petit tum distinctionem agentis à suo termino, tum aliquam dissimilitudinem secundum speciem, inter subiectum & agens, ad hoc vt istud possit suum effectum in illud inducere: nemo enim agit in sibi simile, vt idem Arist, docet 1. Phys. &c 1. de Gener. cap. 9. text. 50. &
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CHAP. 4. It taught that only mixed bodies, composed of the elements, are perfect for becoming the nourishment of living things, and that in this business the pure elements can contribute nothing, since their qualities, being more intense, cannot be altered by the qualities of living things, and thus conquered, etc., nor pass into the substance of the thing nourished, as we also note elsewhere. If therefore all mixed bodies were made up of the qualities of the elements, or indeed by these alone, it would follow that no mixed body is more powerful than the elements. But we see many things endowed with powers far stronger, many far different, which cannot be reduced to those first qualities. Thus we see the Heraclean stone attract iron, not indeed by any hot or cold quality, because experience has never seen iron, or anything else so heavy, attracted by so great a force either by heat or by cold; but neither by the secondary qualities, both because these arise from the primary ones, and also because no one has ever seen rarity or density, heaviness or lightness, thickness or thinness, hardness or softness, do anything similar. In the same way, amber draws straws, the marine hare affects the lung, cantharides ulcerate the bladder, not the other parts, especially however the softer and nearer liver; the torpedo fish strikes the hand of the fisherman with numbness; the echeneis, a small fish, holds fast a ship flying with swollen sails, etc. Who then, if he is of sound mind, would think that these wonderful operations are brought about by heat, cold, dryness, or moisture, or by the other consequent qualities? Therefore these admirable powers must either arise from the very substance of things, which immediately has the capacity to produce these wondrous effects, or certainly from some higher and hidden quality that does not lie open to the senses. But that they do not proceed immediately from the substance of things; besides the common consensus of almost all philosophers and theologians, who say that no substance acts immediately, but through its own powers as through proportional instruments; as, above all, St. Thomas most evidently proves, 1st part, q. 77, art. 1, and in 1 Sent., dist. 3, q. 4, art. 2, reason plainly suggests this and experience confirms it in many ways. For the operative powers are placed by the Philosopher in the category of quality, a genus which differs in nature and essence from substance: and this because action by its nature requires both a distinction of agent from its term, and some dissimilarity according to species between subject and agent, so that the latter may be able to bring its effect into the former. For no one acts upon what is like himself, as the same Aristotle teaches, Phys. 1 and Gen. 1, ch. 9, text 50, and
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MATHEMATICVM. 415 implicita, (hoc enim considerare pertinet ad Philoso- phos;) sed provt dicit extensionem partium, & est mensura quædam apta, vt & alia quanta per ipsam metiamur, & vt ipsa vicissim ab aliis menturetur. Et ideò Mathesis pro- priè considerat quantum, hoc est quantitatem non in ab- stracto, sed in concreto, provt in subiecto reperiur: Phi- losophi autem quantitatem abstractam, provt dicit aliquid in corporibus quantis, inhærens substantiæ, ab ipsa eorum substantia, & qualitatibus distinctum, faciensque illam im- penetrabilem: quo pacto definitur ab Aristotele 5. Metaph. c 13. esse id quod est diuisibile in ea qua in sunt: quorum vnumquodque, vnum quid aptum est esse: quibus verbis in- dicare voluit extensionem partium in ordine ad te, ita vt Quantitas constet ex partibus diuisibilibus, & diuisibilibus in infinitum, quatum profecto quælibet apta sit esse vnum quid totum respectu aliarum partium, in quas est etiam diuisibilis; ita vt nullum sit assignare terminum huius diui- sibilitatis, sed quæuis minima quantitas consideretur, vt semper extensa sit, & sit vltra in alias partes extensas di- uisibilis. Quare Philosophus negat puncta indiuisibilia in- extensa, sed in omni minima quantitate considerat omnem extensionem cogitatione saltem apprehensam, licet fortè Physicam diuisionem non sit capax admittere. Mathemati- cus autem, quoniam rationem Mensuræ solum considerat in quantire, ideò parum illi refert, an Quantitas constet ex partibus diuisibilibus in infinitum, vel punctis indiuisibi- libus, sed minimam quantitatem, quæ non sit actu capax trinæ dimensionis vocat punctu indiuisibile, illam quæ vni- cam dimensionem admittit, appellat lineam, primamq[ue] hanc dimensionis rationem, quæ aliam non supponit, longitu- dinem: quæ duplicem habet dimensionem, vocat superficiem, longam quidem, & latam; ita vt latitudo secunda dimensionis ratio supponat semper in corpore mensurabili longitudinem: Si verò Quantum omnis dimensionis sit ca- pax, & in longum, & in latum, & in altum dicitur corpus, tertiaque hæc dimensionis species dicitur profunditas, quæ supponit reliquas duas longitudinem, & latitudinem. Hoc autem attendiur solum in quantis continuis, licet in discretis aliqualem earumdem dimensionum similitudinem inueniat Arithmetica, vt nos in loco aduertimus, ac di- ctum est etiam in Verbo Proportionalitas. Porrò, ex diuersa quanti provt rationem mensuræ habet, 18. consideratione varia, & diuersa Mathematicarum discipli- narum genera orta sunt. Siquidem vel Quantum considera-
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MATHEMATICVM. 415 implicit; for to consider this belongs to the Philosophers; but as it signifies the extension of parts, and is a certain measure fitted so that other quantities may be measured by it, and so that it in turn may be measured by others. And therefore Mathematics properly considers quantity, that is, quantity not in the abstract, but in the concrete, as it is found in a subject: whereas philosophers consider abstract quantity, insofar as it signifies something inhering in quantified bodies, distinct from their substance itself and from qualities, and making it impenetrable: in which way Aristotle defines it in Metaph. 5, c. 13, as that which is divisible into the things in which they are; each of which is apt to be one thing: by these words he wished to indicate the extension of parts in relation to each other, so that Quantity consists of divisible parts, and divisible to infinity, since indeed each part is apt to be one whole thing in relation to the other parts into which it is also divisible; so that no limit can be assigned to this divisibility, but any smallest quantity is considered as always extended, and as further divisible into other extended parts. Wherefore the Philosopher denies indivisible, unextended points, but in every smallest quantity he considers every extension apprehended at least in thought, although perhaps it is not capable of admitting physical division. But the Mathematician, since he considers only the notion of Measure in quantity, therefore it matters little to him whether Quantity consist of parts divisible to infinity, or of indivisible points; but the smallest quantity, which is not actually capable of a triple dimension, he calls an indivisible point; that which admits a single dimension he calls a line, and he calls this first mode of dimension, which presupposes no other, length; that which has a double dimension he calls a surface, namely long and broad; so that breadth, the second mode of dimension, always presupposes length in a measurable body. But if Quantity is capable of every dimension, and is said to be in length, breadth, and height, it is called a body, and this third species of dimension is called depth, which presupposes the other two, length and breadth. This, however, is considered only in continuous quantities, although in discrete quantities Arithmetic finds a certain likeness of these same dimensions, as we have noted in the place, and as was also said in the word Proportionalitas. Moreover, from the diverse consideration of quantity, according to the way it has the notion of measure, various and diverse kinds of mathematical disciplines have arisen. For either Quantity is considered
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LEXICON 418 quem assumo ad diuidendum viginti per quatuor, vel quaternarius, cum eosdem viginti velo, distribuere per tot quinque. Quod si è contra vice versa numerum quinarium assumam ad multiplicandum quatenarium, & è contra numerum quaternarium ad multiplicandum quinarium; tunc numerus 10. prosiliens dicitur productus, quia profectò est ductus vnius in alium quoadusque numerus maior confletur, vtrumque in se includens, quod tunc heri intelligitur, cum alter ipsorum toties augetur, quoties in altero continetur vnitas: vt patet in exemplo allato; vbi quia in numero quaternario quater continetur vnitas, ideò quater adaugeo numerum quinarium, ex quo tandem prouenit numerus vicesimus productus è quaternario in quinarium. Plura de hac re vide in Clauio in Epicome Arithmetica præctica cap. 1. RA 1. RABDÆ, vel Rabdi, Græcè sunt de eorum genere ostentorum, quæ in sublimi videntur, ex collisione radiorum Solis in auqua nube rorida, sed æquabili, quæ proinde ex reflexione ignitum aliquod referunt ad modum Trabis; reuera tamen nullam substantiam habent, sed sunt meræ apparentiæ, & visus deceptiones, non secus ac Iris, Area, Vrge, quæ prætet nubem à sole illuminatam, nil amplius sunt. Vide in V. Vrge. 2. RADIUS communiter dicitur fulgor ille à sole, vel quocumq[ue] corpore luminoso per rectam lineam immissus ad aliquod aliud corpus seù opacum, seù similiter luminosum, densum tamen, quod excipiat quidem immisum spiculum, & vlteriùs progredi non permittat. Ab Opticis verò definitur esse linea recta luminosa, vel illuminatio facta per lineam rectam. 3. Differt à lumine, & à luce, per hoc quod lux est prima passio, & insuper instrumentum corporis luminosi, quo lumen, & radius producuntur; lumen verò sit à luce congrenta per sui diffusionem, qua immisso radio recipitur in corpore diaphano illuminato: At Radius se habet admodum spiculi, (vnde est, quod spiculum etiam appelletur) traiecti à corpore luminoso in corpus illuminandu[m], & interim parit etiam lumen, illudque diffundit per medium diaphanum. Quare lariùs patet lumen, quam Radius, & lux: quandoquidem illud potest esse sine radio, vt in crepusculis, & in domo illuminata aëre ambiente: lux sine radio in corpo-
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LEXICON 418 whom I assume for dividing twenty by four, or by fours, when the same twenty I wish to distribute by five. But if, on the contrary, I take the number five for multiplying four, and on the contrary the number four for multiplying five; then the number 10. is said to spring forth as produced, because it is indeed the leading of one into the other until the larger number is formed, each including the other in itself, which is then understood when one of them is increased as many times as the unity is contained in the other: as is clear in the example given; where because in the number four unity is contained four times, therefore I increase the number five fourfold, from which at last arises the twentieth number produced from four into five. See more on this matter in Clavius, in Epicome Arithmetica præctica, ch. 1. RA 1. RABDÆ, or Rabdi, in Greek, are among those signs or apparitions which, seen on high, appear from the collision of the sun’s rays in a watery, dewy, but even cloud, and therefore by reflection they show some fiery thing in the manner of a beam; yet in truth they have no substance, but are mere appearances and deceptions of sight, not unlike the Rainbow, Halo, and other such things, which before a cloud illuminated by the sun are nothing more. See under V. Vrge. 2. RADIUS is commonly called that brightness from the sun, or from whatever luminous body, sent in a straight line to some other body, whether opaque or likewise luminous, yet dense, which indeed receives the sent shaft, and does not permit it to proceed further. But in Optics it is defined as a straight luminous line, or illumination made by a straight line. 3. It differs from brightness and from light in this, that light is the first affection, and moreover the instrument of the luminous body, by which light and radius are produced; brightness, however, comes from light suitably by its diffusion, whereby, the ray having been sent in, it is received in the illuminated diaphanous body: but Radius behaves much like a shaft (hence it is also called a shaft) thrown from a luminous body into a body to be illuminated, and meanwhile it also produces light, and spreads it through the diaphanous medium. Therefore brightness is more extensive than Radius and light: since that can be without a ray, as in twilight, and in a house illuminated by the surrounding air: light without a ray in a body-
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MATHEMATHICVM. 419 te luminoso, sed impediro, ne lumen suum diffundat, non autem radius sine luce, à qua est effectiuè, aut sine lumine, quod habet effectiuè, vt instrumentum lucis producendæ. < 4.> Triplex est radius, rectus modò explicatus; qui à corpore luminoso rectè discedit, & terminatur in aliud: reflexus, qui à corpore illuminato transmittitur, siue in ipsum corpus illuminans, siue in aliud quid sibi aduersum: & refractus, cum à medio minus raro, in rarius dissultat, vel etiam rariore in minus rarum, seù crassum progreditur, vt cum ab aëre in aquam diffonditur. Hæc autem triplex radiorum consideratio fundat triplicem scientiam, Dioptricam, Catoptricam, seù Anacampticam, & Anaclasticam, de qui- quibus. Vide Vitell. lib. 10. Opticæ, & nos suis in locis. Hinc < 5.> Ratius apud Astronomos audit aspectus, & configu-ratio duorum siderum in certa ab inuicem distan[n]ia è quâ vtrinque sibi immittunt radios, quibus communicata luce se muiuò roborant, aut oppugnant, provt similibus, aut dissimilibus qualitatibus fuerint præditi; vnde etiam est quod influxum erga isthæc inferiora aut augent, aut at- temperant, aut perueriunt. Sunt autem sextilis, Quadra-tus, Trinus, Quintilis, & alij, quos supra enumerauimus in V. Aspectus. 10: Regiomonranus vult huiusmodi radios immiti per circulos in latum protensos, quorum centrum sit Astrum intuens (excepta tamen oppositione, quæ sit per dia-metrum) finis verò vbi terminatur mensura, & distantia horum radiorum, in quem si inciderit aliud Astrum dicetur accipere, & vicissim immittere talem radium, vnde est, quod quilibet radius sumi debeat in puncto horum circu-lorum, quo intersecant Eclipticam. Blanchinus verò con-tendit esse circulos in longum descriptos, qui transeant per corpora siderum intuentium: sicque radios sumi tamquam puncta super hos circulos in distantiis consuetis, vt pro sex-tili gr. 60. pro quadrato gr. 90. &c. Quapropter prima sen-tentia concludit in directionibus nullam seruandam esse latitudinem occuisantium siderum, sed eius solius, quod recipit radium; quod profectò vbi peruenerit ad circulum radij, siue habeat latitudinem, siue non, recipit immissum radium, atque inde etiam ad inuentem planetam remittis. Secunda verò vult consequenter radios immitti in certa distantia, qua orbitas planetarum intersecet; atque adeò pro sextili, & trino accipiunt dimidium latitudinis planèæ intuentis; in quadrato nullam, cum necessariò incidat in
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MATHEMATICVM. 419 for the luminous body, not to hinder it, however, lest it diffuse its own light, not however a ray without light, from which it is effected, or without luminosity, which it has effectually, as an instrument for producing light. < 4.> There is a threefold ray: the direct, now explained, which departs straight from a luminous body and ends in another; the reflected, which is transmitted from an illuminated body, whether back to the same illuminating body or to something else opposite to it; and the refracted, when it leaps from a less rare medium into a rarer one, or even from a rarer into a less rare, or dense one, as when it is diffused from air into water. And this threefold consideration of rays grounds a threefold science: Dioptrics, Catoptrics, or Anacamptics, and Anaclastics, concerning which. See Vitell. lib. 10 Optics, and us in their proper places. Hence < 5.> Among astronomers, aspect means the configuration of two stars at a certain distance from one another, from which they mutually send out rays, by communicated light they either strengthen or oppose one another, according to whether they are endowed with similar or dissimilar qualities; whence also it comes that toward these lower things they either increase, moderate, or corrupt the influence. These are sextile, square, trine, quintile, and others, which we have enumerated above in V. Aspects. 10. Regiomontanus holds that such rays are sent through circles extended broadly, whose center is the observing star (except for opposition, however, which is through the diameter); but the end is where the measure and distance of these rays terminates, and if another star falls upon this, it is said to receive and in turn send back such a ray, whence it follows that each ray ought to be taken at the point of these circles where they intersect the ecliptic. Blanchinus, however, contends that there are circles described lengthwise, which pass through the bodies of the observing stars; and thus the rays are to be taken as points on these circles at the customary distances, as for sextile 60 degrees, for square 90 degrees, etc. Therefore the first opinion concludes that in directions no latitude of the eclipsing stars is to be observed, but only that of the one which receives the ray; which certainly, when it has reached the circle of the ray, whether it has latitude or not, receives the sent ray, and from there also sends it back to the finding planet. The second, however, wishes accordingly that the rays be sent at a certain distance, where they intersect the orbits of the planets; and therefore for sextile and trine they take half the latitude of the observing planet; in square, none, since it must necessarily fall in
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420 LEXICON Eclipticam. Hanc controuersiam fusè agitat Titus in Cælesti Philosophia lib. 2. cap. 4 addito etiam demonstrationis schemate. Vide ipsum. Similiter 7. RADIVS apud Geometras appellatur sinus maximus, qui est semidiameter circuli, & semisses chordæ subtensæ integro semicirculo, post quem sequuntur alij sinus semper minores, & minores vsque ad co[m]plementum arcus, cui subtenditur, ex quo per regulam propotionum venamur quantitatem reliquorum sinuum, arcus, cui singuli subtenduntur, nec non lineæ tangentis, atque secantis. 8. RADIVS ASTRONOMI S s, seù Geometr. cui est instrumentum Mathematicum factum ad speculanda sidera per radios visuales, eorumque distantiam, diametros, longitudines, aliaque permulta venanda. Eius vsum, atque virtutares fusè tradit Gemma Fræsius integro opusculo, Regiomontanus, Tycho, aliique; cui postea non nihil innouato successit. 9. RADIVS LATINVS sic dictus à Latino-Vrsino eius inuentore, quem vberrimis Commentariis illustrauit Egnatius Dantes celebris Mathematicus. 10. RADIIX communiter dicitur initium rerum, sumpra analogia ab radice arboris, quæ est initium plantæ ramusculorum, foliorum, & omnium denique, quæ in radice fundantur. Hinc apud Astronomos frequentissimè vsurpatur pro fundamento, vnde hauritur ratio cælestis motus instituendi. Sic Natiuitas, seu Thema Genethliacum dicitur Radix in ordine ad reuolutiones, directiones, progressiones, aliasque operationes, quæ tum in exlis ab stellis, tum in terris ab istorum motuum observationibus fiunt, & fundantur in prima cælorum constitutione, vnde homo, aut alia quæcumque res sumpsit initium. Quæ de re vide Auctores in Isagogieis. 11. RAMPHISTES, teste Kitchero, in Oedipo Ægyptiaco, dicitur Pica Brasilica Indorum vocabulo, Toucan, fidus in exlo ad australem plagam non ita pridem à recensioribus Astronomis detectum, habens stellas 8. infimæ notæ. 12. RAS apud Arabes idem sonat, ac caput. Hinc Ras Aben ab ipsis dicitur stella fixa in capite Draconis consistens: Ras Alangue stella irem in capire Serpentarij. Ras Algesi stella in capite Hereulis: Ras Eleced stella in capite Leonis, &c. de quibus omnibus suis in locis. 13. RATIONALIA SIGNA dicuntur eadem quæ humana, sumpta analogia à definitione hominis, qui dicitur Animal rationale:
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420 LEXICON Eclipticam. Titus discusses this controversy at length in Celestial Philosophy, book 2, chap. 4, with the addition also of a diagram of the demonstration. See him. Likewise 7. RADIUS is called by geometers the greatest sine, which is the semidiameter of a circle, and half of the chord subtended by the entire semicircle, after which follow other sines, always smaller and smaller, until the complement of the arc to which it is subtended; from this, by the rule of proportions, we seek the quantity of the remaining sines, the arc to which each is subtended, as well as the tangent and secant line. 8. RADIUS ASTRONOMICAL, or Geometrical, is an instrument made for mathematical observation of the stars by visual rays, and for searching out their distances, diameters, lengths, and many other things. Gemma Frisius has fully set forth its use and virtues in a separate treatise, as have Regiomontanus, Tycho, and others; and afterwards something innovated on it followed. 9. RADIUS LATINUS, so called from its inventor, Latino-Vrsinus, and illustrated with very abundant commentaries by Egnatius Dantes, a celebrated mathematician. 10. RADIIX is commonly said to be the beginning of things, by analogy from the root of a tree, which is the beginning of the plant’s little branches, leaves, and finally of all things that are founded in the root. Hence among astronomers it is very frequently used for the foundation from which the reason for establishing celestial motion is drawn. Thus the Nativity, or Genethliac Theme, is called the Radix in relation to revolutions, directions, progressions, and other operations, which are carried out and founded both in the heavens from the stars, and on earth from the observations of those motions, and are based on the first constitution of the heavens, from which a man, or any other thing whatsoever, took its beginning. On this matter, see the authors in the Isagogics. 11. RAMPHISTES, according to Kitcher in the Egyptian Oedipus, is the name given in the Indians’ language to the Brazilian Magpie, the Toucan, a faithful constellation in the southern sky, discovered not long ago by more recent astronomers, having 8 stars of the lowest magnitude. 12. RAS among the Arabs means the same as head. Hence Ras Aben is said by them to be the fixed star situated in the head of Draco: Ras Alangue, a star likewise in the head of Serpentarius. Ras Algesi, a star in the head of Hercules: Ras Eleced, a star in the head of Leo, etc., all of which are treated in their proper places. 13. RATIONAL SIGNS are called the same as human, taken by analogy from the definition of man, who is called a rational animal:
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MA THEMATICVM. 42 rationale: quæ enim signa humanam figuram præseferunt, nedum æquiuocatione nominis rationalia esse dicuntur, sed etiam per quandam attributionem, ac similitudinem, quoniam ad rationem, atque humanitatem habent influere. Vide quæ diximus in Verbo Humana signa. RATIONA I QUANTITAS, seu etiam irrationalis dici- <14> tur apud Geometras omnis quæcumque proposita quantitas, quæ cum alrera sit commensurabilis, aut incommensurabilis. Qua de re vide Euclid. lid. 10. à defin. 5. & seqq. neconon ea quæ nos tradidimus in V. Apotome, & in V. Proportionalitas. RATIONALIS VIA erigendi cælestem figuram, distribuendique <15> domorum spatia celebris est apud Astronomos, præsertim recensiores, quo nomine Regiom[an]otanus insigniuit methodum ab Abraham Auenesra primum inuentam, ab ipso mordicus propugnatam, acque in tabulas redactam constituendi situs moderatorum in cælesti figura, accipiendoque similitudines locorum ad cardines super lineis, & circulis parallelis Verticali magno, qui transit per puncta orius, & occasus æquatoris; itavt totum fundamentum similitudinum locorum constituatur in huiusmodi circulis parallelis ad verticalem descriptis. Et quia eam facilem, & præ cæteris rationi consonam comprobauit, seu potius suo captui maximè atridentem eam audacter rationalem appellauit; eiusque sectatores rationales dixit; quasi modò cæteræ methodi tum à Ptolema[co], tum ab aliis traditæ irrationales sint, ab ratione abhorrentes, & ex cerebro cuiusque auctoris confictæ. Igitur rationales ducunt duos circulos magnos per communes intersectiones finitoris, & meridiani, qui habeant solum dispescere æquatorem in duodecim partes æquales, nulla habita ratione ad reliquas proportionales distantias à cardinibus sed eoipso, ac sidus aliquod, aut plura coincidunt in vnum huiusmodi hemicyclum dicunt esse in consimili proportionali distantia ad cardines, eoquia seruant eandem ad illos figuræ qualitatem, licet non quantitatem. Ad hanc methodum Regiomontanus magno studio, & labore extruxit, vt dixi tabulas ascensionum, ac descensionum obliquarum à primo gradu eleuasionis poli vsque ad 60. quasmirum in modum ampliarunt, Canonibusque & Commentariis illustrarunt Magius, & Argolus. Huic tamen constituendorum situum rationi opposita ex diametro est methodus Ptolemaica, quæ circulos positionis non definit per communes intersectiones Finitoris, & Dd
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MA THEMATICVM. 42 rationale: for those signs which bear the human figure are called rational not merely by an equivocation of the name, but also by a certain attribution and resemblance, since they have an influence upon reason and humanity. See what we said under the word Humana signa . RATIONAL QUANTITY, or also irrational, is said by geometers of every proposed quantity, whether it be commensurable or incommensurable with another. On this matter see Euclid, Book 10, from Def. 5 and following; and also what we have set down in V. Apotome and in V. Proportionalitas . RATIONAL WAY of erecting the celestial figure, and distributing the spaces of the houses, is celebrated among astronomers, especially the more recent ones; by which name Regiomontanus distinguished the method first invented by Abraham Avenezra, stoutly defended by him, and reduced to tables, for determining the positions of the significators in the celestial figure, and for taking the likenesses of places at the angles by means of lines and parallel circles to the great Vertical, which passes through the points of rising and setting of the equator; so that the whole foundation of the likenesses of places is established in such circles described parallel to the vertical. And because he proved it easy and, more than the rest, consonant with reason, or rather because it most suited his understanding, he boldly called it rational; and he called its followers rational, as though the other methods, both those handed down by Ptolemy and by others, were irrational, abhorrent to reason, and fabricated from the brain of each author. Therefore the rational ones draw two great circles through the common intersections of the finitor and the meridian, which need only divide the equator into twelve equal parts, with no regard paid to the remaining proportional distances from the angles; but as soon as a star, or several, coincide in one such hemisphere, they say it is in a like proportional distance from the angles, because it preserves the same figure-relation to them, though not the quantity. For this method Regiomontanus, with great study and labor, constructed, as I said, tables of oblique ascensions and descensions from the first degree of elevation of the pole up to 60°, which Magius and Argolus greatly enlarged and illustrated with Canons and Commentaries. Against this way of determining positions, however, the Ptolemaic method is directly opposed, which does not define the circles of position by the common intersections of the finitor and the meridian, Dd
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MATHEMATICVM. 421 quod ab illis accepit: hoc autem fieri potest, & cum pro- ficuo & cum malo: qua de re vide Abraham Iudæum in suo Introductorio pag. 4. REDITVS. Vide Ingressus, aut Resolutio. 22. REFLEXIO est reduplicatio actionis, vel qualitatis immis- 23. sæ ab aliquo agente in passum, qua eadem actio, aut qua- litas producta in passo, intenditur, & reproductur, maiori nisi tendens in ipsum agens. Sic lumen à Sole immisum in speculum cum ad ipsum peruenerit intenditur, & revertitur numeris auctum, per idem medium, per quod venerat: quod quidem magnum est Naturæ prodigium, vt quod agens na- turale vires suas omnes exerens directè assequi non est potis, hoc in iactu ferè oculi præstet passum de se nihil ad- dens, sed solum resistens productioni agentis, seu receptio- ni effectus in ipsum. Quandoquidem corpus opacum, in quod reflectitur radius corporis luminosi, nil haber lucis, quò possit ipsam intendere in medio interposito; speculum vistorium in se nec formaliter, nec virtualiter ignem conti- net, qui tamen, ex reflexione solarium radiorum, quæ stat in eo, statim prosilit in materia proportionata inter ipsum, & solem constituta: quod ergò radij solis per ipsam tran- scuentes directè præstare non potuerunt, hoc præstant iidem, vt reflexi: qua virtute? qua virium adauctione, equidem ignoratur. Videtur tamen causam effectiuam actionis re- flexæ esse ipsummet effectum quatenus ita producitur in ter- mino, vt inde possit alium rursus effectum producere sibi similem; at quosum nobiliorem? non video. Cæterum ex reflexione solarium radiorum habemus, quod tot luminibus cælum exornetur, quot sunt in eo sidera: ipsa enim in se lucem vllam non habent, sed sunt corpora opaca, in quibus lumen à sole immisum recipitur, & subiectatur, quod po- stea qualitatibus eorum affectum, hanc varietatem effectuum gignit, quam demirantes, stupendaque Naturæ opera col- laudantes, videmus. Sed de hac re, quæ non minus extra aleam nostram est, quam penè suprà captum, satis sint di- cta. Plura de Reflexiæ virtutis prodigiis habet Vitellion lib. 10. & Kircheius in Arte Magna lucis, & Vmbra. REFRACTIONIS nomine venit inter Astronomos, & Per- 24. spectiuos diuersitas illa aspectuum, & aberratio visus, quæ accidit in siderum contemplatione, seu etiam quorumcum- que corporum quæ de longè aut instrumentis opticis, aut per aliud interpositum corpus diaphanum speculamur, quan- do per illud transeuntes radij, aut species obiecti visibilis in- fringuntur, & representant illud aliter, ac reuera est. Patet D d ij
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MATHEMATICVM. 421 which it has received from them: but this can happen both for good and for ill; on this matter see Abraham the Jew in his Introductorio, page 4. RETURNS. See Entry, or Resolution. 22. REFLEXION is the reduplication of an action, or of a quality transmitted by some agent into a patient, whereby the same action, or quality produced in the patient, is intensified and reproduced, unless tending back upon the agent itself. Thus light sent from the Sun into a mirror, when it has reached it, is intensified and returns augmented in number, by the same medium through which it had come: and this indeed is a great prodigy of Nature, that what a natural agent, exerting all its powers, cannot achieve directly, this the patient, in almost the twinkling of an eye, accomplishes, contributing nothing of itself, but only resisting the production of the agent, or the reception of the effect into itself. For since the opaque body into which the ray of a luminous body is reflected has no light by which it can intensify it in the intervening medium, the mirror of vision contains in itself neither formally nor virtually fire, which nevertheless, from the reflection of solar rays that is fixed in it, immediately bursts forth in the matter proportioned and placed between it and the sun: therefore what the rays of the sun, passing through it directly, could not accomplish, the same rays accomplish as reflected: by what virtue? by what increase of power? indeed it is unknown. Yet it seems that the efficient cause of reflected action is the very effect itself, insofar as it is thus produced in the terminus, so that from it another similar effect may again be produced; but for what nobler purpose? I do not see. Moreover, from the reflection of solar rays we have the fact that the heavens are adorned with as many lights as there are stars in them: for they themselves do not have any light in themselves, but are opaque bodies, in which the light sent from the sun is received and subjected, and which afterwards, being affected by their qualities, produce that variety of effects which we behold with wonder and praise as the astonishing works of Nature. But concerning this matter, which is no less beyond our reach than almost beyond our capacity, enough has been said. More on the wonders of the power of Reflection is found in Vitellio, book 10, and Kircher in the Great Art of Light and Shadow. The term REFRACTION, among Astronomers and Perspectivists, denotes that diversity of appearances, and deviation of sight, which occurs in the contemplation of stars, or also of whatever bodies we observe from a distance, either with optical instruments or through some other transparent body interposed, when the rays passing through it, or the species of the visible object, are bent and represent it otherwise than it really is. It is clear Dd ij
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LEXICON bendus est circa eam circulus à centro ipsius ad angulos, cu- ius circumferentia, si æquè tangat omnes angulos, figur a erit regularis, sin minùs, irregularis. 33. REGVLVS, Basiliscus, Cor Leonis Arabicè Alhabor, stella fixa de natura Martis, & Iouis, omnium ferè, quæ sunt in Firmamento potentissima, ac notissima, inter Regias com- purata, existens nunc temporis in gr.25. Leonis, quasi in ipsa Ecliptica, ideoque existimatur maximæ inter reliquas effi- cacæ; quippe quę semper cum Sole congreditur singulis an- nis, & habet cum cæteris etiam planetis aliquando congre- di, quod non aliis datum est. Et quidem ea non multi cor- poris est, vt videre licet ex ipsius diametro, quæ non exce- dit earum magnitudinem, quæ secundi honoris dicuntur, verum ob sui præstantiam, & robur, solet inter primæ ma- gnitudinis numerari. 34. Quinimò aduertit Titus eam solam non modo accipere, sed & remittere radios omnes ad planetas, ac pro eorum qualitate diuersam naturam induere; quod in aliis fixis, siue ob radiorum exilitatem, siue ob aspectus deviationem, qui quoniam extrà Eclipticam numquam assequuntur vt sint partiles, minimè obseruetur. Obseruat etiam campanella lib.2.cap.3. art.2. ex Ptolemæi doctrina, quod, quia Leoni Italia subiecta est, sicut Græcia Virgini, propterea quando stellæ, quæ sunt in Leone transierunt in Virginem, tunc im- perium Italæ in Græciam transit; at quoniam in eo adhuc perseuerauit Regulus, vt dictum est potentior, & in Ecli- ptica; ideò Italia fuit quidem depressa, sed adhuc in ea per- seuerauit dominatus, & Imperium saltem Ecclesiasticum: Quando verò etiam Regulus in signum Virginis commi- grabit, quod erit post 600. circiter annos, tunc fortè Ita- liæ virtus, & dominatus deficiet; nisi fortè ex ingressu Ca- niculæ in Leonem accidat conseruari, quod tamen haud sperant cum sit latitudinis multæ. Cæterum Regulum in ho- roscopo, iugi obseruatione compertum est ferè semper tri- buere naturalem quandam animi, morumque gravitatem, prudentiam, atque in rebus bellicis strenuitatem, vt inter alios obseruauit Argolus de diebus erit lib.1.cap.6. Vide etiam in V. V. Basiliscus, & Cor Leonis. 35. REMVNERATIO apud Astrologos, teste Abraham Auenar- te, est cum Planeta, qui cum primum ex puteo, aut alia quavis depressione alterum eripuerit aspiciatur postmodum ab extracto; quo tempore ipse etiam cadat in puteum, aut aliam depressionem ex qua planeta à se primùm adfutus, cum vicissim eripia: quì sit vt reddat ei quodammodo
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LEXICON A circle drawn around it from its center to the angles, whose circumference, if it equally touch all the angles, the figure will be regular; if not, irregular. 33. REGULUS, Basiliscus, Heart of the Lion, in Arabic Alhabor, a fixed star of the nature of Mars and Jupiter, among all those in the Firmament almost the most powerful and well-known, counted among the royal stars, now being in 25 degrees of Leo, almost upon the Ecliptic itself, and therefore thought to be of the greatest efficacy among the rest; for it always comes into conjunction with the Sun every year, and also has, unlike the other stars, the ability at times to come into conjunction with the other planets, which is not granted to others. And indeed it is not of much bulk, as may be seen from its diameter, which does not exceed the magnitude of those called of second rank; yet because of its excellence and strength, it is usually numbered among those of first magnitude. 34. Nay, Titus observes that it alone not only receives but also reflects all the rays to the planets, and assumes a different nature according to their quality; which in the other fixed stars, either because of the thinness of their rays, or because of the deviation of the aspect, which since they never attain beyond the Ecliptic so as to be partile, is not observed at all. Campanella also observes, lib. 2. cap. 3. art. 2, from Ptolemy's doctrine, that because Italy is subject to Leo, just as Greece is to Virgo, therefore when the stars which are in Leo have passed into Virgo, then the empire of Italy passes into Greece; but since Regulus had still persevered there, as has been said, more powerful and on the Ecliptic, Italy was indeed brought low, but in it there still continued dominion, and at least ecclesiastical Empire. But when Regulus too shall migrate into the sign of Virgo, which will be after about 600 years, then perhaps the strength and dominion of Italy will fail; unless perhaps by the entrance of the Canicula into Leo it should happen to be preserved, which however they do not hope, since it is of great latitude. Otherwise, in a horoscope, by constant observation it has been found that Regulus almost always grants a certain natural gravity of mind and character, prudence, and in military matters valor, as among others Argolus observed, de diebus erit lib. 1. cap. 6. See also under V. V. Basiliscus, and Heart of the Lion. 35. REMUNERATION among astrologers, according to Abraham Avenarte, is when a planet, which at first has delivered another from a pit or any other depression, is afterward aspected by the one extracted; at which time he also falls into a pit, or another depression from which the planet first assisted him, with the result that in turn he gives back to him in a certain way that which
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MATHEMATICVM. 429 eo quia, inquiunt, materialiter se habet ad radicem, nec vllam similitudinem retinet cum situ radicali reliquorum planetarum, aut cum motu directionum, ex quo totam diuidicandi segiem expiscandum est Et in Aph. 114. segment. 5. de reuolutionibus agens, tripliciter ait eas considerari posse, & in Zodiaco ad idem punctum, vt est reditus Solis initio cuiusque anni ad idem punctum equinoctij, & in Mundo, vt ipse, ait, & est reditus ad eandem fixam; & in Genituris, & est reditus eiusdem Solis ad priorem locum: verum addit, in hac debere addi tantam partem eclipticæ, quantam peragare potest in vna die naturali. Igitur reuolutio annua Natiuitatis, aut inceptionis alicuius rei, non debet attendi solum in reditu Solis ad eundem gradum Zodiaci, sed requirit aliquid amplius, scilicet additionem partis Eclipticæ singulis annis, quantum acquirit Sol singulis diebus successivè à die radicali cæpti operis, quod tamen, qua ratione fiat, & quid connexionis habeat cum themate radicali non explicat. Et sanè, vt benè discurrit accutissimus quidam Astronomus Gallus communis hæc ratio, accipiendæ reuolutionis annum ex reditu Solis ad idem punctum Zodiaci, in quo erat in radice operis; atque exinde posteà suuros euentus diiudicandi, quàm sit inanis, fallax, erroribusque multis obnoxia, & ratio probat, & euincit experientia. Quid enim, inquit in hoc retum ordine tam firmum, ac stabile dici potest, quod planè in dies singulos ex fortuita rerum emersione notabilem non subear mutationem? Ipsa Genesis & si rerum omnium in vita euenientium prima radix sit, & fundamentum; nihilominus miro ordine & successivo motu transit mox in directiones, in ingressus impingit, & per varios significatorum transitus variatur. Igitur Thema reuolutionis ad summum erit illius tantum differentiæ temporis, in qua erigitur, & non alius mox successuræ: sic nec ipsæ reuolusiones consistunt immobiles, sed perpetua vertigine agitantur, perinde ac ipsa radicalis figura, constituunt, que cum ea tam disformem conformitatem, vt inde eiusmodi effectus prodeant, quos nemo vnam excogirauerit, Porrò quisnam sit hic reuolutionis motus, & quomodo cum radice, & cum effectibus inde emanaturis connexionem habeat, operæ pretium est, vt paulò fusiùs explicemus. Igitur erecta, & ritè comprobata cælesti Natiuitatis, seu alterius incipientis rei figura, erigendum est itidem Thema reuolutionis quinti voluentis anni in eodem momento temporis, in quo erectum est thema Natiuitatis, nullo ha-
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MATHEMATICUM. 429 because, they say, it is materially related to the radix, and retains no similarity to the radical position of the other planets, or to the motion of directions, from which the whole series of dividing must be investigated. And in Aph. 114, segment 5, treating of revolutions, he says they can be considered in three ways: and in the Zodiac to the same point, as is the return of the Sun at the beginning of each year to the same point of the equinox; and in the World, as he says, and it is a return to the same fixed star; and in Nativities, and it is the return of the same Sun to its prior place: but he adds that, in this case, so much of the ecliptic must be added as it can traverse in one natural day. Therefore the annual revolution of a Nativity, or of the beginning of some thing, ought not to be considered only in the return of the Sun to the same degree of the Zodiac, but requires something more, namely the addition of a part of the Ecliptic each year, as much as the Sun gains each day successively from the radical day of the begun work; yet he does not explain in what manner this is done, or what connection it has with the radical theme. And indeed, as a certain most acute French Astronomer has well argued, this common method of taking the year of revolution from the return of the Sun to the same point of the Zodiac at which it was in the radix of the work, and then from that judging future events, is as vain, deceptive, and subject to many errors as both reason proves and experience demonstrates. For what, he says, in this order of things can be called so firm and stable that it does not plainly, in every single day, undergo a notable change from the accidental emergence of events? Genesis itself, although it be the first root and foundation of all things that happen in life, nevertheless by a marvelous order and successive motion soon passes into directions, strikes upon ingresses, and is varied through the various transits of significators. Therefore the Theme of the revolution will at most be only of that difference of time in which it is erected, and not of another that is soon to follow: thus even the revolutions themselves do not remain fixed, but are stirred by perpetual whirl, just as the radical figure itself constitutes, which with it forms such a dissimilar conformity that from this such effects arise as no one would have devised. Moreover, what this motion of revolution is, and how it has connection with the root and with the effects to be emanated from it, it is worth our while to explain somewhat more fully. Therefore, once the celestial figure of the Nativity, or of some other beginning thing, has been erected and properly verified, the Theme of the revolution of the fifth ensuing year must likewise be erected at the same moment of time in which the theme of the Nativity was erected, with no ha-
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LEXICON 430 bito respectu ad gradum Solis in Zodiaco, atque earundem tabularum subsidio (vt idem ordo seruetur) quo illud erectum est, quas inter experientia probauit præstare Tychonicas. Huius igitur Ascensio Medij Cæli subtrahenda est ab Ascensione recta, itidem Medij Cæli radicalis figuræ, & prosi- liet numerus graduum, quos supra Naturam perfecit coelum in his quatuor interiectis annis, qui erunt ferè 448. Hos autem diuide in quatuor partes, & habebis numerum gra- duum, & minutorum singulis annis competentium, & quos coelum sua circulatione præteriit, qui erunt quasi gr. 87. In super hors gradus singulis annis competentes in duodecim partes æquales dispesse, & habebis numerum singulis men- sibus competentem, septem videlicet grad. cum minutis 15. ac tandem si velis id etiam ad dies deducere habebis minu- ta eorum singulis competentia. Ex his perspicuum fiet, quàm appositè hoc revolutionis nomen iugi coelorum circulationi, quam super res ab earum exordio coelestia corpora faciunt, indirum sit, quia profectò per eam singulis quadriconiis, ad idem ferè punctum reditur. 43. Præterea eum Sol in hisce singulis revolutionum quadriennis quibus ad idem punctum radicale reuertitur augescat duobus ferè minutis, hinc est vt quinquaginta ferè horæ minuta antequam perueniat ad tempus revolutionis, ipse iam tetigerit locum suum radicalem in Zodiaco, quæ minu- ta in gradus æquatoris conuersa exhibebunt duodecim cir- citer annos. Nunc defectus horum annorum duodecim gra- dibus respondentium, signat terminum naturalem, quem Deus constituit vitæ hominum, vt propterea non ab re mul- ti existimauerint, eam naturaliter extendi posse ad centum viginti vsque annos, nec vlteriùs sine miraculo progredi. Siquidem defectus totius circuli spatio quatuor an norum dat 30. quaternas; quæ per quatuor productæ dant 120. Et quidem rationi consonum est, vt cum corpora coelestia, quæ suis motibus quasi quodam vehiculo suas communicant humanis corporibus qualitates; proindeque influendo in illa dant illis esse, & conseruari, quòd à causis secundis prouenit; consequens inquam est, vt dum illa suis in re- volutionibus deficiunt, & ista tandem quæ ab illis pendent, deficiant; qui defectus toties repetitus, necesse est, vt ex- tinguat tandem influxum vitalem, qui à sideribus viventi- bus communicatur. 44. Modò vt hæc Theoria reducatur ad praxim, oportet ad gradus æquatoris accipere gradus Zodiaci respondentes, ac distribuere per singulos annos succedentes, & menses; in-
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LEXICON 430 with respect to the degree of the Sun in the Zodiac, and, by the help of the same tables (so that the same order may be preserved) by which it was erected, those which experience has proved to be superior to the Tychonic ones. Therefore this Ascension of the Midheaven is to be subtracted from the right Ascension, likewise of the Midheaven of the radical figure, and there will emerge the number of degrees which the heavens have completed above Nature in those four intervening years, which will be about 448. Divide these however into four parts, and you will have the number of degrees and minutes corresponding to each year, and which the heavens have passed by in their circulation, which will be about 87 degrees. Moreover, divide the degrees corresponding to each year into twelve equal parts, and you will have the number corresponding to each month, namely seven degrees with 15 minutes. And finally, if you wish to carry this even down to days, you will have the minutes corresponding to each of them. From these things it will be clear how aptly this name of revolution has been applied to the continuous circulation of the heavens, which the heavenly bodies perform over things from their beginning, because indeed by it, every four years, one returns to nearly the same point. 43. Furthermore, since the Sun in each of these four-year revolutions, by which it returns to the same radical point, increases by about two minutes, hence it comes about that about fifty minutes of an hour before it reaches the time of revolution, it has already touched its radical place in the Zodiac, which minutes, converted into degrees of the equator, will make about twelve years. Now the deficiency of these twelve years corresponding to degrees marks the natural limit which God has established for the life of human beings, so that many have not without reason thought that it can naturally be extended up to one hundred and twenty years, and not progress further without a miracle. For the deficiency of the whole circle over the space of four years gives thirty four times, which, multiplied by four, gives 120. And indeed it is consonant with reason that, since the heavenly bodies, by their motions as by a kind of vehicle, communicate their qualities to human bodies; and thus, by influencing them, give them being and preservation, which arises from secondary causes; it follows, I say, that when they fail in their revolutions, these also finally fail, which depend on them; and this deficiency, repeated so often, must finally extinguish the vital influx which is communicated from the living stars. 44. Now, in order that this theory may be reduced to practice, it is necessary to take the degrees of the Zodiac corresponding to the degrees of the equator, and to distribute them through the successive years and months;
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432 LEXICON eadem die radicis, sed tot diebus post, quos anni interfluxerunt eum eo gradu Solis in Zodiaco, quem successiuè acquisiuit in singulos dies à Natiuitate: cuius gradus Ascensio recta quærenda est, eique addenda vel subtrahenda distancia quam habebat in radice à meridiano, proverat vltra vel citrà, nam numerus constatus, aut reliquus erit Ascensio recta Medij coeli figuræ revolutionis, ad quam postè à more solito erigenda est figura, constituis planeris in iis Zodiaci gradibus, in quibus reperiuntur ea die sub dera hora radicis. Atque hæc est figura revolutionis respondens eius initio, hoc est radici, vnde cæpit hic regularis motus institui, quatenus incedit ordine directionis, arque adeo potius dicenda esset revolutio annuæ cuiusque directionis. 47. Parietiam ratione, si inter annum incidat notabilis quædam directio alicuius significatoris, voluerisque cognocere habitudinem planearum ad locum directionis, nec non ad inuicem videndum est, quotus sit arcus directionis, & quot annos, & menses ad amussim appellet iuxta regulam superius traditam rum pro annis tot dies, pro mensibus tot binæ horæ adiiciendæ sunt ad annos qui interim effluxerunt, seu figuræ revolutionis annuæ Solis ad idem puctum Zodiaci, quod in radice tenebat, atque ad eam diem & horam in quam incidit erigenda erit figura more solito, vbi pro miraculo conspicieitur Promissor ad locum significatoris quem in radice habebat ad amussim deuolutus: videbitur quomodo se habeant foriunæ ad dictum locum, quomodo infortunæ: atque adeo non temere coniectari poterit de prospero, vel in fausto enentu illius directionis. Sed hæc doctrina melius forte percipietur per reductionem ad praxim, ad quam lectorem remiro. 48. Rhombus græcè significat figuram geometricam quadrilateram, cuius quidem latera æqualia sint, anguli vero inæquales, quorum duo sibi diametraliter oppositi, acuti sint, duo item obiusi. Talis est forma quam præse fert planus quidam Piscis, ob id Rhombus communiter appellatus. Differt autem à Rhomboide, & perfecto quadrato, quod hoc iam larera, quam angulos habet æquales, & rectos, illa autem etsi cum Rhombo conueniat in hoc quod angulos obliquos habeat, & partim acuros, parrim obtusos; disconuenirtamen in hoc, quod & latera habet inæqualia: vnde medium quid est inter quadratum, & Rhomboidem de vtrisque æquè aliquid participans, atque ab vtrisque in aliquo etiam disconueniens.
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432 LEXICON on the same day of the radix, but after so many days as years have elapsed since that degree of the Sun in the Zodiac, which it successively acquired in each day from Birth: for which degree the right Ascension must be sought, and to it must be added or subtracted the distance which it had in the radix from the meridian, whether beyond or short of it, for the resulting number, or the remainder, will be the right Ascension of the Midheaven of the figure of the revolution, to which afterward, in the usual manner, the figure is to be erected, with the planets set in those degrees of the Zodiac in which they are found on that day under the hour of the radix. And this is the figure of the revolution corresponding to its beginning, that is, to the radix, from which this regular motion began to be established, insofar as it proceeds in the order of direction, and therefore it would rather be called the revolution of each annual direction. 47. Likewise, if within the year there occurs some notable direction of any significator, and you wish to know the relation of the planets to the place of the direction, as well as to one another, it must be seen what the arc of the direction is, and how many years and months it precisely calls for according to the rule given above, namely, one day for years, two hours for months, are to be added to the years which have meanwhile elapsed, or to the annual revolution figure of the Sun to the same point of the Zodiac, which it held in the radix, and for that day and hour into which it falls the figure must be erected in the usual manner, where, as if by miracle, the Promissor will be seen devolved exactly to the place of the significator which it held in the radix: it will be seen how the fortunes stand in relation to the said place, how the infortunes stand; and thus one will not rashly be able to conjecture the prosperous, or the unfavorable event of that direction. But this doctrine will perhaps be better understood by reduction to practice, to which I refer the reader. 48. Rhombus in Greek signifies a quadrilateral geometric figure, whose sides are equal, but whose angles are unequal, of which two diametrically opposite to one another are acute, and the other two also obtuse. Such is the form presented by a certain flat Fish, for which reason it is commonly called a Rhombus. It differs however from the Rhomboid, and from the perfect square, because this has now equal sides as well as equal angles, and right ones, whereas that, although it agrees with the Rhombus in this, that it has oblique angles, and partly acute, partly obtuse; it differs nevertheless in this, that it also has unequal sides: whence it is something intermediate between the square and the Rhomboid, partaking equally of both and also in some respect differing from both.
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436 LEXICON & in dulcedinem concoctus transit. Siquidem, vt habet Galenus, 4. de simplicium Medicamentor. facultatibus c. 9. moderatus ealot dulcedinem facit; & omnia dulcia miti calore sunt prædita. 56. Ro 5. apud Astronomos dicitur genus quoddam Cometæ corpore magni, ac figuræ instar faciei hominis, mixti coloris ex aureo & argenteo. Est de natura Solis, & cum apparuerit portendit mortem Principum, & hominum potentiorum, rerumque mutationem in melius. Vide quæ diximus in V. Pseudostella. 57. 6. RO 7. apud Astronomos dicitur genus quoddam Cometæ corpore magni, ac figuræ instar faciei hominis, mixti coloris ex aureo & argenteo. Est de natura Solis, & cum apparuerit portendit mortem Principum, & hominum potentiorum, rerumque mutationem in melius. Vide quæ diximus in V. Pseudostella. 58. 7. RO 8. apud Astronomos dicitur genus quoddam Cometæ corpore magni, ac figuræ instar faciei hominis, mixti coloris ex aureo & argenteo. Est de natura Solis, & cum apparuerit portendit mortem Principum, & hominum potentiorum, rerumque mutationem in melius. Vide quæ diximus in V. Pseudostella. 59. 7. ROTA IXIONIS, sidus in Cælo ad Australem plagam, alio nomine Corona Australis. Vide ibi. 60. 7. RUBALL arabicè, Latinè Canopus stella fixa primæ magnitudinis in Argonauti, de qua multa diximus in V. Canopus. 61. 7. RVVABAH Ismaelitis audit stella polaris in extremo eaudæ vrsæ minoris sita, nomine à toto asterismo desumpto. 62. 7. RVMINANTIA SIGNA, apud Astronomos dicuntur quæ animalium ruminantium speciem præseferunt, qualia sunt Aries, Taurus, & Capricornus. Hæc enim Animalia, sicut & omnia cornigera, quoniam in superiore mandibula dentibus eatent, cibum summatim carpunt, atque in iugulo seruant, quem posteà ad o[mn]es iterum reuocantes lente ruminant & comminuunt. In his ergò signis consistens Luna consimilem in nobis effectum progignit, & ideò cautum est ab Astrologis Medieis, ne potiones sumantur Luna signa ista tenente, quæ ideo ruminantia vocauere, atque animantium ruminantium nomine, & figura insigniuere, vt eorum innotescat natura, siquidem, vt iugis semper experientia probauit, potiones eo tempore diù in stomacho retineri non possunt, sed citò euomuntur. Econtrà Vomitoria quamdiù Luna in signis ruminantibus reperitur, appositè exhibentur, vt præ cæteris aduertit Ganiuetus cap. 2. differ. 3. quia tunc Luna virtutem expultricem toborat. Inter ruminania signa aseribi solet etiam Leo, non quod is vere ex ruminantibus sit, sed quia, vt obseruat Origanus, cum sit Domicilium Solis, præest cordi, ac proinde eundem effe- ctum
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436 LEXICON & being digested passes into sweetness. Indeed, as Galen says, 4. de simplicium Medicamentor. facultatibus c. 9. a moderate heat produces sweetness; and all sweet things are endowed with mild warmth. 56. Ro 5. among the Astronomers is said of a certain kind of Comet, with a large body, and in the shape of a human face, of mixed color from golden and silvery. It is of the nature of the Sun, and when it appears it portends the death of Princes, and of more powerful men, and a change of affairs for the better. See what we said under V. Pseudostella. 57. 6. RO 7. among the Astronomers is said of a certain kind of Comet, with a large body, and in the shape of a human face, of mixed color from golden and silvery. It is of the nature of the Sun, and when it appears it portends the death of Princes, and of more powerful men, and a change of affairs for the better. See what we said under V. Pseudostella. 58. 7. RO 8. among the Astronomers is said of a certain kind of Comet, with a large body, and in the shape of a human face, of mixed color from golden and silvery. It is of the nature of the Sun, and when it appears it portends the death of Princes, and of more powerful men, and a change of affairs for the better. See what we said under V. Pseudostella. 59. 7. ROTA IXIONIS, a star in the heavens toward the southern region, by another name Corona Australis. See there. 60. 7. RUBALL in Arabic, in Latin Canopus, a fixed star of the first magnitude in the Argonaut, concerning which we said much under V. Canopus. 61. 7. RVVABAH is called by the Ishmaelites the pole star situated at the very end of the tail of the lesser bear, the name being taken from the whole asterism. 62. 7. RUMINANTIA SIGNA, among Astronomers, are called those which bear the appearance of ruminating animals, such as Aries, Taurus, and Capricorn. For these animals, as well as all horned animals, because they have no teeth in the upper jaw, nibble their food in small bites, and keep it in the throat, which afterward they bring up again and slowly chew and grind. Therefore, when the Moon is in these signs it produces a similar effect in us, and for that reason physicians and astrologers have cautioned that drinks should not be taken while the Moon holds these signs, which they therefore called ruminant, and marked them with the name and figure of ruminating animals, so that their nature might be known; indeed, as constant experience has shown, drinks at that time cannot remain long in the stomach, but are quickly vomited up. On the other hand, emetics are suitably administered while the Moon is found in the ruminant signs, as Ganiuetus especially notes, cap. 2. differ. 3. because then the Moon strengthens the expulsive power. Among the ruminant signs Leo is also usually included, not because it is truly among the ruminants, but because, as Origanus observes, since it is the domicile of the Sun, it presides over the heart, and therefore the same effect
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LEXICON 440 ribus radiis conueniant, eò minus apta, & infelix dicenda est Id autem semper intelligendum, quatenus ipsa Luminatia, præcipuè autem Sol cæteros vincat in fortitudine, ac dignitate. Nam cum ipsa sinr naturales honorum significa- tores, iuxta alibi dicta, ad hoc vt ritè eos possint decerne- re, debent eisdem ipsa dignitatum numeris cumulari, atque alios vestigales habere. Quod si alius Planeta fortior fuerit supràque ipsa luminaria eleuatus; iam non ipsa principatum tenebunt, sed potius fortiori subseruient, & sua lumina tribuent. Vt proinde eius qui fortior fuerit, manifesta in genitura impressa vestigia conspiciantur. 3. SATELLITIVM etiam dicitur comitatus, quem non ita pri- dem compertum est facere ad Iouem, & Saturnum, minores vt ita dicam planetas, seu erraticas stellulas, quæ circa ip- sos rotantur ac retinent pro centro eorum corpora, non se- cus ac Venus, & Mercurius solem: Qui proinde vel ob id Iouis, aut Saturni stipatores, & Satellites appellantur. Hi primùm detecti sunt in Ioue quatuor à Galileo, quos stel- las Mediceas nuncupauit, provr in loco diximus. Postmo- dum in Saturno alij duo, qui aliquando cum eo figuram elli- pticam, aliquando vnum corpus omnino sphæricum effor- mant, aliquando etiam ab eo feiuncti apparent. Neque vero-credendum est reliquos planetas sine comitatu incede- re, præsertim aurem Martem, nam Venus & Mercurius sunt propriissimi Solis satellites, cum ab ipso non multum elon- gentur, neque omnes aspectuum configurationes ad ipsum possint habere vt reliqui planetæ) sed ob stellarum exilita- tem hoc satellitium non posse oculis discerni Vide quæ ad hanc rem diximus in V. Mars. Hoc etiam modo. 14. SATELLITES dici possunt omnes planetæ ad Solem (excepta Luna) max mè in sententia Tychonis, qui in Mundi systemate solem ponit erraticarum omnium centrum, has- que perpetuò circa ipsum rotari, provt dicemus suo loco. 15. SATVRNVS græcè Phaton dicitur planera omnium tardissi- mus atque à terra remotissimus, cuius sphæra est immediatè fixarum orbi subiecta, Stella proinde inter erraticas aspectu omnium minima colore plumbeo, albicante, & suboscuro, natura rigens, ac frigida, hominibus vniuersoque animan- tium perfectorum generi inimica. Adeò vt si is ab albo pla- netarum eraderetur, vt etiam eius inimicus Mars, calidæ nimis, & exsiccantis naturæ, homines (inquit Hermes apud Argolum de diebus criticis cap 9) æuiterni forent, & immortales. Sed hoc noluit prouidentissimus rerum om- nium artis ex constituere; quia hominem, ad cælestem glo-
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LEXICON 440 if they agree with the far-flung rays, it is all the less fitting, and must be called unfortunate. But this is always to be understood insofar as the Luminaries themselves, and especially the Sun, surpass the others in strength and dignity. For since they are by nature the indicators of honors, as has been said elsewhere, in order that they may rightly discern them, they ought to be endowed with the same numerical dignities, and to have other vestigial signs. But if another planet be stronger and lifted above the luminaries themselves, then they no longer hold the principate, but rather serve the stronger and lend him their light. Thus, therefore, the manifest traces impressed in the nativity of the one who is stronger may be seen. 3. SATELLITIVM is also called a retinue, which it has recently been discovered to apply to Jupiter and Saturn, the smaller planets, or so-called wandering little stars, which revolve around them and keep their bodies as their center, no otherwise than Venus and Mercury do the Sun. They are therefore called the attendants and satellites of Jupiter or Saturn for this reason as well. These were first discovered in Jupiter, four by Galileo, whom he named the Medicean stars, as we said in the proper place. Later, two others in Saturn, which sometimes with it form an elliptical figure, sometimes a wholly spherical body, and sometimes also appear separated from it. Nor indeed should it be believed that the remaining planets move without a retinue, especially Mars, for Venus and Mercury are the Sun’s most proper satellites, since they do not depart from it by much, nor can they have all the configurations of aspects toward it as the other planets do; but because of the small size of the stars this satellite-hood cannot be discerned by the eyes. See what we said on this matter in V. Mars. In this way also. 14. SATELLITES may be called all the planets relative to the Sun (except the Moon), especially in the opinion of Tycho, who in his system of the world places the Sun at the center of all the wandering stars, and says that these perpetually revolve around it, as we shall say in the proper place. 15. SATURN is called in Greek Phaeton, the slowest of all the planets and the most distant from the Earth, whose sphere is immediately beneath the sphere of the fixed stars. It is therefore the smallest in appearance among the wandering stars, of a leaden, whitish, and somewhat dark color, by nature rigid and cold, and hostile to human beings and to the whole genus of perfect animals. So much so that if it were erased from the white planets, as also its enemy Mars, of excessively hot and drying nature, human beings, says Hermes apud Argolum, de diebus criticis, chap. 9, would be everlasting and immortal. But the most provident Artificer of all things did not wish to establish this; because man, toward the celestial glo-
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MATHEMATICVM. 44f modò radiis illustratæ mortuo, vt ita dicam modo resplendent. Quæ mihi ratio præ cæteris arridet, ac diu hærenti probabilior tandem, ac verior visa est, quoad vsque alij me- liorem proferant. SCIRON sic dictus est à rupè quadam vnde exsustare potissimum solebat, atque Athenas plurimum infestare Corus ventus occidentalis, lateralis Fauonio, spirans ab occasu æstivali. de quo plura diximus in verbo Caurus. Eo nunc maximè infestatur Iapygia regio in Italiæ vlt. mis finibus constituta, vnde & Iapygis illi nomen adhæsit. SCORPI octauum ab Ariete signum aqveum fixum, do- micilium Marris & eiusdem Trigonum, vnaque Veneris & Lunæ; sic dictum à mira quam habet cum Scorpionem terrestris sympathia. Siquidem Luna hoc signum inq[ue] ess[enti]a scorpionem maximè feri tunc, & infensi; Domusque (quod valdè mirum est) ædificari ecepta scorpionem in horoscopo existente, experientia teste scorpionum nidus euadet Est item signum venenosum, turpe, prolificum, mendax: vnde Almansor in Aphorismis ad regem Saracenorum propos. 106. Auerte, inquit, oculos tuos à figura, in qua fuerit ascendens Scorpio. Habet ex membris humanis regere pudenda. Scorpij fidus in octaua sphæra, amplitudine sua duo signa complectitur; Libram videlicet, & scorpium, vnde olim vndecim signa Zodiaci enumerabantur, & stellæ in Libra existentes, etiamnum chelæ seu branchia scorpij ab aliquibus appellantur: Sic enim Iudit nobiscum Natura, vt quæ stellæ ob aliquam connexionem occultam ab Scorpionem terrestri nomen hauserunt, in vnum conglomeratæ efforment fidus omnium maximum, quando is qui nomen indidit, inter huius generis animantes inuenitur omnium minimus. Continet sub se stellas Ægino vndeuiginti. Prolemao 21. & adhuc tres sporades, Keplero 28. Baiero autem 29. mixtæ naturæ: Nam chelæ sunt de natura Iouis, & Mercurij, & vna potissimum Martis. Similiter tres in fronte sunt Martix, & Saturninæ: Antares, seù cot scorpij potissimâ in hoc side-re cum aliis duabus in corpore Martem, & Iouem referunt; Nebulosa est Martia, & Lunaris: reliquæ in flexu caudæ Saturninæ sunt, & Venereæ, præter aculeum, qui est de natura Martis, & Mercurij. Vnde nil mirum si ob tantam varietatem, & qualitatum mixtionem dicatur signum fallax, ac venenosum mixtio enim qualitatum præsertim contrariarum in cælis corruptionem humorum infert. Primæ eius partes frigidæ sunt, & nuius generant; Mediæ temperatæ, vltimæ turbulentæ: Pars borealis calida est; Australis humida. Inci
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MATHEMATICVM. 44f now, so to speak, illuminated by the rays of the dead, they only shine back. That interpretation seems to me preferable to the rest, and while I long remained uncertain it finally appeared more probable and more true, until others bring forward a better one. SCIRON was so called from a certain rock from which it was chiefly wont to blow up, and greatly to trouble Athens; Corus, a western wind, lateral to Favonius, blowing from the summer west. Of this we have spoken more at length in the word Caurus. That region is now most greatly afflicted by it, Iapygia, situated in the farthest bounds of Italy, whence the name Iapygis has also attached itself to it. SCORPIUS, the eighth sign from Aries, a watery fixed sign, the do- micile of Mars and his Trigon, and likewise of Venus and the Moon; so called from the marvelous sympathy it has with the terrestrial Scorpion. For the Moon in essence strikes this sign most strongly as scorpion and hostile. And the house too (which is very remarkable), once begun to be built while the scorpion is in the horoscope, as experience testifies, will become a nest of scorpions. It is also a sign poisonous, ugly, fertile, deceitful: hence Almansor in the Aphorisms addressed to the king of the Saracens, proposition 106: “Turn away,” he says, “your eyes from the figure in which Scorpio is ascendant.” It has, from among the human members, governance over the private parts. The fixed star of Scorpius in the eighth sphere, by its breadth, contains two signs; namely Libra and Scorpius, whence once eleven signs of the Zodiac were enumerated, and the stars existing in Libra are even now called by some the claws or pincers of Scorpius: for thus Nature plays with us, that the stars which, because of some hidden connection, have taken their name from the terrestrial Scorpion, gathered together into one, form the greatest of all constellations, when he who gave the name is found among creatures of this kind the smallest of all. It contains under itself eighteen stars according to Æginus; Ptolemy says 21, and still three sporades; Kepler 28, but Bayer 29. Of mixed nature: for the claws are of the nature of Jupiter and Mercury, and one especially of Mars. Likewise the three in the forehead are Martian and Saturnine; Antares, or the heart of the scorpion, in this star especially, together with the other two in the body, represent Mars and Jupiter; the nebulous one is Martian and Lunar; the rest in the bend of the tail are Saturnine and Venusian, except for the sting, which is of the nature of Mars and Mercury. Hence it is no wonder if, because of such great variety and mixture of qualities, it is said to be a deceitful and poisonous sign: for the mixture of qualities, especially contrary ones, in the heavens brings corruption of the humors. Its first parts are cold, and generate naught; the middle parts are temperate; the last turbulent: the northern part is hot; the southern humid. Inci
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MATHEMATICVM. 449 pter vt obseruat Arist. lib. 2 Meteor cap. 4. ipsi solum quo- libet anni tempore spirant, quando alij certis tantum tem- poribus. Hunc nos Itali vulgò Tramontanam vocamus Græci Aparctias. Est de natura sua frigidus & siccus, adeo- que salubris omnia à corruptione præseruans, licet ob ni- miam frigiditatem cuadat floribus, & germinanti vineæ per- niciosus. Vide quæ diximus in V. Aparthias. SERPENS Arab. Alangue sidus in cælo ad borealem pla- < 50.> gam propè æquarote constans stellis 18. licet Baierus addens illi quæ propè illum extant informes in sua Vranometria enumeret omninò 37. omnes ferè de natura Veneris, & Sa- turni: vt proptereà contrariis qualitatibus præditæ euadant noxiæ, corruptiæ, ac venenosæ. De hoc sidere horoscopan- te sic cecinit Pontanus in sua Vrania. Exoriens facit Marsos, qui vulnera cantu, Qui sanent morlus, nigro qui sorte veneno Vnguine Poenio, & succis medicentur, & herbis. Si verò fuerit in occasu, sequitur idem Pontanus, ipsum portendere mortem ex morsu Serpentis, aut ex ictu venena- tæ sagittæ, aut sane ex propinatione veneni. SERPENTARIVS aliud sidus representas hominem Marsum, < 51.> siue Æsculapium manu supradictum Serpentem gestantem: Alionnbmine Ophiucus, in quo multa diximus. In hoc si- dere apparuit noua stella anno 1604. & durauit ad multos annos, quæ sui nouitate multam Astronomis fecit materiam speculandi, scribendi, eiusque effectus prognosticandi: quemadmodum aliæ duæ vna in pectore Cygni, altera in fede Cassiopeæ. Sed & de hac, quæ apparuit in genu Ser- pentatij scribit Keplerus, se magnoperè addubitare, num importet Mahometricæ sectæ desitionem, num Indi vniuersaliter conuertendi essent ad fidem; num monarchia aliqua reliquis omnibus imperatura sit, num Religionis ingens, & vniuersalis mutatio instet, num denique mundi finis. Et aduertit, tres omninò genuinas, veras, & nouas stellas in Firmamento intra paucos annos apparuisse, post maximam superiorum coniunctionem in Piscibus: Et quemadmodum primus Trigonus igneus mundi creatione, quintus Christi domini n iuitate nobilis extitit; ita hunc postremum haud temerè credendum esse Ecpyrosi, atque incendio Mundi se- cundum Christi aduentum denunciaturo præluxisse. Tan- dem pia quadam parenæsi ad lectores facta, concludit. In- terim non sanè peccant si hac stella commonefacti vitam in- siaurent Christianam; itaque se comparent, vt Christum Dominum iam iam excepturi. SERVUM PYPILLÆ sidus. Vide Corona Gnossia < 52.>
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...because, as Aristotle observes in book 2 of the Meteorologica , chapter 4, they alone breathe at any time of the year, whereas others do so only at certain seasons. We Italians commonly call this wind the Tramontana; the Greeks call it Aparctias . By nature it is cold and dry, and therefore wholesome, preserving everything from corruption, though because of its excessive cold it is harmful to flowers and to a vine that is beginning to sprout. See what we said under V. Aparthias . SERPENS , Arab. Alangue , a constellation in the sky near the northern part of the equator, consisting of 18 stars, although Bayer, adding to it those dim stars that lie near it in his Uranometria , counts altogether 37. Almost all are of the nature of Venus and Saturn; and for that reason, being endowed with contrary qualities, they become noxious, corrupting, and poisonous. Of this constellation, when it rises at the horoscope, Pontanus sang thus in his Urania : Rising, it makes Marsi, who heal wounds by song, Who cure ailments, who with dark fatal poison May be treated with Punic ointment, and with juices and herbs. But if it be setting, the same Pontanus says that it portends death from the bite of a serpent, or from the strike of a poisoned arrow, or indeed from taking poison. SERPENTARIVS , another constellation, representing a Marsian man, or Aesculapius, holding the aforesaid serpent in his hand; otherwise called Ophiuchus , concerning which we have said much. In this constellation a new star appeared in the year 1604, and it lasted for many years, and by its novelty gave astronomers much material for speculation, writing, and forecasting its effects: just as did two others, one in the breast of Cygnus, the other in the chair of Cassiopeia. But Kepler also writes of this one, which appeared in the knee of Serpentarius, that he greatly doubts whether it signifies the end of the Mohammedan sect, whether the Indies are to be universally converted to the faith; whether some monarchy is to arise and rule over all the rest; whether some great and universal change of religion is at hand; or whether, finally, it heralds the end of the world. And he notes that three entirely genuine, true, and new stars have appeared in the firmament within a few years, after the greatest conjunction of the superior planets in Pisces; and just as the first fiery trigon was nobly extant at the creation of the world, and the fifth at the nativity of Christ the Lord, so this last, he says, should not rashly be thought to have preceded the ecpyrosis and the conflagration of the world, which will announce the second coming of Christ. At last, after a pious exhortation addressed to his readers, he concludes: meanwhile they do not sin if, warned by this star, they renew their Christian life; and so let them prepare themselves, as if they were now about to receive Christ the Lord. SERVVM PYPILLÆ , constellation. See Corona Gnossia .
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LEXICON 452 commouent ventos, vt suo loco dicemus. <61.> SIDERATIO aliquando accipitur pro siderum coaptatione in coelesti themate, aliquando etiam idem sonat, ac sideris percussio, quales sunt certi morbi à determinatis constellationibus, quæ terris proximè iusident, prouenientes, Auctor est Varro. <62.> SILENS LVNA dicitur in coniunctione cum Sole toto eo tempore, quo non lueet tam ante quam post partitem congressum; eo quia iunc temporis nulla, vel saltem exigua virtute pollet; vnde quasi ortiosa, & silens esse videtur. Hinc Columella lib. 2. cap. 10, Silente inquit, Luna fabam vellito ante lucem. Durat autem id tempus quovsqve à sole liberaratur, exurgitque in cornua; quam Lunæ phasim Græci Menoidem appellant. Toto hoc tempore Formicæ nil operantur. <63.> SIGNA apud Astronomos, (vt paulò ante explicatum est) sunt notæ quædam in Zodiaco per duodenas æquales partes diuisæ, quarum singuiæ triginta gradibus constant in longum, atque in latum duodecim, atque vt eorum natura dignoscatur, siue ratione stellarum fixarum, quæ in iis sunt, siue ex effectibus, quos parit in hilce inferioribus Sol per illas discurtens variis animalium, aliarumque rerum imaginibus insigniæ. Sunt autem Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. Dicuntur autem omnia sidera esse in aliquo signo non modo quæ intra latitudinem Zodiaci consistunt, sed etiam quæ extra vagantur, quatenus si Ecliptica in duodecim partes æquales diuidatur, atque à punctis divisionum per polos Zodiaci circuli describantur; quidquid inter duos semicirculos includitur, seu in superficie, quam duo semicirculi ab vno in alterum Zodiaci polum claudunt, ad signum illud dicitur attinere, quod in Zodiaco inter duos illos semicirculos intercluditur. <64.> Porrò hæc distinctio signorum Zodiaci, vt benè aduertit Titus in lib 1. cap. 10. Coelestis Philosophiæ, non est fictitia, nec sine vlla ratione excogitata, sed vera & realis, per realem astrorum influxum à locis vnde incipiunt influere primas qualitates, vel vnde emittunt radios efficaces, quibus intenditur, aut remittitur efficacia talis influxus. Siquidem Planetæ à punctis mobilibus Zodiaci incipiunt influere primas qualitates; atque à punctis proportionalium distantiarum attingunt proportionales gradus talium qualitatum: Quandoquidem initium Tauri est in Trino ad initium Capricorni, & in sextili ad initium Cancri, vnde incipiunt planetæ
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LEXICON 452 moving winds, as we shall say in its place. <61.> SIDERATIO is sometimes taken for the conjunction of the stars in the heavenly figure; sometimes it also means the striking of a star, such as certain diseases arising from determined constellations, which lie very near the earth. Varro is the author. <62.> SILENT MOON is said to be in conjunction with the Sun during that whole time in which it does not shine, both before and after the exact encounter; because at that time it has no power, or at least very little; whence it seems, as it were, idle and silent. Hence Columella, book 2, chapter 10: “When the Moon is silent, pull the beans before dawn.” But that time lasts until it is freed from the sun and rises into the horns; which phase of the Moon the Greeks call Menoides. During this whole time ants do nothing. <63.> SIGNS among Astronomers, as was explained a little before, are certain marks in the Zodiac divided into twelve equal parts, each of which consists of thirty degrees in length and twelve in breadth; and in order that their nature may be recognized, either by reason of the fixed stars that are in them, or from the effects which the Sun produces in the lower world while passing through them, they are distinguished by various images of animals and other things. They are Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces. And all stars are said to be in some sign, not only those which lie within the latitude of the Zodiac, but also those which wander outside it, insofar as, if the Ecliptic be divided into twelve equal parts and circles be described from the points of division through the poles of the Zodiacal circle, whatever is enclosed between the two semicircles, or on the surface which the two semicircles close from one pole of the Zodiac to the other, is said to belong to that sign which is enclosed in the Zodiac between those two semicircles. <64.> Moreover, this distinction of the signs of the Zodiac, as Titus rightly notes in book 1, chapter 10 of Celestial Philosophy, is not fictitious, nor invented without reason, but true and real, through the real influx of the stars, from the places where they begin to influence the primary qualities, or from where they emit effective rays, by which the efficacy of such influx is intensified or diminished. For the planets begin to influence the primary qualities from the movable points of the Zodiac; and from points of proportional distances they reach proportional degrees of such qualities. For the beginning of Taurus is in trine to the beginning of Capricorn, and in sextile to the beginning of Cancer, whence the planets begin
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MATHEMATICVM. 433 planeta influere qualitates passiuas: & initium Geminorum est in Trino ad initium Libræ, & in sexuili ad initium Arjetis, vnde incipiunt influere qualitates actiuas: quod idem in aliis signis videre est. Igitur distributio ista signorum realis est, ac nomenclatio non inanis sed iure excogitata ad eorum naturam exprimendam. Similiter non ab re quædam ex ipsis dieuntur masculina, alia fæminina, aliqua humana, aliqua ferina, hæc pulchra, illa deformia, &c. ob diuersos respectus, & effectus, quos habent parere in hisce inferioribus sidera in ipsis constituta. Sie etiam ratione situs dicuntur præsidere super certas regiones & ciuitates, vel quia ipsis sint verticalia, vel quia in earum ædificatione fuerint ascendentia. Ex membris etiam humanis habent singula singulis præesse; item certa certis animantibus, lapidibus, ac plantis: vt in loco sæpius diximus, idque vel ratione, vel sanè ex iugi & nunquam fallente experientia. Quæ autem signa singulis membris præsideant eleganter expressit Manilius in Astronom. lib. 1. his versibus. Namque Aries capiti; Taurus Cervicibus heret; Brachia sub Geminis; censentur pectora Cancro: Te scapula Nemae vocant: teque Ilia Virgo: Libra colis clunes; & Scorpius inquineregnat: Et femur Arcitenens; genua & Capricornus amauit: Cruraque defendit luvianis: vestigia Pisces. Horum etiam dominatus est per planetas distributus, ita vt luminaria, quæ potiora sunt, potiora sibi vendicent, ea videlieet in quibus potentiores fiunt, & manifestos effectus pariunt, & quidem singula suum, & vnicum, Sol nempe Leonem, Luna Cancrum: reliqui planeæ bina singuli obtineant, pro habuiudine ad ipsa luminaria, provt provt susè dictum est in V. Domicilium. Hinc etiam. SIGNIFER dicitur circulus obliquus Zodiaci, in quo huiusmodi signa consideramur, & quem motu suo cuique proprio ab Occidene in Orientem Planetæ statis temporibus peragrant, & percurrunt. Qui, profectò circulus consideratur in primo mobili latus, vt dictum est sex, aut certè nouem hinc inde gradibus ad omnium planetarum per suam latitudinis orbium incedentium viam concludendam: itavt extra illum nusquam exorbitent. Nam in Firmamento, seu octava sphæra intelligitur esse alius Zodiacus huic iam dicto substratus, qui similiter in duodecim signa, seu potiùs Asterismos dispescitur eiusdem nominis, & figuræ, quoniam olim, vt dictum est, erant illis immediate subie- F f
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MATHEMATICVM. 433 planets to influence passive qualities; and the beginning of Gemini is in trine to the beginning of Libra, and in sextile to the beginning of Aries, from which active qualities begin to influence: the same thing may be seen in the other signs. Therefore this distribution of the signs is real, and the naming not empty but rightly devised to express their nature. Likewise not without reason are some called masculine, others feminine, some human, some bestial, these beautiful, those deformed, etc., because of the diverse respects and effects which the stars placed in them are held to produce in these lower things. Thus also, by reason of their position, they are said to preside over certain regions and cities, either because they are vertical to them, or because in their founding they were ascendant. Likewise among the human members each has been set to preside over a particular one; likewise certain stars over certain animals, stones, and plants: as we have often said in the place, and that either by reason, or certainly from constant and never-failing experience. Which signs preside over the individual members Manilius elegantly expressed in Astronom. book 1, in these verses. For Aries clings to the head; Taurus to the neck; Under Gemini are the arms; the chest is assigned to Cancer: Virgo claims your shoulders; and your loins, Libra: You, Scorpius, rule the groin; and Sagittarius the thigh; Capricorn has loved the knees; and Jupiter defends the legs: Pisces the feet. Their dominion too has been distributed through the planets, so that the luminaries, which are more powerful, claim the more powerful parts for themselves, namely those in which they become stronger and produce manifest effects, and each indeed its own, and a single one: the Sun namely Leo, the Moon Cancer: the remaining planets each hold two, in proportion to their relationship to the luminaries, as was said above in V. Domicilium. Hence also. SIGNIFER is the oblique circle of the Zodiac, in which we consider such signs, and which the planets with their own motion pass through and traverse at fixed times from West to East. This circle, indeed, is considered in the first mobile to be broad, as was said, six, or certainly nine, degrees on either side, to encompass the path of all the planets moving by means of their orbital latitudes: so that they may nowhere stray outside it. For in the Firmament, or eighth sphere, there is understood to be another Zodiac lying beneath this one already mentioned, which likewise is divided into twelve signs, or rather Asterisms, of the same name and figure, because formerly, as was said, they were immediately sub- F f
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MATHEMATICVM. 461 septentrione in Austrum, atque ab Austro in septentrionem moueretur sub Coluro solstitiorum primi mobilis per min. 24. vltrò, cirroque remeans, & circulum non perficiens: cuius morus inæqualitas obseruata est in stellis fixis, & maxima Solis declinatione. Censebant autem huius librationis spatium esse annorum 3432. Nona Sphæra erat quæ motu quoque librationis ab ortu ad occasum & iterum ab occasu ad ortum concipiebatur moue- ueri sub Ecliptica decimæ sphæræ, & super polos eiusdem per minuta 40. spatio annorum 1716. Octava Sphæra est Firmamentum, & locus fixarum de quo sæpius dictum, quam præter triplicem motum à supe- rioribus sphæris acceptum, dabaúr moueri super Eclipticæ polis spario annorum 25798. obseruabant enim distâtias stel- larum fixarum à punctis solstitialibus, & æquinoctialibns non manere semper easdem, sed successiuè crescere, & au- geri versus orientales partes. Sequebantur postea planerarum propriæ cuique sphæræ, Saturni, quæ præter quatuor iam dictos motus haberet suum proprium ab occidente in oriennem annis ferè 36. Iouis, quæ similiter ab occasu in ortum circulationem suam compleret in annis ferè 12. Martis, quæ in duobus, Solis, quæ integro anno, seu diebus 365 & ferè sex horis. Veneris, & Mercurij quæ ferè in vno anno. Tandem Lunæ, quæ cir- culum suum perageret ferè in mense hoc est diebus 17. & horis ferè 8. Et hæc quidem communis Astronomorum sententia fuit, & etiam nùm apud plurimos viget de plurali- tate, ac distinctione coelestium orbium, quoniam, vt dixi cælos constituebant solidos, nec poterant alioqui saluare motuum apparentias. Verum quia modò ex tempore Tychonis iam Cæli fluidi facti sunt, & optimè salvari possunt omnes apparentiæ non < 96.> modò per vnum coelum, per cuius expansum sidera omnia suo quæque motu discurrant, sed etiam per vnicum mo- tum, ideò nos vnicam tantum sphæram mobilem cum re- censiorum peritissimis constituimus, & vnum motum Qua < 97.> de re vide iam dicta in V. Calum, & in V. Motus. Sphæra etiam dicitur à Philosophis, atque Astronomis sparium quoddam orbiculariter definitum, ad quod se ex- tendit virtus agentis, atque in sideribus exrensio lueis, intrà cuius ambitum dicunrur habere familiaritarem, atque aspe- ctus platicos: ita vt extensio lucis Sarurni sit ad gr. 10. Iouis ad 1. Martis ad 7. cum dimidio. Solis ad 17. veneris ad 8 Mer- curij ad 6. Saturni ad 11. cum dimidio. Fixaru[m] primæ magnitu-
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MATHEMATICVM. 461 from the north toward the south, and from the south toward the north, it would move beneath the solstitial colure of the first mobile by 24 minutes beyond, and returning in a circuit, it would not complete the circle: the inequality of whose motion was observed in the fixed stars, and at the greatest declination of the Sun. Moreover, they judged that the period of this libration was 3432 years. The ninth sphere was that which, by a motion also of libration, was conceived to move from east to west and again from west to east beneath the ecliptic of the tenth sphere, and over its poles, by 40 minutes in the space of 1716 years. The eighth sphere is the Firmament, and the place of the fixed stars, of which it has been often said, which, besides the triple motion received from the higher spheres, was said to move over the poles of the ecliptic in the space of 25,798 years; for they observed that the distances of the fixed stars from the solstitial and equinoctial points did not always remain the same, but successively grew and increased toward the eastern parts. There followed afterwards the proper spheres of the planets, each one’s own sphere: of Saturn, which, besides the four motions already mentioned, had its own proper motion from west to east in about 36 years. Of Jupiter, which likewise would complete its circulation from west to east in about 12 years. Of Mars, in two years. Of the Sun, in a full year, or 365 days and almost six hours. Of Venus and Mercury, in about one year. Finally of the Moon, which would complete its circle in about a month, that is, in 17 days and almost 8 hours. And this indeed was the common opinion of astronomers, and even now among many there prevails the plurality and distinction of the heavenly orbs, because, as I said, they used to make the heavens solid, and otherwise they could not save the appearances of the motions. But since now, from the time of Tycho, the heavens have become fluid, and all the appearances can very well be saved not only by one heaven, through whose expanse all the stars may move each with its own motion, but also by a single motion, therefore we have established only one mobile sphere, together with the most skilled of the more recent writers, and one motion. On this matter see what was said above in V. Heaven, and in V. Motion. The sphere is also called by philosophers and astronomers a certain space defined circularly, to which the power of the agent extends, and in the stars the extension of light, within whose bounds they are said to have familiarity and “platic” aspects: so that the extension of the light of Saturn is to 10 degrees; of Jupiter to 1; of Mars to 7 and a half; of the Sun to 17; of Venus to 8; of Mercury to 6; of Saturn to 11 and a half. Of the fixed stars of first magnitude
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LEXICON 466 dumque mouentur, quatuor in eo designant puncta dehontantia varias passiones, quibus afficiuntur eireâ motum, & illustrationem à Sole. Primò Apogæum, vbi maximè remouentur à terra, & sunt omnes supra Solem in gradu ecliptico eidem coniuncti, vnde incipiunt fieri Superiores quidem orientales, inferiores occidentales, & augeri lumine. Secundum punctum est Perigæum, vbi sunt infra solem maximè terræ vicini: item coniuncti eidem Soli in gradu Ecliptico, arque exinde incipiunt esse superiores quidem occidentales, inferiores verò orientales, & lumine minui. Reliqua duo puncta hinc inde ad angulos rectos, in quibus planetæ maximè à Sole elongantur, dicuntur stationes, quia ascendentes ad Apogæum, ac descendentes ab eo ad Perigæum, videntur quodammodò stare, dum non permutant situm in Zodiaco: Et prima quidem statio dicitur, cum à dextris Solis consistunt, & incipiunt retrocedere in Zodiaco transeundo per Perigæum vsque ad secundam stationem. Hæc verò dicitur secunda statio, quia existentes à sinistris Solis incipiunt fieri directi, & moueri in consequentiam signorum per totam illam medietatem Epicycli vsque ad primam stationem. Hoc totum expressè videtur in Systemate Tychonis, ac præsertim in duobus satellitiis Solis, Venere, & Metcurio. Hinc 105 STATIONAR. vs dicitur planeta existens eireà primam, & secuudam stationem, vt modò explicuimus, ascendens vel descendens in suo Epicyelo ad Apogæum, vel Perigæum; iiavre in Zodiaco vel nullatenus, vel certè insensibiliter moueatur, sed persistat diu in eodem gradu quamdiù ascendit; vel descendit in partibus illis sui orbis, quæ directè subsunt vni gradui Zodiaci. 106 STELLA, græcis Astrum est corpus sphæricum lucidum, siue sua, siue aliena luce præfulgens in ætherea regione, ac sua pulehitudine mirè intuentium oculos rapiens, & præstringens: ex quo Astri nomen deriuatum existimat Plato in Cratilo. Dicitur autem promiscuè tam de erraticis quinque, quarum singulæ suo motu proprio ab aliis differente mouentur ab oceasu ad ortum, quam de fixis in Firmamento, quæ mouentur omnes simul eum suo orbe motu itidem proprio, ab oceidente in orientem. Et hæ stellarum sibi nomen retinent, (nam illæ proprio nomine Planetæ appellantur) & sunt propemodum infinitæ in expanso Firmamenti dispersæ, arque in varios asterismos, quæ sidera dicta sunt, dispositæ, & ordinatæ. Guius autem substantiæ sint, est prorsus ignotum. Hoc planè certum est, eas neque igneas esse, vt volebat
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while they move, they mark in it four points indicating various phases, by which they are affected by motion and illumination from the Sun. First, Apogee, where they are most remote from the earth, and are all above the Sun, joined to it in the ecliptic degree; from there they begin to become superior, indeed eastern, inferior western, and to increase in light. The second point is Perigee, where they are below the Sun and nearest the earth: likewise joined to the same Sun in the ecliptic degree, and from there they begin to be superior indeed western, but inferior eastern, and to diminish in light. The other two points here and there at right angles, in which the planets are most distant from the Sun, are called stations, because, ascending to Apogee and descending from it to Perigee, they seem in a certain way to stand still, while they do not change their position in the Zodiac: and the first station is indeed said to be when they stand at the right of the Sun and begin to move backward in the Zodiac, passing through Perigee until the second station. This, however, is called the second station, because, being on the left of the Sun, they begin to become direct and to move in the order of the signs through that whole half of the epicycle until the first station. This whole matter is expressly seen in the system of Tycho, and especially in the two satellites of the Sun, Venus, and Mercury. Hence 105 STATIONARY is said of a planet existing around the first and second station, as we have just explained, ascending or descending in its epicycle toward Apogee or Perigee; so that in the Zodiac it moves either not at all, or certainly imperceptibly, but remains for a long time in the same degree as long as it ascends or descends in those parts of its orbit which lie directly under one degree of the Zodiac. 106 STAR, in Greek Astrum, is a spherical luminous body, shining either by its own light or by another's, in the ethereal region, and by its beauty wonderfully drawing and captivating the eyes of those who behold it: from which the name Astri is thought by Plato to be derived in the Cratylus. It is used indiscriminately both of the five wandering stars, each of which moves by its own motion, different from the others, from west to east, and of the fixed stars in the Firmament, which all move together with their sphere by a likewise proper motion, from west to east. And these retain the name of stars for themselves, (for those are called by the proper name Planets) and are dispersed throughout the expanse of the Firmament in almost infinite number, and arranged and ordered into various asterisms, which are called constellations. Of what substance they are is altogether unknown. This is certainly clear, that they are neither fiery, as
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MATHEMATICVM. 475 hanc rerum connexionem, mirumque ordinem in vniuersa penè natura inter dissita quæuis comperimus. Hinc iure meritò eruditissimus Campanella hanc Vniuersi < 123.> faciem demirans, ita philosophatur lib. 2 cap. 5. Nescio inquit, qua sympathia nobis cum tota Naturæ serie inest: nam cum vna calcatur, solent grassari pralia, & sanguis humanus effundi. Plerumque cum putantur vineæ capita truncari humana & suffocatiui catharri grassari sueuerunt. Cum florent arbores, semina corporis, & ingenij turgent, florentque, & ad quasdam incitantur fructificationes: cum colliguntur sterilescimus: Vnde signum Virginis sterile vocatur. Cum venti plurimi diò flant, colligimur in penetralia domorum, & tunc consilia pessima ineuntur: vnde foemina solent insidiosa moliminæ prognosticari. Quid cum humano sanguine multi expressio, & non potiùs ouium pecudumque mactatio? Quid capitum detruncatio cum vineæ putatione? Quæ arborum efflorescentiæ cum ingenij seruore connexio? Quæ ventorum vis cum pessima consiliorum molitione? Verum hæc altissima dispositione præordinata sunt, atque vnam superiorem causam appellant, respiciuntque: subdit enim sapientissimus vir. Nec ista ratione vacant: nam etsi respectu causarum secundaru[m] & per accidens fiat, vt hæc herba simul cum illa floreat, inquit S. Thomas super 6. Metaph. ) tamen respectu cali habem causam: similes enim affectus corporeos influunt omnibus stella corporibus, sed modificantur pro genere, & qualitate recipientium Hæc ille. Ergò stellarum induxus vniuersales sunt, æque omnibus < 124> corporibus subiectis communicantur; æquè omnes mundi partes afficiunt, sed non eosdem, pares, aut similes in omnibus subiectis habent effectus producere, quando ista aut genere aut specie diuersificantur, sed pro qualitate recipientium in aliquibus connexos, complexos, consimiles, sibi mutuò corsepondentes; in aliis dissitos, alienos, æquiuocos, sibi inuicem aduersantes. Sic vbi Naturæ conformitas, tum mixtorum ad inuicem, tum ad causam superiorem, ibi communicatio, consensus, & amicitia; vbi diffotmitas & nullus ordo, contrariæ affectiones, dissidium, atque iniuicitia. Qua de re alibi me dixisse recordor, Luminaria, quæ sunt causæ vniuersales & æquiuocæ omnium producibilium, cum Ioue, aut Venere Naturæ humanæ conformibus producere mixta hominibus opportuna, cum Saturno verò fossilia, venenata, foetida, vitæ hominum aduersantia. G g iii
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MATHEMATICVM. 475 this connection of things, and the marvelous order throughout almost the whole of nature among whatsoever is far separated, we discover. Hence with justice and merit the most learned Campanella, admiring this face of the Universe <123.>, philosophizes thus, lib. 2 cap. 5. “I know not,” he says, “what sympathy is in us with the whole series of Nature: for when one is trodden down, battles are wont to rage and human blood to be poured out. Most often, when it is thought that the tops of the vines are to be cut back, human catarrhs and suffocating catarrhs have been wont to prevail. When trees flower, the seeds of body and genius swell and flower too, and are stirred toward certain fruitions; when they are gathered, we become sterile: whence the sign of Virgo is called sterile. When very many winds blow for a long time, we shut ourselves within the inner parts of our houses, and then the worst counsels are devised: whence women are accustomed to prognosticate insidious plots. What is the relationship of much expression of human blood, and not rather the slaughter of sheep and cattle? What is the cutting off of heads in relation to the pruning of vines? What connection is there between the blossoming of trees and the barrenness of genius? What force of winds with the worst contriving of counsels? But these things are ordained by the highest disposition, and they look to and invoke one superior cause,” says that most wise man. “Nor are these things without reason: for although, with respect to secondary causes and by accident, it happens that this herb flowers together with that one,” says St. Thomas on the 6th Metaphysics, “nevertheless with respect to the heaven we have a cause: for similar bodily affections are infused into all the bodily stars, but they are modified according to the nature and quality of the recipients.” This is his statement. Therefore the influences of the stars are universal, and are equally communicated to all subject bodies; they affect all parts of the world equally, but they do not produce the same, equal, or similar effects in all subjects, when these differ either in genus or species, but according to the quality of the recipients, in some they are connected, compounded, and similar, mutually corresponding to one another; in others they are distant, alien, equivocal, and mutually opposed. Thus where there is conformity of Nature, both among mixed things with one another and with a higher cause, there is communication, agreement, and friendship; where there is dissimilarity and no order, there are contrary affections, discord, and enmity. On this matter I remember having said elsewhere that the luminaries, which are the universal and equivocal causes of all things producible, when joined with Jupiter or Venus, which are conformable to human nature, produce mixtures suitable for human beings; but with Saturn they produce fossil, poisonous, foul things, contrary to the life of men. G g iii
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LEXICON <127> His igitur ita constitutis, iam ad omnem sympathiæ rationem, quæ inter Vniuersi istius partes inuicem colligatas inspicitur explicandam deueniamus. Siquidem ita hominem constituit summus Opifex vt esset veluti Vniuersi ipsius compendium, atque ex eius consideratione vniuersam mundi faciem, inimicamque constitutionem contemplemur. Omnis igitur sympathia reru[m] aut ex naturæ similitudine, viciniâque; aut ex familiaritate operis, actuumque conformitate; aut demum ex genere, quod ex vno eodemque principio promanent, sintque veluti aliquo superiori vinculo colligatæ, originem trahit. Ex naturæ similitudine habetur, quod homo alteri homini condoleat, pecus pecudi, quod vinum in doliis fluctuet, cum vites in vincis efflorescunt. Ex naturæ similitudine sit, quod in morbis contagiosis alter alterum lædat aspectu, voce, contactu; quod primo sanguine menstruo, aut secundinis in loca exnosa deiectis, foemina[m] malè habeant, quod cineribus calidis super recens excretas hominis fæces impositis: ille mox dissenteria corripietur, quod mox sistatur lac in vberibus, si foemina eiusdem lactis modicum in prunas emulgeat: & cætera quorum longam seriem affert Kircherus in Artemagnetica, & non quotidie non sine stupenti oculo experimur. Item ex vicinitate accidit, quod vna provincia peste infecta: altera illi propinquior, quamuis non sub eodem cælo eodem morbo afficiatur; quod aër calidus aquam propinquiorem magis quam remotiorem, etsi qualitatibus primis non discrepent, calefaciat, quod magnes, qui polum naturaliter aspicit, ad eam partem, quamuis ab ipso polo remotam feratur, cui, & quantò est ipse vicinior, &c. <128> Secundò ex familiaritate operis, tum etiam ex naturæ similitudine est sympathia illa quam in rebus videmus, cum scilicet, vno aliqvid operante, videmus aliquem ad idem opus quamuis nil tale cogitantem excitari. Vt cum altero oscitante, & ipsi mox oscitamus, altero mingente cietur & nobis lotium, quod ex imagine obscæna, Venus in aspiciente extimuletur. Nec dicas cum Valesio vbi supra hæc, & similia Naturæ arcana ex imaginationis vi, quatenus mens in cerebro residens per facultatem animalem in singula membra influit, atque operari facit, pendere. Nam etsi id vt plurimum verum sit, tamen non semper: quandoquidem videmus sæpè aliquem nil tale cogitantem, vt dixi, quin & ab altero oscitante vultu, aux animo auersum, vel oculis captum, (quò sit, vt nil de oscitatione recogitet) nihilominus oscitare; quod argumento est, ipsam naturam
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LEXICON <127> Since these matters have thus been set in order, let us now proceed to explain every kind of sympathy, which is observed among the parts of this whole Universe bound together with one another. For the supreme Workman so fashioned man that he should be, as it were, a compendium of the Universe itself; and from consideration of him we may contemplate the entire face of the world, and its opposing constitution. Every kind of sympathy among things therefore takes its origin either from similarity and nearness of nature; or from familiarity of operation and conformity of actions; or finally from kind, because they proceed from one and the same principle, and are, as it were, bound together by some higher bond. From similarity of nature comes it that one man feels compassion for another, cattle for cattle; that wine in barrels is agitated when the vines blossom in the wine-press. From similarity of nature it comes that in contagious diseases one harms another by sight, voice, or touch; that women are made ill by the first menstrual blood, or by the afterbirth thrown into foul places; that if warm ashes are placed upon fresh human excrement just voided, the man will soon be seized with dysentery; that milk is soon stopped in the breasts if a woman milk a little of that same milk into the embers; and the rest, of which Kircher gives a long series in the Artemagnetica, and which we do not experience every day without a wondering eye. Likewise from nearness it happens that one province infected with the plague: another, nearer to it, although not under the same sky, is afflicted with the same disease; that hot air warms water nearer to it more than more distant water, though they do not differ in primary qualities; that the magnet, which naturally looks toward the pole, is carried to that part, although remote from the pole itself, to which, the more nearly it approaches, &c. <128> Secondly, from familiarity of operation, and also from similarity of nature, is that sympathy which we see in things when, namely, one thing being operated upon, we see someone else, though thinking nothing of the sort, stirred to the same action. Thus, when another yawns, we soon yawn ourselves too; when another urinates, our own urine is moved; and from an obscene image Venus is aroused in the beholder. Nor should you say with Valesius, in the place cited above, that these and similar secrets of Nature depend on the force of imagination, insofar as the mind, residing in the brain, flows through the animal faculty into each of the members and causes them to act. For although this is for the most part true, yet not always: since we often see someone, as I said, thinking nothing of the kind, and even with his face turned away from another yawning, or with his eyes captured, so that he gives no thought to yawning, nevertheless yawn; which is an argument that nature itself
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MATHEMATICVM. 41 firare facit non illa Hac etiam ratione, inquit, cor citius afficeret septum transuersum, quam os ventris; nam viciniam cum corde non habet minorem, & insuper habet motum sed videmus ex affectionibus oris ventriculi promptissimè fieri sincopes, ex affectione septi deliria: ergò non trahunt hac membra alia in sympathiam his rationibus communibus in quibus superantur ab aliis, qua non faciunt perinde, sed intercedit propria aliqua natura, qua hac fiunt inter septum & cerebrum; os vetriculi, & cor, quam nos ignoramus. Hæc igitur in hac mutua facultatum conspiratione consistit, quæ vt dixi, ab vno animæ pendet regimine, atque analogiam non ineptè appellarunt, cum in rebus longè dissimilibus, ac disparatis, quandam nihilominus similitudinem ferret. <132.> Simili modo in hac Mundi, & Macrocosmi istius constitutione videre est hanc rerum analogiam, quæ non in sola similitudine, vicinitate, operis familiaritate, aut noto quodam vinculo saluari potest, cum hæc eadem sympathia in rebus longè maiori vinculo nxis minimè videatur, quia tamen eam experimentis sentimus, aliquam longè istis superiorem esse euidenti ratione deducimus, atque adeò in mundi formam, & conuentionem in vnum quoddam vniuersale principium iure merito importamus. Vnde enim uerò est, vti dicebam, quod Galli semper, & vbique sunt Hispanis infensi, moribus, colore, genio diuersissimi? illi subiti, isti graues: illi corpore vt plurimum magni, isti breuiusculi; illi colore candidi, & capillitio d[omi]nui isti nigro? Scoti quamuis eiusdem religionis, eiusdem Insulæ acolæ semper nihilominùs Anglis infensissimi excitere; itavt ne facta quidem regnorum vnione, potuerint vnquam animos temperare, & in mutuæ necessitudinis nexum venire. Itali olim Orbi imperitabant; nunc autem diuersarum gentium imperio, ac ludibrio subsunt, Sed quid est, quod canis vel minimus gallinam fugat, & deuorat; quam tamen postquam pullos exclusit, adeò reformidat, vt eâ visa fugam quantumuis generosus arripiat, hæcque in illum audax prosiliat? hæc enim verò Naturæ ludentis arcana sunt, quæ tamen suam causam, nostro captu superiorem habent. <133.> Sed age, eam vtcumque explicare conemur. Ptolemæus in Quadrip lib 4. cap. 7. causam omnem amicitiæ, & inimicitiæ naturalis, adeoque consensus, dissensusve rerum, in coelestium corporum constitutionem refundit. Cùm enim eadem seu se solis, seù, cum aliorum adiumento sint differe-
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MATHEMATICVM. 41 does not make it happen in that way. For this reason also, he says, it would affect the heart more quickly than the diaphragm, than the mouth of the stomach; for it has no less proximity to the heart, and besides, it has motion. But we see that from affections of the mouth of the stomach, syncope is produced most readily; from an affection of the diaphragm, delirium. Therefore these members do not draw the others into sympathy by these common reasons, in which they are surpassed by others, which do not act in the same way; rather there intervenes some proper nature, by which these things are brought about between the diaphragm and the brain, the mouth of the stomach and the heart, which we do not know. This, then, consists in this mutual agreement of faculties, which, as I said, depends on the governance of one soul; and they not ineptly called it analogy, since in things very unlike and disparate it nevertheless bears a certain likeness. <132.> In a similar way, in this constitution of the World and of that Macrocosm, one may see this analogy of things, which cannot be preserved by mere similarity, nearness, familiarity of work, or some known bond, since this same sympathy seems by no means to exist in things bound together by a far greater tie; yet because we perceive it by experiment, we infer by clear reasoning that there is some principle far superior to these, and thus we rightly and justly refer the form and agreement of the world to one universal principle. For whence is it, as I was saying, that the French are always and everywhere hostile to the Spanish, though they are most different in customs, complexion, and temperament? the former quick, the latter grave; the former for the most part tall in body, the latter shorter; the former fair in complexion and dark-haired, the latter black-haired? The Scots, though of the same religion and inhabitants of the same island, are nevertheless always most hostile to the English, so that not even after the union of the kingdoms could they ever moderate their feelings and come into the bond of mutual obligation. The Italians once ruled the world; now, however, they are subject to the empire and mockery of different nations. But what is it that a dog, even the smallest, drives off and devours a hen, although after she has hatched her chicks he fears her so much that at the sight of her he takes flight however bold he may be, while she boldly leaps upon him? These indeed are the hidden mysteries of Nature at play, which nevertheless have their cause, superior to our grasp. <133.> But come, let us try to explain it however we can. Ptolemy, in Quadrip. lib. 4, cap. 7, refers the whole cause of natural friendship and enmity, and therefore of the agreement or disagreement of things, to the constitution of the heavenly bodies. For since the same, whether by themselves or with the help of others, are differe-
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LEXICON tentium tum genere, tum specie effectuum causæ, exque vniuersalissimæ, & æquivocæ; cumque etiam inter ipsa intercedat mutua amicitia, aut inim citia, inde est, vt effectus ipsi eandem inter se proportionem, atque analogiam seruent, quam superiùs lux causæ, & eò maiorem quò maior inter illa intercedit necessitudo. Sic Iupiter exempli gratia habet sub se ex membris humanis pulmonem, costas, arterias, eartilagines, hepar, &c. I x lapidibus pretiosis Smaragdum, Sapphyrum, Amethystum, Tureoidem; ex animalibus Elephantos, Damas, Ceruos, Tauros, Columbas, Turtures, Corturnices. Mars autem sinistram, fel, renes, adamanthem, iaspidem, magnetem, euphorbium, scammoncan, &c. Et hæc prima sympathiæ generis radix: quæ enim ab vno eodemque principio originem trahut ea inter se mutua necessitudine vinciuntur. Item Planetæ inter se, idque ratione qualitatum quibus pollent, sunt amore, odio, vel nullo vinculo colligati. Saturnus & Iupiter, Iupiter, & Sol, Mercurius cum in Sole, & Saturno sunt adinuicem amici. Iupiter autem amicus Mercurio, at non ipsi vicissim Mercurius, sed neque inimicus: Martis sola Venus amica, cum tamen Veneri non solum Mars, sed & Sol, & Luna, & Iupiter sint amici: Mercurius Veneri neque amicus, neque inimicus; Lunæ solus Sol inimicus, amici Venus & Iupiter, at ipsa non ei vicem rependit, sed neque alteri inimica, aut amica, excepta vt dixi Venere. Hinc, cum semper effectus aliquam similitudinem referre debeat suæ causæ, hanc eandem necessitudinem inter se Planetarum effectus seruare necessum est, quam servant inuicem suæ causæ. Prætereà cum pro diuerso siderum positu tam in Zodiaco, quam in Mundo diuersas contrahant familiaritates, vt suo loco diximus, easdem per quandam analogiam rebus sibi subiectis communicant: quæ verò nulla familiaritate nectuntur, vt in signis inconiunctis, ea nullum etiam amicitiæ vinculum in suos effectus derivant, & hic cardo omnis sympathiæ atque antipathiæ. Hinc ire Ptolemæus loco citato præcipit in amicitiis, & inimicitis hominum dignoscendis respicienda esse Ascendentia vtrisque nati, commutationes planetarum, præsertim Luminarium, aspectus, coniunctiones, Antiscia, seu Intuentia, seu Imperantia, atque obedientia, & ex his de hominum amicitiæ, inimicitiaque iudicium profetendum. Nam si Ascendentia in Genituris consenserint; erit inter natos necessitudo & sympathia; si fuerint inconiuncta erunt naturaliter auersi, si vero fuerint in quadrato, aut opposito erit adhuc inter
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LEXICON ... therefore, both in the kind and in the species of effects, from causes, and from the most universal and equivocal ones; and since even among themselves there exists mutual friendship, or enmity, it follows that the effects themselves preserve among one another the same proportion and analogy as the cause, as was said above, and that all the greater in proportion as the necessity between them is greater. Thus Jupiter, for example, has under him, from the human members, the lungs, ribs, arteries, cartilages, liver, &c. I from precious stones, the Emerald, Sapphire, Amethyst, Turquoise; from animals, Elephants, Deer, Stags, Bulls, Doves, Turtledoves, Quails. Mars, however, [has] the left side, gall, kidneys, adamant, jasper, magnet, euphorbium, scammony, &c. And this is the first root of sympathy of the kind: for those things which draw their origin from one and the same principle are bound together by mutual necessity. Likewise the planets among themselves, and that by reason of the qualities with which they are endowed, are joined by love, hate, or by no bond at all. Saturn and Jupiter, Jupiter and the Sun, Mercury in the Sun, and Saturn are mutually friendly. Jupiter is friendly to Mercury, but Mercury in turn not to Jupiter, yet not hostile either: Mars alone is friendly to Venus, although to Venus not only Mars, but also the Sun, and the Moon, and Jupiter are friendly: Mercury is neither friend nor enemy to Venus; the Moon has the Sun alone as enemy, but Venus and Jupiter as friends, yet she does not repay him in kind, nor is she hostile or friendly to any other, except Venus as I said. Hence, since an effect must always bear some likeness to its cause, it is necessary that this same relationship among the planets’ effects be preserved, which their causes observe among themselves. Moreover, since according to the different position of the stars, both in the Zodiac and in the World, they contract different familiarities, as we said in the proper place, they communicate the same through a kind of analogy to the things subject to them: but those which are bound by no familiarity, as in the disjoined signs, also impart no bond of friendship to their effects; and this is the pivot of all sympathy and antipathy. Hence Ptolemy in the cited place orders, in recognizing the friendships and enmities of men, that regard be had to the Ascendants of both the nativities, the exchanges of the planets, especially of the Luminaries, aspects, conjunctions, Antiscia, or Intuentia, or Imperantia, and obedience, and that from these a judgment concerning the friendship and enmity of men be delivered. For if the Ascendants in the nativities have agreed, there will be kinship and sympathy between the born; if they are disjoined they will be naturally averse; but if they are in square, or opposite, there will still be among
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MATHEMATICVM. 485 SYSTEMA, Græcè audit Vniuersi proba constitutio, & harmonia cælestium corporum inter se, & ergà tellutem ita dispositorum vt situs, ordo, motus, ac passiones apparentiis, ac demonstrationibus tum philosophicis appriscè respondeant. Ricciolus lib. 9. ß. 3. cap. 2. sic illud describit. Systema Mundi nihil aliud est quam coordinatio, seu compositio magnarum mundi partium, videlicet elementorum, ac calorum; cuius veluti materia est numerus calorum, atque elementorum tum totalium, tum partialium; forma autem est ordo, ac situs eorum inter se, ac relatiuè ad centrum Vniuersi. Celebertium olim fuit quod co[n]cinnavit Mercurius Trismegistus, admiserunt Timocharis, Epimenides, Hipparchus, Archimedes, ac Ptolemæus in Almagesto insigniter commendauit, probauit, stabiliuitque hoc ordine; vt tetra simul cum aqua vnum globum efficiens foret Vniuersitatis centrum; mox aëre circumquaque ambiretur, quæ vt leuius elementum, minus tamen quam ignis secundum locum teneret; inde sphæræ ignis; cuius regionis terminè constituerentur ab vltima superficie supremæ regionis aëris, vsque ad concauum Lunæ: Postea succederet orbis Lunæ, & per ordinem alij superiores Mercurij, Veneris, Solis, Martis, Iouls, & Saturni; eodem ordine & habitudine ad tellurem tamquam ad omnium centrum, post quos sequeretur Firmamentum, seu Orbis fixarum, ac tandem Primum Mobile omnes concentricos habens, & complectens. Inueterata hæc mundi constitutio perdurauit vsque ad Nicolai Copetnici ingeniosissimi alioqui Astronomi tempora, qui ex nouis obsetuationibus videns, non posse subsistere prædictum Systema Ptolemaicum, aliud excogitauit seu potius exsu citauit à paucis olim antiquis Philosophis excogitatum, sed cum ipsis emortuum. In eo constituitur sol immobilis in Vniuersi centro: Post orbis Mercurij, qui diebus 80. suam integram revolutionem perficeret. Secundo loco succederet Venus nouem mensium spatio suum circuitum complectis. Tertio loco terræ globus vna cum Lunâ, quæ itidem continuè ergà tellurem circumagatur. Atque huic triplicem motum assignant; diurnum, quò ex Occidente in Orientem ducitur spatio 14. horarum (quem nos motum raptui p[er]tini mobilis damus:) annuum, quem nos soli: ac tertium, quem vocant librationis, quo inæqualitas æquinoctiorum ostenditur, atque Eclipticæ obliquatio ab Æquatore. Sequitur postea Mars, revolutionem suam ergà solem in annis duobus perficiens: inde Iupiter in Hh
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MATHEMATICVM. 485 SYSTEM, in Greek, signifies a right constitution and harmony of the celestial bodies among themselves, and in relation to the earth, so disposed that position, order, motion, and properties correspond, both in appearances and in demonstrations, as well philosophical as exact. Ricciolus, lib. 9, §. 3, cap. 2, describes it thus. The System of the World is nothing other than the coordination, or composition, of the great parts of the world, namely the elements, and the heavens; of which the matter, as it were, is the number of the heavens and the elements, both total and partial; the form, however, is their order and position among themselves, and in relation to the center of the Universe. The most celebrated of old was that which Mercury Trismegistus devised; it was admitted by Timocharis, Epimenides, Hipparchus, Archimedes, and Ptolemy in the Almagest especially recommended, proved, and established it in this order; that the earth together with water, making one globe, would be the center of the Universe; then it would be surrounded on every side by air, which, as the lighter element, would nevertheless hold a lower place than fire; then the sphere of fire; the bounds of whose region would be established from the outer surface of the highest region of air, as far as the concavity of the Moon: after that would follow the orbit of the Moon, and in order the other superior spheres of Mercury, Venus, the Sun, Mars, Jupiter, and Saturn; in the same order and relation to the earth as to the center of all things, after which would follow the Firmament, or Sphere of the fixed stars, and finally the Primum Mobile, having and including all the concentric spheres. This long-established constitution of the world endured until the time of Nicolaus Copernicus, a man otherwise most ingenious in astronomy, who from new observations, seeing that the aforesaid Ptolemaic System could not stand, devised another system, or rather revived one formerly devised by a few ancient philosophers, but dead with them. In it is established an immovable sun in the center of the Universe: after it, the orbit of Mercury, which would complete its entire revolution in 80 days. In the second place would follow Venus, completing its circuit in a span of nine months. In the third place the globe of the earth together with the Moon, which likewise continually revolves around the earth. And to this they assign a triple motion: a daily one, by which it is carried from the West into the East in the space of 14 hours (which we assign to the motion of the raptus of the mobile sphere); an annual one, which we assign to the sun; and a third, which they call the motion of libration, by which the inequality of the equinoxes is shown, and the obliquity of the Ecliptic from the Equator. After this follows Mars, completing its revolution around the sun in two years: then Jupiter in Hh
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annis 12. Tandem Saturnus in annis 30. Post quos potre[m] mam omnium constituunt sphæram fixarum immobilem. <141> Et hæc est constitutio Vniuersi, ex Philolai primum, mox ex Copernici placitis excogitata, in quam mirum est, quam multi ex neothericis conspirantes adhæserint, ac magno plausu receperint. Et sanè si modum spectemus, quo optimè saluantur omnes apparentiæ, ad cuius normam institutæ radices cælestium motuum, isti ad amussim respondent, eâ certè vsque ad Phychonis tempora, nulla visa est concinnior, pulchrior, & vsui accommodatior. Verum hoc systema intolerabilem errorem admittit, terram viique mobilem; quod experientiæ, & (quod magis interest) vni sacræ scripturæ testimonio aduersatur, terram omninò immobilem asserentis. Scio equidem nonnullos esse, qui dicant sacram scripturam vsu humano loqui provt in multis perspicuum est, proindeque ea testimonia huic assertioni minimè refragari. Quin etiam Didacus Astunica ex illo Iobi 9. vbi de Deo dicitur: Qui commouet terram de loco suo, & columna eius concutiuntur; hanc terræ mobilitatem probere nititur, additque nullum esse in tota scriptura locum, qui tam disertè dicat terram non moueri, quam hîc moueri dicit. Sed, vt optimè ostendit Pineda in hunc locum, inde potiùs euinci potest naturalis terræ firmitas, & habitudo, quæ cum ea sit, vt loco minimè dimoueatur, Dei potentia sit, vt contremiscat, atque ad eius nutum concutiatur, quod de terræ motibus, quibus terra à facie Domini trepidare dicitur intelligendum est, vt communiter explicant Parres: eò maxime quod columnæ, (de quibus hic sermo est) quandam stabilitatem magis quam commotionem significant. Quod autem terræ stabilitas à scripturis disertissimè astruatur; patet id apertissimè, & nos in loco adnotabimus: & omnes huiusmodi loquutiones, Sancti Patres communiter ad literam de terræ stabillitate, qua in centro Mundi omninò immobilis constituta est, explicant, & intelligunt: à quibus profectò recedere temerarium foret. Quare iure meritò hoc systema Copernicum, tamquam falsum, sacræ scripturæ aduersum, atque à veræ Philosophiæ principiis alienum, damnatum fuit à sacra Congregatione Cardinalium peculiari decreto: atque in Galilæum, qui illud nihilominus semel & iterum sustinere ardentius quam Christiano homini par erat, annitebatur, seuerius animaduersum. <142> Tandem Tycho Brahe Danus verus Astronomiæ instaurator, post longam quinquaqinta ampliùs annorum obser-
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12 years. Then Saturn in 30 years. After which they establish the sphere of the fixed stars, immobile, as the greatest of all. <141> And this is the constitution of the universe, first devised from Philolaus, and afterward from the tenets of Copernicus, to which it is surprising how many of the moderns, conspiring together, have adhered and received with great applause. And indeed, if we consider the method by which all appearances are best preserved, according to which the roots of celestial motions were established, these correspond exactly; and certainly, up to the time of Phychonis, none has seemed more orderly, more beautiful, and more suited to use. But this system admits an intolerable error, namely that the earth is moved; which is contrary to experience and, what is more important, to the testimony of Holy Scripture, which asserts that the earth is altogether immobile. I do indeed know that there are some who say that Holy Scripture speaks in human fashion, as is clear in many passages, and therefore that those testimonies do not in the least oppose this assertion. Nay, even Didacus Astunica, from that passage in Job 9, where it is said of God: “Who moves the earth from its place, & and its pillars are shaken,” seeks to prove this mobility of the earth, and adds that there is no passage in the whole of Scripture which says so plainly that the earth does not move as this one says that it does move. But, as Pineda shows very well on this passage, it can rather be inferred from it that the natural firmness and stability of the earth is such that it is not moved from its place, while it is by the power of God that it trembles and is shaken at His nod, which must be understood of the movements of the earth, by which the earth is said to tremble before the face of the Lord, as the Fathers commonly explain it; especially since the pillars, of which there is here mention, signify a kind of stability rather than a shaking. But that the stability of the earth is most clearly established by the Scriptures is plainly evident, and we shall note it in the proper place; and all such expressions the Holy Fathers commonly explain and understand literally, as referring to the stability of the earth, by which it has been placed immovably at the center of the world. To depart from them would surely be rash. Therefore, with good reason, this Copernican system, as false, contrary to Holy Scripture, and alien to the principles of true philosophy, was condemned by a sacred Congregation of Cardinals by a special decree; and Galileo, who nevertheless strove to uphold it more ardently than was fitting for a Christian man, was dealt with more severely. <142> At last Tycho Brahe, the Dane, the true restorer of astronomy, after a long observation of more than fifty years...
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MATHEMATICVM 137 uationem, adiutus à pluribus petitissimis Mathematicis primus omnium cælum liquauit, hæteream omnem regionem fluidam constituens ad morem aeris permeabilem, sed longè aere ipso subtiliorem, ac leuiorem: in cuius expanso, & palluie omnia cælestia corpota collocauit, suo quodcumque ordine & loco, motuque proprio præditum, p[er]tovt ex apparens iis cuinci potest. Hinc nouum systema excogitauit sa etæ Rom. Ecclesiæ constitutis inhærens, obseruationibus apprimè respondens, ac sacra scripturæ oraculis, Patrum dictis, veræque Philosophiæ principiis maximè consonum: in quo terram statuit amborum luminarium, ac Firmamenti, seu Orbis stellati centrum: Solem vetò reliquorum quinque planè arum: qui proinde omnes eccentrici essent ad terram; & per vastissimam illam Ætheris regionem constantissimè, & numquam fallente gradu perpetuò rotarentur ad oleum; itavt Mars quando fieret Achronicus in solis oppositione respectu nostri in Zodiaco, fieret etiam ter proximior ipso sole, & consequenter corpore et am grandior videatur uam constitutus in Apogæo, Venerem ipsam magnitudine superet, vmbram faciat, ac trium minutotum paralaxim patiatur, vt ego semel, & iterum obseruaui. Sicque exhibira hæc cæli facies omnes motus, & apparentias saluat, nouis Phænomenis in Æthere visis, haud egrè locum, & materiam tribuit, difficultates omnes soluit, atque humanum captum in rei veritate roborat, & obscurat Alia item Mundi systemata circumferuntur, quæ, quoniam à prædictis parum deuiant, vel non ita communi plausu recepta sunt, ideò breuitati consulentes omisimus. SYRH in sphæra barbarica dicitur secundus decanus Cancri manens sub dispositione Mercurij; iocositatis, confabulationis musicum, diuitiarum, vbertatis, &c. SYZ gis apud Gtæcos significant cælestes siderum copulationes; non modò per corporalem coniunctionem, vt aliqui rigorosè nimis intelligunt, sed etiam per aspectum, & quamcumque familiaritatem: quâ videlicet fiat radiorum commixtio, & virtutis in vnum coadunatio. Et ita rem radicitus explicat Valentinus Naiboda in Alchabitium.
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MATHEMATICVM 137 ...having been assisted by several of the most eager Mathematicians, first of all liquefied the heavens, constituting the whole aethereal region fluid, permeable after the manner of air, but far subtler and lighter than air itself; and in its expanse, and vault he placed all the celestial bodies, each in its own order and place, endowed with its own motion, so that as it appears from them it can be construed. Hence he devised a new system, adhering to the constitutions of the Roman Church, responding most exactly to observations, and most consonant with the oracles of Holy Scripture, the sayings of the Fathers, and the principles of true Philosophy: in which he established the earth as the center of the two luminaries and of the Firmament, or Starry Sphere; and the Sun as the center of the remaining five planets. Therefore all of them would be eccentric to the earth; and through that vast region of the Aether they would rotate perpetually, steadfastly, and with never-failing degree, without error, so that Mars, when he became Achronicus in opposition to the sun with respect to us in the Zodiac, would also become three times nearer to the sun itself, and consequently appear greater in body and size than when placed in Apogee, surpass the very Venus in magnitude, cast a shadow, and suffer a parallax of three minutes, as I have observed once and again. And so this face of the heavens, as exhibited, preserves all motions and appearances, gives easy place and material to new phenomena seen in the Aether, solves all difficulties, and strengthens human understanding in the truth of the matter, and obscures it. Other systems of the world are likewise circulated, which, since they deviate little from the foregoing, or have not been received with such common applause, therefore, attending to brevity, we have omitted. SYRH in the barbaric sphere is called the second decan of Cancer, remaining under the disposition of Mercury; of cheerfulness, conversation, music, riches, abundance, etc. SYZ among the Greeks signifies celestial conjunctions of the stars; not only by corporal conjunction, as some too strictly understand it, but also by aspect, and by any sort of familiarity: namely, whereby there is a mingling of rays and a union of virtue into one. And thus Valentinus Naiboda in the Alchabitium explains the matter from the roots.
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MATHEMATICVM. 48. sed pigri & ingenio rudes, fronte elata, atque vtrinque prominentes, quales sunt boues: sed adhuc alia ratio suppetit, quia hoc signum specialiter eius generis animantes afficit, vt eo malè affecto atque ab infortunis possesso, malè futuram esse pecudibus expectandum sit. Narrant quippe Pontanus ac Niphus in cõment. Apotelesm. Ptolemæi, suo tempore Saturni & Martis coniunctionem in Tauro, horridissima hyemis frigora suscitasse, ma-gnamque bobus calamitatem, perniciemque inuivisse; & quanquam oves tolerando frigori sint imbecilliores, ni-hilominus in boues maximè pestem illam desæuiisse, pro-pter signum coeleste ad quod terrestris bos refertur, vt Arieti bones & armamenta subsun, Caniculę canes terrestres, &c. quapropter si in Ariere ea synodus maleficaru celebrata fuisset vtiq[ue] in oves potiùs ea pestis debachata fuisset. Eius Asterismus in octaua sphæra continet stellas 33. & vndecim in formes: Quamquam Bayerus in eo sidere enumeret stellas 48. & Keplerus 52. inter quas celeberrimæ sunt Pleiades, Hyades-que, hæ in capite, illæ in genibus constitutę: nitium sumit à gr. 17. Tauri primi mobilis, ac protenditur vsque ad gr. 25. Geminorum. Natura eius diuersa est ob diuersitatem stellarum, quę in eo sunt: nam primę eius partes, in quibus sunt Pleyades stellæ procellosę, violentę sunt, & ma-lescicæ: mediæ temperatæ, & aliquantò humidiores: Po-stremæ calidæ in quibus hyades, fulgura, coruscationes, & similia adducentes. De stellis in eo consistentibus in parti-culari suis quibusque locis differuimus. TE ESCOPIVM est instrumentum opicum ex tubis, ac duplici, vel etiam multiplici vitro, concauo quidem pri-mo, conuexis autem, ac lenticularibus aliis, per cuius me-dium in determinata distantia exceptæ obiecti visibilis spe-cies refranguntur, ac mirum in modum dilatentur, referatque obiectum longè potentiæ visuæ approximatum, cu-ius ope factum est, vt corpora cælestia, eorum maculæ for-ma, luminis qualitas, aliæque affectiones probè nostris temporibus internosci potuerint, infinitæ propemodum stellæ in Firmamento obseruaræ, noua Phoenomena circa Iouem & Saturnum item detecta sint, quæ priùs ob sui exilitatem, & loci distantiam oculorum aciem fugiebant. Huius admirabilis instrumenti inuentionem, aut sanè di-lucidarionem debemus Galilæo Galilæi insigni Mathematico, à quo apud nos Italos nomen accepit; licet nostris temporibus ab Fontana, aliisque ingeniosis viris mirum in modum ampliatum sit, vt iam nil amplius in eo gene- Hh iij
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MATHEMATICVM. 48. but sluggish and rude in mind, with a lifted brow and projecting on both sides, such as oxen are: but there is another reason as well, because this sign especially affects animals of that kind, so that when it is ill-affected and possessed by misfortunes, it must be expected that cattle will fare badly. For Pontanus and Niphus relate in their commentary on Ptolemy’s Apotelesmata that in their time the conjunction of Saturn and Mars in Taurus stirred up the most dreadful cold of winter, and brought great calamity and destruction upon oxen; and although sheep are weaker in enduring cold, nevertheless that pestilence raged most fiercely against oxen, because of the heavenly sign to which the earthly ox is referred, just as to Aries belong rams and harness, to the Dog Star earthly dogs, and so forth. Wherefore, if that assembly of witches had been held in Aries, that plague would surely rather have raged against sheep. Its asterism in the eighth sphere contains 33 stars and 11 in the forms; although Bayer enumerates 48 stars in that constellation, and Kepler 52, among which the most famous are the Pleiades and the Hyades, these being placed in the head, those in the knees. It begins from the 17th degree of Taurus of the first mobile, and extends as far as the 25th degree of Gemini. Its nature is diverse because of the diversity of the stars that are in it: for its first parts, in which are the Pleiades, are stormy stars, violent and unhealthful; the middle parts are temperate and somewhat more humid; the last are hot, in which are the Hyades, bringing thunderbolts, flashes, and the like. We have spoken in particular, in their proper places, of the stars that are contained in it. TELESCOPIUM is an optical instrument made of tubes and of a double, or even multiple, glass, the first concave indeed, but the others convex and lenticular, through the middle of which the visible species of an object, received at a fixed distance, are refracted and wonderfully enlarged, so that it presents the object as though brought very near to the power of sight. By its aid it has come about that celestial bodies, their spots, the form, the quality of light, and other properties could be well recognized in our times, nearly infinite stars were observed in the Firmament, and new phenomena around Jupiter and Saturn were also discovered, which formerly, because of their smallness and the distance of their place, escaped the eye’s sight. We owe the invention, or rather the clarification, of this admirable instrument to the distinguished mathematician Galileo Galilei, from whom it took its name among us Italians; although in our times it has been wonderfully enlarged by Fontana and other ingenious men, so that now nothing further in that kind...
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LEXICON re desiderari posse videatur. 1. TELVM, sagitta, iaculum, Demon Meridianus, fidus ad borealem plagam propè Aquilam: de quo satis dictum est sub his dictionibus. 2. TEMPERAMENTVM communiter dicitur proportio, & mixtio quatuor primarum qualitatium, quæ constituunt vniuersa corpora mixta, aique à maiori vel minori vnius super aliam qualitatem prædominio, & excessu, diversificatur, vnde & complexio apud nos, & apud Græcos appellari solet. Eius nouem species ab Hippocrate, Galeano, aliisque Medicis assignari solent: aut enim in corpore mixto istæ qualitates omnes in gradu remisso sunt & æqualis omnium est proportio, & constituit iustum, perfectum que temperamentum, quo melius excogitari nequit, quodque est reliquorum veluti canon, & norma: aut hæc proportio est inæqualis, itavt non sit par intensio qualitatum, & id duobus modis euenire potest, primò vt cæteris tribus moderatè se habentibus vna qualitas superemineat, & sic, vti quatuor qualitates sunt, quatuor etiam differentias temperamenti specificant, atque à seipsis denominant, calidum videlicet, aut frigidum, aut humidum, aut siccum. Secundò, vt duæ reliquis duabus præualeant, quemadmodum in elementis videre est, & sic alias quatuor mixtorum species statuunt ab elementis denominatas, sicqu dicimus illum complexionis esse sanguineæ, quia in eo abundant caliditas, & humiditas; alium esse cholericum, quia in eo flava bilis, & sic calor & siccitas, alium Phlegmaticum, quia flegma, hoc est humor aqueus frigidus, & humidus: alium denique melancholicum, quia præcellit in eomelancholia, & atra bilis cum siccitate & frigiditate. Porrò hæ qualitates, etsi in pluribus mixtis elementares sint, in cælestibus etiam inueniunrrur eminentiori modo, quæ etiam diuersam cælestium corporum constitutionem indicant pro diuersa earum mixtura, quæ ab effectibus innotescit. Vnde & probabile est mirabiles qualitates aliquorum mixtorum quas videmus elementaribus longe præcellere, non ab elementis, sed à cælelestibus ortum ducere, qua de re plura diximus in V. Mixta. TEMPVS quid sit, adeò difficile est explicaru, vt iure dixerit Augustinus lib. 1 Confess. cap. 14. Quid est tempus. si nemo ex me quarat scio, si quarenti explicare velim, nescio. Eius quidditatem obscurissimè tradit Philosophus 6. Phj siccor. text. 10. Tempus est, inquit, numerus morus secundum prius, & posterius: indicat enim rerum fluxibilitatem,
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LEXICON it may seem that something can be desired. 1. TELVM, arrow, dart, Meridian Demon, faithful to the northern quarter near Aquila: enough has been said of this under those terms. 2. TEMPERAMENT is commonly called the proportion and mixture of the four primary qualities, which constitute all mixed bodies, and it is diversified by the greater or lesser predominance and excess of one quality over another; whence also complexion among us, and among the Greeks it is usually called. Its nine species are usually assigned by Hippocrates, Galen, and other physicians: for either in a mixed body all these qualities are in a moderate degree and the proportion of all is equal, and it constitutes a just, perfect temperament, than which nothing better can be devised, and which is as it were the canon and rule of the rest: or this proportion is unequal, so that there is not equal intensity of the qualities, and this can happen in two ways: first, when the other three are moderately balanced, and one quality stands out above them; and thus, since there are four qualities, there are also four differences of temperament, and they are named from themselves, namely hot, or cold, or moist, or dry. Second, when two prevail over the other two, as may be seen in the elements, and thus they establish four other species of mixtures, named from the elements; thus we say that one is of a sanguine complexion, because in it heat and moisture abound; another is choleric, because in it yellow bile, and thus heat and dryness; another phlegmatic, because phlegm, that is, watery humor, cold and moist: another finally melancholic, because melancholy prevails in it, and black bile with dryness and coldness. Moreover, although these qualities are elemental in many mixed things, they are also found in heavenly bodies in a more eminent way, and they also indicate the diverse constitution of heavenly bodies according to their diverse mixture, which becomes known from their effects. Whence also it is probable that the marvelous qualities of certain mixtures which we see far surpass elemental ones do not arise from the elements, but from the heavenly bodies; on which matter we have spoken more in V. Mixta. TEMPUS, what it is, is so difficult to explain that Augustine rightly said, book 1 of the Confessions, chap. 14: What is time? If no one asks me, I know; if I wish to explain it to one who asks, I do not know. The Philosopher in book 6 of the Physics, text 10, gives its quiddity in the darkest manner: Time is, he says, the number of motion according to before and after: for it indicates the fluxibility of things,
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MATHEMATICVM. 495 TEPISATRAS LVNA. ibidem dicitur tertius Decanus 17. Aquarij, significator detractionum, & deceptionum, sub dis- posirione Lunæ. TEPISEVTH SOLIS. ibidem est secundus Decanus Scorpij, 18. deceptionis, detractionis, nouas inimicitias inter homines ferendi, & veteres confirmandi, cuius dominium spectar ad Solem, TERMINI, seu Fines Planetarum sunt certi quidam, & 18. limitari gradus signorum, in quibus repertos planeras ob- servauir Antiquitas vires suas augere, ac maximas habere prærogariuas De iis multa diximus in V. Fines. Hic autem nostr: curæ erir huiusmodi distributionis congruentem ra- tionem reddere, quam nuper excogitauit Tius in Cælesti, Philosophia: ac non de finibus modò, sed & de iure Domicilij, Altitudinis, ac Trianguli, Sic enim habet lib. 2. cap. 12. Cauendum est, quod quinque Planeta Saturnus, Iu- piter, Mars, Venus, & Mercurius ratione suarum, proprietatum, & maximè coloris sui lumnis habent inter se deter- minatos quosdam qualitatum gradus similis naturæ gradibus illis, quos Luminaria producunt omnibus suis lationibus. Di- xi similis naturæ; intelligo saltem quoad gradus, non quoad naturam qualitatis: Nam Luminaria non efficuunt quali- litates, quas Mars, & Saturnus, qua omninò corruptiua sunt, &c. Et censeo, quod Iupiter habeat illos gradus qua- litatis caloris, qui ex radio trino oriuntur; humiditatis verò illos gradus, qui ex radio sextili fiunt, humiditatis vero, qui ex trino: & hinc quod sit fortuna minor ratione maioris qualitatis passi- ua. Saturnus, quod habeat illos gradus frigiditatis, qui ex oppositione fiunt, id est summos, siccatis verò illos gradus, qui ex quadrato oriuntur, & idcirco quod sit Infortuna Ma- ior, ratione excessus frigiditatis supra siccatatem: Tandem Mars obtineat illos gradus ariditatis, qui ex oppositione emer- gant & caloris destructui illos gradui, qui ex quadrato; & ideò quod sit Infortuna minor. Mercurius, quia inconstantis apparet coloris, inconstantis natura censetur esse, & ex- perimento constat. Cuius rei triplicem rationem assignat: primò quod Luminaria suis lationibus generant quauor primas qualitates à primo gradu vsque ad octauum, & sum- mum: Secundò quia Luminaria eo quod exhibent omnes colores sua uce, consequenter veniunt exhibere etiam il- los gradus qualitatum, quos singulari planetæ exhibent
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MATHEMATICVM. 495 TEPISATRAS of the Moon. There it is called the third decan of Aquarius, 17. signifying detractions and deceits, under the disposition of the Moon. TEPISEVTH of the Sun. There it is the second decan of Scorpio, 18. of deception, detraction, bringing new enmities among men and confirming old ones, whose dominion pertains to the Sun. TERMINI, or Bounds of the Planets, are certain and limited degrees of the signs, 18. in which the planets found therein were observed by antiquity to increase their powers and to have the greatest prerogatives. We have said much about them in V. Fines. Here, however, it will be our task to give a suitable account of this kind of distribution, which Tius has recently devised in Celestial Philosophy; and not only concerning bounds, but also concerning the law of Domicile, Altitude, and Triangle. For thus he writes in lib. 2, cap. 12. One must beware that the five planets, Saturn, Jupiter, Mars, Venus, and Mercury, by reason of their properties, and especially of their own color and light, have among themselves certain determined degrees of qualities of a nature similar to those degrees which the Luminaries produce in all their motions. I said of a similar nature; I mean at least as to degrees, not as to the nature of the quality. For the Luminaries do not produce the qualities which Mars and Saturn, being altogether corruptive, do, etc. And I think that Jupiter has those degrees of warmth which arise from the trine ray; of humidity, however, those degrees which are produced from the sextile ray, and of humidity also those which come from the trine: and hence that he is a lesser fortune by reason of a greater passive quality. Saturn has those degrees of coldness which arise from opposition, that is, the highest; of dryness, however, those degrees which arise from the square, and therefore that he is the greater misfortune, by reason of the excess of coldness over dryness. Finally, Mars possesses those degrees of aridity which emerge from opposition, and of destructive heat those degrees which come from the square; and therefore that he is the lesser misfortune. Mercury, because he appears of an inconstant color, is judged to be of an inconstant nature, and experience confirms it. He assigns a triple reason for this matter: first, because the Luminaries, by their motions, generate the four primary qualities from the first degree up to the eighth and the highest; second, because the Luminaries, in that they exhibit all colors by their light, consequently also come to exhibit those degrees of qualities which they exhibit to the individual planets
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MATHEMATICVM. 47 quintilis sit ferè in medio finium Louis, & Veneris: reliqua dua Martis. In Scorpione septem Martis ex quadrato ad Leo- nem: quatuor Veneris ratione trini ad tropicum Cancri: octo Mercurij, quas censeo maleficas esse ob sesquiquadratum ad initium Cancri, & Arietis: quinque Louis ex biquintili ad tropicum Cancri: sex Saturni. In Sagittario duodecim sunt Louis, quinque Veneris propter trinum ad initium Arietis, & quintilem ad initium Libræ, qui inter fines Louis, & Veneris ad vnquem ponitur: quatuor Mercurij indifferentes: reliqua Saturni & Martis. In Capricorno septem Mercurij, quas potius Veneris putarem cum Chaldais propter initium aug- mentationis d[e]erum: inde septem Mercurij, septem Louis, sine sint Veneris ob quintilem ad initium Arietis, reliqua infortu- narum. In Aquario septem Mercurij ob sextilem ad Arietem: sex Veneris, septem Louis: sed ego censeo esso Saturni propter sesquisquadratum ad Cancrum; & ad Libram: & quinque sequentes Louis, ob radium biquintilem ad Libram: vltima Martis sunt. In Piscibus duodecim sunt Veneris ob trinum ad Cancrum, & sextilem ad Capricornum; qui radium est in medio finium Veneris. & Louis exquisitè: tres Mercurij in- differentes: reliqua infortunarum. In qua finium vniuersa distributione tantum in medio signi Aquarij videtur aliqua difficultas; in reliquis omnibus correspondent fines miro mo- do, iuxta radios partium signorum ad puncta mobilia, unde incipiunt Astra influere primas qualitates. Hucusque Titus: cuius ratiocinationem eisi pro nostro in- stituto longiusculam, volui nihilominus ipsissimis eius ver- bis referre, ne fortè alienis verbis expressa, quicquam suæ maiestatis, atque energiæ deperderet. TERNVELLES in Tabulis Persicis significat Aërculem, seu < 20.> Ingeniculum sidus ad borealem plagam coastans stellis 28. secundum Ptolemæum, at iuxta Bayerum 48. de quo satis alibi dictum. TERRA Vniuersi istius Centrum, ac basis, suprà quam < 21.> cætera elementa innixa sunt, & circà quam cælestes orbes rotantur quando ipsa vt ait Poëta. Ponderibus librata suis immoblis haret. Constituit cum elemento Aquæ vnum corpus sphæricum, cuius / rotunditari non plus officiunt montium altitudines, valliumque cauitates, quam in aurantij pomo tuberculi prominentes: quod magno Diuinæ prouidentiæ consilio fa- ctum, censendum est; quò homines, & animantia probè ibi possent consistere, & omnem eius regionem inhabitare. Quandoquidem cum primò creata est ea perfectè sphærica
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MATHEMATICVM. 47 the quintile is almost in the middle of the bounds of Jupiter and Venus: the remaining two are of Mars. In Scorpio there are seven of Mars from the square to Leo: four of Venus by reason of the trine to the tropic of Cancer: eight of Mercury, which I judge to be malefic because of the sesquiquadrate to the beginning of Cancer and Aries: five of Jupiter from the biquintile to the tropic of Cancer: six of Saturn. In Sagittarius there are twelve of Jupiter, five of Venus because of the trine to the beginning of Aries, and the quintile to the beginning of Libra, which is placed by a hair’s breadth between the bounds of Jupiter and Venus: four of Mercury, indifferent: the rest are of Saturn and Mars. In Capricorn there are seven of Mercury, which I would rather think of Venus with the Chaldeans, because of the beginning of the increase of days: then seven of Mercury, seven of Jupiter, whether they be of Venus because of the quintile to the beginning of Aries, the rest are of the infortunes. In Aquarius there are seven of Mercury because of the sextile to Aries: six of Venus, seven of Jupiter: but I think they are of Saturn because of the sesquiquadrate to Cancer; and to Libra: and the five following, of Jupiter, because of the biquintile ray to Libra: the last are of Mars. In Pisces there are twelve of Venus because of the trine to Cancer, and the sextile to Capricorn; which is the ray in the middle of the bounds of Venus and Jupiter exactly. Three of Mercury, indifferent: the rest of the infortunes. In this entire distribution of the bounds there seems to be only one difficulty, in the middle of the sign of Aquarius; in all the rest the bounds correspond in a marvelous way, according to the rays of the parts of the signs toward the movable points, whence the stars begin to influence the primary qualities. Thus far Titus: whose reasoning, although somewhat long for our purpose, I nevertheless wished to relate in his very own words, lest perhaps, if expressed in other words, it should lose something of its majesty and energy. TERNVELLES in the Persian Tables signifies Hercules, or the kneeling constellation, situated toward the northern part, with 28 stars according to Ptolemy, but according to Bayer 48. Enough has been said elsewhere about this. THE EARTH, the center and base of this whole universe, upon which the other elements rest, and around which the heavenly spheres revolve, when it itself, as the poet says, Weighed down by its own weights, it lies unmoving. It forms with the element of water one spherical body, to whose roundness the heights of mountains and the hollows of valleys do no more harm than the projecting bumps on an orange: and this, one must judge, was done by the great wisdom of Divine Providence, so that men and living creatures might properly dwell there and inhabit its whole region. For since at its first creation it was perfectly spherical
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MATHEMATICVM. 308 Existimauit Origenes, vt videre est in eius Commentar. super Ezechielem, terram esse magnum quoddam Animal sensu, & ratione prædi um, eoquod ibi cap.1. dicatur coram Deo peccasse: Quæ dicta per prosopopeiam ipse littera- liter inrellexit. Sed & Keplerus in Epitome Astronomiæ Copernicæ terrestrem globum vita præditum, & sua anima non quidem intellectiua, aut sensitiva, sed longe ab his diuersa informarum constantissimè autumat. Cuius rei nul- lum manifestius argumentum proferre se putat, quam Ma- ris fluxum & refluxum, qui magni istius corporis sit velut[ur] vita, & respiratio. Cuius ratiocinationes fusè expendit Ricciolus lib.9. sect.4. cap 4. & fusiùs cap 7. aitque num. 11. in hanc eandem de telluris anima opinionem ex magnetico sibrarum ductu processisse Guillermum Gilbertum lib.5. de Magnetecap.11. vbi vim magneticam ob tam varios, & mi- rabiles motus, aut quamdam animam esse, aut facultatem animæ imitatice[m] contendit, & lib.6. cap.4 experimentis Terrellæ ostendere conatus erat telluris globum esse ma- gnum magnetem. <24> Est aurem Terrella nil aliud, quam magnes in globi for- mam contornatus, in quo deprehendere licet id experiri vo- lenti duos polos, ac facies axem ipsius terminantes: & acus magnetice superimpositæ semper congruunt illius axi secundum sui longitudiuem: sed quoad altitudinem inclinantur magis, minusque versus polos terrellæ p[er] ovt magis, minus- que distant ab ipsis. Cum ergò similia eueniant in acubus magneticis respectu axis mundi & terræ, hinc sibi satis probabiliter visus est colligere terram esse magnum magne- tem: & sicut terrellæ globus pyxidi lignæ inclusus, vt su- pernatare possit, & aquæ superpositus, itavt eius polus bo- realis in Austrum tendat circulari motu se circà sui centrum conuertit, donec ipsius polus boreus boream respiciat; ita iudicat tellurem revolutioni magneticæ aptum esse, vt posi- tionem suam ad Mundi polos, quam semel habuit conseruet. Quod adhuc verius esset, si, vt affitmat Petrus Peregrinus terrellæ globus super polos suos in meridiano suspensus re- uolueretur in horis 24. Cæterum hanc Kepleri opinationem de terræ anima largo modo sumptâ pro principio intrinseco vitæ, sunt qui existimant non omninò falsam, nec Sacra Paginis, aut Philosophiæ principiis contrariam, qua de re vide quæ de Mundi forma diximus in V. Mundus. <25.> Credibile est terrestrem globum illuminari à Sole non se- cus ac coelestia corpora, quæ item in se ipsis opaca sunt, & densa, sed à Solis radiis in eorum superficie plana, ac leui- I i
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MATHEMATICVM. 308 Origen thought, as may be seen in his Commentary on Ezekiel, that the earth is a certain great animal endowed with sense and reason, because there it is said that it sinned before God in chapter 1: words which he himself understood literally, though they were spoken by way of prosopopoeia. And Kepler too, in the Epitome of Copernican Astronomy, most steadfastly maintains that the terrestrial globe is endowed with life, and with a soul of its own, not indeed intellectual or sensitive, but very different from these. He thinks he can present no clearer argument for this than the flow and ebb of the sea, which are, as it were, the life and respiration of that great body. Riccioli examines these reasonings at length in book 9, section 4, chapter 4, and more fully in chapter 7; and he says, no. 11, that William Gilbert advanced into this same opinion concerning the soul of the earth from the magnetic drawing of the fibers, in book 5 of On the Magnet , chapter 11, where he argues that the magnetic force, because of so many various and wonderful motions, is either some kind of soul, or a faculty imitating soul; and in book 6, chapter 4, he had tried by experiments with the terrella to show that the globe of the earth is a great magnet. <24> A terrella, however, is nothing other than a magnet fashioned into the form of a globe, in which one can perceive, for anyone wishing to test it, two poles and the ends of its axis: and magnetic needles placed upon it always align with its axis along their length; but in height they incline more or less toward the poles of the terrella, according as they are more or less distant from them. Since, therefore, similar things happen in magnetic needles with respect to the axis of the world and of the earth, he thought he could quite probably infer from this that the earth is a great magnet; and just as the globe of the terrella, enclosed in a wooden box so that it may float, and placed upon water, turns around its center by circular motion until its northern pole faces north, while its northern pole is directed toward the south; so he judges the earth to be fit for magnetic revolution, so that it may preserve its position with respect to the poles of the world, which once it has had. This would be even truer if, as Peter Peregrinus asserts, the globe of the terrella, suspended over its poles in the meridian, were to revolve in 24 hours. Meanwhile, there are some who think that this opinion of Kepler about the soul of the earth, taken broadly as an intrinsic principle of life, is not altogether false, nor contrary to Sacred Scripture or the principles of philosophy; on this matter see what we said about the form of the world in V. Mundus . <25.> It is credible that the terrestrial globe is illuminated by the Sun no less than the heavenly bodies, which likewise are opaque and dense in themselves, but are illuminated by the Sun’s rays on their flat and smooth surface, I i
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504 LEXICON. immortalis miserere nobis, mox diuinitus cessauisse. Sed & Cordubæ terremotum tres annos durasse tradit Auerroes: quo tempore scribit Ioannes Anglicus Hispaniam ab Africa, & Ossam ab O. ympo sciunctam tuisse. <27.> Multa sunt Terræmotus signa, quæ nos, vt contrà ipsum præmuniamus edocent. Imprimis eum naturaliter prænoscunt muta animantia, vt mures, qui è domibus mox casuris aufugiunt: item Gallinæ, & Pauones hac illac inordinatè discurrentes ac volitantes, atque siue in montes, siue in ædium superiora contendentes: quo signo refert Suessanus in sua Meteorologia præmonium Anaximenem Philosophum terræmotum mox futurum prædixisse. Cuius rei rationem afferunt tetrum odorem ab ipsis alioqui acutissimi olfactus, è terræ visceribus ob pessimam illam exhalationem prosilientem exceptum, atque adeo ob id animalia loco aufugere. Secundò ipsum terremotum præueniunt leues quædam concussions, mox aliquando, vt supra diximus sonitus, quibus quasi vocibus naturæ Author nos admonet vt fugamus à sacie arcus. vt liberentur electi. Tertiò si aqua in puteis ex se fiat turbida, ac tetrum odorem mittat; si ebulliet, & quodammodo subsiliat, & sursum ascendat: etenim hæc omnia effectus sunt exhalationis foras exire contendentis. Item si fiat tranquillitas aëris intempestiua: si interdiu, aut paulò post Solis occasum sereno cælo appareat nubecula quædam tenuis instar lineæ in longum protensæ: si media æstate ingruat insolitum frigus. Si mare absque ventis subito intumescat; & alia huiusmodi, quorum longam seriem affert Arist. loco citato, Seneca in quast. naturali. lib. 6. Plin. lib. 2. cap. 38. Sed omnibus abundantior est Resta de Meteoris lib.... <28.> Porrò contra terremotus præsidium nullum in Natura extare rectiùs existimauerim. Est enim Dei Vindicis flagellum, quemadmodum & pestilentia, aduersus quam nullum planè datur antidotum. Si vllum esset, id sane foret terram cauernis, & pluribus puteis aperire quò perniciosus illehalitus viam sibi ad exeundum parare possit: vti in vbium obsidionibus per aduersos cuniculos subiecti tormentarij pulueris, atque incensi impetum aliò declinari non si ne fructu videmus. Antiqui carbonum, ac lanarum vim in ædium fundamentis iactam unissimum contrà huiusmodi motus præsidium existimabant: vnde & in celebri illo Dianæ Ephesiæ Fano, vno ex septem Orbis Miraculis idipsum factum legimus, ne terræmotibus quateretur. Alij Domus humiliores habitare consueuerunt, istæ enim difficiliùs
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504 LEXICON. immortalis, have mercy on us, had soon ceased by divine intervention. But Averroes says that the earthquake at Corduba lasted three years: at which time Johannes Anglicus writes that Spain was separated from Africa, and Mount Ossa from Olympus. <27.> There are many signs of earthquakes, which teach us how to be forewarned against them. First, dumb animals naturally perceive them in advance, such as mice, which flee from houses about to collapse; likewise hens and peacocks, running and flying hither and thither in disorder, and making for either the mountains or the upper parts of buildings: on this sign Suessanus reports in his Meteorologia that Anaximenes the philosopher foretold an earthquake as about to occur. The reason they give for this is a foul odor, perceived by those animals whose sense of smell is otherwise very keen, rising from the bowels of the earth through that evil exhalation, and so the animals flee from the place. Secondly, earthquakes are preceded by certain slight shocks and, as we said above, sometimes by sounds, by which, as though by the voices of nature, the Author admonishes us to flee from before the face of the bow, that the elect may be delivered. Thirdly, if the water in wells of itself becomes turbid and emits a foul smell; if it boils and in some measure leaps up and rises upward: for all these things are effects of an exhalation striving to come out. Likewise, if there is an untimely stillness in the air; if by day, or a little after sunset, a certain thin cloud appears in a clear sky, stretched out in length like a line; if in midsummer unusual cold comes on. If the sea suddenly swells without winds; and other such signs, a long list of which Aristotle gives in the passage cited, Seneca in the Naturales Quaestiones, book 6, Pliny, book 2, chapter 38. But more abundant than all is Resta de Meteoris, book.... <28.> Moreover, I would rightly judge that there is no defense against earthquakes to be found in nature. For they are the scourge of the avenging God, just as pestilence is, against which absolutely no antidote is given. If any existed, it would surely be to open the earth with caves and many wells, so that that harmful exhalation might make a way for itself to escape; as in the sieges of cities, by countermines, we see the force of the gunpowder and fire applied below diverted elsewhere not without result. The ancients thought that the force of charcoal and wool thrown into the foundations of buildings was the only defense against such movements: whence also in that famous temple of Diana of Ephesus, one of the seven wonders of the world, we read that the same thing was done, lest it be shaken by earthquakes. Others used to live in lower houses, for these are more difficult
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MATHEMATICVM. 305 runt : vnde & Traianus iussit ne Domus sexaginta pedes excederent. Suessanus econtrà perpendens periculum hali- tuum pestilentialium è terræ hiatibus erumpentium, putat opportunius esse edita palatiorum inhabitare, hæcque ob validissima & profundissima fundamenta difficilius ruere. Linesius nullum maius effugium fore asserit, quam in mare contendere, atque in Nauibus se recipere. Vetum nullum validius antemurale, quam in Deum confugere, & lachrimis, aepiis operibus eius misericordiam implorare. Scribit Nicephorus lib. 17. cap. 3. cum magnus adesset Antiochiae terremotus sub Iustino Imperatore, eas Domos minimè læsas, in quibus præ foribus, aut in angulis hæc breuis oratio scripta esset: Christus nobiscum, state. Potentissimum etiam est quod suprà ex Baronio retulimus Gloriosum Trisagium à puero diuinitùs decantatum, nosque in nuperis Regni nostri motibus mirabilis efficaciæ experti sumus. < 29.> Denique plurima etiam terræ motus effecta connumerantur. Vrbes integræ solo æquatæ; pestilentia mox sequuta: Montium arietatio, & in vnum coëtio, quemadmodum in cremo Sabbæ, circà annum Domini 734. Scribit Theophanes Isauricus apud Anastasium Bibliothecarium: & in Agro Mutinensi factum fuisse memoriæ tradit Plin. lib. 2. cap. 38. In agro, inquit, Mutinensi montes duo inter se concurrunt crepitu maximo assultantes recedentesque inter eos, flamma, fumoque in coelum exeunte interdiù, eo concurfu villa omnes elise, animalia permulta, qua intra fuerant exanimata sunt; Nouæ aquarum scaturigines, vt scribit idem Plinius: fluviorum in contrarias partes conuersio: eorumdem exsiccatio: nouarum Insularum, & Montium eruptio, atque ad alia loca translatio; vt de quædam regione refert Suessanus vi terræ motus fuisse in Mare asportatam, sibique cum permensem stetisset supernatans viuis adhuc hominibus, ob Soli ariditatem, & materiam pumicosam, demum demersa fuit omnibus hominibus illis miserè pereuntibus. Memorabile est etiam quod refert Plato in Timæo in hæc verba. Atlannis Insula vasto gurgite mersa est, quam ob causam in- navigabile pelagus illud propter absorpta Insulua limum reli- ctum tunc pelagus illud navigabile erat; Insulam enim hab- bat ante ostium, quod vos columnas Herculis appellatis. Quod tamen fabulosum existimat Ioseph Acosta li. 1. Histor. Indic. Nicephorus quoque testatur foeminas sæpissimè ab- orsum passas: idque facilè credi potest contingere siue ex timore concepto, huc etiam ex noxio halitu quem excipe- rent: sicut etiam quod notat Eurgerius apud Antiochion Ii iii
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MATHEMATICVM. 305 runt : whence Trajan also ordered that houses should not exceed sixty feet. Suessanus, on the other hand, considering the danger of pestilential vapors bursting forth from the openings of the earth, thinks it more suitable to inhabit the higher parts of palaces, these being less likely to fall because of their very strong and very deep foundations. Linsius asserts that there will be no greater refuge than to make for the sea and take shelter in ships. But no stronger bulwark exists than to flee to God and, with tears and pious works, implore His mercy. Nicephorus writes, book 17, chapter 3, that when a great earthquake was present at Antioch under the Emperor Justin, those houses were least damaged in which, before the doors or in the corners, this brief prayer had been written: Christ is with us, stand fast. Most powerful also is that which we have related above from Baronius, the glorious Trisagion sung by a child by divine inspiration, and which we ourselves in the recent movements of our kingdom have experienced to be of marvelous efficacy. < 29.> Finally, many effects of earthquakes are also counted. Entire cities leveled to the ground; pestilence soon followed: The collision of mountains and their coming together into one, as in the city of Sabbæ, around the year of the Lord 734. Theophanes the Isaurian writes, as cited by Anastasius the Librarian; and Pliny, book 2, chapter 38, records that it happened in the Mutinian plain: “In the Mutinian plain, he says, two mountains rushed together with a tremendous crash, then withdrew, and between them fire and smoke rose into the sky by day; in that collision all the villages were crushed, and many animals, which had been within them, were killed.” New springs of water, as the same Pliny writes; the changing of rivers into contrary directions; their drying up; the eruption of new islands and mountains, and their transfer to other places; as Suessanus relates of a certain region, by force of an earthquake it was carried into the sea, and, after remaining afloat for a month and still containing living men, because of the dryness of the soil and the pumice-like material, it finally sank, with all those men miserably perishing. It is also noteworthy what Plato relates in the Timaeus in these words. The island of Atlantis was swallowed by the vast whirlpool, on which account that sea was then navigable; for after the island was absorbed, the mud left behind made that sea unnavigable; for it had an island before the mouth, which you call the Pillars of Hercules. However, Joseph Acosta considers this fabulous. Nicephorus likewise testifies that women very often suffered miscarriage; and this can easily be believed to happen either from fear conceived, or also from the harmful vapor which they inhaled: as also what Eurgerius notes among the Antiochians. Ii iii
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MATHEMATICVM. 307 horoscopum: linnetum ratio, studiorum, ac præsertim me- mori[us] hinc auspiciati solet, nec sanè abque fundamento: hæc enim temperamentum sequuntur, quod quando est siccum retentiuam adjuuat, quemadmodum humidum de- struit, licet citò capere faciat: Atqui Planetæ ex Nona domo cadentes, ac siccis qualitatibus præditi respicientes de trino horoscopum iisdem qualitatibus nascentis animum im- buunt. Gaudet in hac Domo Iupiter, qui cum naturaliter ad religionem, ac pietatem propellat, nil mirum, si præ- stet vt & ista Domus sit naturalis Religionis significatiux. THEM: apud Firmicum aliosque Astrologos passim signi- < 37.> cat delineationem cælestis Signorum, Planetarum, aliorum- que siderum positus in cælesti figura erecta ad aliquod tem- poris momentum, vnde rei alicuius tunc temporis coeptæ af- fectiones expiscari solent. THEMESO in sphæra barbarica audit primus Decanus Ca- < 38.> pricorni, manens sub dominatu Iouis, habensque signi- ficata spatiandi, perpendi cum debilitate, & vtilitate gauden- di, &c. Item THESOGAR in eadem sphæra dicitur primus . decanus Ge- < 39.> minorum sub dispositione eiusdem Iouis, cuius est indicium tabellionatus, calculi dati, & accepti, petitionum, scien- tiarum inutilium, &c. Item THEOPIBV ibidem dicitur secundusDecanusPiscium quem < 40.> similiter gubernat Iupiter, haberque significare gloriatio- nls genium, animi elati iramiscendis se rebus arduis. Si- militer. THOPITVS in eadem sphæra barbarica audit secundus de- < 41.> canus Virginis sub dominatu Veneris adducens genium quæstus, opum cogendarum, auaritiæ, &c. THRASCIAS alias Circius Ventus vehementissimus, Septen- < 42.> trioni lateralis, mediusque inter ipsum & Borolybicum: de quo alibi fusè diximus. Nomen istud ad Thracia sortitus est, eo quod ex ufflando per illam prouinciam transeat: qua etiam ratione ab Hispanis ventus gallicus dictus est. Flare solet in Verisinitio, & in fine Autumni, quibus tempori- < 43.> bus fuimina, nimbos, & procellas adducit: nocet musculis, neruis, articulis; adeoque causat pleuritides, lassitudines, arruumque contractiones. TRHONVM, Solium, atque Carpentum, appellant Astro- < 43.> nomi multiplicem, aut saltem duplicatam dignitatem Pla- nete quam runc is obtinere dicitur, cum repetitur in loco vbi plures dignitates essentiales habet: puta Domicilium, exaltationem, fines: vide in V. Carpentum. Ii iiiij
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MATHEMATICVM. 307 horoscope: a sign of the mind, studies, and especially memory is commonly inferred from it, and not indeed without foundation: for these follow temperament, which when it is dry helps retention, just as humidity destroys it, although it causes quick apprehension. But planets falling from the Ninth house, and endowed with dry qualities, regarding the horoscope by trine, imbue the mind of the native with the same qualities. Jupiter rejoices in this House, and since he naturally impels to religion and piety, it is no wonder if it should also be a natural significator of Religion. THEM: among Firmicus and other astrologers it commonly signifies the delineation of the heavenly arrangement of the Signs, Planets, and other stars in a celestial figure erected for some moment of time, from which they are accustomed to infer the circumstances of some matter then begun. THEMESO in the barbarous sphere is called the first decan of Capricorn, remaining under the dominion of Jupiter, and having the significations of walking about, of weighing, together with frailty, and of delighting in usefulness, etc. Likewise THESOGAR in the same sphere is called the first decan of Gemini under the disposition of the same Jupiter, whose indication is of notarial work, accounts given and received, petitions, useless sciences, etc. Likewise THEOPIBV there is called the second decan of Pisces, which likewise Jupiter governs, and it is said to signify the spirit of glorying, and a lofty mind mingling itself with arduous matters. Likewise. THOPITVS in the same barbarous sphere is called the second decan of Virgo under the dominion of Venus, bringing the spirit of gain, of amassing wealth, of greed, etc. THRASCIAS, otherwise Circius, a very violent wind, lateral to the north and midway between it and the Borolybicus: of which we have spoken at length elsewhere. This name he derived from Thrace, because it passes by blowing through that province: for the same reason it is also called by the Spaniards the Gallic wind. It usually blows at the beginning of spring and at the end of autumn, at which times it brings rains, downpours, and storms; it harms the muscles, nerves, and joints; and thus causes pleurisy, weariness, and contractions of the sinews. TRHONVM, Solium, and Carpentum, astrologers call the multiple, or at least doubled, dignity of a planet, which it is said to have when it is repeated in a place where it has several essential dignities: for example, domicile, exaltation, terms: see under V. Carpentum. Ii iiiij
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114 LEXICON 70. TRIQUETRUM PTOLEMI est instrumentum Mathematicum, perantiquum cuius authorem faciunt Ptolemæum, aptum ad metiendas rerum distantias, altitudines, longitudines, declinaciones. Eius vsum fusè tradit Galluuius de Instrum. Mathemat. 71. TROPÆI Venti sunt Altari de quibus refert Plin. lib. 2. cap. 43. quod etsi in terra alioqui generentur, tamen semper è maris regione perflant. sunt eiusdem rationis ac Apogæi. Verum illi tunc dicuntur, cum ad mare tendunt; cum verò inde redeunt vocantur Tropæi, ex Græca notione tropos, quæ significat conversionem. Venti sunt nimium violenti, qui maria ex improviso commouent, & pluuias repentinas faciunt; quæ tamen momento siniunt. Familiares sunt in Æstate in toro tractu Italiæ, ac præsertim Neopoli; vbi has repentinas pluuias Tropæas vocant. 72. TROPICI appellantur duo circuli minores in sphæra æqualiter ab æquatore distantes, hoc est per gr. 23. cum dimidio, hinc inde qui sunt limites cursus solis, & deviationis ab æquinoctiali circulo: quos cum attigerit, sistit, & convertit iter ad æquatorem: hinc Tropicorum iis nomen est indium. Quorum alter est, qui declinat ab boream, & dicitur Tropicus Cancri, vbi sol efficit maximum diem artificialem, noctemque è contra breuissimam: alter ad Austrum inflectens dictus Tropicus Capricorni, in quo existens sol facit Hyemem, diemque minimum, noctemque longissimam. Quod tamen intelligendum est de nostris regionibus borealibus citra æquatorem Nam in Australibus totum oppositum accidit. 73. TRVTINA HERMETIS apud Astrologos antonomasticè audit artificiosa methodus rectificandi natalitium thema per indagationem dici conceptionis, ab Hermete primum inuenta, ac posteà à Ptolemæo (siue alioquouis Centiloquij Auctore) suo Aphorismo 51. firmata. In quo, inquit, signo Luna est genitura tempore, illud in conceptu fac Ascendens: & in quo signo inuenta fuit in conceptu, illud, aut eius oppositum fac Ascendens imparts. Docet itaque Hermes, magnam intercedere connexionem & rythnum inter diem conceptionis & diem natuitatis, ira vt ordinatissimo semper & constanti motu præcedat Luna à die conceptionis; expletoque dierum numero, quot requiruntur ad maturandum fætum; tum demùm in lucem edat, quando fuerit in eo signo, quod conceptionis tempore orientalem angulum occupabat. Porrò numerum dierum quibus moratur foetus in vtero, auspicandum præcipit à distantia, quam
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114 LEXICON 70. TRIQUETRUM PTOLEMI is a mathematical instrument, very ancient, of which Ptolemy is made the author, suitable for measuring the distances, heights, lengths, and declinations of things. Galluuius gives a full account of its use in De Instrum. Mathemat. 71. TROPÆI are winds of the altar, concerning which Pliny relates in book 2, chapter 43, that although they are otherwise generated on land, they always blow from the region of the sea. They are of the same nature as the Apogæi. But they are called thus when they move toward the sea; when, however, they return from it, they are called Tropæi, from the Greek notion tropos, which signifies a turning. They are excessively violent winds, which suddenly agitate the seas and cause sudden showers, which nevertheless end at once. They are familiar in summer throughout the whole tract of Italy, and especially at Naples, where these sudden showers are called Tropæan. 72. TROPICI are the two smaller circles in the sphere equally distant from the equator, that is, by 23 and a half degrees on either side, which are the bounds of the sun’s course and of its deviation from the equinoctial circle: when it has reached these, it stops and turns its path back toward the equator; hence they are called Tropics. One of them bends toward the north and is called the Tropic of Cancer, where the sun brings about the longest artificial day and, on the contrary, the shortest night; the other, turning toward the south, is called the Tropic of Capricorn, in which, when the sun is there, it makes winter, the shortest day, and the longest night. This, however, must be understood of our northern regions on this side of the equator; for in the southern regions the exact opposite occurs. 73. TRUTINA HERMETIS among astrologers is, by antonomasia, the artful method of rectifying a nativity chart by investigating the day of conception, first invented by Hermes and afterward confirmed by Ptolemy (or, as some say, by the author of the Centiloquium) in Aphorism 51. In that aphorism, he says: “In whatever sign the Moon is at the time of the nativity, make that sign the Ascendant at conception; and in whatever sign it was found at conception, make that sign, or its opposite, the Ascendant when dividing the houses.” Hermes therefore teaches that there is a great connection and rhythm between the day of conception and the day of birth, so that the Moon always precedes by the most orderly and constant motion from the day of conception; and when the number of days required to mature the fetus has been completed, then at last it brings forth into the light when it is in that sign which, at the time of conception, occupied the eastern angle. Moreover, he instructs that the number of days the fetus remains in the womb should be estimated from the distance, which
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LEXICON Tabula Moræ Fætus in vtero. Signa. Grad. Dies Mora. Dies Mora. 0. 0. 273. 0. 12. 274. 0. 24. 275. 1. 6. 276. 1. 18. 277. 2. 0. 278. 2. 12. 279. 2. 24. 280. 3. 6. 281. 3. 18. 282. 4. 0. 283. 4. 12. 284. 4. 24. 285. 5. 6. 286. 5. 18. 287. 6. 0. 288. Luna sub terra. Luna supra terram. Atque hæc est via rectificandi natalitium Thema per diem conceptionis ab Hermete Trismegisto inuenta; quæ tamen aliud non est quam rythmus, & numerorum correspondantia ex ordinatissimo Lunæ circuitu circa tellurem: Qui fit,
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LEXICON Table of the Delay of the Fetus in the womb. Signs. Grad. Days of Delay. Days of Delay. 0. 0. 273. 0. 12. 274. 0. 24. 275. 1. 6. 276. 1. 18. 277. 2. 0. 278. 2. 12. 279. 2. 24. 280. 3. 6. 281. 3. 18. 282. 4. 0. 283. 4. 12. 284. 4. 24. 285. 5. 6. 286. 5. 18. 287. 6. 0. 288. Moon under the earth. Moon above the earth. And this is the way of rectifying the natal theme by the day of conception, invented by Hermes Trismegistus; which nevertheless is nothing other than rhythm, and correspondence of numbers from the most orderly circuit of the Moon around the earth: Which is done,
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MATHEMATICVM. 317 fit, vt semper in idem recidar, atque adeo variato nimium natalitio themate, variari etiam necessariò debet dies con- ceptionis. Tum demum quia ob diuersa accidentia, quæ extrinsecùs aduenire possunt facilè etiam, aut immaturè, aut seriùs edi potest foetus, vt patet experientia: in quo casu nims enormiter fallit hæc methodus. Quapropter so- lidiori fundamento est innitendum. TSAMANGADIV GRIESARA, hoc est, via straminis, apud < 75.> Æthyopes & Hebræos dicitur via lactea, teste Kirchero in Oedipo Ægyptiaco: apud Arabes verò Almagires quasi fluxûs, seu tractus ex sparsapaleâ. TVBERONI, apud Plinium dicitur Stella regia in pectore < 76.> Leonis dicta communiter Regulus, & cor Leonis: sic enim ait, lib 18. cap. 26. Octauo Calendas Februarij Stella regia appellata Tuberoni in pectore Leonis occidit matutino. Nescimus qua ratione, & vnde tandem excerpserit. TURBO, apud Geometras dicitur figura solida, quæ ex < 77.> lato in acutum desinit, seu ex parte verticis lata est, atque inferiorem partem acutam habet: ei contrarius est conus, qui pyramidalem formam referens latum habet pro basi, acutum pro vertice. Nomen hausit turbo ab instrumento lusorio, quod à pueris scutica, vel funiculo circumagitur. Hinc etiam Turbineum appellatur quidquid ex lato desinit in acutum. TURBO etiam dicitur Ventus vorticosus, procellæ species, < 78.> obuia quæque impetens, ac deturbans: Gtæcis Typhon; à Plinio, Vibratus venius, ab aliis Vortex; ab Aristotele Ven- tus indigestus vocatus, hoc est non adhuc perfectè separa- tus à nube: quippe qui semper afferre secum solet aliquam nubium partem. Differt ab Ecnephia; quod is non rectè ascendit: vt ille, sed potiùs in gyrum voluitur secum ele- uans saxa, & alia ingentia corpora; vnde sit postea pluura lapidum, & similium. Plinius aduersus hunc ventum affert pro remedio acerum, quod præcipit debere circum effundi, quia vis, inquit, aceti frigidissima, & subtilissima est; sic- que ardorem turbinis extinguit, crassitiemque eludit. Nau- tæ è contrà bombardarum explosione turbinem disper- dunt. TYMPANA appellantur Tabulæ in Planisphærio, seu Astro- < 79.> labio, in quibus ad quascumque poli eleuationes sunt des- cripti circuli altitudinum, & verticales, vt exiis ortus; & occasus siderum, declinaiones, Cæli inedia:iones, aliaque facilè erui possint. Siquidem singula eorum immediatè subjeciuntur reti seu Voluello, quod cæli stellarumque Kk
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MATHEMATICVM. 317 it happens that I always fall back on the same thing, and thus, if the natal theme is changed too much, the day of conception must also necessarily be changed. Finally, because, owing to various accidents that may happen from outside, the fetus can also be born easily either too early or too late, as experience shows: in which case this method fails enormously. Therefore one must rely on a sounder foundation. TSAMANGADIV GRIESARA, that is, the way of straw, is called the Milky Way among the Ethiopians and Hebrews, as Kircher testifies in the Oedipus Aegyptiacus; among the Arabs, however, Almagires, as it were a flow or tract from scattered chaff. TVBERONI, among Pliny, is called the royal star in the breast of Leo, commonly called Regulus and the heart of Leo: for thus he says, book 18, chap. 26. On the eighth day before the Kalends of February the royal star, called Tuberoni, in the breast of Leo, set in the morning. We do not know by what reasoning, nor whence, in the end, he extracted it. TURBO, among geometers, is called a solid figure which ends from broad to pointed, or which is broad at the top and has a pointed lower part: opposed to it is the cone, which, representing a pyramidal form, has a broad base and a pointed summit. The name turbo was borrowed from the toy instrument which boys spin around with a whip or string. Hence too anything that ends from broad to pointed is called turbine-like. TURBO is also called a whirling wind, a kind of storm striking and driving down whatever stands in its way: among the Greeks, Typhon; by Pliny, a vibrated wind; by others, a vortex; by Aristotle, an undigested wind, that is, not yet perfectly separated from the cloud: indeed one that is usually accompanied by some part of the clouds. It differs from the ecnephia in that this does not rise straight up, as that does, but rather whirls around in a circle, lifting along rocks and other huge bodies; whence afterward comes a shower of stones and the like. Pliny offers, against this wind, vinegar as a remedy, which he says should be poured around, because, he says, the force of vinegar is very cold and very subtle; and so it extinguishes the heat of the whirlwind and eludes its thickness. Sailors, on the other hand, disperse the whirlwind by the discharge of cannon. TYMPANA are the plates in a planisphere, or astrolabe, on which, for whatever elevations of the pole, are described circles of altitude and verticals, so that from them the rising and setting of the stars, declinations, meridians of the heavens, and other things may easily be drawn out. For each of them is immediately placed beneath the rete, or volvelle, which of the heavens and of the stars...
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MATHEMATICVM. 51 tionalium, Iupiter borealium: Saturnus Orientalium, Mars Occidentalium. Vbi aduertendum omnes ventos ex sui intrinseca ratione < 14.> eiusdem esse naturæ, & qualitatis: extrinsecus autem habere, quod iste sic calidus, ille frigidus, hic morbosus, ille salubris, hic lenis ille impetuosus, &c. Cum enim ventus formaliter aliud non sit, quam aer commotus, consequenter pro qualitate aeris, & regionis vnde exsufflat, aut pertransit ventus, naturam induit morbificam, aut salubrem, calores facit, aut frigora, exsiccare sit aptus, aut humores adducere. Sic venti Septentrionales, quoniam à frigidis regionibus, atque ab altissimis montium iugis spirantes ad nos aduentant, ideò frigidi, & sicci sunt: Meridionales, quia à Mari proueniunt, ac per Zonam torridam transeunt, ideo calidi, & humidi magis aut minus prolocorum varietate, & qualitate distantiæ. Vnde Syroccus magis humidus est Genuæ, quam Neapoli, coquia ibi amplior est sinus maris maioremque humorum copiam habet asserre. Econtrà in Sicilia calidus & siccus est, quia ad eam insulam non per mare, sed per continentem Africæ tractum permeat; adeoque omnem humorem ex Oceano haustum linquit in Africa, Africanumque aerem calidum siccumque in Insulam illam opportat Quod adeo vetum est, vt in Regno Chile, & in aliis terræ < 15.> Australis nuper detectæ regionibus accolæ contrarias no, bis experiuntur ventorum naturas, & qualitates: vr testis est Alphonsus de Oualles in descriptione Regni Chile Nam ibi Auster perinde est ac nobis Aquilo, imperuosus, frigidus, & siccus: hic verò è contrà, & ei collaterales venti, qualitates assumunt calidas, & humidas, eo prorsus modo, quo nobis experiri est Syrocum, & Austrum, quia profectò illis à Polo Antartico, & stigida Zona, cuius naturam indunt Auster, & reliqui laterales aduentant, Aquilo verò circius, & Septentrio per Zonam torridam, atque Oceanum transeuntes aerem humoribus repletum, & caloribus feruidum illuc asportant. Quod & nos alibi adnotauimus. Similiter Aquilo in Lusitania, & Neapoli nubes cogit, & pluuius est; in Africa nubes dissipat, ac serenitatem adducit. Septentrio è contrà in Hellesponto, & apud Cyrenen pluuiam creat, in Italia serenus est. Porrò venti cardinales quatuor sunt à totidem mundi < 16.> partibus flantes. Septentrio, de sub Polo Arctico: Auster à Meridie: Subsolanus, ab exortu æquinoctiali: Fauonius ab occasu item æquinoctiali, quibus totidem intermedios a ?- K k ij
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MATHEMATICVM. 51 tional winds: Jupiter, of the northern; Saturn, of the eastern; Mars of the western. Here it is to be noted that all winds, in respect of their intrinsic nature, <14.> are of the same kind and quality; but extrinsically they have this property, that one is thus hot, another cold, one unhealthy, another wholesome, one gentle, another impetuous, and so forth. For since wind formally is nothing other than air in motion, consequently, according to the quality of the air and of the region from which it blows or through which it passes, the wind takes on a morbific or wholesome nature, produces heat or cold, is apt to dry things out or to bring moisture. Thus northern winds, because they blow from cold regions and from the highest mountain ranges and come to us, are therefore cold and dry: southern winds, because they come from the sea and pass through the torrid zone, are therefore hot and more or less humid, according to the variety of places and the degree of distance. Hence the Sirocco is more humid at Genoa than at Naples, because there the gulf of the sea is broader and it has a greater supply of moisture to bring. On the other hand, in Sicily it is hot and dry, because to that island it passes not by sea, but over the tract of the African mainland; and thus it leaves in Africa all the moisture drawn from the Ocean, and brings the hot and dry African air to that island. This is so well known that in the Kingdom of Chile, and in other regions of the recently discovered <15.> southern lands, the inhabitants experience contrary winds in nature and quality, as Alphonsus de Ovalle testifies in his description of the Kingdom of Chile. For there the Auster is to them as the Aquilo is to us: powerful, cold, and dry; while here, by contrast, it and the winds adjacent to it assume hot and humid qualities, precisely in the same way in which we experience the Sirocco and Auster, because indeed for them winds come from the Antarctic Pole and the frigid Zone, from whose nature Auster and the other lateral winds derive their character, whereas Aquilo, the Circius, and the Septentrio, passing through the torrid Zone and the Ocean, carry there air filled with moisture and heated with fire. This we have also noted elsewhere. Likewise Aquilo in Lusitania and Naples gathers clouds and is rainy; in Africa it disperses clouds and brings clear weather. Septentrio, on the other hand, in the Hellespont and near Cyrene produces rain, while in Italy it is clear. Moreover, the cardinal winds are four, blowing from the four corresponding parts of the world <16.> Septentrio, from beneath the Arctic Pole; Auster from the South; Subsolanus, from the equinoctial rising; Favonius from the equinoctial setting likewise, to which correspond the same number of intermediate winds a ?- K k ij
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LEXICON dunt Geographi Bortholybicum, Borthapeliotem, Notapeliotem, & Notolybicum: Addiderut postea & alios quatuor laterales Subsolario, & Fauonio hinc inde grad 13. & semis distantes, hoc est qui spirarent à quatuor punctis ortus & occasus vtriusque Solstitij. Et ab ortu quidem Æstuiali Cæciam, ab Hyemali Vulturnum, ab occasu Æstuiali Corum, ab Hymeali Africum: Pari etiam ratione deprehenderunt quauor alios hinc inde laterales septentrioni, & Austro in eadem distantia ac sunt prædicti à suis cardinibus: Et Circium, & Aquilonem dederunt Septentrioni, illum ad occasum conterminum Borrolybico, istum ad ortum adiacentem Græco. Phoenicem autem, ac Lybanotum Austro: hunc ad occasum, illum ad ortum: ac tandem singulis lateralibus binos hincinde minores ab iisdem lateralibus denominatos Neotherici appinxerunt, vt Africo verbi gratia Ypasticum & Mefafricum: coro Ypocorum, & Mesocorum, &c. qui tamen venti propriè non sunt ab aliis distincti, sed potius quaræ ventorum. Ergò numerus ventorum olim erat 10. postea excreuerunt ad 14. inde ad 16. ac tandem adiectis omnibus collateralibus, iam modò sunt omninò 12. Quorum omnium schema passim exhibent scriptores tabulæ Geographicæ, & nos singulorum naturam in loco quem sibi quisque vendicat explicamus. Quantiæ autem sint ventorum commoditates eleganter explicat Seneca lib. 5. quast Natural: cap. 10. Inter cætera, inquit, Prouidentia opera ex una causa ventos aut inuenit, aut per diuersa dispasuit: sed primùm, vt aëra non sinevent p[er] grescere, sed assidua vexatione vtilem redderent: deinde, vt imbrem terris subministrarent, ij denique nimios compescerens. Nam modò adducunt nubes, modò deducunt, vt per totum orbem pluuia diuidi possent. In Italiam Auster impellit, Aquilo in Africam reijcit: Etesia non patiuntur apud nos nubes consistere: ijdem totam Indiam & Ætiopiam continuis per id tempus aquis irrigant. cap. 16. Ob idque alibi aduerrit, nullam planè regionem esse, quæ non habeat aliquem flatum ex se nascentem, aut circa se cadentem. Tanta est numinis prouidentia in orbe isto suauiter per causas secundas administrando. Sed & hic, (quoriam de ventis agitur,) non erit fortè lectoribus iniucundum, nec à nostro instituto abhorrens colæ, seu orbis piscis Mari Ægyptio familiaris miram naturæ affectionem in medium ferre, & causam inuestigare. Hic enim, & viuus & mortuus se vento semper obuerit, ac pyxide quamuis inclusus, domi è filo pendens,
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LEXICON The Geographers gave them Bortholybicum, Borthapeliotem, Notapeliotem, and Notolybicum. Afterwards they added four others, the lateral ones Subsolario and Fauonio, on either side, 13½ degrees distant; that is, those which blow from the four points of the rising and setting of both solstices. And from the summer rising Cæcias, from the winter rising Vulturnus, from the summer setting Corus, from the winter setting Africus. In like manner also they found four other lateral winds on either side toward the North and the South, at the same distance as those aforesaid are from their cardinal points: and they assigned Circius and Aquilo to the North, the former adjoining Bortholybicus on the west, the latter adjoining Graecus on the east. To the South they gave Phoenices and Lybanotus: the one on the west, the other on the east. And finally they attached to each of the lateral winds two smaller ones on either side, named from those same lateral winds, the Neotherici; as to Africus, for example, Ypasticus and Mefafricus; to Corus, Ypocorus and Mesocorus, etc. These winds, however, are not properly distinguished from the others, but are rather kinds of winds. Therefore the number of winds was once 10; later it grew to 14; then to 16; and finally, with all the collateral ones added, there are now in all 12. The charts of all these are displayed everywhere by writers on geographical tables, and we explain the nature of each one in the place that each claims for itself. The advantages of winds are elegantly explained by Seneca, book 5 of the Natural Questions, chapter 10. Among other things, he says: Providence, by one cause, either invented the winds or dispersed them in different ways: first, so that the air might not merely be blown about, but be made useful by continual agitation; then, so that they might supply rain to the lands, and at last restrain excessive heat. For sometimes they bring down clouds, sometimes carry them away, so that rain may be distributed throughout the whole world. Into Italy the South Wind drives them, the North Wind throws them back into Africa; the Etesian winds do not allow clouds to settle among us; the same winds water all India and Ethiopia with continuous rains during that season. Chapter 16. And for this reason he elsewhere notes that there is absolutely no region which does not have some breeze born from itself or falling around it. So great is the providence of the divine power in governing this world pleasantly through secondary causes. But here also, since the subject is winds, it will perhaps not be unpleasant to readers, nor foreign to our purpose, to present and investigate the cause of the colæ, or fish-wheel, a fish familiar to the Egyptian Sea, and its remarkable natural property. For this creature, both alive and dead, always turns itself toward the wind, and, though enclosed in a box, hanging at home by a thread,
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MATHEMATICVM. 523 clausis adhuc cubiculi foribus, ac fenestris ad eam nihilominus mundi plagam se rictu convertit, vnde ven- tus exsufflat. Hunc ego vidi Veronæ in Musæo Excel- lentissimi Medici ac Philosophi Petri deCastromihi cum primis familiaritate coniuncti, nec sine admiratione rei perieulum hisce oculis feci. Athanasius Kircherus in Arte magnetica rem susè pertractat, aitque id oriti ex Sympathia, ac naturali propensione quam habet piscis ad ventum, quo nimium oblectatur: proindeque ei rictum obuertit, vt eius refrigerantem auram auide excipiat frui- turus, at enim ego, pace tanti viri, potiùs in Antipathiæ ge- nium huius insitæ conversionis causam refundendam censeo. Quæ enim affectio, quæ conuenientia esse poterit huius piscis ad Ventum, quæ illum naturaliter moueat ad eius affectandam auram, hæcque illi sit oppotura? < 19.> Etsi enim non detrectauerim pisces multos pulmone præ- ditos aëris respiratione gaudere; non tamen id eovsqve con- cesserim, vt admittam etiam ventum præsertim violentissi- mum iis commodum cedere: idque maxime in pisce isto haud mole magno, quique respirationis beneficio carere, tum ex eo quod pulmone caret, tum quia extra aquam non diu vi- uit, eensendus est. Itaque Antipathiam potiùs dixerim hanc miram piscis affectionem: ad quod asserendum me mouet tum aquaticorum omnium natura, & interior constitutio, qua illis aqua connaturalis, aër exitialis est, tum etiam ipsa particularis piseis exterior forma, quæ vt nomen indicat. Orbicularis est nisi quantum breuis rictus ex parte prominet, atque ex aduerso cauda magis lata, quam oblonga respon- det, quæ eidem per amplissimos maris sinus discurrenti pro- temone deseruit. Quia igitur forma orbicularis, vt experien- tia docet, nauigationi non admodum idonea est, etiam huic pisci inopportuna aceidit ad natandum. Atqui Venti, quibus mare percellitur, piscibus omnibus, vel iis etiam, qui respirationis vsu fruuntur, eniusmodi sunt Delphini, Pho- eæ, &c. sunt incommodi, (qui sit, vt tempestates præ- sentiant, atque ad eas declinandas in penitiora se maris loca recipiant) sed huic maxime pisci, qui à Natura minus omnibus ad se tutandum, & forma adnandum apta, & au- xiliaribus pinnis fuit instructus, ventus cedit infensus: vn- de est quod aduersus eum eomodo quo potest se communiat, ac resistat, quod sanè præstat ei rictum obuertendo: tum na- turali omnium animantium impetu, quò se ad ea à quibus ex improuiso impetuntur [conuertunt, tum etiam quia in ea, positione magis declinat venti exsufflantis iniuriam: turatur K k iiiij
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MATHEMATICUM. 523 with the doors of the room still closed, and the windows nonetheless turned toward that quarter of the world from which the wind blows. I saw this in Verona, in the Museum of the Most Excellent Physician and Philosopher Peter de Castro, with whom I was closely acquainted, and I made trial of the matter with these eyes no less with admiration. Athanasius Kircher, in his Magnetic Art, treats the matter at length, and says that it arises from a sympathy and natural inclination which the fish has for the wind, by which it is greatly delighted; and therefore it turns its mouth toward it, so as eagerly to receive and enjoy its cooling breeze. But I, with due respect to so great a man, think that the cause of this innate turning should rather be referred to the spirit of antipathy. For what affection, what suitability can there be between this fish and the wind, what can naturally move it to seek that breeze and make it agreeable to it? <19.> For although I have not denied that many fishes furnished with lungs take pleasure in breathing air, I have nevertheless never conceded that even wind, especially the most violent, can be useful to them; and this above all in that fish, which is not of large size, and which must be judged unable to do without the benefit of respiration, both because it lacks lungs and because it does not live long out of water. Therefore I would rather call this strange disposition of the fish antipathy. To assert this, I am moved both by the nature of all aquatic creatures and by their inward constitution, by which water is natural to them and air destructive, and also by the fish’s own outward form, which, as the name indicates, is round, except insofar as a short mouth projects on one side, while on the opposite side there is a tail broader rather than longer, serving it as a kind of prow as it runs through the widest bays of the sea. Since, therefore, a round form, as experience teaches, is not especially suitable for navigation, it is likewise ill-suited to this fish for swimming. But winds, by which the sea is buffeted, are troublesome to all fishes, even to those such as dolphins, porpoises, and the like, which enjoy the use of respiration, because they sense storms in advance and withdraw into deeper parts of the sea to avoid them; but they are especially troublesome to this fish, which Nature has furnished less than all others with means both of defending itself and of swimming, and with auxiliary fins. Hence it is that it protects and resists itself against it as best it can, which indeed it does by turning its mouth toward it; both by the natural impulse of all living creatures, by which they turn toward those things by which they are suddenly attacked, and also because in that position it more readily escapes the injury of the blowing wind. turatur K k iijij
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etiam eius color ac fulgor, mollis & emissitius electro similis. Sed & obseruatione dignum est quod ex Platone notat < 22.> Ficinus in Timæcab. 19. Veneris nempè & Mercurij potentiam contrariam esse Soli; quia, inquit, opposito ad illum motu quandoque mouentur progredientes: Sol occulta prodit, illi econtrà: prætereà Solis potentia cum rebus incomparabilis est, ipsi comparabiles moderantur, comparabilemque efficiunt: Venus conciliationis, & amicitia, Mercurius proportionis, & & commixtionis est author. Hæc Ficinus. De Veneris Astro testatur Varro apud D. August. Deciuitate < 23.> Dei lib. 21. cap. 8 aliquoties murasse colorem, magnitudinem, figuram, & cursum, quod pro portento habitum fuisse ait: Verum inde iure colligit Augustinus non esse contrà naturam, cum in aliqua re, cuius natura innotuit aliquid ab eo, quod erat notum incipit esse diuersum. Et sanè cum Veneris motus, vti & Martis sit maximè irregularis, adeo vix Tychonis temporibus sit compertus, & quandoque extrà Eclypticam diuagetur ad gr. 9. item Mars in Perigeo sub sole fiat, in eodem ferè situ, vbi semper apparet Venus, maximè terris vicinus, proindeque magnitudine Venerem ipsam exæquet, nil mirum si tunc temporis genti sideralis scientiæ minus peritæ, nouis suis irregularitatibus, ac Phoenomenis imposuerit, creditumque fuerit Veneris astrum colorem igneum induisse, locum, motum, ac figuram murasse. Quandoquidem hoc ipsi Tychoni, hoc est homini ad speculanda sidera facto, tantum negotium primò obseruanti facessit, vt diù multumque hæsitauerit, num Martis, aut Veneris Astrum, an potius nouum Phoenomenon coelo pridem natum extiterit. VER Anni initium, & apud Astronomos, & apud Orientales < 24.> dicitur Quanta omnium temperatissima, in qua cuncta florent, omnia exhilarantur, & Mundus ipse exordium sumpsisse creditur: vnde Poëta. Non alios prima nascentis origine Mundi Illuxisse dies, a iumve habuisse tenorem Crediderim: Ver illud erat. Dicitur Ver, vt ait Varro à Virore, quod tum Virgulta omnia virere incipiant: vel vt alij volunt à Vertendo, quod tum vertere se incipiat anni tempus. Diuiditur autem, quemadmodum reliqui Anni quadrantes in tres portiones pro qualitate signorum, quæ tunc temporis perambulat Sol: atque adeo in Ver nouum, hoc est Veris initium, quod computatur toto eo mente quo Sol est in Ariete, qui proinde dicitur
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even its color and brightness, soft and like emitted amber. But it is also worthy of note what Ficinus remarks from Plato <22.> in his commentary on the Timaeus, ch. 19, namely that the power of Venus and Mercury is contrary to that of the Sun; because, he says, they are sometimes moved in an opposite motion when advancing: the Sun reveals hidden things, they, on the contrary; moreover the power of the Sun, though incomparable with things, does not act in a comparable way, and makes them comparable: Venus is the author of reconciliation and friendship, Mercury of proportion and and of mixture. Thus Ficinus. Varro, cited by St. Augustine in De Civitate Dei book 21, ch. 8 <23.> testifies of the star of Venus that it changed color, size, shape, and course on several occasions, which, he says, was regarded as a portent: but Augustine rightly concludes from this that it is not against nature, when in some thing, whose nature has become known, something begins to be different from what was known. And indeed, since the motion of Venus, as well as that of Mars, is highly irregular, so much so that it was scarcely ascertained in Tycho's time, and sometimes wanders outside the ecliptic by 9 degrees, likewise when Mars is in perigee under the Sun, in nearly the same position in which Venus always appears, being very close to the Earth, and therefore equal to Venus herself in magnitude, it is no wonder if at that time it deceived a people less skilled in sidereal science, with its new irregularities and phenomena, and if it was believed that the star of Venus had assumed a fiery color, and had changed its place, motion, and form. For this gave Tycho himself, that is, a man made for observing the stars, so much trouble at first when he observed it, that for a long time he hesitated whether it were the star of Mars, or of Venus, or rather some new phenomenon long before born in the heavens. VER. The beginning of the year, both among astronomers and among the Orientals <24.> is called the most temperate of all seasons, in which everything blooms, all things are enlivened, and the world itself is believed to have taken its beginning: whence the poet: I should not believe that at the first origin of the newborn world other days had shone forth, or that it had had any other season. That was spring. It is called Ver, as Varro says, from viror , because then all shoots begin to grow green; or, as others wish, from vertendo , because then the season of the year begins to turn. It is divided, however, just as the remaining quarters of the year, into three portions according to the quality of the signs which the Sun then traverses: and thus into the new spring, that is, the beginning of spring, which is reckoned throughout that whole period in which the Sun is in Aries, who therefore is called
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MATHEMATICVM. 329 ipsum Albertus cognomento Magnus apud Sixtum Senen- tem in Bibliotheca Sancta tom. 2. lib. 6. annotat. 10. Cæterum primæ huius Asterismi partes calidæ sunt, ac noxię: medię temperatæ: postremæ humidiores. VERUASO LVNAE in Sphæra barbarica dicitur secundus De- <40.> canus Tauti cuius Dominium, ac dispositio spectat ad Lu- nam, & habet significare potentiam, nobilitatem, Imperium in gentes, &c. Hæc, & his similia, Araóum nugæ sunt, qui eò dementiæ deuenerunt, vt singulis decanis signorum Sin- gulos Genios assignarent, singulos suo nomine insignitos, quos qui animi causa leuandi ab grauiotibus cuiis, ac studiis videre voluerit Consulat Oedipum Ægyptiacum Athanasij Kircheri, qui ex fide dignissimis exemplaribus, hæc monu- menta excerpsit, & in curiosorum gratiam edidit. VMELI VS ANDROMEDÆ arab. Mirach dicitur ab Astrono- <41.> mis stella fixa valdè insignis, tecundæ magnitudinis, de na- tura Veneris, in cingulo Andromedæ constituta, de qua fusè dictum in V. Mirach. VOCIFERATOR sidus in Vociferantis formam exprætum <42.> alio nomine Bubulcus, Boores, Plaustri ductor, &c. VOLVELLVM à voluendo dictum est Rete in Astrolabio <43.> motum primi mobilis, ac singulos Solis parallelos, quos in singulos dies describit, necnon fixas insigniores eosque diurnes circulos repræsentans: de quo vide in V. Rete. VORTEX vide Typhon: in idem quippe recidit: & Plinio <44.> auctore, non plus differt à turbinę, quam stridor à fragore: est enim, vt nominis etymon præsefert, ventus vorticinosus omnia in gyrum rapiens, & attollens: dicitur etiam Pinea, vt est Apuleius in lib. de Mundo; qui eum sic describit. Cum scilicet torquetur humus arida, & ab infimo erigitur ad supremum. VRANISCOS, hoc est calum paruum, teste Kircherol in <45.> Oedipo dicitur græcè apud quosdam Rota Ixionis, seu Co- rona Australis sidus ad austrum, de quo al:bi dictum. VRNA Sidus vide Vas, Crater. VRSA Sidus in coelo duplex ad borealem plagam circa po- <46.> lum arcticum: quorum alterum dicitur Vrsa minot, & Cy- <47.> nosura, quæ polo proximius adhæret, & eum denominat arcticum, constans stellis tantummodò septem; (licet Ke- plerus in eo enumeret omninò 10.) quarum postrema in cauda est polaris, & Nautarum Directrix: Alterum dictum Vrsa maior, Helice, à priore non longè distans, sed contra- rio positu, habens stellas omninò 5. iuxta eiusdem Keple- ri obseruationes, sed septem similiter clariores, omnibusque
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MATHEMATICVM. 329 Albertus himself, surnamed Magnus, notes this in Sixtus Senensis, in Bibliotheca Sancta , tom. 2, lib. 6, annot. 10. Moreover, the first parts of this Asterism are hot and harmful; the middle moderate; the last more humid. VERUASO of the MOON in the barbarous sphere is called the second De- <40.> can of Tauti, whose dominion and disposition belong to the Moon, and it is said to signify power, nobility, rule among nations, etc. These, and such like things, are the follies of the Arabs, who have gone so far into madness as to assign to each decan of the signs individual Genii, each marked with its own name; whoever wishes, for the sake of amusement, to see these things rather than heavier labors and studies, let him consult Kircher’s Oedipus Aegyptiacus , who, from the most trustworthy exemplars, gathered these memorials and published them for the benefit of the curious. VMELI VS ANDROMEDÆ, called in Arabic Mirach by astronomers, is a fixed star of very notable brightness, of the second magnitude, of the nature of Venus, situated in the girdle of Andromeda; much has been said of it under V. Mirach. VOCIFERATOR, a star represented in the form of a vociferating man, <42.> also called Bubulcus, Boötes, the driver of the wagon, etc. VOLVELLVM, so called from winding, is the rete in the astrolabe <43.> representing the motion of the first mobile, and the several parallels of the Sun, which it traces on each day, as well as the fixed stars of greater note and those daily circles; see under V. Rete. VORTEX, see Typhon: for it comes to the same thing; and, according to Pliny, <44.> it differs from a whirlwind no more than a hiss from a crash: for it is, as the etymon of the name indicates, a whirling wind snatching everything into a circle and lifting it up. It is also called Pinea, as Apuleius has it in his book De Mundo ; he describes it thus: Namely, when dry earth is twisted and raised from the lowest point to the highest. VRANISCOS, that is, a little heaven, according to Kircher in <45.> the Oedipus , is called in Greek by some the Wheel of Ixion, or the Southern Crown, a star toward the south, of which elsewhere. VRNA, see Star, Vase, Crater. VRSA, a double star in the heavens toward the northern region around the <46.> Arctic Pole: one of them is called Ursa Minor, <47.> and Cynosura, which clings closest to the pole and gives it the name Arctic; it consists of only seven stars, although Kepler counts altogether 10 in it, the last of which, in the tail, is the polar star and the guide of sailors. The other is called Ursa Major, Helice, not far distant from the former, but in the opposite position, having altogether 5 stars according to Kepler’s observations, but likewise seven brighter ones, and all the
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MATHEMATICVM. alibi dicit, ipsum nempè esse turbidum, & caligine plenum: Dum igitur caligo intercipitur inter obiectum visibile, & oculum, consequenter species illius per refractionem alterantur, & obiectum amplius repræsentant, quam reuerat sit. X XIPIHIAS cometæ species colore pallidi in mucronem (à 1. quo illi nomen est inditum) fastigiati, qualem fuisse scribunt qui apparuit anno 1532. De eo mentionem facit Plin lib. 2. cap. 15. Cum apparet portendere solet Infensissimos ventos, qui & Domos subuertant, & arbores eradicent, ariditatem, maximam frumenti penuriam: ex his famem, & quæ ex famè ac terræ sterilitate oriri possunt, inala. XIPIHIAS item dicitur sidus ad polùm Antarcticum, Indo- rum vocabulo Dorado , retroacto sæculo ab Americo Vespuccio vna cum aliis vndecim detectum: constat stellis septem in longitudine sub signo Capricorni: quarum tamen dix, spectant potius ad nubeculam illi proximam: quæ verò in ventre est, maximè accedit ad polum Eclipticæ, & nunc temporis vix vno gradu ab eo distat. Y YPAPHRICVS græcolat. ex & Africo vento, cui est 1. collateralis est enim vns est minus principalibus, qui nouissimè ad ventorum seriem adiecti sunt, & vocantur potius quartæ ventorum, quam Venti: medius est inter Zephirum, & Africum, cui ad dexteram adiacet alius ventus collateralis dictus Masafricus, quarta itidem ipsius Africi ad meridiem tendens, & proxima Vento-Lybico. Sic etiam quotquot sunt venti cardinibus laterales totidem & habent binos ventos minores collaterales sibi hinc inde adiacentes ad dexteram, & sinistram. Vnde Aquiloni adiacet Ypaquilo ad Septentrionem, Masaquilo ad Borrhapeliotem, seu Græcum: Coeciæ, Ypocæcias ad Borrhapeliotem, Meso-Cæcias ad Orientem. Euro Ypoeurus ad Subsolanum, Mesoeurus ad Notapeliotem, seu Syrocium. Phoenici, Ypophoenix ad Notapeliotem, Mesophoenix ad Austrum. Lybanoto Ypolybanotos ad Notolibycum, Mesolybanotos ad Austrum. Coro, seu Argestæ, Mesocorus ad Fauonium, Ypocorus ad Borrolybicum, tandem Circio Ypocircius ad Borrolibicum, Mesocircius ad Septentrionem. Quorum
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MATHEMATICVM. Elsewhere he says that it is indeed turbid and full of haze: therefore, when the haze intervenes between the visible object and the eye, the species of that object are consequently altered by refraction, and represent the object as greater than it really is. X XIPIHIAS, a comet’s appearance, pale in color, tapering into a point (from which it is named), as those who appeared in the year 1532 wrote that it was. Pliny makes mention of it, lib. 2, cap. 15. When it appears, it is usually a sign of the most hostile winds, which both overthrow houses and uproot trees, of drought, and of the greatest scarcity of grain: from these, famine, and the evils that can arise from famine and sterility of the earth. XIPIHIAS is also the name given to a star toward the Antarctic pole, discovered in a former century by Amerigo Vespucci together with eleven others under the Indian name Dorado . It consists of seven stars in length under the sign of Capricorn, of which six, however, seem rather to belong to the small cloud near it; but that which is in the belly comes closest to the pole of the Ecliptic, and at present scarcely stands one degree away from it. Y YPAPHRICVS, from the Greek and the African wind, of which it is a collateral; for it is one of the less principal winds, which were most recently added to the series of winds, and are rather called the quarters of the winds than winds. It lies midway between Zephyrus and Africus, and to its right there adjoins another collateral wind called Masafricus, likewise the fourth from Africus, tending toward the south, and near the Vento-Lybicus. So also, as many winds as are lateral to the cardinal points, so many lesser collateral winds do they have adjoining them on this side and that, to the right and left. Hence to Aquilo there adjoins Ypaquilo toward the north, Masaquilo toward Borrhapeliotem, or the Greek wind; to Coecias, Ypocæcias toward Borrhapeliotem, Meso-Cæcias toward the east. To Eurus, Ypoeurus toward Subsolanus, Mesoeurus toward Notapeliotes, or Syrocius. To Phoenices, Ypophoenix toward Notapeliotes, Mesophoenix toward the south. To Lybanotus, Ypolybanotos toward Notolibycum, Mesolybanotos toward the south. To Corus, or Argestes, Mesocorus toward Fauonius, Ypocorus toward Borrolybicus, and lastly to Circius, Ypocircius toward Borrolibicum, Mesocircius toward the north. Of which
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MATHEMATICVM. 557 solem habeat horizonti proximum semper intra lineam crepusculinam commorantem, atque adeo numquam obscuram noctem, numquam tenebras, numquam etiam intolerabile frigus. < 13.> Vbi quidem magnam connendandc Diuinæ sapientiæ argumentum nobis sit considerandi bus, quod vbique locorum res ita disposuit, vt æstus immoderantiam æqua diei, noctisque vicissitudo, ac frequentes pluuiæ temperarent; & ex alia parte frigoris intoleranda scuitias, & maximus solis recessus à vertice iugi eiusdem suprà, vel circà terram consistentiâ compensaretur. < 14.> Sed & illud mirari licet, quod æstas in Zona torrida tepidior est, tolerabiliorque quam Hyems: quamuis enim Sol ibi verticalis existens deberet maximos æstus adducere, tamen hoc regionibus illis prouidens Natura concessit, vt quamdiù Sol vertici appropinquaret nubibus semper obtegeretur, atque assiduis fastidiosisque cadentibus pluuijs subiecta tellus irrigaretur; cum verò à vertice elongatur, cum eo nubes attrahat, quò cursum dirigit, consequenter alias oras inopertas linquit, quas proinde constanti æstu, continuisque radiis percutit. < 15.> Quod mihi plurium annorum experientia edoctus testatus est oculatus testis omni exceptione dignus Antonius Pema Clericus Regularis Apostolicus ad indos Missionarius ad nos redux, vt alios item operarios in Domini vineam conduceret, vix humanissimus, pijssimus, ac rerum vsu longè instructissimus. Ait enim in Golgondæ Regno se id expertum; quin & in Goa ciuitate totius Orientis Principi, ac celebri emporio, mense Maio, quo Sol Tauri signum percurrens sit ei verticalis, continuis integri mensis pluuiis locum repleri, vnde aquarum copia certos quosdam cyniphes producit hominibus nimium infensos: cum tamen in Hyeme magni calores sint, nullæque pluuiæ. Nec id ratione vacat à Natura desumpta: Videmus enim in arte distillatoria, quid non absimile fieri: vbi enim calor ad summum vasis distilatorij contenderit, atque adunatus fuerit, omnes ad se subiecti humoris vapores trahit, atque in odoratam pluuiam vertit. Sic profecto Sol verticalis euadens ad se omnes terræ vapores attrahit, nubibus conuestitur, pluuias creat, atque ad subiectas regiones demittens eas vberrimè lauat, & rigat. Quo sanè remedio Deus ita orbi prouidit, vt nulla esset Prouncia in qua homines æquè bene non possent consistere, suaque munificentia frui. Ll iii
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MATHEMATICVM. 557 the sun should always have the horizon nearest, always dwelling within the twilight line, and so never darkness, never gloom, never even intolerable cold. <13.> Here indeed there is for us a great argument for considering the divine wisdom, in that everywhere it so arranged things that the excess of heat was tempered by the equal succession of day and night, and by frequent rains; and on the other hand the intolerable sharpness of cold, and the greatest recession of the sun from the summit, were compensated by the sameness of the region lying above or about the earth. <14.> But this also may be wondered at, that summer in the torrid zone is milder and more tolerable than winter: for although the Sun, being there vertical, ought to bring very great heat, nevertheless Nature, providing for those regions, granted that as long as the Sun approached the zenith it should always be covered with clouds, and that the earth beneath should be watered by continual and wearisome falling rains; but when it departs from the zenith, the clouds, which it draws along with it as it directs its course, consequently leaves other shores uncovered, which it therefore strikes with constant heat and continual rays. <15.> This was testified to me as something experienced over many years by a witness worthy of every exception, Anthony Pema, Regular Cleric, Apostolic missionary to the Indies, returned to us, in order that he might also recruit other laborers into the Lord's vineyard, a man scarcely human in his kindness, most pious, and far advanced by long experience of things. For he says that he had experienced it in the Kingdom of Golconda; and even in the city of Goa, the principal city of the whole East and a famous emporium, in the month of May, when the Sun, traversing the sign of Taurus, is vertical there, the place is filled with continual rains for a whole month, from which abundance of water certain gnats are produced that are excessively hostile to men: whereas in winter there are great heats and no rains. Nor is this without reason drawn from Nature: for we see something not unlike this happening in the art of distillation: for when the heat has striven to the highest point of the distilling vessel and has been gathered together, it draws to itself all the vapors of the moisture beneath, and turns them into fragrant rain. Thus certainly the vertical Sun, becoming hot, draws to itself all the vapors of the earth, is clothed with clouds, creates rains, and, sending them down to the lower regions, washes and waters them most abundantly. By this remedy indeed God so provided for the world that there should be no province in which men could not dwell equally well and enjoy his bounty. Ll iii
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PHYSIO-THEOLOGICA pugnat ex Medicis Carolus Rapinius peculiari libello edita de Puluere sympathico. Ioannes Baptista Helmont. Daniel Becherus, Fabritius Hildan, Basilius Valentinus, Ioannes Vritichius, Ioann. Baptista Sitonus, & alij. Ex Theologis verò admittit Paulus Vecchi in obseruationibus Medicis in sacram script. obseru. 60. pro vtraque parte rationes affert Illuminatus Moronus in respons. moral. resp 95. n. 167. sed præ omnibus defendit Bertrandus Loth. Dominicanus in resolut. Theolog. tr. 14. quast. 1. art. 3. Ioan. Petrus Crescentius in Prassiæ. Rom. lib. 3. num. 11; & Ignatius Lupus in edictum sancta inquisit. part. 3. lib. 19. quibus etiam tam pro Philo- sophis, quam pro Theologis meritò annumerandus est. P. Nicolaus Cabæus de Meseoris lib. 4. text. 4. quast. 2. qui ex occasione in hanc eurandi vulnera methodum per sym- pathiam in quacumque distantia incidens hæc haber. Sunt aliqui effectus de quibus videtur ab aliquibus dubitatum, vtrum absoluans omninò à medio, vt est illa ratio medenda vulneribus, qua vulnera curantur applicando medicinam crustis sanguino infectis: dicunt enim sic curari vulnera in quacumque distantia equaliter. Nec res omninò superstitioni obnoxia censeri debet: nullus enim interuenit actus religionis, nec vera, nec falsa; nec medicamentum ipsum ullam habet speciem falsi cultus: est enim omninò simplex medicamentum, omninò simplici modo applicatum, neque ex eo quod causam ignores debes statim damoniacum exclamare; quasi verò om- nia noueris naturalia, & sint in te omnis sapientia apices transfusi. Hæc illi: quæ omnia, addiâ tantorum virorum, qui pro naturali pulueris efficientia stant, authoritate, satis sunt, ad aliquam saltem probabilitatem ipsi conciliandam. Ego verò hic non subsisto; sed in primo limine hærens, si- denter me ostensurum spondeo, absolutè liberum cuique esse pulueris sympathici, omnisque magneticæ curationis vsum, in idque vel adversarios ipsos ex suismet principiis debere conuenire. < II.> Moucor quia commune est Theologorum omnium axio- ma. vt quandocumque dubitatur an effectus sit superstitio- sus, an naturalis à causa naturali etsi nobis ignota proue- niens, censendus semper est naturalis, idque ex eo quia no- bis non notæ sunt omnes naturæ vires, omnes lapidum, mi- neralium, herbarumque virtutes, modusque & celeritas ope- randi: quandoquidem vt author est Plinius Multa sunt Na- tura miracula incomperta adhuc rationis, & in Natura ma- iestate penitus abdita. Ergò fieri potest, vt effectus sit natu- ralis, & nobis in comperta sit eius causa: possessio enim stat
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PHYSIO-THEOLOGICA Charles Rapinius argues among the physicians in a special treatise published On the Sympathetic Powder. Johannes Baptista Helmont, Daniel Becher, Fabritius Hildan, Basilius Valentinus, Johannes Vritichius, Johann Baptista Sitonus, and others. Among theologians also Paulus Vecchi admits it in Medical Observations on Sacred Scripture, Obs. 60, offering reasons for both sides; Illuminatus Moronus in Respons. moral. resp. 95, no. 167. But above all, Bertrandus Loth., a Dominican, defends it in Resolut. Theolog. tr. 14, quast. 1, art. 3; Ioan. Petrus Crescentius in Prassiæ Rom. lib. 3, no. 11; and Ignatius Lupus in the edict of the Holy Inquisition, part 3, lib. 19. Among these he must rightly be counted both among philosophers and among theologians. P. Nicolaus Cabæus, de Meseoris lib. 4, text. 4, quast. 2, who on this occasion, concerning this method of healing wounds by sym- pathy at any distance, has these words: There are some effects about which it seems that some have doubted whether, entirely without any medium, as is that method of healing wounds by which wounds are cured by applying medicine to blood-stained crusts, they say that wounds are thus healed in any distance equally. Nor should the matter be judged altogether tainted with superstition; for no act of religion intervenes, neither true nor false; nor does the medicine itself have any appearance of false worship. For it is altogether a simple medicine, applied in an altogether simple manner; and because you do not know the cause, you ought not at once cry out that it is demoniacal, as though you knew all things natural, and all wisdom had been poured into you. Thus far he. All these things, together with the authority of so many men who stand for the natural efficacy of the powder, are sufficient to win it at least some probability. But I do not stop here; rather, standing at the very threshold, I confidently promise that I shall show it to be absolutely free for anyone to use the sympathetic powder, and indeed every magnetic cure, and that even the opponents themselves ought to agree to this from their own principles. <II.> I am moved because it is a common axiom of all theologians that whenever it is doubted whether an effect is supersti- tious or natural, arising from a natural cause though unknown to us, it must always be judged natural; and this because we do not know all the powers of nature, all the virtues of stones, minerals, and herbs, nor the manner and speed of their working. For as Pliny says: Many miracles of Nature are as yet undiscovered by reason, and are hidden in the majesty of Nature itself. Therefore it can happen that the effect is natural, while its cause is unknown to us; for possession stands
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DE SYMPATHIA. 13 sui sauorem allatus, qui, vt causa æquiuoca, & vniuersalis, plures effectus habet, & multiplicem operandi modum, alium nobis cognitum, alium incognitum. Sic lucem, calorem & his similia sol operatur modo nobis vtiue cognito, & eo pacto, quo ignis, & cætera luminosa intrà suam amplissimam sphæram; & eò ampliùs quò propius, aut rectius fiat ei passum; & si inter ipsum, & passum ponatur obex, impeditur actio illuminandi, aut calefaciendi: alios effectus habet sol, qui non hac regula mensurantur, & alium operandi modum nobis planè incomprehensibilem; producit enim aurum, & mineralia in visceribus terrę posito quocumque obice: dat animantibus vitam, siue e[ss]e longè sint, siue propè, siue ipse in nostro sit, siue in inferiori hemisphærio delitescat, & equè benè, siue nubibus tectus, siue ijs discussis. An autem & in his casibus operetur per contra- stum, ac transmittendo actiuitatem suam per medium, (quamuis in eo nil simile operetur) dubium est: affirmo ego, sed explicare non audeo. Incomperta adhuc rationis hæc sunt, inquit Plinius, & in Natura maiestate penitùs abdita. Quis non in Lunaria, in selenitel pide, atque in <20.> conchilijs non demiretur lunares motus, & maculas? Lunares vices subeunt, & luna crescente crescunt, ea decrescente decrescunt. quorsum hæc actio? à Luna ne, an potiùs ex insita eorum natura? Si à Luna, quonam pacto hæc in minimis quibusque rebus exquisitissimè operatur, & non in alijs? Quomodò non eius actiuitati obest paries interjectus, quin imò & totus terrarum orbis, quando Luna inferius hemisphærium lustrat? Quomodò eius vim sentit selenites in scrinijs, ac domorum penetralibus inclusa? Si immediatè, & ab intrinseca eorum ratione id procedit, quomodò ad operandum ex Lunæ motibus excitantur? Quomodò tam constanter eiusdem affectiones sequuntur? Quod belli describit Marbodæus Poëta Gallus in selenite, sic inquiens: Lunares motus, & menstrua tempora seruat: Crescit enim Lunâ crescente minorque minutâ Efficitur, tamquam calestibus anxia damnis. Pari igitur ratione poterit puluis sympathicus vulneribus opitulari, actionemque suam immediatè in sanguinem exerere atque inde in vulnus transmittere. Respondetur tertio ad argumentum: nullam hîc, & in <21.> similibus casibus dari operationem intermediam, sed omnem immediatè fieri à natura rerum, modo quidem ineffabili, sed quem nos in tertia quæstione explicare conabimur.
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ON SYMPATHY. 13 brought in because of the force of the effect; which, as an equivocal and universal cause, has many effects and a manifold mode of operating, one known to us, another unknown. Thus the sun produces light, heat, and the like, in a way known to us, and in that manner in which fire and other luminous bodies act within their own most ample sphere; and the more so the nearer, or more directly, the patient is disposed toward it; and if an obstacle be placed between it and the patient, the act of illuminating or heating is hindered. The sun has other effects which are not measured by this rule, and another mode of operation altogether incomprehensible to us; for it produces gold and minerals in the bowels of the earth, with any obstacle placed there. It gives life to living creatures, whether they be far off or near, whether it be itself in our hemisphere or hidden in the lower hemisphere, and equally well whether covered by clouds or with them dispersed. Whether in these cases it acts by contrast and by transmitting its activity through the medium, though it produces nothing similar in that medium, is doubtful: I affirm it, but I do not dare explain it. “These things are still unknown to reason,” says Pliny, “and deeply hidden in the majesty of Nature.” Who would not marvel, in lunaria, in selenite, and in shells, at lunar motions and spots? They undergo lunar changes, and as the moon waxes they wax, and as she wanes they wane. Whence comes this action? From the moon, or rather from their innate nature? If from the moon, how does it operate so exquisitely in the smallest things, and not in others? How does the wall interposed between not hinder its activity, and indeed not even the whole earth, when the moon illuminates the lower hemisphere? How does selenite enclosed in caskets and in the inner chambers of houses feel its force? If immediately, and if this proceeds from their intrinsic nature, how are they stirred to act by the motions of the moon? How do they so constantly follow its affections? The Gallic poet Marbodus describes this in the selenite, saying: It preserves lunar motions and monthly times: For it waxes with the waxing moon and becomes smaller with the waning, As though troubled by celestial losses. By the same reasoning, then, sympathetic powder may be able to help wounds, and exercise its action immediately in the blood and from there transmit it to the wound. Thirdly, the argument is answered: in these and similar cases there is no intermediate operation, but everything happens immediately from the nature of things, indeed in an ineffable manner, but one which we shall try to explain in the third question.
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DE SYMPATHIA. 15 morborum intima medicatrix; & cui cæteri omnes præsto sunt adiumenra suppeditantes. Quod si Natura nimium deiecta est, ita vt nullo prorsus 24. adumento leuari valeat, tunc profectò cura omnis euadit inurilis, & si demum perficitur, miraculosa est, non naturalis, nec Sathanica, sed Diuina. Quod autem non quidem subitò (vt falsò quidam prætendunt) sed citius habeatur curatio, & eirà vllam molestiam, aut dolorem per hæc sympathica medicamenta, quam per methodica; non eò ipsò arguitur pulueris inefficacia, ac Dæmonis assistentia; quandoquidem omne id quod facere potest Dæmon per internam, & probam remediorum applicationem potest & ipsa natura per eadem, vel longè suauiora media hominu[m] arte suffecta: vt videmus in præcoci fructuum productione, in olerum ad semihoram eruptione, & alijs miris, quæ abunde exhiber Porta in sua Magia naturali, & nos quotidie experimur, adeóvt iam nobis vilescant, quæ olim in admirazione erant, & arte Dæmonis facta estimabimur. Quod eruditè expressit Barclaius in Argenide lib. v. introducens perbelle Arsidam apud Mauros hospitanrem, atque in mensa Iubæ poma non ita pridem ex arboribus pendentia, mox subita glacie circumdata demirantem: qui posteà rem intelligens ex antiperistasi factam, sale videlicet niui admixto, omnem stuporem abjecit. Sic profectò Natura, arte obstetricante, breui temporis interuallo curationem poterit perficere; via quidem nobis imperscrutabili, sed sibi plana, & facili: Vt proprereà liberum nobis sit, eius semitis inhærendo, eandem viam cæco quamuis ductu fectari. Dices: in dubijs tutior pars est eligenda, ne quis temerè etoris periculo se exponat. Cap. Ad audientiam. & Cap. significasti. 2. de Homicidio. Ergò in dubio num puluis naturaliter agat, an arte Dæmonis, eius vsus est omittendus, atque ad noriora, & tutiora remedia confugiendum: aliàs illum, his prætermisssis, adhibens temerè se exponet periculo errandi, & communicandi cum Dæmone. Contrà quia id procedit in facto, non autem in iure, 26. vt benè aduertit idem Diana, parse 4. tract. 3. resol. 3. & parte 5. tract. 9. resol. 94. cum aliàs sit regula longè vniuersalior, quod in dubijs benigna fieri debet interpræratio. Cap. Estote 2, de regulis iuris. & quod in dubijs melior est conditio possidentis. req. 61. de regulis iuris in 6. quod etiam notat Bonacina, de Censoris disp. 2. quæst. 2. puncto
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The innermost healer of diseases; and to it all the others are at hand, supplying assistance. But if Nature is too much cast down, so that she can by no means be relieved by any aid whatever, then indeed all treatment becomes useless; and if in the end it succeeds, it is miraculous, not natural, nor satanic, but divine. But that the cure is brought about not indeed suddenly (as some falsely claim), but more quickly, and with no disturbance or pain by these sympathetic medicines than by methodical ones, does not on that account prove the inefficacy of the powder, or the assistance of a demon; since whatever the demon can do through the internal and proper application of remedies, nature herself can also do by the same means, or by far more pleasant ones supplied by human art: as we see in the early production of fruits, in the bursting forth of vegetables in half an hour, and in other wonders, which Porta abundantly exhibits in his Natural Magic, and we experience daily, so that now we despise things which were once matters of admiration, and we shall be judged to have been done by the art of a demon. This Barclay elegantly expressed in the Argenis, book V, where he very neatly introduces Arsida lodging among the Moors, and at Juba’s table marveling at apples that not long before were hanging from the trees, but were soon covered by sudden ice: when afterward, understanding the matter to have been done by antiperistasis, namely snow mixed with salt, he cast aside all wonder. So indeed Nature, with art as midwife, will be able in a short interval of time to accomplish a cure; a way indeed inscrutable to us, but plain and easy to itself: so that it is therefore permitted us, by adhering to its paths, to follow the same road, though with blind guidance. You will say: in doubtful matters the safer side must be chosen, lest anyone rashly expose himself to the danger of error. Cap. Ad audientiam. and Cap. significasti. 2. de Homicidio. Therefore, in doubt whether the powder acts naturally or by the art of a demon, its use must be omitted, and recourse must be had to safer and more certain remedies; otherwise one who employs it while neglecting these will rashly expose himself to the danger of error and of communicating with a demon. On the contrary, because this applies to a matter of fact, not of law, as the same Diana rightly notes, part 4, tract. 3, resol. 3, and part 5, tract. 9, resol. 94; and since there is otherwise a far more general rule, that in doubtful cases a favorable interpretation ought to be made. Cap. Estote 2, de regulis iuris. And that in doubtful cases the condition of the possessor is the better. req. 61, de regulis iuris in 6, which Bonacina also notes, de Censoris disp. 2, question 2, point
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PHYSIO-THEOLOGIA, Nos eadem quæ Demon operatur, operari possemus, si eandem, quam ipse habet rerum naturalium notuiam habemus. n. 29. Paracelsus ab omnibus maledictis vindicatus. Nec maiorismihi negotij erit Vnguenti Armarij vsum, atque efficaciam in curandis vulneribus propugnare: quippe quod etsi non parum à memorato puluere discrepet (componitur enim ex diuersis simplicibus aliisque ex humano corpore comparatis, vt videre est apud Auctores, qui de eo ex professo scripserunt, quorum adhuc singuli non eandem componendi methodum tradunt, sed pro suo quisque genio quod lubet, aut magis ad rem facere videtur, Vnguento studet ingerere quiatamen non eo vulnus, sed telum vulneris infflictium inungitur, aut etiam pannus, quo cruor è vulnere manans excipitur; ideo sympathico pulueri valde affinis est, & eandem cum eo difficultatem inuoluit propter miram illam curationem in distans factam, quo virtus vnguemi ferro, aut linteis applicata transfertur, magneticè in ipsum vulnus, illudque etsi distans consolidat. Qua propter eadem ferè argumenta, quibus in asserenda probabilitate lieitoque vsu pulueris sympathici vsi sumus, militant etiam pro vnguento armario, quod eadem sane virtute agit, habetque plurimos ex Medicis, ac Philosophis qui pro eo scribunt, ac naturali virtute illud operari demonstrant. Inter quos Petrus Seruius in Romana Sapientiæ Academia Professor primarius peculiari libello de Vnguento Armario Rodulphus Goclenius senior, atque etiam Iunior in Synarchrosi Magnetica, Osuualdus Gabelchoneurus in Practica Germanica, Cæsar Nagatus de rara vulnerum curatione. Burggrauius in Biolychnio, Psellus, Colerus, Schenchius, Patrisius, Basilius Valentinus, & alij multi. Verumtamen, quia, vtdixi, non æquè ab omnibus traditur; non idem cum puluere parandi modus, ac tempus: multas habet circumstantias, quæ videntur planè inutiles, ac manifestè superstitiosæ, quas non puluis sympathicus: ac tandem, quia in illum longè maiore nisu scriptores multi iique piissimi, ac scientissimi conspirarunt: idcircô operæ pretium erit de eo peculiarem quæstionem instituere, atque eius partes, vsum, curandi vim distinctiùs examinare. Est igitur Vnguentum Armarium conflatum ex diversis ingredientibus; præcipuè verò pinguedine humana sangui-
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PHYSIO-THEOLOGIA, We could do the same things as the Demon performs, if we had the same knowledge of natural things that he has. n. 29. Paracelsus vindicated from all curses. Nor will it be a greater task for me to defend the use and efficacy of the Armary Ointment in curing wounds: for although it differs not a little from the aforesaid powder (for it is compounded of various simples and of others prepared from the human body, as may be seen in the authors who have written on it expressly, of whom each still does not hand down the same method of composition, but according to his own bent puts into the ointment whatever he likes, or whatever seems more useful for the purpose), yet it is applied not to the wound itself, but to the weapon that inflicted the wound, or even to the cloth by which the blood flowing from the wound is received; therefore it is very akin to the sympathetic powder, and involves the same difficulty with it, because of that marvelous distant cure, by which the virtue of the ointment, applied to the iron or to linens, is transferred magnetically to the wound itself, and, though at a distance, consolidates it. Wherefore the same arguments almost, which we used in asserting the probability and lawful use of the sympathetic powder, also hold for the Armary Ointment, which surely acts by the same virtue, and has many physicians and philosophers who write in its favor and demonstrate that it operates by natural power. Among them are Peter Servius, chief professor in the Roman Academy of Wisdom, in a special little book on the Armary Ointment; Rodolphus Goclenius, the elder, and also the younger, in Synarchrosis Magnetica; Oswald Gabelchoneurus in the German Practice; Caesar Nagatus on the rare curing of wounds; Burggrauius in Biolychnion; Psellus, Colerus, Schenchius, Patrisius, Basilius Valentinus, and many others. Nevertheless, because, as I said, it is not handed down alike by all, nor is the method and time of preparation the same as with the powder; and because it has many circumstances which seem plainly useless and manifestly superstitious, which the sympathetic powder does not have; and finally because many writers, and those very pious and learned, have conspired in its favor with far greater effort: therefore it will be worth the trouble to institute a particular inquiry about it, and to examine more distinctly its parts, use, and healing power. Thus the Armary Ointment is compounded of various ingredients; chiefly, however, human fat, blood-
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18 PHYSIO-THEOLOGIA, ad tertium quæstionis caput attinet id discutere. Pro nunc sufficiat demonstrasse multiplicem vnguenti præparationem non arguere eius inefficaciam. <10.> Deinde, cum prædicti Auctores pluribus experimentis suam quisque compositionem probauerint, & ipsa vulnera non omnia eiusdem rationis, sed alia leuia, alia grauiora esse necessum sit: Item & hominum naturæ, (quæ vt ait Hippocrates sunt morborum medicatrices, quasque ego in hoc negotio potissimam partem habere, vnguentum autem leuissimo solum præsidio naturas ipsas subleuare, peculiari quæstione ostendam.) Cum inquam naturæ hominum non sint æquales, sed aliæ robustiores, aliæ nimis deiectæ: mirum non est, si quod hi præcipuam vnguenti materiam dixere, hoc alij suis experimentis edocti in fortis naturæ hominibus, vulneribusque non tam profundis, quæ forte natura se sola potuisset agglutinare, superuacuncum prædicarint, at longe leuiere vnguenti præparatione vbi, eundem planè effectum adepti sunt. Non igitur ex eo quod Natura huius se sola curationem feliciter aggressa est, vnguentum quamvis leuissimum inefficax dicendum erit; si cut non per hoc cætera vulneraria medicamenta prorsus inefficacia exclamarem Philippus Palatius, Petrus Parisius, aliique, eoquod ipsi solo balsamo communi ex oleo, & vinò, aut etiam aqua simplici, & turundis ex cannabe, aut ex lino confectis, etiam deploratæ spei vulnera se curasse testentur. Nam in aliis fortè deiectæ, atque imbecillis naturæ hominibus id ipsum non assequuti fuissent. Quare in hoc etiam à Petro Seruio acerrimo. Vnguenti huius propugnatore dissentio, qui vnguentum à Ioanne Viticchio excogitatum, eo quod Mumiam, cæteraque ex humano corpore fulcimenta prætereat, tanquam inefficax & nullius roboris reijcit asserens nullam tunc ipsi cum ægro intercedere Sympathiam; sed si fortè æger salutem consequatur, eam soli Naturæ acceptam ferendam esse. Non inquam, id placet; nam fieri potest, vt licet Natura multoties se sola salutem asserre sit apta, quandoque tamen ita debilis reperiatur, vt se sola non satis sit, at vel leui præsidio fulta, vires suas exserat atque opus perficiat. Sed de his fusius sequenti quæstione. <11.> Quoad secundum caput, de modo, ac tempore vnguentum parandi, etsi reverâ tot, tantasque circumstantias superuacaneas dixerim, atque earum plurimas à Goclenio, Crolio, Gabelehouero, nescio, nùm animosè magis an scrapulosè præceptas, omninò vitandas suadeam, eo ma-
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18 PHYSIO-THEOLOGIA, As regards the third chief point of the question, it remains to discuss this. For the present it will suffice to have shown that the manifold preparation of the ointment does not prove it to be ineffective. <10.> Then, since the aforesaid authors have each confirmed their own composition by numerous experiments, and since wounds themselves are not all of the same kind, but some slight, others more serious; likewise, since the natures of men too are different, (which, as Hippocrates says, are the healers of diseases, and which I shall show in this matter to play the principal part, whereas the ointment itself only supports nature with the very slightest aid.) Since, I say, the natures of men are not equal, but some more robust, others excessively weak: it is no wonder if what these men called the principal material of the ointment, others, taught by their own experiments, in men of strong constitution and in wounds not so deep, which nature perhaps could have closed by itself, declared to be superfluous, though with a far simpler preparation of the ointment they nevertheless achieved the same result. Therefore, from the fact that Nature has happily undertaken the cure of this wound by herself, the ointment, however slight, must not be called ineffective; just as on this account I would not cry out that all other vulnerary medicines are altogether ineffective, as Philippus Palatius, Petrus Parisius, and others did, because they testify that with nothing but the common balsam made of oil and wine, or even simple water, and with pledgets made of hemp or flax, they have cured wounds of desperate condition. For in other men, perhaps of depressed and weak constitution, they would not have achieved the same. Therefore, in this also I disagree with Petrus Servius, the most ardent defender of this ointment, who rejects the ointment devised by Ioannes Viticchius as ineffective and of no strength, because it omits mumia and the other supports taken from the human body, asserting that then no sympathy exists between it and the sick person; but if by chance the patient recovers, this must be attributed to Nature alone. This, I say, does not please me; for it may happen that although Nature is often capable of bringing about health by herself, at times she is nevertheless found to be so weak that she is not sufficient by herself, but, supported even by slight aid, she exerts her strength and brings the work to completion. But more on these matters in the following question. <11.> As for the second chief point, concerning the manner and time of preparing the ointment, although in truth I have said that so many, and such great, circumstances are superfluous, and although I advise that most of those things prescribed by Goclenius, Crollius, and Gabelehouerus—whether, I know not, more boldly or more scrupulously—be altogether avoided, therefore ma-
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30 PHYSIO-THEOLOGICA, to est, vt ipse posseà indubitato credidit, opus natura duce perfici, quamuis via nobis ignota. Neque verò periculum est, in tali casu circumstantiam fortassis inutilem, quæ adhibetur, Dæmonem in lædus aduocaturam, cumque præsto ad sanitatem donandam affuturum: Nam vt sæpè dixi, Dæmon non est tàm bonus, tamue munificus, vt vel rejectus velit assistere, aique hominem sibi inimicum præsertim cum res culpa vacat, & eius ope rejecta suo vtentem iure velit beneficiis promereri. Patet id satis in memoratis modo experimentis à prædictis Theologis factis: patet id etiam ex implacabili odio, atque inuidia, qua totum hominum genus prosequitur. Nec clementissimus Deus id vnquam permitteret, vt nobis veritates causarum naturalium inuestigantibus, adeoque Deum ipsum, vt Auctorem Naturæ aduocantibus, callidus hostis suis præstigiis in præiudictum veritatis imponeret, falsamque protruderet sed nec permittere potest, vt Theologi omnes consentiunt. 13. Moueor secundò quia huiusmodi circumstantiæ, qualis forte erit vnguentum istud parandum esse Lunâ crescente, in bona domo constituta, & in signo humanæ signuæ; Sole etiam libræ signum, vel certos quosdam eiusdem signi gradus permeante, non sunt prorsùs euanidæ, ac proinde vti suspectæ reijciendæ. Quandoquidem negare non possumus in vniuersum inferiora isthæc occulta quadam vi à superioribus regi, vt patet præsertim in aliorum medicamentorum præparatione, ægrorum decubitum, pharmacorum sumptione venæ sectione, plantarum insitione, alij quæ rerum electionibus, in quibus à peritis, & quidem legumè, vt in loco diximus, plurimum obserua ur situs cælestium corporum ac præcipuè luminarium, à quorum bona vel mala constitutione, configuratione, ac positu pendet bonus, vel malus euentus rerum, provt fuse probat Galenus de diebus Dectatorijs, atque erudiè prosequitur Maginus in lib. de legisimo Astrologia in medicina vsu. Non ergò ob id quod vnguentum in certa syderum constitutione fieri præcipiatur, vanitatis proinde, ac superstitionis erit damnandum. 14. At, inquies. Quid sibi vult humanæ figuræ signum in quo constituta Lunâ præcipitur vnguenti præparatio? Quid Sol in Libra, adhoc vt felix, & auspicata prodeat compositio? Ex signis quidem cælestibus, vt & planetis, alia esse humanæ naturæ amica, alia inimica, alia ignea, alia terrea, alia aliis qualitatibus prædita, verum est, at quod
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30 PHYSIO-THEOLOGICAL, that is, that it itself could, as he had previously undoubtedly believed, be carried out by nature as guide, though the way is unknown to us. Nor indeed is there any danger that, in such a case, a circumstance perhaps useless, which is employed, will call the Demon to aid, and that he will be present ready to grant health: for, as I have often said, the Demon is not so good, nor so generous, that, even when rejected, he would wish to assist, and to help a man hostile to himself, especially when the matter is free from blame, and because his help is rejected he wishes by rights to earn favor through benefits from one using it. This is sufficiently clear from the experiments just mentioned, made by the aforesaid Theologians: it is also clear from the implacable hatred, and envy, with which he pursues the whole human race. And most merciful God would never permit this, that, when we investigate the truths of natural causes, and so call upon God himself as the Author of Nature, a crafty enemy should by his tricks impose upon us to the prejudice of truth and produce falsehood; nor can He permit it, as all Theologians agree. 13. I am moved secondly because circumstances of this kind, such as perhaps the requirement that this ointment be prepared while the Moon is waxing, in a good house, and in the sign of human form; and also the Sun passing through the sign of Libra, or certain degrees of the same sign, are not altogether vain, and therefore are not to be rejected as suspect. Since we cannot deny in general that these lower things are governed by some hidden force from the higher, as is especially evident in the preparation of other remedies, in the lying down of the sick, in taking medicines, in venesection, in grafting of plants, and other choices of things, in which, as experts, and indeed lawfully, as we said in the place, the positions of the heavenly bodies, and especially of the luminaries, are greatly observed, on the good or bad constitution, configuration, and position of which depends the good or bad outcome of things, as Galen proves at length in his book On Critical Days, and Maginus discusses learnedly in the book On the most lawful use of Astrology in medicine. Therefore, because the ointment is ordered to be made under a certain constitution of the stars, it should not on that account be condemned as vain or superstitious. 14. But, you will say, what is meant by the sign of a human figure, in which the preparation of the ointment is ordered to take place while the Moon is positioned? What does the Sun in Libra mean, in order that the composition may come forth fortunate and auspicious? Indeed, from the heavenly signs, as also from the planets, some are friendly to human nature, others hostile, some fiery, others earthy, others endowed with other qualities; this is true, but that which
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DE SYMPATHIA. 51 hoc hominis figuram, illud Arietis, aliud Leonis referat, &c. Hoc planè fictitium est, hominum placitum, ac nugæ vt plurimum à Poëtis excerptæ: idque factum est vel quia stellæ in tali asterismo positæ talem figuram quodammodo referebam, vel potiùs, quia Poëtæ, ne sua figmenta ab hominum memoria exciderent, sideribus appinxerunt, quò in cælestibus perennarent. Cæterum tàm nocet homini canis sidereus quod in eum sirij Fabula translata est, quam canis pictus aut marmore exsculptus: si quid autem nocet, id potius habet à qualitatibus intempetatè calidis, quam à cognomento, aut similitudine canis, quam præ se fert, non quod aliquid commune cum eo habeat. Verum, vt his satisfaciam, notandum est, ex iis, quæ < 15.> in nostro Lexico diximus, huiusmodi fictiones, ea nomina, non temerè à priscis illis Astronomis esse excogitata, ac sideribus attributa, sed vt aliquid sub fabulæ cortice nobis degustandum præberent, eorumque prauas; aut benè has qualitates notas facerent. Nam neque Asta calida sunt, aut frigida, humida, aut sicca, provt communiter dicuntur esse, cum hæ qualitates propriæ elementorum sint, ac solum in sublunaribus hisce, à quibus cælestia longe discrepant, reperiantur. Sed quia nostri antiqui experimentis multis edocti agnouerunt has primas qualitates à certis planetis, ac sideribus gigni, destui, conseruari, &c. Ideò non ineptè eas dictis planetis & sideribus attribuerunt. Sic quia viderunt aliqua signa suis benignis influxibus humanum potissimum genus afficere, vt id nobis significarent, placuit eis in humanam figuram redigere, & his veluti hieroglyphicis eorum naturam explicare: quia viderunt maleficis in primo Zodiaci signo constitutis, aut luminatium defectionibus in eodem signo incidentibus, arietes malo aliquo laborare, cane sidereo exoriente, canes nostros in rabiem agi, &c. Quamuis nil habeant cum Ariete, aut cane commune præter nomen æquiuocum, & aliqualem effectuum similitudinem, eadem talibus nominibus indigitarunt. Et hinc prodiit tanta signorum nomenclatura, atque distinctio in humana, ferina, deformia, pulchra, mutilata, ruminantia, mutà, vocem habentia, &c quæ passim memorant Astronomi. & obseruant in curationibus Medicis. Hinc singulis membris humanis singula Zodiaci signa præfecerunt; obseruationibus quippe cautum est, ea ta ibus membris, nescio qua virtute præesse, itavt nefas sit illud tangere ferro, cum Luna permeat signum quod tali membro
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DE SYMPATHIA. 51 whether this one refers to the figure of a man, that one to Aries, another to Leo, and so on. This is plainly made up, a matter of human fancy, and trifles for the most part taken from the Poets; and this was done either because the stars placed in such a constellation somehow resembled such a figure, or rather because the Poets, lest their inventions should slip from men’s memory, affixed them to the stars, so that they might endure in the heavens. Moreover, a starry dog harms a man just as much as the story of Sirius has been transferred to him, as does a painted dog or one carved in marble: if it does harm at all, it has this rather from unseasonably hot qualities than from the name, or from the likeness of a dog which it bears, not because it has anything in common with it. But, to satisfy these points, it must be noted, from what we have said in our Lexicon <15.> that such fictions, those names, were not rashly devised by those ancient Astronomers, and attributed to the stars, but so that they might offer us something to be tasted beneath the bark of the fable, and make their bad, or rather good, qualities known. For the stars are not hot, or cold, moist, or dry, as they are commonly said to be, since these qualities belong properly to the elements, and are found only in these sublunary things, from which the heavenly bodies differ greatly. But because our ancestors, taught by many experiments, recognized that these primary qualities are generated, destroyed, preserved, and so on, by certain planets and stars, therefore they not unwisely attributed them to the said planets and stars. Thus, because they saw that certain signs, by their benign influences, affect the human race in particular, so that they might signify this to us, it pleased them to represent them in human form, and to explain their nature by these hieroglyphics as it were: because they saw that the malicious powers placed in the first sign of the Zodiac, or the eclipses of the luminaries falling in that same sign, cause rams to suffer some evil, and at the rising of the starry dog, our dogs are driven into madness, and so forth. Although they have nothing in common with Aries or with the dog except the equivocal name, and a certain similarity of effects, they designated them by such names. And from this arose that great nomenclature and distinction of the signs into human, beastly, deformed, beautiful, mutilated, ruminant, mute, speaking, and so on, which Astronomers commonly mention and observe in Medical cures. Hence they appointed particular signs of the Zodiac to individual parts of the human body; for observation has shown that these signs somehow preside over such members, so that it is a sacrilege to touch that member with iron, when the Moon passes through the sign which to that member
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32 PHYSIO-THEOLOGIA, præficitur. Sic etiam abstinendum à potionibus medica- mentorum per aluum euacuantium Lunâ versante in siguis animalium ruminantium, nam tunc vomitus excitatur, vt experientia docuit, & ipsemet semel, & iterum obseruaui. Non quod ruminatio illa, quæ eius nominis animalibus competit sit cælestibus signis aliquo pacto communis, sed quia obseruario vomitus semper occurrentis cum Luna permeat dicta signa, causa fuit, vt eadem signa, vt nota fierent, ruminantia dicerentur. Notum etiam est, Luna in Scorpionis signo versante scorpionibus nostris vires augeri, ac tunc temporis infensissimos esse, vt suo malo probauit amicissimus Petrus de Castro Medicus eruditissimus, de quo sæpè in nostro libro meminimus: exorientibus stellis in Delphino positis, in Arginaui, in ceto, & cæteris eiusdem generis, tempestates in Mari excitari. Numquid ne id aceidit, quia Delphini in mati exultantes tempestates præsignant, ideo & stellæ tali nomine insignitæ ex hor capite etiam tempestates decernent? non equidem, sed ideo hoc illis nomen inditum, quia talis naturæ sunt, qua tempestates cum Luna exorientes faciunt, quas Delphini pisces exultatione præsagiunt; vnde æquum fuit, vt eo nomine appellarentur, &c. Neque istæ aniles fabulæ sunt, vt benè aduertit Argotus in Astronomicis lib. 2. cap. 14. Sed obseruationes propè infallibiles longissimi temporis vsu comprobatæ, quæ quidem licitæ sunt, & verissimæ. Nam quamuis Ecclesia damnarit Astrologiam iudiciariam, quæ de hominis vita, & iis quæ à libera voluntate dependent, temerè quicquam pronunciat, (quandoquidem ea impia est, ac planè superstitiosa) tamen quatenus tradit præcepta in Medicina obseruanda, quemadmodum etiam circà Artem navigatoriam, & agticulturam, permisis, & sua permissione probauit. <17.> Nunc igitur non mirum cuiuis esse debeat, si vnguentum nostrum præcipia ur fieri crescente Luna, in bono signo humanam figuram præseferente, & in bona domo constituta. Nam licet id fortè nimis scrupulosum sit, & quandoque superfluum, non est tamen superstitiosum, aut à legitimis Astronomorum præceptis alienum: quando certum est ideo hæc signa talibus figuris, ac nominibus insigniri, quia cum rebus, quæ talem figuram præseferunt, aut nomen obtinuerunt, aliquam seruant analogiam. <18.> Potiùs superstitiosæ dicendæ erunt reliquæ circumstantiæ à Crolio præceptæ: vt scilicet ferrum potius inungatur, quam
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32 PHYSIO-THEOLOGIA, is prescribed. Thus also one must refrain from taking medicines that purge through the bowels when the Moon is in the signs of the ruminant animals, for then vomiting is stirred up, as experience has taught, and I myself have observed it once and again. Not because that rumination, which belongs to animals of that name, is in any way common to the celestial signs, but because the observation of vomiting, which always occurs as the Moon passes through the said signs, was the reason why those same signs were called ruminant, so that they might be known. It is likewise known that, when the Moon is in the sign of Scorpio, our scorpions are strengthened and are then most dangerous, as my very dear friend Peter de Castro, a most learned physician, whom we have often mentioned in our book, experienced to his cost; and that when the stars set in the Dolphin, the Argo, the Whale, and others of the same kind are rising, storms are stirred up in the sea. Or did this happen because dolphins, leaping in the sea, foretell storms, and therefore the stars distinguished by that name from this fact also indicate storms? Not at all; rather, they were given that name because they are of such a nature that they cause storms to arise with the Moon, storms which the fish called dolphins foretell by their leaping; whence it was fitting that they should be called by that name, etc. Nor are these old wives’ tales, as Argotus rightly notes in the Astronomica, book 2, chapter 14. Rather they are observations, almost infallible, confirmed by the use of very long time, which are indeed lawful and most true. For although the Church has condemned judicial astrology, which rashly pronounces on a man’s life and on those things that depend on free will, since that is impious and altogether superstitious, nevertheless, insofar as it delivers precepts to be observed in Medicine, just as also in navigation and agriculture, it has been permitted and approved by its own permission. <17.> Now therefore no one ought to be surprised if our ointment is prescribed to be made while the Moon is waxing, in a favorable sign bearing the human figure, and placed in a good house. For although this may perhaps be too scrupulous, and at times superfluous, it is nevertheless not superstitious, nor alien to the legitimate precepts of astronomers: since it is certain that these signs are distinguished by such figures and names because they preserve some analogy with things that bear such a figure or have obtained such a name. <18.> Rather, the remaining circumstances prescribed by Crolius should be called superstitious: namely, that the iron should rather be anointed, than
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DE SYMPATHIA. 35 Alij enim id fieri autumant per igniculos quosdam cælestes, seu portiunculam substantiæ illius lucidæ simplicis, & homogeneæ quæ in prima rerum sublunarium formatione sit illis congenita, & admixta, cuius solius ope cælestes influxus participant; vnde etiam sit omnis sympathiæ vis, & cælestium corporum cum terrenis consentio. Alij per effluuium corpusculorum è sanguine medicato ad partem læsam sibi affinem rectà, & naturali impetu commeantium. Alij præsupponunt dari quemdam spiritum Mundi per totum orbem diffusum, qui sit vector occultarum potentiarum, & operationum, quique omnes mundi partes connectat, ac mirum illum consensum, quem nos sympathiam vocamus, pariat, exciterque. Atque per has, & consumiles hypothesium fictiones, rum vnguenti miram virtutem, rum reliqua naturæ arcana, quæ hominum captum fugiunt, explicare contendunt Verum etsi hæc in aliquibus locum habeant, atque ad scopum aliquo pacto colliment, tamen in vnguento armario, & in aliis plerisque nemo ex mea sententia illum tenere potuit. Nam primò, quoad spiritum Mundi vectorem huiusmodi qualitatum, si hunc velimus cum Gotlenio, Auctore Mosaicæ Philosophiæ, & aliis quibusdam, Centralissimum illum Diuinitatis spiritum dicere, qui ab initio vt habetur, Gen. 1. ferebatur super ignas, hoc profectò vel inde impietatem redolet, quod videtur maximè pium. Nam, vt benè Kircherus arguit, iam correret vniuersa Philosophia; iam nulla in causis secundis foret actiuitas, nulla virtus, nulla in rebus proprietas, nulla actiuitatis sphæra, nulla denique in Natura ipsa, hoc est ordinata illa causarum congerie operositas, & causalitatis ratio, proindeque omnia refunderentur in Deum, vt causam immediatam & (quod blasphænum est) etiam peccata; cum rum potentiæ perinde se haberent, vt mera organa; & instrumenta Deo omnia in omnibus operanti inseruientia. Si verò hunc spiritum mundi latiùs sumptum connexionem illam dicamus, qua in vniuersa natura res cognatæ inter se mirum in modum afficiuntur, contrariæ sibi inuicem aduersantur, vna alteri condolet, hæc illi fatali genio subest, altera prædominatur, ita vt in hoc verè saluetur mira illa sympathiæ, antipathiæque vis, ac dissitarum quantumuis rerum nexus, & colligatio, tunc profectò à vero non aberramus vt nos fusè tradidimus, in V. Sympathia, & in V. Mundus, eum de eius forma ageremus, & alibi sæpè: neque à nobis dissentit præcipua Philosophorum schola, neque ipse Kircherus, qui par. 9. cap. c ij
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ON SYMPATHY. 35 For some suppose that this comes about through certain heavenly sparks, or a small portion of that lucid, simple, and homogeneous substance which, in the first formation of sublunary things, is innate and mingled with them, by the sole aid of which they participate in celestial influences; whence also arises the whole power of sympathy, and the accord of heavenly bodies with earthly ones. Others explain it by an efflux of little corpuscles from medicated blood, moving straightway and by a natural impulse toward the affected part that is akin to them. Others suppose there exists a certain Spirit of the World diffused through the whole orb, which is the bearer of occult powers and operations, and which connects all the parts of the world and produces and excites that marvelous agreement which we call sympathy. And by these and similar fictional hypotheses they attempt to explain now the wondrous virtue of the ointment, now the other secrets of nature that escape human understanding. But although these may have a place in some cases and in some way point toward the goal, yet in the ointment of the cabinet, and in most other matters, no one, in my opinion, could hold that view. For first, as regards the Spirit of the World as the bearer of such qualities, if we wish, with Gotlenius, author of Mosaic Philosophy, and certain others, to call this that central spirit of divinity which, as is said at the beginning, Gen. 1, was carried upon the waters, this indeed smells of impiety, even from the very fact that it seems most pious. For, as Kircher rightly argues, then the whole of philosophy would already collapse; there would be no activity in secondary causes, no virtue, no property in things, no sphere of action, and finally no industry and causal order in nature itself, that is, in that ordered heap of causes; and so all things would be referred back to God as the immediate cause and, which is blasphemous, even of sins, since powers would stand as mere organs and instruments serving God, who works all in all. But if we take this spirit of the world in a broader sense and call it that connection by which, throughout universal nature, akin things are affected by one another in a marvelous way, contraries oppose one another, one thing has compassion for another, this one is subject to a fatal genius, another predominates, so that in this way that marvelous power of sympathy and antipathy, and the bond and connection of things however distant, is truly preserved, then indeed we do not depart from the truth, as we have explained at length in V. Sympathy and in V. World, when we treated of its form, and often elsewhere; nor does the principal school of philosophers disagree with us, nor does Kircher himself, who in part 9, chapter
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DE SYMPATHIA. 57 reducta, & inferiore sacrario clausa. Ex quibus aliud hac atas, aliud, qua post subibit accipies. Omnes ad verum collineamus: qui propiùs accedit, gaudeat se in Naturæ penetralia introductum assequi quod cæteris negatum est; qui aberrat, reique veritatem tenere non valer, neque animum suum firmant quæ ab aliis proficiscuntur, fateatur cum Seruio hæc sibi abmirari potiùs datum esse quam nosse: nec proinde ignorantiæ suæ tenebras in potestatem tenebrarum refundar, inde causam tantæ operationis exquirens, quod Philosopho æquè indignum est, ac in primam omnium causam tanquam ad sacram anchoram aduolare. Neque verò mihi vsquequaque probandum est (vt contendit sennertus) dari in vnguento talem vim, quæ vt < 26.> agat non requirit corporum contingentiam, quando id à posteriori per effectus videmus; atque in aliis rebus ipsemet sennertus non diffiteretur. Neque enim, air, sequitur, dantur aliarum rerum tales actiones mirabiles; ergò & vnguentum talem vim habet: sed adhuc id probandum. Nam peto ab ipso: Vnde hahes mi homo, dari in rerum natura huiusmodi actiones mirabiles, quas non à Dæmone; sed ab ipsa maiestate Naturæ esse intelligas, & vnde demum id homini protritæ frontis probares? Cerrè, inquiet, ab experientia, & quia sæpius mirabiles huiusmodi effectus emanare vider. Quod si quis adhuc obstinatior effectus quidem admitteret, de causa verò dubitaret, atque à Dæmone esse contenderet, vel sanè à Deo miraeulosè suprà naturæ vires; vtique ipse statim subiungeret, non esse recurrendum ad causam primam aut ad Dæmonem, quando effectus videtur, nec implicat à Naturæ viribus proficisei, nam tunc censendus est naturalis. Pari igitur ratione effectum eurationis per vnguentum armarium, & alia id genus medicamenta præstitum, naturalem debemus supponere, quando illum sæpè videmus, & veram causam omninò ignoramus. Illi potiùs probandum venit, curationem naturalem non esse, neque naturali via posse haberi, cui inest genius impugnandi, elucetque disparitatis ratio inter hæc & alia naturæ areana: Quod neque à Sennerto, neque ab alio, quod sciam, hactenus factum est. Cum aliàs possessio stet pro Natura; ac tum ratio, tum sexeenta in eodem genere experimenta suppetant, quæ naturalem vnguenti virtutem probant, nec minus pro eo, quam pro aliis Naturæ miraculis militent, vt discurrenti pater. Verum adhuc scrupulus est; Vnguentum istud Paracelsus c iii
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DE SYMPATHIA. 57 reduced, and enclosed in the lower shrine. From these, you will receive one thing in the following place, another in the one that comes next. Let us all aim at the truth: whoever comes nearer, let him rejoice that he has been introduced into the inner sanctum of Nature and has attained what is denied to others; whoever strays and is unable to hold to the truth of the matter, and whose mind is not strengthened by what proceeds from others, let him admit with Servius that it has been granted him rather to marvel at these things than to know them; and therefore let him not pour back the darkness of his own ignorance into the power of darkness, seeking from thence the cause of so great an operation, which is as unworthy of a philosopher as to fly to the first cause of all things as though to a sacred anchor. Nor, indeed, is it altogether acceptable to me, as Sennertus contends, that in an ointment there is such a power which, so as to act, requires no contiguity of bodies, since we see it a posteriori from the effects; and in other matters Sennertus himself would not deny it. For, says he, it does not follow that there are such wondrous actions in other things; therefore the ointment too has such a power: but that still must be proved. For I ask him: Where do you get this, my good man, that there are in nature such wondrous actions, which you understand to be not from the Devil, but from the very majesty of Nature itself, and from where at last would you prove this to a man of brazen forehead? Surely, he will say, from experience, and because such marvelous effects are seen to arise more often. But if someone, even more obstinate, should admit the effect indeed, yet doubt the cause, and maintain that it is from the Devil, or indeed from God miraculously beyond the powers of nature, he would at once add that one must not have recourse to the first cause or to the Devil when the effect is seen, and it does not imply that it proceeds from the powers of Nature; for then it must be judged natural. By the same reasoning, therefore, we ought to suppose the effect of cure brought about by the armarium ointment, and by other medicines of that kind, to be natural, whenever we often see it, and are altogether ignorant of the true cause. Rather, it is for him to prove that the cure is not natural, and cannot be had by natural means, in which there is an inborn tendency to resist; and the reason for the disparity between this and other hidden things of nature is evident: this has not yet been done by Sennertus, nor by anyone else, so far as I know. Since, in other respects, possession stands for Nature; and then both reason and countless experiments of the same kind are available, which prove the natural power of the ointment, and no less fight on its behalf than on behalf of the other wonders of Nature, so that it may be evident to the reader as he proceeds. But still there remains a scruple; this ointment Paracelsus c iii
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PHYSIO-THEOLOGIA, primus in orbem inuexit, hoc est homo supectæ fidei, auctor damnatus, & cui Dæmonem familiarem suisse scribunt, à quo tandem, pacto tempore, strangularus, non leue dedit indicium, se quidquid sciret, quidquid operaretur arcani, à diabolo accepisse. Sed enim ego rem ipsam considero, non vnde sit: parum de soli bonitate curo, dummodò bonam mihi segetem proferat: Naturæ opus agnosco, eam veneror, ipsius munera insequor, auctorem detestor, modum quo arcanum hoc comparauit abominor: est ipsum arcanum tamquam Dei donum in Natura prouisum ad humani generis tutamentum complector. Do vtique Paracelsum suspectæ fidei auctorem suisse; do fædus cum Dæmone iniisse; do etiam huius secreti notitiam auctore diabolo comparasse: at quid inde? nùm mihi idcircò eius vsus prohibitus, quando solis naturæ viribus factum agnosco? non equidem: astipulantur mihi omnes Theologi vno ore docentes, licitum mihi esse vti scientia, seu rerum naturalium notitia semel à me, sive ab alio ope Dæmonis acquisita, dummodo tamen vsus à Dæmonis auxilio non dependeat; quia rerum naturalium cognitio per se bona est, & peccatum quo parta fuit, pertransit. Ita in specie Suar. de superstit. lib 2. cap. 17. Sanchez, in opere moralib 2. cap. 41 Valentia, 1. 2. disputat. 6. quest. 13. puncto. Bonac. hic disput. 2. quest. 5. puncto 4. num 6. & alij. Sat mihi ad omnem culpam euadendam, si Dæmonis operibus non assentior, si eius opem reiicio, & quod ipse ex mirabili rerum qua præditus est cognitione assequitur, id ego parta vt cumque viarum suarum notitia tentare adnitor: < 9.> Neque enim operatio Dæmonum sua est sed naturæ, & ideò, (vt benè aduertit Abulensis, in cap. 7. Exodi quest. 10. in fine.) non est valde miranda, benè autem scientia, qua aliquid faciunt, nam & nos eadem quæ ipsi faciunt, faceremus, si tantam rerum notitiam haberemus: non enim aliud faciunt quam applicare actiua passiuis, sicut faciunt medici, probè colentes rerum naturam consensum, atque dissensum, quid agere possit, & quid & à quo pati, & vbi hoc fieri debeat, & quo tempore; atque adeò hæc illis debito ordine applicantes, quod vtique & nos facere, aut imitari possumus per eam quam vt cumque adepti sumus notitiam: quem etiam longo vsu, experientia, & ingenij < 30.> acumine fortè adeptus est Paracelsus in hac mira vnguenti huius inuentione, quem profectò ab omni inuidiæ nota vindicat egregiè Helmontius afferens luculentissimum de eo testimonium Archiepiscopi Salisburgenus in
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PHYSIO-THEOLOGIA, first introduced into the world by one who was, that is, a man of suspect faith, a condemned author, and of whom they write that he had a familiar demon, by whom at last, after a pact in due time, he was strangled, gave no slight indication that whatever he knew, whatever secret thing he worked, he had received from the devil. But as for me, I consider the thing itself, not whence it comes: I care little for the goodness of the soil, provided it yields me a good harvest: I acknowledge the work of Nature, I revere it, I pursue its gifts, I detest the author, I abhor the manner by which he obtained this secret: I embrace the secret itself as a gift of God provided in Nature for the safeguarding of mankind. I indeed grant that Paracelsus was an author of suspect faith; I grant that he entered into a pact with the Devil; I grant also that he acquired knowledge of this secret with the devil as author: but what follows from that? am I therefore forbidden to make use of it, when I recognize that it was done by the forces of nature alone? Certainly not: all the Theologians support me, teaching with one voice that it is lawful for me to use a science, or knowledge of natural things, once acquired by me, whether by myself or by another through the aid of a demon, provided however that the use does not depend on the Demon’s assistance; because the knowledge of natural things is in itself good, and the sin by which it was acquired passes away. Thus in particular Suar. de superstit. lib. 2. cap. 17. Sanchez, in opere moralib. 2. cap. 41 Valentia, 1. 2. disputat. 6. quest. 13. puncto. Bonac. hic disput. 2. quest. 5. puncto 4. num. 6. and others. It is enough for me to avoid every fault, if I do not assent to the works of the Demon, if I reject his help, and what he himself achieves from the marvellous knowledge of things with which he is endowed, that I, with whatever knowledge of his ways I have acquired, strive to attempt: < 9.> For the operation of Demons is not theirs but nature’s, and therefore, (as Abulensis rightly observes, on chapter 7 of Exodus, question 10, at the end) it is not greatly wonderful; rather is the knowledge by which they do something wonderful, for we too should do the same things that they do, if we had such great knowledge of things: for they do nothing other than apply active things to passive things, just as do physicians, who carefully observe the agreement and disagreement of things, what one thing can do, and what and by whom it can suffer, and where this ought to be done, and at what time; and thus applying these things to them in due order, which indeed we also can do, or imitate, through whatever knowledge we have attained: which Paracelsus perhaps also attained through long use, experience, and acumen of intellect < 30.> in this marvelous invention of this ointment, whom indeed Helmontius splendidly vindicates from every stain of envy by citing a most lucid testimony about him from the Archbishop of Salzburg in
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42 PHYSIO-THEOLOGIA, xi, res longè natura diuetsas, loco separatas, tempore diffitas, inuicem colligatas & mutuo amore connexas, è contrà alias specie, forma, natura, qualitatibus similes dissidere, vnam ad alterius præsentiam pati, approximatam, interna vi, quamuis sensus expertem diuelli, deficere alteram, alteram ad inimici præsentiam alterari, atque ad illius 2. exitium toris viribus niti. Enimuerò quid natura magis dissonum, quam materiale, ac spirituale? Et r amen quæ maior connexio, quæ sympathia potior, quam corporis, & animæ? quam mentis, & phantasiæ? quam voluntatis, & voluptatis? appetitus videlicet sensitiui, qui liberam voluntatem, cui aliàs parêre natus est, ad sibi placita trahit, præuenit, obtenebrat, fascinatque vt de se lugens testatur Apostolus ad Romanos scribens, ac paucis expressit Poëta cum cecinit Buchol. 2 Trahit sua quemque voluptas? Quæ imaginatiuæ proportio cum membris inferioribus, quæ colligatio inter fæcum & visam à Matre rem seu concupitam, seu exosam, quæ mox ex oceulta sympathiæ, antipathiæue vi transeat in affectum, & quod mitabilius, non in concipiente faciat casum, sed in conceptu, statim que appareant vestigia rei quantumuis absonæ in corpusculi membris impressa? Mitto Malacæ affectiones ex immoderato desiderio exortas, vtpotè frequentes, & cuilibet noras; afteram auer- sioni exempla, quæ nihilominus eosdem in concepto fætu effectus dederunt, & ne fides authorem deserat, desumam 3. ex Helmontio cap de iniectis materialibus ipsissimis verbis, quæ propriis ipse oculis hausit. Sartoris vxor, inquir, Mechlinia, præ foribus vidit in conflictu, manum amittero: statim perculsa horrore poperit filiam una manu, altero autem cruentoque brachio extinctam quod manus eius non reperiretur, & hamorrhagia infantem interimeret. Vxor Marci de Vogelor Mercatoris Antuerpiensos anno 1692. videns militem mendicantem cuipila ferrea in obsidione Ostendana dexterum brachium abstulerat, illudque adhuc cruentum circumferebat: mox abinde filiam peperit orbam brachio, & quidem dextero, cuius cruentut adhuc humerus per chirurgum solidam debuit. Nupit Mercatori Amstelodami, cui nomen Hoochamer, illa adhuc anno 1638. superstes. Cæterum nuspiam reperibile fuit brachium dexterum, nec ossa, nec vlla apparuit putris ago, in quam brachium contabuisset parua horula. Attamen nondum conspecto milite fætus bina habebat brachia: nec potuit brachium auulsum annihilari. Ergo clauso vtero ablatum est brachium. Quis autem auulserit naturaliter, & quorsum ablatum sit, certè non quadrant
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42 PHYSIO-THEOLOGIA, things very different in nature, separated in place, apart in time, yet bound together with one another and joined by mutual love, on the contrary others, though similar in species, form, nature, and qualities, to be at variance; one, at the presence of another, to suffer, when brought near, by an inward force, though without sense, to be torn away; one to fail, the other at the presence of an enemy to be altered, and with all its 2. powers to strive toward its destruction. For what indeed is more unlike in nature than the material and the spiritual? And yet what greater connection, what stronger sympathy, than between body and soul? than between mind and imagination? than between will and pleasure? the appetite of the senses, namely, which draws the free will, to which it is otherwise born to obey, toward what pleases itself, goes before it, darkens it, and bewitches it, so that the Apostle, grieving over himself, testifies when writing to the Romans, and the poet expressed this in few words when he sang, Bucol. 2: Trahit sua quemque voluptas? What proportion is there between the imaginative faculty and the lower members, what bond between the soul and the body, or the thing seen by the mother, whether desired or hated, which straightway through the hidden power of sympathy or antipathy passes into affection, and, what is more admirable, not in the conceiving one does it cause the effect, but in the conceived, so that there immediately appear traces of a thing however contrary, impressed upon the limbs of the little body? I pass over the affections of Malacis arising from immoderate desire, as being frequent, and known to everyone; I will take examples of aversion, which nevertheless produced the same effects in the conceived fetus, and lest faith desert the author, I shall quote 3. from Helmont, in the chapter on injected materials, in his very own words, which he drank in with his own eyes. “The wife of a tailor,” he says, “in Mechlin, saw before the door, in the struggle, the loss of a hand: immediately struck with horror she gave birth to a daughter, with one hand, but the other and the bloody arm dead, because her hand could not be found, and the hemorrhage killed the infant. The wife of Marcus de Vogelor, a merchant of Antwerp, in the year 1692, seeing a soldier begging, to whom an iron ball in the siege of Ostend had taken off the right arm, and who was still carrying it around bloody: soon after she gave birth to a daughter without an arm, and indeed the right one, whose shoulder, still bloody, the surgeon had to make whole. She married a merchant in Amsterdam, whose name was Hoochamer; she was still surviving in the year 1638. Moreover, nowhere could the right arm be found, nor the bones, nor did any trace of putrefaction appear, in which the arm would have decayed in a short while. Yet before the soldier had even been seen, the fetus had both arms: nor could the severed arm be annihilated. Therefore the arm was removed while the womb was closed. But who had severed it naturally, and for what purpose it was removed, certainly do not fit
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DE SYMPATHIA. 43 triualos rationes in tanto portento, aut paradoxo. Non sum qui hac dicam: Hæc dicam saltem non fuisse brachium ablatum, vt neque auulsum à Satana. Deinde minoris opera esse deferri alio brachium auulsum, quam fuit brachium à toto auulsisse absque nece. Vxor mercatoris cognita robis, vt audiunt, quod uno mane decapitarentur tredecim (tempore ducis Albani contigis Antuerpiæ) ducunturque inordinatis appetitibus pragnanses, statuit spectare descruncationes. Ascendit ergo cubiculum familiaris sibi vidua in foro morantis; visoque spectaculo, statim illam adorsus est dolor parturientis, peperitque maturum infantem cruento collo, cuius caput nusquam apparuit. Hæc ille: quæ vtiue neque contactui seu Physico, seu Mathematico neque effluuiis, neque similitudini, aut connexioni naturæ accepta referri possunt. Sed tantummodò abditissimo ipsius naturæ mysterio. Item quanta sit cælestium cum terrestribus loci distantia, < 4.> dissimilitudo, & formaru disparitas nemo est qui non videat. Concinunt omnes penè Philosophi nedum formas, sed & materiam corporum cælestium longè esse à sublunaribus diuersam: At enim, hoc non obstante, magna est inter hæc & illa consentio: cursum solis sequitur helitropium, illum, emenso mediæ noctis curriculo, ad nostrum hemisphærium properantem occinens, & exsiliens intelligit Gallus gallinaceus: Lunaria, & selenites Lunæ affectiones persentiunt, easdem prorsus phases, & maculas, provt illa subit, in facie ostendentes: Lunæ cum sole compressum sentit oleæ cinis in fundo argentei vasis aqua pleni consistens, dum mox turbatur, & eorsque in gyrum vertitur, quoad illa à solis complexu se extricauerit: Martis sidere in cælestibus infirmato, aut ab inimicis obesso hebetatur apud nos ferrum, lentescit spiralis throcea in horologiis, & segnius signat horam: econtrà eo benè posito, hoc rigescit, & vires suas duplo auctas resumit. Solè Leonis signum permeante leones febre corripiuntur: Luna in scorpio existente, scorpius noster futit: Cane sidereo ex oriente canes aguntur in tabiem, & alia penè innumera, quæ sparsim habet Plinius, & nos alibi ex occasione retulimus. Sed & temporum vices fato quodam recutrente recurrunt, vnde, vide in Lexico nostro V. Annus Periodicus. & Imperia suas mutationes subeunt, sata quæque ac plantæ statis temporibus germinant, efflorescunt, fructus parturiunt, vt præ cæteris Iuniperus, Aloës, Palma, & tunc miri etiam motus in vniversa Natura insurgunt; ac profectò mirum est, & multorum obseruatione literis consignatum, Neapolita-
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ON SYMPATHY. 43 the rational grounds in so great a marvel, or paradox. I do not mean to say this: I would say at least that the arm had not been cut off, nor yet snatched away by Satan. Then it would be less of an achievement to carry elsewhere an arm that had been torn off, than it was to tear off the arm from the whole body without death. The wife of a merchant, having learned from hearsay that thirteen men were to be beheaded one morning (at the time of the Duke of Alba, as happened at Antwerp), and being pregnant with unruly appetites, resolved to go and watch the executions. She therefore ascended the chamber of a widow, her acquaintance, dwelling in the marketplace; and at the sight of the spectacle she was immediately seized by the pains of labor, and gave birth to a full-term infant with a bloody neck, whose head nowhere appeared. This he says: which, indeed, can be referred neither to contact, whether physical or mathematical, nor to emanations, nor to similarity, nor to connection of nature. But only to the most hidden mystery of nature itself. Likewise, how great is the distance and difference between the heavenly and the earthly, and the disparity of their forms, there is no one who does not see. Nearly all philosophers agree that not only the forms, but also the matter of heavenly bodies is far different from that of sublunary things: but nevertheless, despite this, there is great agreement between these and those: the heliotrope follows the course of the sun; the rooster, when it has completed the circuit of midnight, understands the sun hastening toward our hemisphere by its crowing, and by its leaping up; the lunaria and the selenites perceive the affections of the moon, showing on their face the very same phases and spots as she undergoes: the ash of olive wood, standing in the bottom of a silver vessel full of water, feels the moon compressed together with the sun, and is soon disturbed and turned round in a circle, until she has freed herself from the sun’s embrace: when the star of Mars is weakened in the heavens, or assailed by enemies, iron grows dull among us, the spiral chain in clocks becomes sluggish, and marks the hour more slowly: on the contrary, when it is well positioned, it stiffens and regains its powers, doubled in strength. When the sun passes through the sign of Leo, lions are seized with fever: when the moon is in Scorpio, our scorpion rages: when the stellar Dog rises in the east, dogs are driven into wasting disease, and there are nearly innumerable other things, which Pliny records here and there, and which we have elsewhere mentioned on occasion. But also the alternations of times, by some recurring fate, return again; whence, see in our Lexicon, under V. Periodic Year. And empires undergo their changes; every kind of seed and plant germinates at fixed seasons, blooms, bears fruit, as preeminently do juniper, aloes, palm, and then even wonderful motions arise in all nature; and indeed it is astonishing, and recorded in writing by the observation of many, Neapolita-
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DE SYMPATHIA. 45 titur, ac si in Apulia propè inimicum consisteret. Quartò demum temporis respondentia, quo fit mali recursus nunquam intermittentis, nisi aut alteruter moriatur, aut omne virus penitus extinguatur. Hæc omnia, quæ neque in naturæ similitudinem, aut 7. dissimilitudinem præcise, neque in effluuios spiritus, neque in occultam qualitatem immissam refundi possunt, certò mihi persuadent, atque in mea opinione confirmant, quam alias docui in Lexico V. Mundus, dari aliquam communem formam, quæ Vniuersi istius partes inuicem nectat, atque ad constituendum vnum per se habilitet, tribuatque vnam alteri condolere, aliam ab alia pati, ac diuetsis motibus intrinsecus affici, respondere, in totius conservationem, & ordinem à Natura constitutum viritim conspirare: si enim vniuersum hoc vnum compositum per accidens diceretur, vt quid lapis contrà suam naturam sursum ad replendum vacuum impelleretur, vt quid selenites Lunam, tota substantia, toto cælo diuersam motibus suis imitatetur? Vtque iu humano corpore cum Galeno plures sympathiæ species conspicati sumus, aliam, quæ dicitur operis familiaritatis, aliam generis, & aliam vicinitatis; ex quibus veluti fontibus, omnes internæ memborum affectiones deriuant; ita, & in magno isto corpore Mundi omnes internæ partium affectiones, condolentiæ, dissensiones, mutuæ earum colligationi in vna vniuersali forma acceptæ referri debent, atque ad vnam ex dictis tribus sympathiæ speciebus reduci. Sic aëris contagiones, atque adeo hominum, & iumentorum, vicinitati, sic magneticæ attractiones, & forte fascinus, quæ per medium obicem impediuntur: per effluuios, (vt cerebri affectiones ab stomachi vaporibus sursum elatis) sic etiam ex familiaritate operis, vti in corpore humano mammæ vtero præsertim conceptus tempore sunt colligatæ, ita in Vniuerso, Vere omnia efflorescunt, nedum plantæ, sed & corpora, & ingenia turgent, atque ad quasdam fructificationes mutuò incitantur. Verum vti eodem loco Verbo S. Sympathia num. 128. diximus, sunt aliquæ partium affectiones, & condolentiæ in humano corpore, quæ ad hæc capita omninò reduci non possunt, sed ad aliam occultam virtutem, quæ his tandem accedat, vt pater in delitio mentis, quod ex inflammatione septi transuersi solum oritur, non autem ex obstructione ventriculi, quæ tantum caput dolere facit, ita in hac Vniuersi constitutione plures rerum affectiones sunt, quæ ægè
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DE SYMPATHIA. 45 it is as if in Apulia it were standing near an enemy. Fourthly at length, correspondences of time, by which there comes a recurrence of evil never intermitting, unless either one or the other die, or the whole virus be utterly extinguished. All these things, which can neither be referred precisely to the likeness or unlikeness of nature, nor to effluent spirits, nor to an infused occult quality, do certainly persuade me, and confirm me in my opinion, which elsewhere I taught in the Lexicon V. Mundus, that there is some common form, which binds together the parts of that Universe mutually, and fits them for constituting one thing in itself, and grants that one should feel with another, one suffer from another, and, by diverse motions, be affected inwardly, respond, and, in the preservation of the whole, conspire one by one toward the order established by Nature: for if this whole universe were said to be one composite by accident, to what end would a stone be driven upward contrary to its nature to fill a vacuum, to what end would selenite imitate the Moon, with its whole substance, wholly different from the sky, by its motions? And as in the human body, with Galen, we have observed many kinds of sympathies, one called from the familiarity of the work, another of kind, and another of vicinity; from which, as from sources, all internal affections of the members derive; so also, in that great body of the World, all internal affections of the parts, condolences, dissensions, their mutual conjunction, taken in one universal form, ought to be referred, and reduced to one of the three kinds of sympathy already mentioned. Thus the contagions of the air, and therefore also of men and beasts, are due to vicinity; thus magnetic attractions, and perhaps fascination, which are hindered by a medium obstacle: through effluvia, (as affections of the brain from vapors of the stomach raised upward) thus also from familiarity of work, as in the human body the breasts are especially bound to the womb at the time of conception, so in the Universe, truly all things flourish, not only plants, but also bodies and minds swelling, and mutually provoked toward certain fructifications. Yet as in the same place, in Verbo S. Sympathia no. 128, we said, there are certain affections and condolences of parts in the human body, which cannot at all be reduced to these heads, but to another hidden power, which finally comes to these, as the father in mental delight, which arises only from inflammation of the transverse septum, not however from obstruction of the stomach, which only makes the head ache, so in this constitution of the Universe there are many affections of things, which scarcely
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DE SYMPATHIA. 49 gnatum: quod etiam, quamuis obscurè agnouit Hieronymus Dandinus, Digress. 6. in libros de Anima. asserens florem hunc à principio intrinseco moueri, ad motum solis, sicut lapis ad centrum: quod etiam affirmat de Lunaria sese ad motum Lunæ confoimanre, quam ideò Lunitropium vocat. Similiter in Selenite lapide mira illa mutario macularum ad Phasium Lunarium normam, (cum in solido lapide fiat, nec in externa facie modò sed & in toto corpore, vt eo dissecto videre est,) non nisi ab intrinseco esse potest: mutatur autem per insitam ei cum Luna similitudinem, ac sympathiam quâ, eâ motâ ad similem motum & passionem intrinsecus excitatur. Sic chordæ similes ad alterius contactum resonant non ab aëre moto, vt vult Fracastorius lib. de Sympathia cap. 11. & Aresius de Generat. disp. 1. quast. 41, sect. 7. quandoquidem in alia cythara viciniori, sed non vnisona, & in longe maiori impulsu aëris ad cytharam vsque perueniente non eumdem effectum parit, sed à verissima sympathia intrinsecus chordas vnisonas ad vniformem sonum excitante: neque enim maior dispositio, quam dicunt in istis esse ad recipiendum motum, & edendum sonum, quam in aliis non æquè tensis explicari potest per aliud, quam per istam Naturæ consensione: sed & id contrariâ ratione, Antipathiæ videlicet, euincit alia experientia chordarum ex agni ncruis formatarum, quæ ad cytharæ è lupi chordis compactæ pulsationem statim intrinseca vi dum puncuntur; earum quippe naturâ ad contrarij motum, quod ferre non potest, sese deuiciente. Hinc etiam in plantis idipsum videre est, quæ aliis sibi mutuo amoris nexu deuinctis complantaræ feraciores ac viuidiores redduntur, provt de malo punico, & Myrto testantur Demoeritus, & Mizaldus lib. 1. arcanorum, ac de Ruta sub ficu crescente Plinius lib 19. c.8. ac Dioscorid. lib. 1. cap. 31. Aliarum autem naturâ dissitarum propinquitate læduntur, & sterilescunt, vt præsertim vitis à brassica. Econtrà multæ sunt, quæ ob inimici fruticis, aut oleris viciniam roborantur, & vires conduplicant; vt rosa allio complanta ta odoratior sit, non quod allium, quod alioqui graueolentissimum est, quicquam boni in illam transmittat, eiusque fragrantiam augeat, sed qvia ad inimici præsentiam excitata intime natura rosæ ad pugnandum accingitur, viresque suas omnes exerit. Et sic discurre per singula, in oscitatione, oculorum lippitudine ad caligantis oculi visum dentium stupore ad acidarum rerum aspectum, aut considerationem, atque aliis corporis affectionibus, ac deliquiis, quæ
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DE SYMPATHY. 49 that this is born: which even though Hieronymus Dandinus obscurely recognized, Digress. 6 in books On the Soul, asserting that this flower is moved from an intrinsic principle, in accordance with the motion of the sun, just as a stone is toward the center; which he likewise affirms of the Lunaria, saying that it conforms itself to the motion of the moon, for which reason he calls it Lunitropium. Likewise in the Selenite stone that wonderful change of its spots according to the phases of the moon, since it takes place in a solid stone, and not only on the outer surface but throughout the whole body, as can be seen when it is cut open, can arise only from within: but it is changed by the likeness it has to the moon, and by the sympathy through which, when the moon is moved, it is inwardly stirred to a similar motion and passion. Thus similar strings, when touched by another, resound not from the moved air, as Fracastorius would have it, book On Sympathy, ch. 11, and Aresius, On Generation, disp. 1, q. 41, sect. 7, since in another, nearer cithara, but not in unison, and with a much greater impulse of air reaching the cithara, the same effect is not produced; rather it is from a very true sympathy, inwardly stirring the unison strings to a uniform sound. For the greater readiness, as they say, in these strings to receive motion and produce sound than in others not equally tense, can be explained by nothing else than this consent of Nature. But this is also proved by the opposite reason, namely antipathy, by another experience of strings made from lamb’s nerves, which, when plucked by the strings of a cithara made from wolf’s strings, immediately yield by an inward force, the moment they are struck; for by their nature they give way to a contrary motion, which they cannot bear. Hence also the same thing can be seen in plants, which, when planted with others bound together by a mutual bond of affection, become more fruitful and more vigorous, as Democritus and Mizaldus testify concerning the pomegranate and myrtle, book 1 of Secrets, and Pliny, book 19, ch. 8, concerning rue growing under a fig tree, and Dioscorides, book 1, ch. 31. But when plants of a different nature are nearby, they are harmed and made barren, especially the vine by the cabbage. Conversely, there are many which, because of the vicinity of an enemy shrub or vegetable, are strengthened and double their powers; thus a rose planted with garlic is more fragrant, not because garlic, which is otherwise extremely foul-smelling, transmits anything good into it or increases its fragrance, but because, aroused by the presence of an enemy, the inner nature of the rose is armed for combat and exerts all its strength. And so continue through the individual cases: in yawning, in the dimness of the eyes at the sight of a darkened eye, in the numbness of the teeth at the sight or contemplation of sour things, and in other affections and faintings of the body, which
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55 PHYSIO-THEOLOGIA, tim sympathiam, partim antipathiam: sympathiam intel phangium, & certam speciem harmoniæ, colores, arma, &c. atque eriam in percussio id euenire ob qualitatem immissam, quæ proinde totam naturam insicit, antipathiam inter ipsam veneficam qualitatem, & hominem, talem tamen quæ facilè in ipsam naturam redundet, præsertim cum ex Arist. septim Metaph. cap. 6. contrariorum eadem forma fit, atque adeo intercedat necesse est aliqua similitudo, & connexio. <10.> Hinc ad obiecta in naturalem pulueris sympathici actiuitatem, cæterotum eiusdem generis medicamentorum, facilis est responsio: quomodo enim, inquiunt, tam modicus puluis sanguini iam emortuo applicatus, magnum alioqui vulnus, idque dissimum sanare potest? quomodo vnguendum ferro illium, in quo vix sanguinis vestigia extant, eadem virtute pollet? Quomodò in vulneribus à sclopetis factis eadem miracula non experimur? Verum, vti dicebam. curatio immediatè à natura fit, extrinsecis hisce fulcis effectiuè in vulnus ne minimum quid operandibus, sed solum in ea quibus immediatè applicantur, puta sanguinem, pus, & similia, ad quorum tamen alterationem natura, ob substantiæ similitudinem, & conformitatem alteratur, intrinsecùs excitatur & maiori nisu curationem perficit; eo prorsus pacto, quo per morbum deiecta solo sufficiu, aromatum, vini, aliorumque id genus extractorum, quæ spirituales magisque æthereas rerum portiones seruant, natura erigitur, spiritusque nostri corporis aliàs torpentes momento temporis excitantur, & pro naturæ affinitate proficiunt, & instaurantur. Sic profectò Natura per eius pariis, quæ quatuus excisa, retinet nihilominus aliquid primigeniæ substantiæ, veluti somno expergefacta, & amica voce erecta accingitur ad curationem perficiendam morbumque superandum, eò faciliùs, quo ad id aliàs prona est, vt vel leuissimo adiumento, (eo maximè quod non, vt cætera medicamenta immediate applicata naturam premit) suffulta alacrior exit ad opus perficiendum. <21.> At cum vulnus igneo globulo lavata rota à sclopetis infilgitur, instrumentum, quod ad explosendum dumcavas globum inseruit, nullam contrahit cum vulnete sympathiam; cum non corpus attingat, non uulnus per seipsum faciat sed per immissum plumbum; ac proinde nil mirum, si ineptum prorsus euadat ad curationem magneticè perficiendam, benè autem opus feliciter fortè prodiret, si globus extrahi pollet, atque in vnguentum immitti; militat enim pro eo,
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55 PHYSIO-THEOLOGIA, partly sympathy, partly antipathy: sympathy of the intelligence, and a certain kind of harmony, colors, arms, etc.; and even in the blow this occurs by reason of the quality imparted, which therefore infects the whole nature; antipathy between the venomous quality itself and man, yet such as easily redounds into nature itself, especially since, from Aristotle, Metaph. 7, cap. 6, opposites have the same form, and thus there must necessarily intervene some likeness and connection. <10.> Hence, in answer to the objections against the natural activity of the sympathetic powder, and other medicines of the same kind, the response is easy: for how, they ask, can so small a powder, applied to blood already dead, heal a great wound otherwise, and a very deep one? how can that ungent for iron, in which scarcely any traces of blood remain, possess the same power? How is it that in wounds made by muskets we do not experience the same wonders? But, as I was saying, the cure is effected immediately by nature; these outward supports do not operate in the wound in the least, but only in those things to which they are immediately applied, namely blood, pus, and the like, for the alteration of which, however, nature, on account of the similarity and conformity of the substance, is altered, is stirred inwardly, and with greater effort brings the cure to completion; in exactly the same way as, after being brought low by disease, nature is raised up by a sufficient supply of aromatics, wine, and other extracts of that kind, which preserve the spiritual and more ethereal parts of things, and our bodily spirits, otherwise drowsy, are roused in a moment of time and, according to their affinity with nature, are strengthened and restored. Thus indeed nature, through its parts, which, when cut off, nevertheless retain something of the original substance, as if awakened from sleep and roused by a friendly voice, sets itself to complete the cure and overcome the disease, and all the more easily the more it is otherwise inclined to this, so that with even the slightest aid—especially because it does not, like other medicines when applied directly, press upon nature—it is supported, and goes forth more eagerly to accomplish the work. <21.> But when a wound is inflicted by a fiery bullet fired from a musket, the instrument which inserted the hollowed-out bullet to be discharged contracts no sympathy with the wound; since it does not touch the body, it does not make the wound by itself, but through the lead introduced; and therefore it is no wonder if it proves utterly unfit for curing by magnetic means; but perhaps the work would go well if the bullet could be extracted and put into the ointment; for this speaks in its favor,
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34 PHYSIO-THEOLOGIA, præsentiam rei vtcumque similis commouetur, & feruet, quæ est causa iracundiæ commouendæ: siquidem hæc aliud non est quam accensio sanguinis circa cor. Qua etiam ratione Galenus lib. de suppurat. empyrica vetat Ipuenti sanguinem aut hæmorrhagiam patienti aspectum ipsius sanguinis aut alterius rei rubræ, & ad cærulea & nigra rubet oculos conuertere: præcipit contra exanthematis iuxta cætem laborantibus rubris vestimentis operiri Non quod hæc quidquâ conferant aut immittant intus in sanguinem aut contraponant, sed ipsum fiat quia, spiritus in sanguine consistentes ob sympathiam alliciuntur splendore illo sanguini prorsus consimili, ac sanguinem ipsum commouent, vnde est quod sic agitatus, aut circa cor adunatur, aut alias cum exiium sic foras erumpit. Id quod etiam eo modo in rebus inanimis videmus vt in purpura, in corallio quæ cum aliis eiusdem coloris, aut naturæ seruantur in naviuo splendore persistunt, atque perficiuntur. Mitto alia experimenta passim obvia, sed non minus admiratione digna. 13. Cogeris itaque iam, vel reluctans frequenti demonstrationi assentiri, quod sanguini, & pari excisæ quamuis emortuæ aliquid remanet primitiuæ substantiæ, quo himirum seruatur huiusmodi proportio & consensus cum reliquo corpore, cuius virtute magneticæ istæ operationes in Natura intrinsecus excitentur. Ex quo, vt id obiter dicam, non modò planè euincitur contra Thomistas in corruptione compositi non dari resolutionem vsque ad materiam primam, sed adhuc in corupto perseverare plures formas substantiales, quas vocant partiales partium similarium distinctas, vt puta, carnis, ossis, nerui, &c. vt volebat Scotus in 4. distinct. 11. quæst. 3. quem sequuntur Maiorius in 2. distinct. 16. ß 15. Niphus primo de Generat. comment. 78. Piccolominus lib. de multitudine formarum cap. 2. Hieron. Dandinus digress. 8. par. 3. 2. de anima Antonius Trombeteta 8. Metaph. 9. & passim recentiores, quam sententiam acriter, & egregiè propugnat ex nostris Aresius in lib. 1. Generat disp. 2. quæst. 10. sect. 3 asserens hanc fuisse mentem Aristotelis pluribus in locis præsertim primo de Anima textu 58. ac plurium veterum Peripateicorum Alexandri, Simplicij, Auerrois quibus Picolomineus addit Galenum, & Platonicos, 14. Et quidem si non alia argumenta suppeterent, certè ipsa torius substantiæ similitudo euincerer, in plantis, lignis, animantibus, aliisque iam corruptis, & exsiccatis aliquam radicalem, maximeque vitalem substantiam reperiri; quæ
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34 PHYSIO-THEOLOGIA, is moved and grows hot by the presence of some similar thing, which is the cause of provoking anger: for indeed this is nothing other than an inflaming of the blood around the heart. For the same reason Galen, in lib. de suppurat. empyrica, forbids, in a person with excessive blood or hemorrhage, the sight of blood itself or of any other red thing, and orders the eyes to be turned away to blue and black objects; on the contrary, he prescribes that those suffering from exanthemata and similar complaints be covered with red garments. Not because these contribute anything or send anything into the blood from within or oppose it, but because this happens: the spirits residing in the blood are, by sympathy, attracted by that brightness altogether akin to blood, and they stir the blood itself; whence it is that, thus agitated, it either gathers around the heart or otherwise, with a certain outburst, bursts forth outward. We also see the same thing in inanimate objects, as in purple, in coral, which, together with other things of the same color or nature, are preserved in a lively brightness and are perfected. I omit other experiments commonly encountered, but no less worthy of admiration. 13. You are therefore now compelled, even if reluctantly, to assent to the frequent demonstration, namely, that in blood, and equally in excised flesh however dead, something remains of the primitive substance, by virtue of which, as it were, this proportion and consensus with the rest of the body is preserved; and by its power these magnetic operations are aroused within Nature. From this, as I may remark in passing, it is not only clearly proved against the Thomists that in the corruption of a composite there is no resolution all the way down to prime matter, but also that in the corrupted thing there still persist several substantial forms, which they call partial, distinct forms of similar parts, such as of flesh, bone, nerve, etc., as Scotus maintained in 4. distinct. 11. quest. 3, whom Maiorius follows in 2. distinct. 16. ß 15, Niphus in the first book De Generat. comment. 78, Piccolominus in lib. de multitudine formarum cap. 2, Hieron. Dandinus in digress. 8. par. 3. 2. de anima, Antonius Trombeteta in 8. Metaph. 9, and many recent writers; this opinion is vigorously and excellently defended by our Aresius in lib. 1. Generat disp. 2. quest. 10. sect. 3, asserting that this was Aristotle’s meaning in many places, especially in the first book De Anima, text 58, and also that of many ancient Peripatetics, Alexander, Simplicius, Averroes, to whom Piccolomineus adds Galen and the Platonists. 14. Indeed, if no other arguments were at hand, surely the very similarity of the whole substance would prove that in plants, woods, living creatures, and other things already corrupted and dried out, some radical, and especially vital, substance is to be found; which
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38 PHYSIO THEOLOGIA, ipsum potius accidir, non in aggressoris, sed in mandantis occisionem præsentiam? cur inquam in aggressoris duntaxat præsentia, & eius solum qui vulnera infixit, non qui venenum propinando, aut alias vitam ademir? Tertiò quia saltem id non nisi post longum temporis spatium vsu, & frequentia compertum est, vnde quoad vsque id plenius innotuerit Dænon suo sine frustratus rem prorsus inutilem ex Dei permissione prosequutus est: cur igitur hoc porius in sanguinis effusione manifestare elegit, eique permissum est, & non in alio potiori argumento, quod rem cuinceret? Quartò demum, quia id nihilominus, quamuis frequens, non est certum indicium rei, cum non constet adhuc qua ratione fiat; & ideò ex hoc præcisè non posset simpliciter animaduerti in huiusmodi indiciatum, nec etiam modò non alia indicia concurrerent ad criminalem inquisitionem procedi, vt multis probant Hippolytus de Mars. in praxi crimin. 9. diligenter. Paris de Puteo, in sindicatu Verbo Tortura, & alij iuristæ apud Maiolum in duabus canicular. colloqu 1. Phys. eò maximè quia aliquando etiam huiusmodi sanguinis effusio subsequua est ad præsentiam amicorum, aut sanguine coniunctorum, vt notat idem Maiolus, de quibus tamen eoquia homicidium publicè fuerat, ab alio factum nulla suspicio inesse poterat, quod ab iis homicidium fuerit perpetratum: Vnde à primo ad vltimum, nulla est ratio credendi hanc sanguinis effusionem in occisi eaduere prætet naturam à Dæmone fieri, ad occisorem manifestandum. 34. Dico igitur consequenter ad superius dicta, id fieri naturaliter ex sympathia operis familiaritatis, non ab vlla antipathia, aut immissione vel regressione spirituum, ex occisi corpore ad occisorem, aut è contrà. Equidem in diversitate casuum, qui referuntur: suppono occisionem fuisse semper factam in aperto conflictu, & sciente, atque adniente contra aggressorem occiso: quo posito, credendum est hunc ira in aggressorem incaluisse; ac demum viribus imparem occubuisse. Cum igitur ira fit accensio sanguinis, circà cor, qui posteà succumbente natura per inflicta vulnera foras prosiliit; & sanguis ira infectus quandam antipathiam cum aggressore contraxit; inde fit, vt eodem præsente sanguis ex familiaritate operis iterum accendatur, ebulliat, ac per eandem vulnerum viam exitum sibi paret, & vtcumque natura duce, in aduersarium adnitratur. 35. Ex quo etiam deduco idipsum quandoque accidere ad præsentiam amicorum, fratrum, &c. Quia profectò com-
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38 PHYSIO THEOLOGIA, would this happen rather in the presence of the killer than of the one who commanded the killing? Why, I say, only in the presence of the aggressor, and of the one who merely inflicted the wounds, and not of the one who, by administering poison or in some other way, took the life? Thirdly, because at least this has not been ascertained except after a long span of time, by use and frequent observation; hence, until it has become more fully known, the demon, frustrated in his purpose, pursued a wholly useless matter by God’s permission. Why then did he prefer to manifest this rather in the effusion of blood, and was it permitted to him, and not in some other more powerful argument that would have proved the matter? Fourthly and finally, because, although frequent, it is nevertheless not a certain sign of the matter, since it is not yet known by what cause it happens; and therefore from this alone it could not simply be concluded in such an accusation, nor even now could criminal proceedings be undertaken unless other indications concurred, as many authors prove: Hippolytus de Mars. in Praxi crimin. 9 carefully; Paris de Puteo, in Sindicatu , under the word Tortura ; and other jurists cited by Maiolus in Duabus Canicular. Colloqu. 1, Phys. especially because sometimes such an effusion of blood also follows upon the presence of friends, or of blood-relations, as the same Maiolus notes; yet, since the homicide had been publicly committed, no suspicion could arise that it had been done by another, that they had perpetrated the homicide. Hence, from first to last, there is no reason to believe that this effusion of blood in the slain occurs beyond nature, by a demon, in order to reveal the killer. 34. I therefore say, consequently to what has been said above, that this happens naturally from the sympathy of a familiar work, not from any antipathy, or from the sending or return of spirits from the body of the slain to the killer, or vice versa. Indeed, in the diversity of the cases that are reported, I suppose the killing to have always been done in open conflict, and with the knowledge and consent of the one killed against the aggressor; which being granted, it must be believed that the latter had grown hot with anger toward the aggressor, and then at length, being unequal in strength, had fallen. Since, then, anger is an inflammation of the blood around the heart, which afterward, as nature yields, bursts forth through the wounds inflicted; and since the blood, infected by anger, contracted a certain antipathy toward the aggressor, it comes about that, when the aggressor is present, the blood, by the familiarity of the act, is again kindled, boils up, and through the same path of the wounds makes an exit for itself, and, as it were, under nature’s guidance, strains toward the adversary. 35. From this I also infer that the same thing sometimes happens at the presence of friends, brothers, etc. Because, indeed...
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DE SYMPATHIA. 35 iunctio sanguinis, aut amoris necessitudo, vt sæpè in nobis experimur ad amatæ rei conspectum facit, vt sanguis in venis ebulliat, alteretur; atque in arteria pulsus inæqualitatem exhibeat: Vnde ex hoc Erafistratus apud Galenum, quandam mulierem agnouit ex nimio amore ergà priuignu[m] decumbere, prolato enim vix Pyladis nomine, statim Nouerca expalluit; vnde ipse apposita ad carpum manu, inuenit pulsum maxima inæqualitate fluctuare, quod erat indicio, cor etiam interiùs, sanguinem, & spiritus fluctuasse ex amoris affectu. Ex quo fieri potest, vt amante iam mortuo, sanguis, & spiritus vitales, qui reliqui sunt in cadauete ob sympathiam operis, atque eiusdem substantiæ vnitatem, ad solam obiecti amati, vel odio habiti præsentiam excitentur ad similem, & aliàs sibi familiarem motum; vnde posteà ex vulneribus, in quibus habet apertum ad exitum viam, vbertim profluat & exsiliant. Quod etia[m] videre est suo modo in cæteror[um] animantium exuuiis, quos enim affectus inter se viuentes habuerunt, hos etiam seruant in morte, horum vmbram videmus adhuc in extis, sanguine, sibitis, corio & similibus. Sic quia ad lupi præsentiam agnus viuus timore interiùs concutiebatur, posteà iisdem mortuis, idem affectus, & contrarietas, in reliquiis cernitur; vnde Lyta, aut tympanum ex ouina pelle, aut intestinis compactum, tacta Lyra, aut tympano è lupi corio, aut neruis constante, dirumpitur. Similiter sonitus lyræ ex vulpeculæ extis, gallinas tertitat, & in fugam vertit, ex serpentium neruis, hominibus, ac præsertim foeminis ob insitam contrarietatem, & inimicitiam, retrorem incutit. Qua ratione Zischas hæreticus infensissimus Catholicorum hostis, cum in pugna oculos amisisset, iterum pugnaturus præcepit suis, vt, si fottè ei occumbere contigisset, detracto sibi corio, tympanum conficeretur, quo bellum inauguratum, hostes, quibus viuens terroli fuit, eodem timore perculsi in fugam conuertentur. Sic igitur in casu nostro contrario affectu, tum odij, tum amoris, fieri potest, vt cuius præsentia viuenti animi motus, & sanguinis fluctuationem circà cor, siue ex amore, siue ex odio suscitabat, in iam mortuo eorumdem effectuum causa sit, sicque sanguis è vulneribus profluat naturaliter tam ad inimici, quam ad amici præsentiam. E contrà in eo, qui aut dormiens, aut quouismodo ignorans occisus est, quia nulla inerat dum adhuc vinebat in aggressorem ita, & odij exardescenda, nulla etiam esse poterit in iam de mortui sanguine operis sympatia; vnde nil mirum, si nulla in eo fiat sanguinis ebullitio, & effusio ad ini-
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DE SYMPATHIA. 35 the union of blood, or the bond of love, as we often experience in ourselves: at the sight of the beloved object it causes the blood to boil in the veins and become altered; and in the arteries it shows an unevenness of the pulse. Whence, from this Erafistratus, as Galen reports, recognized a certain woman to be lying ill from excessive love for her stepson; for when the name of Pylades was scarcely uttered, the stepmother turned pale at once; whereupon he, placing his hand upon her wrist, found the pulse to fluctuate with the greatest irregularity, which was a sign that the heart also within, and the blood and spirits, were fluctuating from the passion of love. From this it can happen that, when the lover is already dead, the blood and vital spirits that remain in the corpse, by sympathy of action and by the unity of the same substance, are stirred up by the mere presence of the beloved object, or of the hated one, to a similar, and otherwise familiar, motion; whence afterwards from wounds, in which there is an open way for خروج, it flows out and springs forth abundantly. This can also be seen in its own way in the remains of other living creatures; for those affections which they had among themselves while living, they also preserve in death, and we still see their shadow in the entrails, blood, sinews, skin, and the like. Thus, because at the presence of the wolf the living lamb was shaken within by fear, afterwards, when they are dead, the same affection and contrariety are seen in the remains; whence a lyre, or drum, made from sheep’s skin or from intestines, when touched by a lyre or drum made of wolf’s skin or consisting of sinews, bursts asunder. Similarly the sound of a lyre made from the entrails of a fox frightens hens and drives them into flight; made from the sinews of serpents, it strikes fear into men, and especially into women, because of an inborn contrariety and enmity. For this reason Zischas, the heretic and most bitter enemy of the Catholics, when he had lost his eyes in battle and was about to fight again, ordered his men that, if perhaps it should happen that he fell, the skin should be stripped from him and a drum made from it, by which war would be inaugurated, and the enemies, whom while living he had been a terror to, would, struck with the same fear, be turned to flight. So then in our case, by the contrary affection, both hatred and love, it can happen that the presence of one who, while living, stirred the motions of the soul and the fluctuation of the blood around the heart, whether from love or from hate, becomes in one already dead the cause of the same effects; and thus the blood from wounds flows naturally both at the presence of an enemy and of a friend. On the other hand, in the case of one who was killed either while sleeping or in any way unaware, because while he was still living there was no such exasperation of hatred against the assailant, there also can be no sympathy of action in the blood of one already dead; whence it is no wonder if there is in him no boiling and effusion of blood to ini-
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63 INDEX Cauda Ceti dat periculum submersionis, ibid. n. 49 Cauda Cygni mirè humores adauger, potissimè sperma, 79. n. 366 Est verticalis Florentiæ Bononiæ alijsque sinitimis Ciuitatibus, ibid. Cauda Leonis dat optimum ingenium, atque honores, 97. n. 53 Ceginus sinister humerus Bootis verticalis Regno Neapol. 99. n. 59 Centiloquij Author an Ptolemæus, ibid. 63 Hali sibi contrarius de Centiloquij Authore, ibid. Illud approbat D. Thomas, ibid. n. 64 Centrum Mundi duplex, 100. n. 65 Solis, & siderum Terræ, ibid. & 500. n. 23 A Centro Telluris sit dimensio siderum à Mathematicis; 100. n. 65 Cepheus in Horoscopo quid significet, 101 n. 67 Ceratias Cometa apparens anno 1618. quot mala intulerit, ibid. 68 Chasma falsò à Plinio in genere Cometaru[m] positu[m] 102. n. 73 Chamæleon sidus directè oppositum Vrsæ, ibid. 78 Chele cur dicantur Stellæ in lancibus libræ, ibid. n. 74 Chile Regnum Ventorum naturam habet nobis contrariam, 76. n. 360 Vbi Auster frigidus, & siccus. Boreas contra calidus, & humidus, ibid. Choreutæ cur dictæ Stellæ du extrema circa Polaré, 103. n. 81 Christiani Daniæ Regis memorabile dictum, 78. n. 362 Chronocatores qui sint, 103. n. 85. Cicuta hominibus exitialis, Sturnis verò commodum pabulum, Qu. Cur frigiditate non interimat, non Nix, aut Glacies, 191. n. 62 Aduersus eam præsens Antidotum Vinum, ibid. Cingulus Orionis in Horoscopo ingeniosos facit, 83. n. 3 Circini Geometrici Galilæi laus, 2. n. 3 Circius Ventus vnde dictus, 104. n. 89 Eius qualitates, ibid. Circulus quid, & in quo differat ab Ellipsa, 105. n. 92 Circuli quadratura an dari possit, & in quo verè consistat, 408. n. 9. & seq. Circumstantiæ multæ superstitiosæ reperiuntur apud aliquos in compositione, & vsu Vnguenti Armarij, Qu. 1. n. 1. & seq. Non tamen per hoc spermendum, ibid. Climata quot costituerint Anti qui, quot recetiores, 107. n. 103
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63 INDEX Tail of Cetus brings danger of drowning, ibid. n. 49 Tail of Cygnus wonderfully increases humors, especially sperm, 79. n. 366 It is vertical at Florence, Bologna, and other neighboring cities, ibid. Tail of Leo gives excellent intellect and honors, 97. n. 53 Left shoulder of Cepheus is vertical in the Kingdom of Naples. 99. n. 59 Whether Ptolemy is the author of the Centiloquium, ibid. 63 Haly contrary to himself concerning the author of the Centiloquium, ibid. St. Thomas approves that, ibid. n. 64 Double center of the world, 100. n. 65 of the Sun and stars, of the Earth, ibid. & 500. n. 23 By mathematicians, the measurement of the stars from the center of the Earth; 100. n. 65 What Cepheus signifies in the horoscope, 101 n. 67 Ceratias comet appearing in the year 1618, how many evils it brought, ibid. 68 Chasma falsely placed by Pliny in the genus of comets, 102. n. 73 Chamæleon, a star directly opposite the Bear, ibid. 78 Why the stars in the scales of Libra are called Chele, ibid. n. 74 Chile, the kingdom of winds, has a nature contrary to ours, 76. n. 360 Where the south wind is cold and dry; the north wind, on the contrary, warm and humid, ibid. Why the two extreme stars around the Pole are called Choreutæ, 103. n. 81 A memorable saying of Christian, King of Denmark, 78. n. 362 Who the Chronocatores are, 103. n. 85. Hemlock is deadly to men, but for starlings a useful food, Qu. Why cold does not kill, nor snow or ice, 191. n. 62 A present antidote against it: wine, ibid. The Belt of Orion in the horoscope makes men ingenious, 83. n. 3 Praise of Galileo’s geometric compasses, 2. n. 3 Whence the wind Circius got its name, 104. n. 89 Its qualities, ibid. What a circle is, and how it differs from an ellipse, 105. n. 92 Whether the squaring of the circle can be achieved, and in what it truly consists, 408. n. 9. & seq. Many superstitious circumstances are found among some in the composition and use of the unguent of the armor, Question 1, n. 1, & seq. Yet it is not to be despised for this reason, ibid. How many climates the ancients established, how many the more recent, 107. n. 103
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70. INDEX In Horoscopo semper affert aliquam corporis discræriam, ibid. Cum luminaribus magnam fortunam adducit. ibid. Sola inter fixas habet, & recipit a pectus ad Planetas, 85. n. 4. & 426. n. 54. In Corde Solis cur Planeta euadat fortis, cum alias combustus aut sub radijs euadat debilis, 98. n. 58. Cor Scorpii, Stella fixa Regia, sed violenta, 124. n. 173. & 46. n. 216 Eius significata in Horosc. ibid. Est directè opposita Pallilitio, ibid. Coro Vento infestissima est Apulia, 126. n. 181 Coronæ aeræ, Quæ. 126. n. 179 Coronæ Septentrionalis in Horoscopo significata, 125. n. 176 Sidus est omnium nobilissimum, ibid. Cæli pupilla, & flos coelestis cur dicta, 16. n. 151 Est tamen sidus tempestuosum, ibid. n 152 Corpora Planetarum, & Globi quare non concaui, sed conuexi, 120. n. 157 Corpora Platonica, Quæ. 131. n. 8 Cosmicè Astra impropriè dicuntur oriri, 126. n. 181 Cosmographia, eius munus, & quomodo differt à Geographia, 117. n. 184 Crateris sidus in Horoscop. significata, 128. n. 186 Crepusculum quid dicatur, 128. n. 187 Noua solis in Crepusculis existentis dirigendi metodus, ibid. n. 188 In spatio Crepusculorum sol constitutus semper vitæ moderationem obtinet, ibid. In Norvegia semper Crepusculi, ibid. Critici dies qui, & vnde exorti, 130. n. 190 Eorum maxima ratio à Medico habenda, ibid. Obseruandi etiam Indicatiui, qui formantur ab aspectibus imperfectis, ibid. Crux sidus Australium Cynosura, 132 n. 194 Culmen seu medium Coeli naturalis Actionum significator, 132. n. 197 Cuspis quæ dicatur, 133. n. 202 Cyclo vtebatur Ecclesia ante Gregorianam correctionem, 133. n. 104 Cygnus in Horosc. quid significet, 79. n. 366 In eo noua Stella apparuit anno 1600. 134. n. 209 Quæ tandem euanuit relicto quodam hiatus in loco, ibid. Cynocephalus horarum inuentor, 232. n. 34
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70. INDEX In the horoscope it always brings some bodily discord, ibid. When with the luminaries it brings great fortune. ibid. Among the fixed stars alone it has, and receives from the chest to the planets, 85. n. 4. & 426. n. 54. In the Heart of the Sun, why a planet becomes strong, whereas otherwise, when combust or under the rays, it becomes weak, 98. n. 58. Cor Scorpii, the fixed royal star, but violent, 124. n. 173. & 46. n. 216 Its significations in the horoscope, ibid. It is directly opposite to the Pallilitium, ibid. Coro Vento is most hostile to Apulia, 126. n. 181 Crown of bronze, what it is. 126. n. 179 The Northern Crown in the horoscope, its significations, 125. n. 176 It is the noblest of all stars, ibid. Why it is called the pupil of heaven, and the flower of the sky, 16. n. 151 Yet it is a stormy star, ibid. n. 152 Why the bodies and globes of the planets are not concave, but convex, 120. n. 157 Platonic solids, what they are. 131. n. 8 Stars are improperly said to rise cosmically, 126. n. 181 Cosmography, its function, and how it differs from geography, 117. n. 184 The star of Crater, its significations in the horoscope, 128. n. 186 What is meant by twilight, 128. n. 187 A new method of directing the sun when it is in the twilights, ibid. n. 188 In the period of twilight the sun established there always preserves moderation of life, ibid. In Norway there is perpetual twilight, ibid. Critical days: what they are, and whence they arose, 130. n. 190 Their greatest importance must be considered by the physician, ibid. The significators likewise are to be observed, which are formed from imperfect aspects, ibid. The Cross, the southern Cynosura, 132 n. 194 The Culmen, or midheaven, the significator of natural actions, 132. n. 197 What is meant by cusp, 133. n. 202 The Church used the cycle before the Gregorian correction, 133. n. 104 Cygnus: what it signifies in the horoscope, 79. n. 366 A new star appeared in it in the year 1600. 134. n. 209 Which at last vanished, leaving a certain gap in its place, ibid. Cynocephalus, inventor of the hours, 232. n. 34
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R E R V M MOBILIVM. 71 In luminariam coitus, nec cibum sumit, nec videt, 460. n. 81 Cynosura, 61. n. 182 D DAmnarorum corpora in Inferno etunt tanquam muria- tici pisces in dolio, 146. n. 39 Dæmon maxima quæque naturæ bona gestit suis tricis co- rumpere, aut suspecta reddere, Qu. 1. n. 26 Quæ ipse agit, & nos agere valeremus, si eamdem quara ipse habet retum notitiam haberemus, Qu. 2. n. 29 Dæmon meridianus cur dicta sagitta sidus, 135. n. 3 Dæmones secundam Aëris regionis inhabitant, & quare, 12. n. 38 Debilitatis gradus an dentur in signis, & qui nam ij sint, 79. n. 367 An fictitia, ibid. Decanorum prærogatiua, Quæ. 135. n. 7 Declinatio quid sit, 136 n. 10 Qvid commodi ex ea eliciatur, ibid. Decubitus figura, an ad indagandum morbi progressum, & qualitates licitè erigatur, 136. n. 11. 12 An erigenda sit initio morbi, an potius à puncto quo quis à morbo prostatus tandem in lecto decumbit. ib. Defectiones luminarium pro qualitate signorum in quibus incidunt, auspicandæ, 235. n. 20 In Arietis signo occurrentes, Arietibus, & pecudi pestem inducunt, ibid. Delphinus cum Planetis exoriens quid indicet, 137. n. 15 Diameter Mundi quæ dicatur, 138. n. 22 In ea eius magnetica se directè ad polum verrit, 81. n. 374 Dies quid. & vnde à diuersis Nationibus computari, incipiat 140. n. 26 Dies Caniculares vnde dicti. & quo tempore incipiant, 91. n. 15 Dies Critici. vide Critici dies. Dies vbi maiores, 107. n. 104. & seq. Digiti Ecliptici quot constituantur in disco Solari, quot in Lunari, 140. n. 28. Dignitates Planetaru[m] aliæ essentiales, aliæ accidètales, 141. n. 30 Quæ potiores, & cur ita dicantur, ibid. Directionis motus quis sit, & an realis, 142. n. 35 Quomodo fiat, & quando compleatur. 143 n. 36 Directio conuersa. vide, conuersa ditectio. Noua doctrina dirigendi solem in spatio crepusculorum e Lij
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R E R V M MOBILIVM. 71 In luminariam coitus, neither takes food nor sees, 460. n. 81 Cynosura, 61. n. 182 D Bodies of the damned in Hell are like salted fish in a barrel, 146. n. 39 The Demon is eager to corrupt with its tricks, or make suspect, whatever is the greatest good of nature, Qu. 1. n. 26 What it itself does, and what we would be able to do, if we had the same knowledge of things that it has, Qu. 2. n. 29 Dæmon meridianus why called the dog-star, 135. n. 3 Demons inhabit the second region of the air, and why, 12. n. 38 Whether degrees of weakness are found in the signs, and which they are, 79. n. 367 Whether they are fictitious, ibid. The prerogative of the decans, Quæ. 135. n. 7 What declination is, 136 n. 10 What advantage is derived from it, ibid. The figure of decubitus, whether it may lawfully be raised up for investigating the progress and qualities of the disease, 136. n. 11. 12 Whether it should be raised at the beginning of the disease, or rather from the point when one at last, having been seized by illness, lies down in bed. ib. Eclipses of the luminaries are to be prognosticated according to the quality of the signs in which they fall, 235. n. 20 Those occurring in the sign of Aries bring plague to the rams and to cattle, ibid. What is indicated by the Dolphin rising with the planets, 137. n. 15 What is meant by the Diameter of the World, 138. n. 22 In it its magnetic part moves directly toward the pole, 81. n. 374 What a day is, and from what point it begins to be reckoned by different nations, 140. n. 26 Whence the Dog Days are so called, and at what time they begin, 91. n. 15 Critical days. see Critical days. Where the days are longer, 107. n. 104. & seq. How many Ecliptic digits are constituted in the Solar disk, how many in the Lunar, 140. n. 28. The dignities of the planets are some essential, others accidental, 141. n. 30 Which are the more important, and why they are so called, ibid. What the motion of direction is, and whether it is real, 142. n. 35 How it is performed, and when it is completed. 143 n. 36 Reverse direction. see, reverse direction. A new doctrine of directing the sun in the space of the twilight e Lij
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72 INDEX existentem, 118. n. 188 Directus Planeta cur validior quam retrogradus, aut stationarius, 74. n. 348. & 148. n. 42. & 417. n. 37 Dispositor alicuius loci quis Planeta dicatur, 149. n. 46 Diurnus, ac Nocturnus Planeta dicitur in ordine ad qualitates actiuan, aut passiuas, 149. n. 49 Domicilij prærogatiua in Planetis Philosophicè probata, 150. n. 52 & 495. n. 19 Dominus Horæ, seu Diepon. 139. n. 25 Dominus Nouenariæ quis, 39. n. 193 Dominus Terminorum, 20. n. 102 Dominus annuæ profectionis an sit Astrologorum figmentum, 152. n. 54 Dominus Genituræ an astruendus. Quinam dicendus, 152. n. 55. & seq. Quas prærogatiuas habere debeat, ibid. Variæ Astrologorum sententiæ, ibid. Auctoris opinio Naturæ, & experimentis conformis, 153. n. 56 An Luminaria ab hac prærogatiua sint excludendi, ibid. 57 An Planeta combustus, cadens, aut sub Solis radijs constitutus, ibid. Dominum Horæ obseruare in rerum electionibus an superstitiosum, 155. n. 59 Domorum Coelestium, quoad situm mundi congruens naturæ distributio, 151. n. 53 Domum ædificare Scorpion in Horosc. existente, ipsa Scorpionum nidus euadet, 445. n. 17 Drago volens Cometæ genus, 158. n. 67 Dubia superstitiosa ne sint an naturalia, naturalia censenda sunt. Qu. 1. n. 29 In Dubijs tutior pars eligenda. Qu. 1. n. 25 Quomodo id intelligi debeat, ibid. Duodecim signa singula singulis membris humanis præsunt, 453. n. 64 E Eclipse quid, & vnde dicta, 161. n. 4 Eclipse Solis à Lunari diuersitas, ibid. Eclipse Solis potius dicenda Telluris Eclipse, ibid. Eclipsantur etiam Planetæ superiores, 163. n. 7 Eclipse Louis anni 1648. quid orbi induxerit, ibid. Eclipses quid in singulis signis occurrentes portendant, ibid. & 233. n. 20
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72 INDEX existentem, 118. n. 188 Directus Planeta cur validior quam retrogradus, aut stationarius, 74. n. 348. & 148. n. 42. & 417. n. 37 What planet is called the dispositor of a certain place, 149. n. 46 A planet is called diurnal or nocturnal in relation to active or passive qualities, 149. n. 49 The prerogative of domicile in the planets, philosophically proven, 150. n. 52 & 495. n. 19 Lord of the hour, or of the day, 139. n. 25 Who is the lord of the ninth house, 39. n. 193 Lord of the terms, 20. n. 102 Whether the lord of the annual profection is a figment of astrologers, 152. n. 54 Whether the lord of the nativity is to be established. Who is to be so called, 152. n. 55. & seq. What prerogatives he ought to have, ibid. Various opinions of astrologers, ibid. The author’s opinion, conformable to nature and to experience, 153. n. 56 Whether the luminaries are to be excluded from this prerogative, ibid. 57 Whether a planet combust, cadent, or situated under the rays of the Sun, ibid. Whether observing the lord of the hour in making choices about things is superstitious, 155. n. 59 A distribution of the celestial houses, as regards the position of the world, in harmony with nature, 151. n. 53 To build a house with Scorpio in the horoscope, it will itself become a nest of scorpions, 445. n. 17 A dragon flying, a kind of comet, 158. n. 67 Whether doubtful things are to be considered natural rather than superstitious, natural things are to be deemed such. Q. 1. n. 29 In doubtful cases the safer part is to be chosen. Q. 1. n. 25 How this ought to be understood, ibid. The twelve signs each preside over single parts of the human body, 453. n. 64 E What an eclipse is, and whence the term is derived, 161. n. 4 The difference between a solar and lunar eclipse, ibid. A solar eclipse ought rather to be called an eclipse of the Earth, ibid. The superior planets are also eclipsed, 163. n. 7 What the lunar eclipse of the year 1648 brought upon the world, ibid. What eclipses occurring in each sign portend, ibid. & 233. n. 20
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R E R V M M O B I L I V M. 73 Eclipse Solis anni 1651. in Ariete, & altera in Leone 1654. 162. n. 6 A præcedentibus Luminarium Eclipsibus Nupera Italiæ pestilentia ortum habuit, ibid. Eclipses non afficiunt ea loca in quibus non apparent, ibid. Eclipsis portentosa quæ erit anno 1681. qua totum cor- pus solare obscurabitur, quæ mala indicet, 141. n. 19 Eclipses non tam malorum, quam maximorum bonorum sunt causæ, 163. n. 6 Eclipsæ duæ, 163. n 9 Eneasias Ventus longè ab cæteris diuersus, 164. n. 10 Eius descriptio ex Aristotele, ibid. Electiones Astrologiæ quid, 165. n 18 An licitè fiant, ibid. Sunt in duplici differentia, ibid. Elementa omnia præter terram mouentur motu vniuersitatis, 169. n. 24 Ea negat Auersa quam benè? ibid. Elementa Geometrica, Quæ. 170. n. 25 Elevatio siderum super sidera in quo consistat, 170 n. 26 Malè explicata à Pontano, n. 27 Varia aliorum explicationes expenduntur, ibid. & seq. Auctoris iudicium, n. 30 Elevationis dignitas an consistat in eo quod Planeta sit eminentior situ in Epicyelo, 23. n. 131 Empirei magnitudo, 174. n. 44 Engonasis in Horoscopo significata, 175. n. 46 Enneatiei dies Naturæ infensi. vide Critici dies. Epacta quid. Eius inueniendi ratio, & quando deficiat, 176 n. 52. & seq. Ephemerides, seu Annotationes, 23. n. 130 Equus in Horoscopo inclinat ad Poësin. 179. n. 63 Equicruia figura quid. vide in V Figura. Eridani Stellæ tempestuosæ, 179. n. 66 Etesiæ Venti quo tempore in diuersis orbis partibus spirent, 180. n. 69 Eurus Ventus vitibus exitialis quonam pacto huic malo oc- curatur, 181. n. 77 Exaltatio Planetarum in quo consistat. 181. n. 79 An sit potior iure domicilij, ibid. Exasteron dicuntur Pleiades, qua ratione, 183. n. 81
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R E R V M M O B I L I V M. 73 Solar eclipse of the year 1651 in Aries, and another in Leo 1654. 162. n. 6 From the preceding eclipses of the luminaries, the recent plague of Italy had its origin, ibid. Eclipses do not affect those places in which they do not appear, ibid. A portentous eclipse which will occur in the year 1681, in which the whole solar body will be obscured; what evils it indicates, 141. n. 19 Eclipses are not so much causes of evils as of the greatest goods, 163. n. 6 Two eclipses, 163. n. 9 Aneasias, a wind long different from the others, 164. n. 10 Its description from Aristotle, ibid. What elections in astrology are, 165. n. 18 Whether they are lawfully made, ibid. They are of a twofold distinction, ibid. All the elements except earth are moved by the motion of the universe, 169. n. 24 Does Auersa deny this well? ibid. Geometrical elements, what they are. 170. n. 25 The elevation of the stars above the stars, in what it consists, 170 n. 26 Badly explained by Pontano, n. 27 Various explanations by others are examined, ibid. & seq. The author’s judgment, n. 30 Whether the dignity of elevation consists in this, that a planet is higher in position in the epicycle, 23. n. 131 The size of the empyrean, 174. n. 44 Engonasis signified in the horoscope, 175. n. 46 The Enneatic days, hostile to nature. See Critical days. What an epact is. Its method of finding it, and when it fails, 176 n. 52. & seq. Ephemerides, or annotations, 23. n. 130 The horse in the horoscope inclines to poetry. 179. n. 63 What an equicrural figure is. See under the letter V. The tempestuous stars of Eridanus, 179. n. 66 The Etesian winds: at what time they blow in different parts of the world, 180. n. 69 The east wind, fatal to vines: by what means this evil is averted, 181. n. 77 In what the exaltation of the planets consists. 181. n. 79 Whether it is superior in right to domicile, ibid. The Pleiades are called Exasteron; for what reason, 183. n. 81
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74 INDEX F Familiaritas inter sidera in quo consistat, 185. n. 3 Eam duplex ratio contrahendi, & in Mundo, & in Zo- diaco, ibid. Inter eas conumeranda sunt etiam Antiscia, 186. n. 6 Omnes Aspectus sunt in genere familiaritatu[m], 68. n. 320 Familiaritatum species ex modis musicis auspicantur, 186. n. 5 Fata Imperiorum, & Monarchiarum vnde, 44. n. 210 Fauonius Ventus in Lusitania an verum sit quod Equas faciat concipere, 14. n. 48 Genitalis Mundi spiritus dicitur, 186. n. 7 Est Venationi contrarius, & quare, 333. n 5 Felices gradus, & infelices in signis an dentur. vide Gradus. Felis abortus ad masculi occisionem vnde sequatur, Qu 3. n 16 Feralia signa sunt feris affinia, 187. n. 9 In Horoscopo faciunt monstra, ibid. Feretrum Lazari quid. 510. n. 47 Fidicula Lucida Stella, excepto Sirio, omnium maxima, & potenior, 187. n. 13 Eius significata in Horoscopo, ibid. Figura sexdecim laterum, quæ dicatur, 188. n. 16 Alstedij in eius explicatione palmalis error, ibid. Figura Æquicurria foetum mortuum excludit, aut diu viuere non permittit, 9. n 30 Explicatur in quo ea consistat, ibid. Figuræ Isoperimentræ quæ dicantur ab Geometris- 188. n. 15 Figuræ decubitus opportunæ in morborum initijs eriguntur, 136. n. 18 In quo puncto ea erigenda sint, ibid. n. 12 Figurarum, ac nominum ex Fabulis in Stellis fixis appinxio, quam ritè, 213. n. 29 Filix vno die florem profert, & fructum, 462. n. 35 Fines. vide Termini. Finitor quid sit, & quotuplex, 190. n. 18 Firmamenti nomine in sacris paginis appellatur Aër. 191. n. 19 Quid eo nomine communiter veniat, ibid. Firmamentum in quo fixæ consistunt an sit solidum, 191. n. 19 Vnde dictum. ibid. Quanra sit eius crassities. ibid. n. 10 Antiqui ob motus tarditatem ipsum à primo mobili non distinguebant, ibid. n. 21
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74 INDEX F Familiarity among the stars, in what it consists, 185. n. 3 It has a twofold method of contraction, both in the World and in the Zodiac, ibid. Among them are also to be counted the Antiscia, 186. n. 6 All Aspects are in general kinds of familiarities, 68. n. 320 The kinds of familiarities are taken from musical modes, 186. n. 5 Whence the Fates of Empires and Monarchies arise, 44. n. 210 Whether the Favonian Wind in Lusitania truly causes mares to conceive, 14. n. 48 It is called the spirit of the Genital World, 186. n. 7 It is contrary to hunting, and why, 333. n. 5 Whether fortunate and unfortunate degrees are given in signs. see Degrees. Whence a cat's miscarriage follows upon the killing of the male, Q. 3. n. 16 Feralia signs are akin to wild beasts, 187. n. 9 In the Horoscope they produce monsters, ibid. What the bier of Lazarus is, 510. n. 47 Fidicula, a bright star, except for Sirius, the greatest and most powerful of all, 187. n. 13 Its significations in the Horoscope, ibid. What the sixteen-sided figure is called, 188. n. 16 A gross error of Alstedius in its explanation, ibid. The Equicurricular figure excludes a dead fetus, or does not allow it to live long, 9. n. 30 It is explained wherein it consists, ibid. What figures of equal perimeter are called by geometers, 188. n. 15 Suitable figures of decumbiture are raised in the beginnings of diseases, 136. n. 18 At what point they should be raised, ibid. n. 12 The fitting of figures and names from fables onto the fixed stars, how rightly done, 213. n. 29 Fern in one day brings forth flower and fruit, 462. n. 35 Boundaries. see Terms. What a terminator is, and how manyfold, 190. n. 18 In sacred pages the name Firmament is used for the Air, 191. n. 19 What is commonly meant by that name, ibid. Whether the Firmament in which the fixed stars exist is solid, 191. n. 19 Whence the term is derived, ibid. What its thickness is. ibid. n. 10 The ancients, because of the slowness of its motion, did not distinguish it from the first mobile, ibid. n. 21
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Rerum MobiliVM 77 Gradus apud Astronomos quid. 213. n. 19 Iidem proportionaliter, ac Geometricè in terra consi- derati, ibid. Quot milliaria in terra singuli comprehendant. ibid. Diuersa eorum denominatio, ibid. n. 30 An, & quinam reales sint, ibid. Eorum aliqua ratio elucet ex Stellis fixis in ijs constitu- tis, ibid. Iam nunc vel ex eo euadunt erroribus multis obnoxijs, ibid. Felicium, & Infelicium subtilis ratio ex Cardano, ibid. Gradus contermini finibus beneficarum felices, malefi- carum verò infelices; ibid. Gradus intermedij signorum fixorum infelices, & quare ibi debilis ad modum euadit Aphera, 80. n. 379 Tabula Graduum augenrium fortunam, 215. n. 32 Lucidorum, & Tenebroforum. n. 33. Putealium, n. 35 Vacuorum, & Plenorum. n. 36. & Debilitatis, 79. n. 367 H HAlon quid memorabilis visus tempore Augusti. 217. n. 314. Hædi Stellulæ in Auriga tempestuosæ, 218. n. 11 Eorum significata in Horoscopo, ibid. Hircus Stella Nautis infesta, 221. n 25 Quid in Horoscopo indicet, ibid. Quibus locis sit verticalis, ibid. Historia memorabilis de Naso adscititio, Qu. 3. n. 16 De muliere solo attactu podagram concipiente, ibid. n. 22 Cuiusdam Medici solis pulueribus ex humano corpore compatatis omnes morbos curantis, ibid. n. 26 Pediculorum sub linea Occidentis morienrium, 82. n. 374 Homines cuiter ni forent, & immortales si ab Albo Planeta- rum eraderentur Mars, & Saturnus, 440. n. 15 Hora quid, & vnde dicta, 222. n. 34 Horarum inuentio, & distributio ex Cynocephalo, ibid. Earum diuersitas, ibid. & seq. Horæ inæquales seu Planetariæ, Quæ. ibid. Quomodo singulis diebus extrahi possint, 139. n. 25 Horæ opportunitarem in tebus agendis contemnere, est potius arbitrij præcipitatio, quam libertas. vide in V. Diepon. Horaria tempora Planerarum Latitudinem habentium, quomodo facile extrahantur, 223. n. 35 Horizontis officia, 225. n. 38,
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Movable Things 77 Degrees among Astronomers, some. 213. no. 19 The same, considered proportionally and geometrically on Earth, ibid. How many miles each contains on Earth, ibid. Their different naming, ibid. no. 30 Whether, and which, are real, ibid. Some account of them appears from the fixed Stars established in them, ibid. Now even from this they become subject to many errors, ibid. A subtle account of Fortunate and Unfortunate from Cardano, ibid. Degrees bordering the limits of beneficent planets are fortunate, but of maleficent planets unfortunate; ibid. Intermediate degrees of the fixed signs are unfortunate, and why there the sphere becomes very weak, 80. no. 379 Table of ascending degrees, fortune, 215. no. 32 Of the bright and the dark. no. 33. Of Puteal degrees, no. 35 Of empty and full. no. 36. And of weakness, 79. no. 367 H A memorable halo seen in the time of Augustus. 217. no. 314. The little kids in Auriga, stormy, 218. no. 11 Their significations in the Horoscope, ibid. The Goat-Star hostile to sailors, 221. no. 25 What it indicates in the Horoscope, ibid. In what places it is vertical, ibid. A memorable history of an added nose, Qu. 3. no. 16 Of a woman conceiving gout by the mere touch, ibid. no. 22 Of a certain physician curing all diseases only with powders compounded from the human body, ibid. no. 26 Of lice dying beneath the line of the West, 82. no. 374 Men would be cutters if they were not, and immortal if Mars and Saturn were removed from the White Planet, 440. no. 15 What an hour is, and whence it is so called, 222. no. 34 The invention and division of the hours from the Cynocephalus, ibid. Their diversity, ibid. and following. Unequal hours, or Planetary hours, what they are, ibid. How they may be extracted for each day, 139. no. 25 To neglect the opportunity of hours in carrying out affairs is rather a rushing of judgment than freedom. see under V. Diepon. The hourly times of planets having latitude, how they may be easily extracted, 223. no. 35 The offices of the Horizon, 225. no. 38,
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RERVM MOBILIVM. 79 Ignis inter omnia agentia naturalia maxime actiùs. Qu. 1. n. 30 Imaginatiuæ vis in rebus timorem incutientibus, Qu 3. n. 3 Imagines Astronomicæ an licitæ, 237. n. 23 Quonam pacto ijs iuiò, ac sine scrupulo vti possimus, ib. Imagines Coelestes instituendi quæ ratio, 234. n. 19 Cur è fabulis potissimum excerptæ, ibid. Cur tanta earum diuersitas, ibid. n. 20 Cur in vna plures, & disparatæ, ibid. Melius nunc cognita plenè Stellarum natura instituiu[m] possent, 333. n. 20 Schillerus easdem in Diuorum Imagines piè commuta- uit, quæ recensentur, 236. n. 20 & 334. n. 21 An non ita appositè, & cum plausu, ibid. Imagines Coelestes an occultam Philosophiam contineant, 236. n. 20 In magna Aula Patauina depictæ, 237. n. 22 An in primo mobili vllæ sint Imagines, & characteres, ibid. & 294. n. 69 Imperatorum, & Monarchiarum fata vnde sint, 44. n. 210 Imum Coeli cur Fouca ab Astronomis appelletur, 202. n. 42 Incidentiæ scrupula in Eclipsibus, quid sint, 162. n. 3 Inconiuncta signa sunt causa Antipathiæ rerum in hisce infe- rioribus, 242. n. 32 Indictio quid sit, & vnde dicta, 245. n. 37 Quomodo singulis annis competens facilè inueniatur, ibid. Indorum vanitas circa Horas coniunctionis Planetarum, 17. n. 79 Inferiora ista à superioribus tanquam à causis vniuersalibus reguntur, Qu. 2. n. 13 Infernus vnde dictus, 246. n. 39 Ex eo verus siderum locus obseruari posset, ni Telluris obstaret crassities, ibid. Quanta sit eius amplitudo, ibid. Tria in se continet receptacula, ibid. Quantum singula diffent à superficie terræ, ibid. An in eo verus ignis corporeus existat, ibid. n. 40 An eiusdem rationis cum nostro, ibid. An sit lumine, alijsque qualitatibus ignis elementaris prædius, ibid. n. 41 Quomodo torqueat Dæmones, & animas separatas, ibid. Quare ignis Inferni sit nostro longè velocior, ibid. An montes Igniuiomi sint Inferni spiracula, è quibus
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RERVM MOBILIVM. 79 Fire, among all natural agents, the most active. Qu. 1. n. 30 The power of imagination in things that arouse fear, Qu. 3. n. 3 Astrological images, whether lawful, 237. n. 23 By what means we may use them freely and without scruple, ib. How the celestial images are to be arranged, 234. n. 19 Why they were taken chiefly from fables, ibid. Why there is such diversity among them, ibid. n. 20 Why in one there are many, and diverse, ibid. Now that the nature of the stars is more fully known, they could be instituted, 333. n. 20 Schiller piously changed the same into images of the saints, which are listed, 236. n. 20 & 334. n. 21 Whether this was not fittingly done, and with applause, ibid. Whether celestial images contain occult philosophy, 236. n. 20 Painted in the great hall of Padua, 237. n. 22 Whether there are any images and characters in the first mobile, ibid. & 294. n. 69 Whence the fate of emperors and monarchies comes, 44. n. 210 Why the lowest part of heaven is called Foca by astronomers, 202. n. 42 What the scruples of incidence in eclipses are, 162. n. 3 The disjoined signs are the cause of antipathy among things in these lower regions, 242. n. 32 What an indiction is, and whence it is so called, 245. n. 37 How the appropriate one for each year may easily be found, ibid. The vanity of the Indians concerning the hour of the conjunction of the planets, 17. n. 79 These lower things are governed by the higher as by universal causes, Qu. 2. n. 13 Whence hell is so called, 246. n. 39 From this the true place of the stars could be observed, if the thickness of the earth did not obstruct it, ibid. How great its extent is, ibid. It contains three receptacles within itself, ibid. How much each differs from the surface of the earth, ibid. Whether there truly exists in it corporeal fire, ibid. n. 40 Whether it is of the same kind as our fire, ibid. Whether it is endowed with light and other qualities of elemental fire, ibid. n. 41 How it torments demons and separated souls, ibid. Why the fire of hell is far more rapid than ours, ibid. Whether fiery mountains are the vents of hell, from which
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80 INDEX naturaliter euaporet Ignis, ibid. 5. 40 Historia de quadam horrisona Voragine in Turingia, n. 41 De Puteo Sancti Patricij in Hybernia, ibid. Cur Deus hæc Inferni ostia pluribus, ac diuersis in locis apparuerit, ibid. Ingressus Planetarum quid sint. n. 250. n. 44 Vaient ad actuandos effectus in radice præordinatos, ibid. Duplicates alij actiui, alij passui, ibid. Instans Natiuitatis elicere quam difficile, 207. n. 12. & seq. Quomodo artificiosè indagari possit, 30. n. 164. & seq. Quodnam dicendum sit verum instans Natiuitatis, 208. n. 14 Instrumentum Gnomonicum, 39. n. 187 Inter lunium quantum temporis amplectatur, 250. n. 46 Inter lunij tempore si sata serantur non sunt vermiculis obnoxia, ibid. Formicæ eo tempore otiosæ 452. n. 63 Interrogationes Astrologicæ an licitæ, 251. n. 47 Iris quid sit, 251. n. 49 Formatur tam à Sole quam à Luna, ibid. Nunquam conspicua in Meridie, nisi in hyeme, & quare, ibid. Eius præsagia, ibid. n. 50 Est serenitatis prænuntia, & quide naturaliter, ibid. n. 51 Cur manè pluuiam, vesperè serenum indicet, ibid. Si in Arbores incubauerit eas odoratiores facit, ibid. Iris Lunæ in quo à Solari differat, n. 49 Est Christi Domini humanitatis symbolum, n. 52 Iuglandis Vmbra cur dormientibus obsit. Qu. 1. n. 16. Iugularum nomine quæ Stellæ veniant, 254. n. 60 Iupiter vnde dictus, 254. 65. eius natura, ibid. In Pharmacis sumendis non est adeò idoneus, & quare, 167. n. 20 Eius astrum duabus Zonis conspicuum, 255. n. 63 Habet suos stipatores, ibid. 284. n. 31 Iouis mira obscuratio anno 1648. 163. n. 7 Quid portendat. ibid. L Lacus quidam cur salsedine præditi, 56. n. 264 Gæteri, etsi vastissimi, qua de re non sint salsi, ibid. n. 265 Laetap
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80 INDEX naturaliter euaporet Ignis, ibid. 5. 40 History of a certain fearsome whirlpool in Thuringia, n. 41 Of the Well of Saint Patrick in Ireland, ibid. Why God has appeared at these gates of Hell in several, and different, places, ibid. Ingressus Planetarum what they are. n. 250. n. 44 They tend to bring about effects preordained in the root, ibid. Some active, some passive, ibid. How difficult it is to elicit the exact moment of Nativity, 207. n. 12. & seq. How it may be skillfully investigated, 30. n. 164. & seq. What should be said to be the true moment of Nativity, 208. n. 14 Gnomonic instrument, 39. n. 187 How much time the interlunium includes, 250. n. 46 If seeds are sown during the interlunium, they are not liable to worms, ibid. At that time the ants are idle 452. n. 63 Whether astrological questions are lawful, 251. n. 47 What a rainbow is, 251. n. 49 Formed both by the Sun and by the Moon, ibid. Never visible at midday, except in winter, & why, ibid. Its omens, ibid. n. 50 It is a herald of fair weather, and why naturally, ibid. n. 51 Why it indicates rain in the morning and clear weather in the evening, ibid. If it has settled on trees, it makes them more fragrant, ibid. In what respect the Moon rainbow differs from the solar one, n. 49 It is a symbol of the humanity of Christ the Lord, n. 52 Why the shade of the walnut tree is harmful to sleepers. Qu. 1. n. 16. What stars come under the name of Jugularum, 254. n. 60 Why Jupiter is so called, 254. 65. its nature, ibid. It is not so suitable in taking medicines, and why, 167. n. 20 Its star visible in two zones, 255. n. 63 It has its attendants, ibid. 284. n. 31 The wondrous obscuration of Jupiter in the year 1648. 163. n. 7 What it portends. ibid. L Why certain lakes are endowed with saltness, 56. n. 264 Why the others, though very vast, are not salty for what reason, ibid. n. 265 Laetap
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Rerum MobiliVM. Eorum luminis intensio, & ex ensio causat actiua. & passiuas qualitates in inferioribus, ibid. Vide, Lux Luminaria quæ dicantur, p. 267. n. 41 An per accessum, & recessum sint causa orius, & interius rerum, ibid. n. 40 Sunt causæ rerum vniuersales & æquiuocæ, ibid. n. 42 Cum diuersis Planetis congruidentia diuersi generis mixta, & animalia producunt, ibid. Quæ Luminarium defectiones pestilentiam, & alia mala adducant, ibid. Quam benè D Dionysius Areopagita, ex miro illo, ac formidabili luminarium defectu in Christi morte, mundi defectionem arguerit, ibid. Luminaribus si forrior, & supra ipsa Planeta eleueretur Satellitium Planeta cedet, p. 440. n. 13 Luna vnde dicta. Eius encomia ex S. Ambrosio, p. 268 n. 44 Efficacia ipsius in hæc inferiora, ibid. & p. 470. n. 113 Agit per lucis extensionem, ibid. Præest Pituitæ, & humido radicali, ibid. & 207 n. 12 Rorem affluenter adducit, 44 n. 53 Cum primum apparet illuminatur ex terræ reflexione, p. 269. n. 43 Triplex Mensis Lunæ. Periodicus, Synodicus, & apparitionis, p. 268. n. 44 Eius diameter quanta, p. 270. n. 47 Quid sin in eius disco maculæ, p. 269. n. 45 Lunæ stationes quæ, p. 271. n. 48 Phases quæ, ibid. An sit locus habitationi congruus, p. 270. n 46 An in eius superficie constituenda sit Paradisus Terrestris, ibid. & p. 355. n. 9. & seq. per 10:um. ibid. An ibi Henochi, & Elias, Si quis in Luna constitueretur ea omnia videret in superficie terræ, quæ nos in Luna conspicimus, p. 168 n 2. Lunæ Eclipsis, Vide Eclipsis, In Lunari Eclipsi Cyclosæpè deceptus, p. 218. n. 4 Lunaria herba Lunæ mutationes servat, qu 1. n 20 Lusitani ob Aeris diuersitatem in India diu viuere nequeunt, nisi eò pergant adolescentes, p. 111. n 131 Lustrum quid sit, p. 245. n 37 Lux quid sit, & in quo à Lumine differat, p. 175. n. 50 Quibus corporibus competat lux, quibus lumen, ibid.
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Movable Things. The intensity and extension of their light cause active and passive qualities in lower things, ibid. See, Light. The luminaries that are so called, p. 267. n. 41 Whether, by their approach and recession, they are the cause of the rise and decay of things, ibid. n. 40 They are universal and equivocal causes of things, ibid. n. 42 How mixtures and animals of different kinds are produced by their agreement with different planets, ibid. What eclipses of the luminaries bring pestilence and other evils, ibid. How well Dionysius the Areopagite, from that marvelous and dreadful eclipse of the luminaries at Christ's death, inferred the world's failing, ibid. If a planet were stronger than the luminaries, and were raised above them, its satellite would give way to the planet, p. 440. n. 13 The Moon, from what it is so called. Its praises from St. Ambrose, p. 268 n. 44 Its efficacy in these lower things, ibid. & p. 470. n. 113 It acts by the extension of light, ibid. It presides over phlegm and the radical moisture, ibid. & 207 n. 12 It abundantly brings dew, 44 n. 53 When it first appears, it is illuminated by reflection from the earth, p. 269. n. 43 The Moon has three months: periodic, synodic, and of appearance, p. 268. n. 44 Its diameter, how great, p. 270. n. 47 What the spots on its disk are, p. 269. n. 45 The Moon's stations, what they are, p. 271. n. 48 The phases, ibid. Whether it is a suitable place for habitation, p. 270. n. 46 Whether Paradise Terrestrial is to be placed on its surface, ibid. & p. 355. n. 9. & seq. through 10:um. ibid. Whether Enoch and Elijah are there, If someone were placed in the Moon, he would see on the surface of the earth all those things which we see on the Moon, p. 168 n 2. Lunar eclipse, see Eclipse, In a lunar eclipse, he was often deceived by the Cythos, p. 218. n. 4 The moonwort herb preserves the Moon's changes, qu 1. n 20 The Portuguese cannot live for a long time in India because of the diversity of the air, unless they go there as young men, p. 111. n 131 What a lustrum is, p. 245. n. 37 What light is, and in what it differs from lumen, p. 175. n. 50 To which bodies light belongs, to which lumen, ibid.
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Rerum MobiliVM. Aliquando pro Venere acceptus, p. 525. n. 24 Tycho in eius obseruatione fatiscens, ibid. An suos Stipatores habeat, vt Saturnus, & Iupiter, p. 279. n. 19 Est in fortuna minor & quare, p. 280. n 20 Mars, & Saturnus si in Cælo non essent, homines immortales forent, p. 440. n. 15 Masculini, & Fæminini ratio in Planetis, & signis Philosophicè probata, p. 280. n. 22. & seq. Mathematica vnde dicta, p. 282. n 27 Eius diuisiones, ibid. Medicamenta vulgaria sunt ad instar Lixirij, quæ naturam purgant quidem, sed simul eneruant, qu. 3. n. 10 Non sic extracta, & alia sublimiora, ibid. Medicamentum non est absolutè relinquendum, eo quod superstitiosis circumstantijs implicetur, si modò alias naturalem vim ad curandum habeat, qu. 2. n. 19 Medicæ stellæ quæ, & vnde denominatæ, p. 284. n. 31. & p. 255. n 64 Medicus Naturæ sub famulatur, qu. 3. n. 10 Semper Ephemeridas præ manibus habere debet, p. 130 n. 191 Medusæ Caput stella perniciosissima, verticalis olim Græcæ, nunc Regno Neapolitano, p. 21. n. 108 Mel præcipuus siderum fructus, p. 185. n. 46. & p. 435. n 55 Sub Cane Sirio salutaris, ibid. Mensium, & Signorum sympathia, & Antipatia, p. 245. n. 36 Mercurius Planeta omnium minimus, p. 285. n. 40 Est naturæ promiscuæ, ibid. Quæ de eo circumferuntur minus certa sunt, quàm quæ de Planetis reliquis, & quare, ibid. n. 41 In domo Saturni profundam dat rerum intelligentiam, ibid. n. 40 Motor ventorum, p. 520. n. 13 Meridiani quot in Cælo concipiendi, p. 286. n. 42 Primus vbi constituendus, ibid. & p. 75. n. 365 Meteora sunt siderum fructus, p. 288. n. 50 Sunt mixta imperfecta, ibid. n. 51 Miles Cometa, quid sua apparitione portendat, p. 289. n. 56 Millaria quot comprehendant singuli gradus in æquatore, p. 213. n. 29 Minutum quid apud Astronomos, p. 289. n. 57
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Movable Things. Sometimes taken for Venus, p. 525. n. 24 Tycho, wearied in observing it, ibid. Whether it has its attendants, like Saturn and Jupiter, p. 279. n. 19 It is in lesser fortune, and why, p. 280. n. 20 If Mars and Saturn were not in the sky, men would be immortal, p. 440. n. 15 The ratio of the masculine and feminine in the planets and signs philosophically proved, p. 280. n. 22. & seq. Mathematics, whence so called, p. 282. n. 27 Its divisions, ibid. Common medicines are like the Elixir, which indeed cleanse nature, but at the same time weaken it, qu. 3. n. 10 Not so those extracted, and other more sublime ones, ibid. Medicine is not to be absolutely abandoned because it is involved in superstitious circumstances, if otherwise it has a natural power to heal, qu. 2. n. 19 What the medicinal stars are, and from where so named, p. 284. n. 31. & p. 255. n. 64 The physician serves Nature, qu. 3. n. 10 He ought always to have ephemerides at hand, p. 130 n. 191 Medusa’s Head, a most pernicious star, formerly vertical in Greece, now in the Kingdom of Naples, p. 21. n. 108 Honey, the chief fruit of the stars, p. 185. n. 46. & p. 435. n. 55 Useful under the Dog-star Sirius, ibid. The sympathy and antipathy of the months and signs, p. 245. n. 36 Mercury, the smallest of all the planets, p. 285. n. 40 It is of mixed nature, ibid. What is reported about it is less certain than what is said of the other planets, and why, ibid. n. 41 In the house of Saturn it gives deep understanding of things, ibid. n. 40 Mover of the winds, p. 520. n. 13 How many meridians are to be conceived in the sky, p. 286. n. 42 Where the first is to be established, ibid. & p. 75. n. 365 Meteors are the fruits of the stars, p. 288. n. 50 They are imperfect mixtures, ibid. n. 51 The comet Miles, what it portends by its appearance, p. 289. n. 56 How many thousand parts each degree in the equator contains, p. 213. n. 29 What a minute is among astronomers, p. 289. n. 57
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RERVM MOBILIVM. Melius oppldò institui posset, ibid. n. 16 Octi mestris partus cur non superuiuat, p. 241. n. 34. & seq Oppositio an sit semper radius Hostilis, p. 340. n. 32 Op. ima quæque sunt magis corruptioni obnoxia, qu. 1. n. 19 Orbis in quo defferat à Globo, & à Sphæra, p. 341. n. 34 Singulorum Planetarium orbis, ibid. c. 35 Orbis piscis mira natura, quæ se ad spirantem ventum con- uertit vel mortuus, & vndè hæc affectio oriatur, p. 313. n. 18. & seq. Origanum aridum appensum, in Brumâ cur redorescat, p. 88 n. 25 Orion sidus tempestuosum, p. 343. n. 42 In Horoscopo quid significet, ibid. Ostensorum quæ in sublimi aere videntur tria genera, p. 119 n. 152 Quid singula portendant, ibid. & in V. Pseudostella, Olympiades vnde, p. 337. v. 26. & seq. P Palilitium cur dicta sit stella in oculo australi Tauri consti- tura, p. 345. n. 1 Paracelsus vnguenti Armarij primus inuentor, qu. 2. n. 5 Ante ipsum tamen apud Antiquos aliqua eius notitia habira, ibid. Paracelsus à maledictis vindicatus, ibid. n. 27. & seq. Paradisus Terrestris an modò erter, & vbi constituatur, p. 270 n. 46. & seq. & p. 346. n. 4. & seq. Parados quid sit, p. 53. n. 248 Parallaxis quid sit, p. 360. n. 15 Quæ sidera Parallaxim habeant, ibid. n. 16 Paralleli declinationis qui sint, & quantæ efficacix, p. 365 n. 17. & p. 48. n. 117 Paralleli Cosmici, siue in mundo ad instar Antisciorum nuper inuenti, non minoris potentiæ. p. 363. n. 18 & seq. Item Paralleli Ascensionales, quorum ratio, & vis ex- plicatur, p. 362. n. 18 Parelia cur signa sint imminentis pluvix, p. 367. n. 25 Pars Fortunæ, Vide Fortuna, & in V. Lunaris Horosc. Fius noua, & subtilis consideratio, ibid. Partes Arabum an admittendæ, p. 367. n 29. & p. 201 n. 41. Parrus Masculinus, & Fæmininus, an, & qua ratione præ- uideri possit, p. 197. n. 30 Partus Septimestris, cur superuiuat, nunquam tamen
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OF MOVABLE THINGS. Could be better established in the town, ibid. n. 16 Why an eight-month child should not survive, p. 241. n. 34. & seq. Whether opposition is always the radius of an enemy, p. 340. n. 32 The lowest things are more subject to corruption, qu. 1. n. 19 How an orb differs from a globe and from a sphere, p. 341. n. 34 The orbs of the individual planets, ibid. c. 35 The strange nature of the fish-orb, which turns itself toward a blowing wind even when dead, and whence this property arises, p. 313. n. 18. & seq. Why dried hanging oregano grows greener again in winter, p. 88 n. 25 The tempestuous star Orion, p. 343. n. 42 What it signifies in a horoscope, ibid. The three kinds of things seen in the upper air, p. 119 n. 152 What each portends, ibid. & in V. Pseudostella, Where the Olympic games originate, p. 337. v. 26. & seq. P Why the star situated in the southern eye of Taurus is called Palilitium, p. 345. n. 1 Paracelsus, the first inventor of the ointment of the armorier, qu. 2. n. 5 Yet before him some knowledge of it was had among the ancients, ibid. Paracelsus vindicated from curses, ibid. n. 27. & seq. Whether the Terrestrial Paradise now exists, and where it is situated, p. 270 n. 46. & seq. & p. 346. n. 4. & seq. What a Parados is, p. 53. n. 248 What parallax is, p. 360. n. 15 Which stars have parallax, ibid. n. 16 What parallels of declination are, and how effective they are, p. 365 n. 17. & p. 48. n. 117 Cosmic parallels, or those lately invented in the world in the manner of antiscions, of no lesser power. p. 363. n. 18 & seq. Likewise ascensional parallels, whose reason and force are explained, p. 362. n. 18 Why parhelia are signs of impending rain, p. 367. n. 25 Part of Fortune, see Fortune, & in V. Lunar Horoscope. Its new and subtle consideration, ibid. Whether Arabic parts are to be admitted, p. 367. n. 29. & p. 201 n. 41. Whether the male and female child may be foreseen, and by what means, p. 197. n. 30 A seven-month child, why it survives, though never yet
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INDEX octimestris, p. 241. n. 34. & seq. Parauij in Magna Aula Monomæriæ depictæ, p. 237. n. 22 Sancti Patritij puteus admirabilis in Hybernia, p. 249. n. 41 Pauones quomodo futurum terræ motum indicent, p. 504 n. 27 Pediculorum Historia sub linea Oceidentis morientium, p 81. n. 374 Pegasus in Horoscopo facit Poëtam, p. 179. n. 63 Perihelium punctum qvid, p. 52. n. 239 Perigæa Planetarum, sicut & Apogæa non semper fixa, p. 53 n. 250 Periscij, & Periæci populi qui dicantur, p. 370. n. 41. & 45 Persei sideris in Horoscopo significata, p. 372. n. 47 Perticæ Cometæ apparciis portenta, p. 374. n. 50 Pestilentia naturaliter sequitur terræ motum, p. 503. n. 26 Phalangij Apuli, seu tarantulæ mira natura, qu. 3. n. 8 Eius variæ affectiones, & istorum ab eo ad ecrtos sonos, ac saltus propensio explicantur, ibid. & seq. Phoenice cur dicta Polaris stella, p. 374. n. 56. & p. 27 n. 154 Phoenomena liber à quibus è Græco in Latinum translatus, p. 60. n. 277 Phoenomena sæpiùs in Coelo visa cuius substantiæ, p. 375 n. 59 Singulis bis mille annis insigne aliquod Phoenomenum apparere solitum, p. 96. n. 36 Piscium signi in Horoscopo significata, p. 379. n. 76 Pisces multi pulmone præditi, p. 513. n. 19 Piscis Orbis mira affectio, qua se ad spirantem ventum conuertit, ibid. n. 18 Vnde hæc affectio, vel in mortuo oriatur, ibid. Kircheri speculatio rejicitur, ibid. Auctoris sententia, ibid. Piscibus vniuersis Ventus nimium importunus, ibid. n. 19 Pithetes Cometæ genus, p. 379. n. 81 Planeta quando dicatur Posthetes, p. 52. n. 241 Planeta in Genethliacis vitæ rationem inhiens, p. 51 n. 238 Quas conditiones habere debeat, ibid. Planeta combustus cur debilis, p. 117. n. 146 An malesici combusti deteriores fiant, ibid. Planetæ quæ stellæ dicantur, p. 379. n. 81 Planetæ se mutuò respicientes contrahunt familiarita-
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INDEX octimestris, p. 241. n. 34. & seq. Parauij depicted in the Great Hall of Monomæria, p. 237. n. 22 The wonderful well of Saint Patrick in Ireland, p. 249. n. 41 How peacocks indicate an impending earthquake, p. 504 n. 27 History of lice dying under the line of the West, p. 81. n. 374 Pegasus in the horoscope makes a poet, p. 179. n. 63 What the perihelion point is, p. 52. n. 239 The perigees of the planets, as well as the apogees, are not always fixed, p. 53 n. 250 Who are called Periscij and Periæci peoples, p. 370. n. 41. & 45 The signification of the star of Perseus in the horoscope, p. 372. n. 47 Portents appearing from a comet’s poles, p. 374. n. 50 Pestilence naturally follows an earthquake, p. 503. n. 26 The Apulian phalangium, or the wondrous nature of the tarantula, q. 3. n. 8 Its various affections, and their inclination toward certain sounds and dances, are explained, ibid. & seq. Why the North Star is called Phoenix, p. 374. n. 56. & p. 27 n. 154 The book Phoenomena, from which it was translated from Greek into Latin, p. 60. n. 277 What substance the frequently seen phenomena in the sky are of, p. 375 n. 59 That some remarkable phenomenon is wont to appear every two thousand years, p. 96. n. 36 The signification of Pisces in the horoscope, p. 379. n. 76 Many fishes are provided with lungs, p. 513. n. 19 The remarkable property of the orb-fish, whereby it turns itself toward the blowing wind, ibid. n. 18 Whence this property arises, even in the dead, ibid. Kircher’s speculation is rejected, ibid. The author’s opinion, ibid. For all fishes, wind is too troublesome, ibid. n. 19 Pithetes, a kind of comet, p. 379. n. 81 When a planet is called Posthetes, p. 52. n. 241 A planet in genethliacs seeking the course of life, p. 51 n. 238 What conditions it ought to have, ibid. Why a combust planet is weak, p. 117. n. 146 Whether evil planets, when combust, become worse, ibid. What stars are called planets, p. 379. n. 81 Planets regarding one another contract familiari-
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RERVM MOBILIVM. tem, p. 85. n. 15 Plantæ multæ ad aliquarum viciniam læduntur, ad aliarum oblectantur, & viuidius efflorescunt, qu. 1. n. 13 Plantæ, quibus iris incubauerit, odoratiores redduntur, p. 251. n. 51 Platonica corpora quæ, p. 231. n. 8 Pleiades stellæ vnde dictæ, p. 38. n. 89 Quot numero sint, p. 183. n. 81 Earum in Horoscopo significata, p. 381. n. 89 In Pleniunio Luna sup[er]ta Horizontem cum Sole sæpiùs visa, p. 424. n. 25 Eius rei rario, ibid. n 26 Pluuiæ iuges in Æstate mira naturæ prouidentia sub Zona torrida habitantibus opportunæ, p. 537. n. 14 Pluuijs Ver cur semper infestum, p. 516. n. 24 Polaris stella cur Phoenice dicta, p. 374. n. 56. & p. 27 n. 154 Olim Nautarum directrix, ibid. Nunc temporis non distat à Polo Mundi plusquam tribus gradibus, ibid. Num aliquando accidat, vt in Polum ipsum coincidat, p. 27. n. 115 Sub Polis nunquam tenebræ, p. 129. n. 118. & p. 516 n 12 Sub Polaribus Regionibus, an eadem sit aëris amoenitas, quam in nostris, ibid. Plinij assertum rejicitur, ibid. Est tamen ibi tolerandum frigus, ibid. Pontanus, Poëta magis, quam Astrologus, p. 383. n. 89 Præsepis stellæ in Horoscopo significata, p 386. n. 101 Sub Procyone difficiles admodum morborum curationes, p. 388. n. 108 Profectionum nomine apud Astronomos quidnam veniat, ibid. n. 110 Earum noua doctrina Philosophiæ consona, ibid. n. 111 Proportionalitatis diuisiones, p. 391. n. 115. & seq. Prorogatores qui dicantur, p. 391. n. 113 Prouincia nulla in Orbe quæ non sit commodè habitabilis, p. 537. n. 15 In hoc mira Numinis prouidentia commendatur, ibid. Puluis Sympathicus quid sit, & quomodo præparetur, qu. 1 n. 3 Vulneribus curandis ad miraculum factus, ibid. Prodest vel ipsis linceaminibus vulneratorum sanguine infectis, quantumuis loco dissitis applicatus, ibid.
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Movable things. item, p. 85. n. 15 Many plants are injured near some, delighted near others, and bloom more vigorously, qu. 1. n. 13 Plants on which the iris has rested are made more fragrant, p. 251. n. 51 Platonic bodies, which, p. 231. n. 8 The Pleiades, whence so called, p. 38. n. 89 How many they are, p. 183. n. 81 Their signification in the Horoscope, p. 381. n. 89 In the full moon, the Moon seen above the horizon with the Sun more often, p. 424. n. 25 The reason for this, ibid. n. 26 Continual rains in summer, a wonderful provision of nature, suitable for those dwelling under the Torrid Zone, p. 537. n. 14 Why spring is always troubled by rains, p. 516. n. 24 The Polar Star, why called Phoenice, p. 374. n. 56. & p. 27 n. 154 Formerly the guide of sailors, ibid. At present it is not more than three degrees distant from the Pole of the World, ibid. Whether it may ever happen that it coincides with the Pole itself, p. 27. n. 115 Under the Poles there is never darkness, p. 129. n. 118. & p. 516 n. 12 Under the Polar Regions, whether the same pleasantness of air exists as in ours, ibid. Pliny’s assertion is rejected, ibid. Yet cold there must be endured, ibid. Pontanus, more a poet than an astrologer, p. 383. n. 89 The signification of the Presepe star in the Horoscope, p. 386. n. 101 Under Procyon, very difficult cures of diseases, p. 388. n. 108 What is meant among astronomers by the name of profections, ibid. n. 110 Their new doctrine, in harmony with philosophy, ibid. n. 111 Divisions of proportionality, p. 391. n. 115. & seq. Who are called prorogators, p. 391. n. 113 No province in the world that is not conveniently habitable, p. 537. n. 15 Herein the wonderful providence of the Deity is commended, ibid. Sympathetic powder: what it is, and how it is prepared, qu. 1 n. 3 Made for the curing of wounds, to a miraculous degree, ibid. It is beneficial even to linen cloths infected with the blood of the wounded, however far away they may be from the place where it is applied, ibid.
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NOTA FILIUM. 59 An aliquando colorem, magnitudinem, motum mutauit, n. 23 Tychonis in ejus obseruatione deceptio, Ibidem. Ver sumendis portionibus opportunum, p. 167 n. 20 Veris qualitates, p. 515 n. 24 In Vere mundus creatus, ibidem. Vestes non sunt sub Leone scindendæ, p. 239 n. 25 Vigiles cur dictæ stellæ in Cynosura, p. 517 n. 35 Vindemi Vbertas, aut raritas à die S. Urbani auspicatur, p. 388 n. 109 Vindemiator cur dicta stella in ala Virginis, p 518 n. 36 Vinum, Cicuræ antidotum, p. 291 n. 61 Vinum indoliis fluctuat sirio exoriente, p. 311 n. 111 Violenta signa, & stellæ quæ sint, p. 517 n 37 Quos effectus pariant, ibidem. Virgæ quid sint, p. 518 n. 38 In quo differant ab ltride, ibidem. Pluviæ ingruentis manifestum judicium, ibidem: Vita Mundi altruitur, & probatur, p. 307 n. 89 Et est perfectior vita omnium animantium, p. 311 n. 94 Vita duplex in homine intellectualis, & animalis, ibidem Vitriolum habet naturalem antipathiam cum sanguine, qu. 1. n. 17 Vmbra in locis Antisciis, Amphisciis, ac Perisciis multi- plex, p. 49 n. 231 Vmbra vbi versatilis, p. 110 n. 117 Vnguenti Armarij descriptio, & virtus, Qu. 2 à n. 4 & seq. Eius aliquam notitiam habuerunt Antiqui, ibidem. n. 3 Diuersimodè à diversis Auctoribus traditur, ibidem. n. 22 & seq. Ab aliquibus non sine superstitionis admixtione, ibi- dem. Quomodo naturaliter operetur, qu. 3. per totam. Vngula Alcis aduersus morbum comitialem, qu. 3. n. 29 Vniones quare soluat Acetum, non Aqua fortis, q. 1. n. 36 Vomitum excitant rumiantia signa, p. 436 n. 61 Vorago in Turingia horisona, p. 249 n. 41 Vrinæ ardorem contrahit ad Siluestrem vrticam mingens; qu. 1. n. 16 Vrta duplex in Coelo, p. 519 n. 47 g ij
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NOTA FILIUM. 59 Sometimes it changed color, size, motion, n. 23 Tycho's deception in its observation, same place. Spring suitable for taking portions, p. 167 n. 20 The qualities of spring, p. 515 n. 24 The world was created in spring, same place. Clothes are not to be cut under Leo, p. 239 n. 25 Why the stars in Cynosura are called watchful, p. 517 n. 35 The abundance or scarcity of the vintage is foretold from St. Urban's day, p. 388 n. 109 Why the star in the wing of Virgo is called the vintager, p. 518 n. 36 Wine, an antidote to Cicuta, p. 291 n. 61 Wine in casks bubbles when Sirius rises, p. 311 n. 111 Violent signs, and what stars they are, p. 517 n. 37 What effects they produce, same place. What the wands are, p. 518 n. 38 How they differ from Irides, same place. A manifest sign of approaching rain, same place: The life of the world is nourished, and proved, p. 307 n. 89 And it is the more perfect life of all living things, p. 311 n. 94 A twofold life in man: intellectual and animal, same place Vitriol has a natural antipathy with blood, q. 1. n. 17 The shadow in Antiscian, Amphiscians, and Periscian places is manifold, p. 49 n. 231 The shadow where it is variable, p. 110 n. 117 Description and virtue of the Armory ointment, Q. 2 from n. 4 and following The ancients had some knowledge of it, same place. n. 3 It is handed down differently by different authors, same place. n. 22 and following By some, not without an admixture of superstition, same place. How it works naturally, q. 3 throughout. The hoof of the elk against epilepsy, q. 3. n. 29 Why vinegar dissolves pearls, not aqua fortis, q. 1. n. 36 Ruminating signs excite vomiting, p. 436 n. 61 A chasm in Thuringia echoes, p. 249 n. 41 Urination contracts a burning pain when one urinates on the wood nettle; q. 1. n. 16 A double Ursa in the sky, p. 519 n. 47 g ij
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INDEX INSIGNIORVM QVÆSTIONVM, quæ in hoc Opere ex occasione examinantur. Numerus appositus & marginalis singulis literis proprius, & cuivis editioni accomodatus. AN Aqua sit terra maior. A. num. 270. An sit Animata A. 269. ß M. 38. An moueatur motu uniuersitatis A. 267. ß 180. ß M. 73. An sub Æquatore sit temperatissimum Clima. C. 119. & Z. 10. An sub Æquatore hyems sit æstate, calidior. Z. 10. Per quid Astra agant in hæc inferiora. L. 38. An Astra vel potius calu in quo sunt moueantur. M. 76. An præter motum uniuersitatis habeant suum peculia- rem motum. M. 75. ß seq. An ullam activitatem habeant in opera artificata I. 23 Astrologicæ Questiones, seu interrogationes an licite. I. 47. Qua ratione Astra cum sensu, ß vegetatione careant vitam sensibilibus ac vegetabilibus tribuant. M. 93. An Calorum substantiasit diversa à sublunarium C 19. ß S. 113. An Cali per motum Vocalem sonum edant. C. 138. An sint Animati C. 140. ß M. 68. An per motum causent calorem in sublunaribus. M. 73.
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INDEX OF THE MOST IMPORTANT QUESTIONS, which in this Work are examined on occasion. The number appended in the margin is proper to each letter, and adapted to every edition. Whether water is greater than the earth. A. no. 270. Whether it is animated. A. 269. ß M. 38. Whether it is moved by the motion of the universe. A. 267. ß 180. ß M. 73. Whether under the Equator the climate is most temperate. C. 119. & Z. 10. Whether under the Equator winter is hotter than summer. Z. 10. By what means the stars act upon these lower things. L. 38. Whether the stars, or rather the heaven in which they are, are moved. M. 76. Whether, besides the motion of the universe, they have their own peculiar motion. M. 75. ß seq. Whether they have any activity in artificial works. I. 23. Astrological questions, or inquiries whether they are lawful. I. 47. By what reason the stars, while lacking sense and vegetation, impart life to things capable of sensation and growth. M. 93. Whether the substance of the heavens is different from that of sublunary things. C. 19. ß S. 113. Whether the heavens produce sound by vocal motion. C. 138. Whether they are animated. C. 140. ß M. 68. Whether by motion they cause heat in sublunary things. M. 73.
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INDEX. nos, [aqua] Masculinos plenos [aqua] vacuos [aqua]c. F. 19. [ aqua] G. 30. An [aqua] quæ ratione Horoscopus sit naturalis Vitæ significator. H. 40. Ignis sphæra an detur [aqua] vbi constituenda. L. 11. 12. [ aqua] 41. Num dicendus sit foecundus an sterilis. I. 10. Num ejus figura sit onalis vel Sphærica. L. 12. Ignis gehennæ an sit corporeus, [aqua] ejusdem rationis cum nostro. L. 40. An luce atque ijsdem qualitatibus ignis elementaris sit præditus. Ibid. Quanta sit inferni Diameter [aqua] amplitudo. I. Ibidem. An montes igninomini sint inferni spiracula. Ibidem. 41. Imagines Astronomicæ an naturali vi præditæ, ac licitè adhiberi possint. L. 23. [aqua] seq. Imagines Cælestes an ullam cum terrestribus connexionem habeant. G. 28. [ aqua] L. 19. [aqua] seq. An laudabiliter in Divorum imagines commutatæ. L. 24. [ aqua] O. 23. Iris cur mane apparens indicet pluviam Vespere antem serenum. L. 51. Latitudinis ratio num habenda sit in Moderatoribus ad siderum radios dirigendis. R. 6. Cur luminarium defectus pestilentiam, [aqua] alia mala naturaliter indicent. E. 6. An sint bonorum etiam Autores, [aqua] signa E. 6. Lumen astrorum an operetur per sui extentionem veram vel apparentem. L. 29. Luna an sit habitabilis. L. 46. Quidnam sint maculæ in Disco Lunari. L. 45. An Mars sit Planeta Masculus, vel femineus. F. 29. M. 17. [aqua] 22. Cur Vespere post Crepusculum, [aqua] mane ante Auroæ e ij
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INDEX. Nodes, [aqua] full masculine [aqua] empty [aqua]c. F. 19. [ aqua] G. 30. Whether, and for what reason, the Horoscope is the significator of natural life. H. 40. Whether the sphere of Fire exists, [aqua] where it is to be placed. L. 11, 12. [ aqua] 41. Whether it should be called fertile or sterile. I. 10. Whether its figure is oval or spherical. L. 12. Whether the fire of hell is corporeal, [aqua] of the same nature as ours. L. 40. Whether it is endowed with light and the same qualities as elemental fire. Ibid. What the diameter [aqua] extent of hell is. Ibid. Whether mountains of fire are the vents of hell. Ibid. 41. Whether Astronomical Images are endowed with natural force, and may lawfully be used. L. 23. [aqua] seq. Whether Heavenly Images have any connection with earthly ones. G. 28. [ aqua] L. 19. [aqua] seq. Whether they have been laudably changed into Images of the Saints. L. 24. [ aqua] O. 23. Why a rainbow appearing in the morning indicates rain by evening rather than clear weather. L. 51. Whether due regard should be had to latitude in directing instruments toward the rays of the stars. R. 6. Why eclipses of the luminaries, [aqua] and other evils, naturally signify pestilence. E. 6. Whether they are also causes of good things, [aqua] signs. E. 6. Whether the light of the stars acts by its true or apparent extension. L. 29. Whether the Moon is habitable. L. 46. What the spots on the lunar disc are. L. 45. Whether Mars is a masculine planet or a feminine one. F. 29. M. 17. [aqua] 22. Why in the evening after twilight, [aqua] in the morning before dawn e ij
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INDEX. Alfazìm. Almanach. Alfèua. Almanàr. Alfelta. Almanèm. Alfridârie. Almauerèth. Algebàr. Almegramèth. Algebra. Almicātharâth Algebûbatàr. Almogiza. Algèdi Denèb. Almàcedeme. Algèmmee. Almìdhebir. Algenìb. Almugèa. Algènsis. Almuri. Algèti. Almusechelet. Algòl. Almustèuli. Algonèysa. Almûthen. Algoràb. Alnisigrèf. Alhàbor. Alosaph. Alhàbor. Alphantia. Alhaisèth. Alphàrd. Alhàntica. Alpheua. Alhàdida. Alpheràtz. Alhùrto. Alphèta. Alìbd. Alramèch. Alichèl. Alràkaba. Alicòrab. Altalisùm. Aìctisal. Altàni. Alìoth. Aluehczît. Alkàir. Alynthiæ signu[m] Alxìa Dapha. Alzimòn. Alxìndus. Amblygòniu[m]. Alkinira. Amfrocraciator. Alkinirem. Annimodar. Allûre. Amphicyrtos. Almagèstum.
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INDEX. Alfazìm. Almanach. Alfèua. Almanàr. Alfelta. Almanèm. Alfridârie. Almauerèth. Algebàr. Almegramèth. Algebra. Almicātharâth Algebûbatàr. Almogiza. Algèdi Denèb. Almàcedeme. Algèmmee. Almìdhebir. Algenìb. Almugèa. Algènsis. Almuri. Algèti. Almusechelet. Algòl. Almustèuli. Algonèysa. Almûthen. Algoràb. Alnisigrèf. Alhàbor. Alosaph. Alhàbor. Alphantia. Alhaisèth. Alphàrd. Alhàntica. Alpheua. Alhàdida. Alpheràtz. Alhùrto. Alphèta. Alìbd. Alramèch. Alichèl. Alràkaba. Alicòrab. Altalisùm. Aìctisal. Altàni. Alìoth. Aluehczît. Alkàir. Alynthiæ signu[m] Alxìa Dapha. Alzimòn. Alxìndus. Amblygòniu[m]. Alkinira. Amfrocraciator. Alkinirem. Annimodar. Allûre. Amphicyrtos. Almagèstum.
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INDEX Aschere alièmin. Auctus lumine. Ascônas. Aucto numero Asèlli. Auellàr. Asicàth. Auis. Asiccàn. Auis Paradisica. Asidà. Aulàx. Aspèctus. Augentes fortunam. Aslabe. Aura. Aslänge, Arnig. Aurea regula. Assub. Astucus. Aùrea numerus. Aster. Astiro. Aùreus numerus. Astrabister. Auriga. Astræa. Aurora Astroôcynos. Aurora Cometes. Astrolabium, Aurora Cometes. Astrologia, Auster. Astron. Autômata. Astrothêmata. Autômata. Astrothêsia. Autùmnus. Astrum, seu Asterismus. Aux. Asymetria. Axis. Atàbulus. Azèlfage. Atazîr. Azimèch. Atèmbui. Azimùth. Aterêchinis. Azôni. Atùn Eltaùr. Azòrum insulæ Athlantides. Azûbenè. Athale. B. Athorâye, seu Altorich. B. Attestationes. Baculus Astronomi- Atmosphæra. . Auctus lumine. cus. Aucto numero Balêna. Auellàr. Bâltheus. Auis. Basiliscus. Auis Paradisica. Batà káytos. Aulàx. Bèd Algense. Augentes fortunam. Bellàtrix. Aura. Beibêniæ. Aùrea regula. Bennenàx. Aùreus numerus. Berenices Comæ, Auriga. Béstia Centauri Aurora Bicorpòreasi-gna, Aurora Come- Biothânatos. Austrum, seu As- Biquintilis. terismus. Bissextilis. Axis. Biûmbres. Azèlfage. Bòlides. Azèmena. Boôtes. Azimèch. Bôreas. Azimùth. Borrhapeliotes Azôni. Borrholibicus. Azòrum insulæ Brîdemif. Azûbenè. Brînèch, vel B. Brînèti. B. Bruma. B. Brûltho. B. Bubûlcus.
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INDEX Aschere alièmin. Auctus lumine. Ascônas. Aucto numero Asèlli. Auellàr. Asicàth. Auis. Asiccàn. Auis Paradisica. Asidà. Aulàx. Aspèctus. Augentes fortunam. Aslabe. Aura. Aslänge, Arnig. Aurea regula. Assub. Astucus. Aùrea numerus. Aster. Astiro. Aùreus numerus. Astrabister. Auriga. Astræa. Aurora Astroôcynos. Aurora Cometes. Astrolabium, Aurora Cometes. Astrologia, Auster. Astron. Autômata. Astrothêmata. Autômata. Astrothêsia. Autùmnus. Astrum, seu Asterismus. Aux. Asymetria. Axis. Atàbulus. Azèlfage. Atazîr. Azimèch. Atèmbui. Azimùth. Aterêchinis. Azôni. Atùn Eltaùr. Azòrum insulæ Athlantides. Azûbenè. Athale. B. Athorâye, seu Altorich. B. Attestationes. Baculus Astronomi- Atmosphæra. . Auctus lumine. cus. Aucto numero Balêna. Auellàr. Bâltheus. Auis. Basiliscus. Auis Paradisica. Batà káytos. Aulàx. Bèd Algense. Augentes fortunam. Bellàtrix. Aura. Beibêniæ. Aùrea regula. Bennenàx. Aùreus numerus. Berenices Comæ, Auriga. Béstia Centauri Aurora Bicorpòreasi-gna, Aurora Come- Biothânatos. Austrum, seu As- Biquintilis. terismus. Bissextilis. Axis. Biûmbres. Azèlfage. Bòlides. Azèmena. Boôtes. Azimèch. Bôreas. Azimùth. Borrhapeliotes Azôni. Borrholibicus. Azòrum insulæ Brîdemif. Azûbenè. Brînèch, vel B. Brînèti. B. Bruma. B. Brûltho. B. Bubûlcus.
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LOCORVM ET VERBORVM. C. Catægis. C Aballus. C Cacodæ- mon. Catogæum. Càdens. Cachétus Cæcias. incidentiæ. Cænàculum, Cathetus refle- Calbèz. xionis. Calculator. Catôptrice. Calippica Pe- Cæsus. riodus. Càstor. Càmmarus. Cauda Capri- Cancer. corni. Canis maior. Cauda Cygni. Canis minor. Cauda Ceti. Canopus. Cauda draco- Capella. sideris. Caper. Cauda delphi- Caput draconis. ni. Caput & cau- Cauda leonis. da draconis. Cauda Vrsæ Caput Apollo. maioris. Caput Hercu- Cauda Vrsæ lis. minoris. Caput seu se- Cegînus. ctio Equi. Centilòquium. Caput Medusæ Centra domo- CaputOphiuci rum. Carcinos. Cèpheus. Carpèncum. Ceràtias. Casmòn. Cèrados. Cassiopêa. Cetus. Catabibazon. Chakitichi.
Transcription: Translated (English)
Of Places and Words. C. Catægis. C Aballus. Cacodæmon. Catogæum. Càdens. Cachétus Cæcias. incidentiæ. Cænàculum, Cathetus reflexionis. Calbèz. Catôptrice. Calculator. Cæsus. Calippica Periodus. Càstor. Càmmarus. Cauda Capricorni. Cancer. Cauda Cygni. Canis maior. Cauda Ceti. Canis minor. Cauda draconis. Canopus. Cauda delphini. Capella. Cauda leonis. Caper. Cauda Vrsæ maioris. Caput draconis. Cauda Vrsæ minoris. Caput & cauda draconis. Cegînus. Caput Apollo. Centilòquium. Caput Herculis. Centra domorum. Caput seu section Equi. Cèpheus. Caput Medusæ Ceràtias. Caput Ophiuci Cèrados. Carcinos. Cetus. Carpèncum. Chakitichi. Casmòn. Cassiopêa. Catabibazon.
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LOCORVM ET VERBORVM. Dichotomos. poris. Diepon. Doryphorîa. Dies. Doza Almogiza. Differentia Ascensionalis. Draco. Digitus Eclipticus. Draconis lunæ caput & cauda. Dignitas. Draco volans. Dimantarcoris. Dabhè. Dimetrius. Ductio. Dioptra. Ductoria. Directio. Duodenària Directus. Planetarum. Discus. Dysis. Disceus. Diulsor. Diurnus. Docus. E Dodecaêdrum. Eclipsis. Dodecatemoron. Ecliptica. Domicilium. Ecptôsis. Dòmus. Edèlen. Dominus anni. Edùb. Dominus genituræ. Effluxus. Dominus Orbis. Elathi. Dominus Horæ. Eldegiagûl. Dominus radiorum. Eleiet. Dominus tèm- Elementum. Elementa Geometrica. Elocuatio. Elhabòr. Elhamnèl. Elhaut. Elgèdi. Elkaùs. Elkèrd. Elkleischèmal. Ellipsis. Eltanin. Eluàrad. Elzegiàle. Embolismus. Embolismica lunatio. Empireum. Engonâsis. Enif alferîts. Eniochus. Ennàgone. Enneàtici dies. Eòsphorus. Epàcta. Ephèmeris. Epicatàphora. Epicyclus. Epigius. Epima. Epitrion. Epochà. Eptàgonum. Equiculus. Equus alàtus. Erègbuo. A iii
Transcription: Translated (English)
Of Places and Words. Dichotomos. poris. Diepon. Doryphorîa. Dies. Doza Almogiza. Differentia Ascensionalis. Draco. Digitus Eclipticus. Draconis lunæ caput & cauda. Dignitas. Draco volans. Dimantarcoris. Dabhè. Dimetrius. Ductio. Dioptra. Ductoria. Directio. Duodenària Directus. Planetarum. Discus. Dysis. Disceus. Diulsor. Diurnus. Docus. E Dodecaêdrum. Eclipsis. Dodecatemoron. Ecliptica. Domicilium. Ecptôsis. Dòmus. Edèlen. Dominus anni. Edùb. Dominus genituræ. Effluxus. Dominus Orbis. Elathi. Dominus Horæ. Eldegiagûl. Dominus radiorum. Eleiet. Dominus tèm- Elementum. Elementa Geometrica. Elocuatio. Elhabòr. Elhamnèl. Elhaut. Elgèdi. Elkaùs. Elkèrd. Elkleischèmal. Ellipsis. Eltanin. Eluàrad. Elzegiàle. Embolismus. Embolismica lunatio. Empireum. Engonâsis. Enif alferîts. Eniochus. Ennàgone. Enneàtici dies. Eòsphorus. Epàcta. Ephèmeris. Epicatàphora. Epicyclus. Epigius. Epima. Epitrion. Epochà. Eptàgonum. Equiculus. Equus alàtus. Erègbuo. A iii
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INDEX. Linea. Malfelcare. Linea incidentiæ. Mamarth. Linea medij motus. Mandebula ceti. Lælaps. Manipulus spicarum. Lælaps. Linea veri motus. Làmpas. Logarithnica. Làmpades. Logarithmi. Lancea. Logistica. Lar. Lógitudo apud Astronomos. Larpitio. Lógitudo apud Geographos. Làterculus. Geographos. Lætio. Lucifer. Latitudo apud Lumen. Mars. Astronomos. Luminaria. Latitudo apud In suo Lumine. Mascula conditio. Geograp 'os . Luna. Latidudo orti- Lunæ mensiones. ua. Lupus. Lelaps. Lux. Leo. Lybicus. Lepus. Lybànotos. Lesath. Lyra. Leucònoti. Leuis. Libànotus. M Liberàlitas. Libra. Magia. Limbus Magistralis ventus. Limbus SS. Patrum. Maleuentum. Linda. Malèficæ.
Transcription: Translated (English)
INDEX. Line. Malfelcare. Line of incidence. Mamarth. Line of the middle motion. Mandebula ceti. Lælaps. Sheaf of ears of grain. Lælaps. Line of true motion. Lantern. Logarithmic. Lanterns. Logarithms. Lance. Logistic. Lares. Length among Astronomers. Larpitio. Length among Geographers. Little tiles. Geographers. Light-bearing. Lucifer. Latitude in Light. Mars. Astronomers. Luminaries. Latitude in its own Light. Masculine condition. Geographers. Moon. Latitude of the rising Measures of the Moon. heavenly body. Wolf. Lelaps. Light. Leo. Lybicus. Hare. Lybànotos. Lesath. Lyre. Leucònoti. Light. Libànotus. M Generosity. Libra. Magic. Border. Master wind. Border of the Holy Fathers. Maleventum. Linda. Witches.
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LOCORVM ET VERBORVM. Mercurius. Musica. Meridianus. Muta signa. Mèrops. Mutàtil. Mesanguo. Mùtutlum. Mescimach. Mutilàta signa. Mèsen. N. Mesaquelo, &c N. Meteora. O. Metònicus annus. N Micromèsa, Naásch, Muros cetàratos. Nadir. Miles. Nahar.Alcharnèr. Minùtum. Naris ceti. Mirach. Natiuitas. Mixta. Natùra. Mobilia signa. Nauis. Moderatòres. Nabolassid. Monomeniæ. Nebulosæ stel- Ægyptiorum. læ. Mosclèk. Nemèr. Motus. Neomànum. Primum Mobi-le. Nèpa. Secundi Mo-biles. Nescher. Mòtlatum. Nigèr. Moznàin. Nigra. Mundus. Nocturnum. Mumir. Nodi. Musatòr. Nona sphæra. Musca. Notapeliotes. Mùscida equi. Notolybicus. Nòrus. Nòtius piscis. Nouenàriæ. Nouilùnium. Nox. Nubes. Numerus. O. Obedien-tiasigna. Obiaculàri. Obliquus Angulus. Obliquus Cir-culus Obliqua signa. Obliquatio. Obscuræ stel-læ. Obsessio. Obrusus angu-lus. Occidens. Occidentales domus. Occidentalis Planeta. Occursantes. Occeànus. Octuèdum. Octuagulus. Octàuasphæra.
Transcription: Translated (English)
OF PLACES AND WORDS. Mercurius. Music. Meridianus. Dumb signs. Mèrops. Mutable. Mesanguo. Mututlum. Mescimach. Mutilated signs. Mèsen. N. Mesaquelo, &c N. Meteora. O. Metònicus annus. N Micromèsa, Naásch, Muros cetàratos. Nadir. Miles. Nahar.Alcharnèr. Minùtum. Naris ceti. Mirach. Nativity. Mixta. Nature. Mobilia signa. Ship. Moderatòres. Nabolassid. Monomeniæ. Nebulous stars Ægyptiorum. Mosclèk. Nemèr. Motus. Neomànum. Primum Mobi-le. Nèpa. Secundi Mo-biles. Nescher. Mòtlatum. Black. Moznàin. Black. Mundus. Nocturnal. Mumir. Nodes. Musatòr. Ninth sphere. Musca. Notapeliotes. Mùscida equi. Notolybicus. Nòrus. Nòtius piscis. Nouenàriæ. Nouilùnium. Nox. Nubes. Numerus. O. Obedien-tiasigna. Obiaculàri. Obliquus Angulus. Obliquus Cir-culus Obliqua signa. Obliquatio. Obscuræ stel-læ. Obsessio. Obrusus angu-lus. Occidens. Occidentales domus. Occidentalis Planeta. Occursantes. Occeànus. Octuèdum. Octuagulus. Octàuasphæra.
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LOCORVM ET VERBORVM. Hermippus. Hypogæum. Hesperus. Hypothenûsa. Heteroscij. Hyppcus. Hexagonum. Hinniculus. I Hiêrezim. I Acha. Hircus. Iàculum. Hircus Meteoron. Iàculum Meteoron. Hircus æquoris. Iapeos. Holométrum. Iapix. Homocentricu. Icnographîa. Homoch. Icosaëdrium. Homôzena. Ictesal. Hóra. Ignis. Horària tempora. Ignis lámbens. Horinæum. Imàgines cælestes. Horizon. Imàgines Astronomicæ. Horoscopus. Imùm Cæli. Horoscopus lunaris. Inathedes. Horoscòpium. Inconiuncta signa. Humàna signa. Inconiuncta signa. Huzìmethon. Imperantia signa. Hydra. Imperantia signa. Hydrus. Intuëtia signa. Hydrographia. Indictio. Hyems. Indus. Hylig. Infernus. Hylegialia loca. Infortùna. Hypaùgus. Ingeniculus. Ingressus. Interluniu m. Interrogationes Astrologicæ. Inuena: if. Iris, irina. Isla: hmi. Isgonius. Isoperimêtræ figutæ. Isomæùnos. Isis. Iògula. Iùgulas. Iugum. Iùpiter. Ixiònis rota. K K, Abàr. Kchütichi. Kàlb. Kaytos. Kaluròps. Kènen. Kertho: Kesil. Ketpholt. Kimach. Kollàsmenon. Kûs.
Transcription: Translated (English)
Of Places and Words. Hermippus. Hypogæum. Hesperus. Hypothenûsa. Heteroscij. Hyppcus. Hexagonum. Hinniculus. I Hiêrezim. I Acha. Hircus. Iàculum. Hircus Meteoron. Iàculum Meteoron. Hircus æquoris. Iapeos. Holométrum. Iapix. Homocentricu. Icnographîa. Homoch. Icosaëdrium. Homôzena. Ictesal. Hóra. Ignis. Horària tempora. Ignis lámbens. Horinæum. Imàgines cælestes. Horizon. Imàgines Astronomicæ. Horoscopus. Imùm Cæli. Horoscopus lunaris. Inathedes. Horoscòpium. Inconiuncta signa. Humàna signa. Inconiuncta signa. Huzìmethon. Imperantia signa. Hydra. Imperantia signa. Hydrus. Intuëtia signa. Hydrographia. Indictio. Hyems. Indus. Hylig. Infernus. Hylegialia loca. Infortùna. Hypaùgus. Ingeniculus. Ingressus. Interluniu m. Interrogationes Astrologicæ. Inuena: if. Iris, irina. Isla: hmi. Isgonius. Isoperimêtræ figutæ. Isomæùnos. Isis. Iògula. Iùgulas. Iugum. Iùpiter. Ixiònis rota. K K, Abàr. Kchütichi. Kàlb. Kaytos. Kaluròps. Kènen. Kertho: Kesil. Ketpholt. Kimach. Kollàsmenon. Kûs.
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INDEX. Regulares figuræ. Samèh. Regulus. Sartài Mesarthia. Remuneratio. Sartàn. Réte. Satellitium. Retrogradus. Satèllites. Reuolùtio. Saturnus. Rhombus. Scalènua. Rhomboides. Scheàt. Riforitas dùnnatu. Schedèr. Régel. Sciographia. Ros. Sciotherium. Rosa Come-tes. Scintillàtio. Rósch Halli-lich. Sciron. Rota Ixiònis. Scorpio. Rubail. Scotomenia. Ruuabàh. Scyphônes. Ruminantia si-gna. Scicans. Rythmus. Sector Circuli. S. Segmentum circuli. Saclàteni. Sectio equi. Sacrarium. Secundi mobi-les. Sàgen. Sedùlli. Sagàtta sidus. Semicirculus. Sagitta sinus. Semilunium. Sagitràrius. Semiquadràtus Salchadài. Sénacher. Saltàtor. Sencinèr. Sephîna. Septangulus. Septentriones. Septentriona-le. Septentrio vé-tus. Serpens. Serpentàrius. Serpens. Sertù pupillæ. Serpens. Scrucuth. Scsquiquadrà-tus. Sexingulus. Sextans Astro-nomicus. Sexagenària di-uisio. Sextans Astro-nomicus. Sextans Astro-nomicus. Sextans Astro-nomicus. Sextilis radius. Sextilis radius. Sidus. Sidus. Sidera discu-rentia. Sideràtio. Silens luna. Silens luna. Signa. Signa. Signifer. Signifer. Significatores Simphasis. Sinaphia. Sinaphia. Sinus. Sinus Abrahæ. Sinus Abrahæ. Sinus Abrahæ. Sirius. Sirius. Sithacèr. Sithacèr. Soail samuni. Soail samuni.
Transcription: Translated (English)
INDEX. Regulares figuræ. Samèh. Regulus. Sartài Mesarthia. Remuneratio. Sartàn. Réte. Satellitium. Retrogradus. Satèllites. Reuolùtio. Saturnus. Rhombus. Scalènua. Rhomboides. Scheàt. Riforitas dùnnatu. Schedèr. Régel. Sciographia. Ros. Sciotherium. Rosa Come-tes. Scintillàtio. Rósch Halli-lich. Sciron. Rota Ixiònis. Scorpio. Rubail. Scotomenia. Ruuabàh. Scyphônes. Ruminantia si-gna. Scicans. Rythmus. Sector Circuli. S. Segmentum circuli. Saclàteni. Sectio equi. Sacrarium. Secundi mobi-les. Sàgen. Sedùlli. Sagàtta sidus. Semicirculus. Sagitta sinus. Semilunium. Sagitràrius. Semiquadràtus Salchadài. Sénacher. Saltàtor. Sencinèr. Sephîna. Septangulus. Septentriones. Septentriona-le. Septentrio vé-tus. Serpens. Serpentàrius. Serpens. Sertù pupillæ. Serpens. Scrucuth. Scsquiquadrà-tus. Sexingulus. Sextans Astro-nomicus. Sexagenària di-uisio. Sextans Astro-nomicus. Sextans Astro-nomicus. Sextans Astro-nomicus. Sextilis radius. Sextilis radius. Sidus. Sidus. Sidera discu-rentia. Sideràtio. Silens luna. Silens luna. Signa. Signa. Signifer. Signifer. Significatores Simphasis. Sinaphia. Sinaphia. Sinus. Sinus Abrahæ. Sinus Abrahæ. Sinus Abrahæ. Sirius. Sirius. Sithacèr. Sithacèr. Soail samuni. Soail samuni.
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INDEX. Transitus. Vagiâh. Translatio luminis. Velzâgora. Trapèziæ. Vazor. Trapezoides. Vazalzene. Triada. Vectox. Triches. Velox cursu. Trigonum. Vêter draconis Trigonocrator Venus. Trigonometria. Ver. Vera. Tritaterum. Veràsua. Trimôrion. Vergiliæ. Trinus radius. Vertex. Triquetrum. Vespèrta. Triquetrum Vespertilio. Ptolemæi. Vesperùgo. Tropæi recti. Via combusta. Trópici. Via lactea. Trutina Hermetis. Vigiles. Tsamàngadu. Vindimiâtor. Tuberòn. Violenta signa. Turbo. Virgæ. Turbo ventus. Virgo. Tympana. Vmbilicus Andromedæ. Typhon. Vociferator. V. Voluellum. V Acuus Vortex. cursu. Vraniscos. FINIS. Vrna. Vrsa. Vvêga. Vultur cædens. Vultur volans. Vultùrns. Y. Xlphias Cometes. Xiphias sidas. Y YPàfricus. Z. Z Amoëtàr. Zàdaron. Zeuith. Zèphirus. Zigeàtus. Zodiacus. Zonæ. Zoodòtes. Zophomenia. Zozàicus. Zubeneschemali.
Transcription: Translated (English)
INDEX. Passage. Vagiâh. Transfer of light. Velzâgora. Trapezia. Vazor. Trapezoids. Vazalzene. Triad. Vectox. Hairs. Swift in course. Triangle. Tail of the dragon. Trigonocrator Venus. Trigonometry. Ver. True. Tritaterum. Veràsua. Trimôrion. Virgo. Triple radius. Vertex. Triquetrum. Vespèrta. Triquetrum Bat. Ptolemy's. Vesperùgo. Right trophies. Burnt road. Tropics. Milky Way. Hermes' balance. Watchers. Tsamàngadu. Grapher. Tuberòn. Violent signs. Whirlwind. Virgins. Wind whirlwind. Virgo. Drums. Navel of Andromeda. Typhon. Shouter. V. Little wheel. Empty Vortex. course. Uraniscos. FINIS. Urna. Ursa. Vvêga. Falling Vulture. Flying Vulture. Vultùrns. Y. Xlphias Cometes. Xiphias sidas. Y YPàfricus. Z. Z Amoëtàr. Zàdaron. Zeuith. Zephirus. Zigeàtus. Zodiacus. Zonæ. Zoodòtes. Zophomenia. Zozàicus. Zubeneschemali.
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I-3.
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I-3.
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1 2
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1 2