…uandas suscepturus est, continet. His quantum de doctrina triangulorum planorum, & sphæricorum suo operi necessarium æstimauit, subiungit.

…[the matters] he is about to undertake [to explain], it contains. To this he appends as much of the doctrine of plane and spherical triangles as he judged necessary for his work.

Secundus, est De doctrina primi motus, & his, quæ de stellis fixis hoc loco dicenda putauit.

The second [book] is On the doctrine of the first motion, and those things which he thought ought to be said in this place concerning the fixed stars.

Tertius, De motu Solis. Et, quia experientia eum docuit, quantitatem anni ab æquinoctijs numerati, ex motu etiam stellarum fixarum dependere, in prima huius Libri parte, vera ratione, & diuina profecto solertia, motus stellarum fixarum, mutationesque punctorum solstitialium & æquinoctialium inquirere ostendit.

The third [book], On the motion of the Sun. And, because experience taught him how greatly the length of the year reckoned from the equinoxes depends also upon the motion of the fixed stars, in the first part of this Book, with true reasoning and indeed with divine skill, he shows how to investigate the motions of the fixed stars and the changes of the solstitial and equinoctial points.

Quartus Liber, est De motu Lunæ, & De Eclipsibus.

The fourth Book is On the motion of the Moon, and On Eclipses.

Quintus, De Motibus reliquorum planetarum.

The fifth, On the Motions of the remaining planets.

Sextus, De Latitudinibus.

The sixth, On the Latitudes.

Priores Libros perdidici, Quarti generalem ideam concepi, reliquorum verò hypotheses primùm animo complexus sum. Quantum ad priores duos attinet, nihil tibi scribendum putaui, idque partim peculiari quodam meo consilio, partim quòd doctrina primi motus nihil à communi, & recepta ratione discedit, nisi quòd tabulas declinationum, ascensionum rectarum, differentiarum ascensionalium, & reliquas ad hanc doctrinam pertinentes, ita de integro construxit, vt obseruationibus omnium ætatum, per partem proportionalem accommodari possint. Quæ igitur in tertio Libro tradit, cum hypothesibus omnium reliquorum motuum, quantum in præsentiarum proingenij mei tenuitate assequi potuero, tibi, Deo dante, dilucidè recitabo.

The earlier Books I have learned thoroughly; of the Fourth I have conceived a general idea; but the hypotheses of the rest I have for the present only embraced in my mind. As regards the first two, I thought nothing should be written to you, partly by a certain particular plan of my own, partly because the doctrine of the first motion departs in no way from the common and received method, except that he has so constructed afresh the tables of declinations, right ascensions, ascensional differences, and the rest pertaining to this doctrine, that they can be adapted by proportional parts to the observations of every age. Therefore the things which he sets forth in the third Book, together with the hypotheses of all the remaining motions, so far as in the present slenderness of my talent I shall be able to attain it, I will, God granting, recount to you clearly.

[margin: Nic. Copernicum natum referunt Anno 1473. die 19. Febr. hora 4. ſcr. 48. p. m. die V[eneris] ante Cathedram Petri. Errat ergo Franc. qui ipſum anno 1472. 29. Ian. natum [eſſe ſcribit]. Mortuus autem eſt anno 1543. die 19. Ian. anno ætatis 70. quo eodem illos libros ſuos Re-uolutionum edi curauerat. (= They report that Nicolaus Copernicus was born in the year 1473, on the 19th day of February, at the 4th hour, 48 minutes p.m., on the Friday before [the feast of] the Chair of Peter. Therefore Franciscus errs, who [writes] that he was born in the year 1472 on the 29th of January. He died in the year 1543, on the 19th of January, in the 70th year of his age, in which same [year] he had had those books of his On the Revolutions published.)]

Cum D. Doctor meus Bononiæ, non tam discipulus, quàm adiutor & conscius obseruationum doctissimi Viri Dominici Mariæ: Romæ autem, circa annum Domini 1500. natus annos plus minus viginti septem, Professor mathematum, in magna Scholasticorum frequentia, & corona magnorum Virorum, & Artificum in hoc doctrinæ genere: hic vacans studijs, summa cura obseruationes annotasset, ex obseruationibus stellarum fixarum elegit eam, quam anno Domini 1525. de Spica Virgi-

When my Lord Teacher at Bologna — not so much a pupil as an assistant and witness of the observations of that most learned man Domenico Maria; and at Rome, about the year of the Lord 1500, being about twenty-seven years of age, a Professor of mathematics, in a great throng of scholars and a crown of great men and craftsmen in this kind of learning — here, devoting himself to his studies, had with the greatest care recorded his observations, from the observations of the fixed stars he chose that one which in the year of the Lord 1525 [he made] concerning Spica of Virgo —

nis habuit. Constituit autem eam elongatam fuisse à puncto autumnali 17. grad. 21. m. ferè, cum ipsius declinationem meridianam non minorem 8. grad. 40. min. deprehenderet. Deinde conferens omnes obseruationes Authorum cum suis, inuenit reuolutionem Anomaliæ seu circuli diuersitatis eo completam, nosque nostra ætate à Timochare vsque, in secunda reuolutione esse. Quare medium motum stellarum fixarum, atque æquationes diuersi motus geometricè constituit. Quia enim Timocharis obseruatio Spicæ, anno 36. primæ periodi Calippi, collata cum obseruatione anni 48. eiusdem periodi, nos docet, stellas illa ætate in 72. annis vnum gradum processisse: deinde ab Hipparcho ad Menelaum septem in centum annis vnum gradum confecisse, constituitque æqualem fuisse motum stellarum à Timochare in postremum quadrantem circuli diuersitatis incidisse, id quò mox apparuerit mediocris diminutus: in tempore autem intermedio inter Hipparchum & Menelaum, motum diuersitatis fuisse in loco tardissimo. Siquidem Menelai obseruationes cum Ptolemæi collatæ, ostendunt in 86. annis per vnum gradum stellas motas: Quare Ptolemæi obseruationes saepe motu anomaliæ existente in primo quadrante, stellasque tunc motu tardo addito, fluxauto. Porrò quia à Ptolemæo ad Albategnium vsque grauissimè, anni respondent, atque nostræ obseruationes collatæ cum Albategnij ostendunt stellas motu diuersi iterum in 70. annis vnum gradum confecere, sed adalias suas in Italia habitas, obseruatio ea, quam suprà dixi, collata ostendit stellas fixas motu diuerso in 100. annis iterum per vnum gradum progredi. Sole quoque clarius à tempore Ptolemæi ad Albategnium, motum diuersitatis, terminum mediocrem præterijsse, totumque quadrantem mediocris addidit, & circa Albategnij tempora fuisse in loco tardissimo: Ab Albategnij autem ad nos tertium quadrantem motus diuersi esse absolutum, & interim stellas progressas motu velociori diminuto, alterum limitem mediocris præregressum, & nostra ætate iterum in quartum quadrantem motus mediocris diminuti anomaliam peruenisse, proinde iam iterum motum diuersum tardissimum limitem appetere. Hac autem D. Præceptor vt ad certam rationem redigeret, quo ordine cum omnibus obseruationibus consentiret, constituit motum diuer-

[she] had. Now he established that she was distant from the autumnal point by about 17 degrees 21 minutes, since he found her southern declination to be not less than 8 degrees 40 minutes. Then, comparing all the observations of the Authors with his own, he found that the revolution of the Anomaly, or circle of diversity, was completed in that interval, and that we in our age, from Timochares onward, are in the second revolution. Therefore he established geometrically the mean motion of the fixed stars and the equations of the unequal motion. For since Timochares's observation of Spica, in the 36th year of the first Calippic period, compared with the observation of the 48th year of the same period, teaches us that the stars in that age advanced one degree in 72 years; then that from Hipparchus to Menelaus they completed one degree in a hundred years; and he established that the motion of the stars from Timochares had fallen into the last quadrant of the circle of diversity, whence it soon appeared diminished toward the mean; but in the time intermediate between Hipparchus and Menelaus the motion of diversity was at its slowest place. For Menelaus's observations compared with Ptolemy's show the stars moved by one degree in 86 years: wherefore Ptolemy's observations [show] the anomalous motion being often in the first quadrant, the stars then moving with slow [motion] added. Further, because from Ptolemy down to Albategnius the years correspond [closely], and our observations compared with Albategnius's show the stars again completed one degree in 70 years by the motion of diversity, but compared with his other observations made in Italy, that observation which I mentioned above shows the fixed stars again advancing one degree in 100 years by the diverse motion. Clearer than the Sun, from the time of Ptolemy to Albategnius the motion of diversity passed the mean limit, and added a whole quadrant of the mean, and about Albategnius's time was at its slowest place: but from Albategnius to us the third quadrant of the diverse motion has been completed, and meanwhile the stars advanced with a swifter diminished motion, having passed beyond the other limit of the mean, and in our age the anomaly has again come into the fourth quadrant of the diminished mean motion, and therefore now again the diverse motion approaches the slowest limit. That my Lord Teacher might reduce this to a fixed rule, so that it would agree in due order with all the observations, he established the diverse motion —

[margin: Prol. lib. 5. cap. 3. Almag. (= Ptolemy, book 5, chapter 3, Almagest.)]

[margin: Albat. cap. 51. (= Albategnius, chapter 51.)]

[margin: Ab anno 1525. ad annum 1525. (= From the year 1525 to the year 1525.)]

[margin: Coper. lib. 3. cap. 6. (= Copernicus, book 3, chapter 6.)]

sum in 1717. annis Ægyptijs compleri, maximámque æquationem 70. ferè minutorum, motum autem medium stellarum in anno Ægyptio 50. secundorum ferè esse, atque integram motus medij futuram reuolutionem in 25816. annis Ægyptijs.

[the diverse motion] is completed in 1717 Egyptian years, and the greatest equation [is] about 70 minutes, and the mean motion of the stars in an Egyptian year [is] about 50 seconds, and that the whole revolution of the mean motion will be in 25816 Egyptian years.

Hanc motuum in stellis fixis rationem comprobant etiam annuæ quantitates à punctis æquinoctialibus obseruatæ, atque getconstat, quare ab Hipparcho ad Ptolemæum dies integer, minus vicesima parte diei, interciderit: ab hoc autem ad Albategnium 7. dies ferè: ab Albategnio ad suas obseruationes, quas anno Domini 1515. habuit, dies 5. ferè, neque hæc omnia instrumentorum vitio, vt sub animis crediderit, sed certa, & consentientibus sibi vbique ratione fieri. Quare minimè ab hypothesi æqualitatem motus sumendam, sed à stellis fixis, vt mirabili consensu omnium ætatum tam de Solis & Lunæ, quàm de reliquorum planetarum motibus obseruationes testantur. Quia à Timochare ad Ptolemæum stellæ processerunt motu tardissimo, dein trecentesimam partem solum diei, quartæ super 365. dies; à Ptolemæo autem ad Albategnium, quia veloces, centesimam sextam partem diei, quadranti decedere receptum est: nostra ætate sic conferentar obseruationes cum Albategnij parte de eius quadranti consentiunt vicesimam octauam quartem. Tardo igitur motui maior anni quantitas ab æquinoctijs respondere videtur, veloci minor, decrescenti velocitati anni augmentum, adeò, vt si accuratè anni quantitas ab Hipparcho nostra ætate examinetur, cum Ptolemæo ferè iterum consentiat. Proinde statuendum puncta æquinoctialia moueri in præcedentia, quemadmodum in Lunanodos, & nequaquam stellas secundum signorum consequentiam progredi. Imaginandum itaque tale punctum æquinoctiale medium, quod procedat à prima stella Arietis orbis stellari, ab eoque æquinoctium medio, ipsum æquinoctium verum nunc diuersò &, regulari discedere, cuius tamen elongationes semidiameter 70. minuta non multum excedat, eoque certam & quantitas anni ab æquinoctijs rationem singulis ætatibus extiterit, & adhuc hodie deprehendi posse, quod hæc ratio exactissimæ, & quasi ad minutum, obseruationibus stellarum fixarum omnium Artificum respondet.

This same account of the motions in the fixed stars is also confirmed by the annual quantities observed from the equinoctial points, and it is established why from Hipparchus to Ptolemy a whole day, minus a twentieth part of a day, dropped out; but from him to Albategnius about 7 days; from Albategnius to his own observations, which he made in the year of the Lord 1515, about 5 days — and that all these things came about not by a fault of the instruments, as some have believed, but by a fixed [rule] and one everywhere consistent with itself. Wherefore the equality of motion is by no means to be taken from a hypothesis, but from the fixed stars, as the observations of every age testify with a wonderful consensus, both concerning the motions of the Sun and Moon and of the remaining planets. Because from Timochares to Ptolemy the stars advanced with the slowest motion, then [there is] only a three-hundredth part of a day, a quarter above 365 days; but from Ptolemy to Albategnius, because [they were] swift, a one-hundred-and-sixth part of a day is accepted as taken away from the quarter: in our age the observations thus compared with Albategnius's agree as to the twenty-eighth part of his quarter. Therefore a greater quantity of the year from the equinoxes seems to correspond to a slow motion, a lesser to a swift, and an increase of the year to a decreasing velocity, so that if the quantity of the year is accurately examined from Hipparchus in our age, it would again nearly agree with Ptolemy. Therefore it must be laid down that the equinoctial points move into the preceding [signs], just as the Moon's nodes do, and that the stars by no means advance according to the sequence of the signs. One must therefore imagine such a mean equinoctial point, which proceeds from the first star of Aries of the starry orb, and that from this mean equinox the true equinox itself now departs in a diverse and regular manner, whose elongations a radius of 70 minutes does not much exceed, and thereby a fixed account of the quantity of the year from the equinoxes has existed for every age, and can even today be detected, since this account corresponds most exactly, and almost to the minute, to the observations of the fixed stars of all astronomers.

[margin: Cop. lib. 3. cap. 6. (= Copernicus, book 3, chapter 6.)]

[margin: Anni consideratio generalis ab æquinoctio. Ptol. lib. 3. cap. 2. Albat. cap. 27. 28. Cop. lib. 3. cap. 13. (= General consideration of the year from the equinox. Ptolemy, book 3, chapter 2. Albategnius, chapter 27, 28. Copernicus, book 3, chapter 13.)]

Vt autem huius rei gustum aliquem tibi, doctissime Schonere, præbeam, en computaui tibi præcessiones æquinoctiorum veras, ad quædam obseruationum tempora.

But that I may give you some taste of this matter, most learned Schoner, behold I have computed for you the true precessions of the equinoxes, at certain times of observations.

| --- | --- | G. | M. | --- |

| Ante natiuitatem Domini | 295 | 2 | 20 | Timocharis |

| | 128 | 4 | 0 | Hipparchi |

| Post natiuitatem Domini | 139 | 6 | 40 | Ptolemæi |

| | 880 | 18 | 10 | Albategnij |

| Domini | 1076 | 19 | 37 | Arzahelis |

| | 1525 | 27 | 21 | Nostro |

[Table — Year | True precession (G[degrees], M[minutes]) | Time: In the year Before the Nativity of the Lord 295 — 2°20′ — Time of Timochares; 128 — 4°0′ — Time of Hipparchus; In the year After the Nativity of the Lord 139 — 6°40′ — Time of Ptolemy; 880 — 18°10′ — Time of Albategnius; In the year of the Lord 1076 — 19°37′ — Time of Arzahel; 1525 — 27°21′ — Our [time].]

Ptolemæi præcessio subtracta à locis stellarum in Ptolemæo positis, relinquit quantum à puncto æquinoctiali Arietis stella distent. Albategnij deinde præcessio addita ostendit verum locum obseruationis. Hoc fit in omnibus alijs similiter. Maximè autem hæc ad amussim obseruationibus omnium Artificum respondent, vbi etiam singula annotantur minuta, vel ex declinationibus positis habentur, autve Lunæ motu ad maiorem præcisionem reducti, vt nostra ætate vix in docendis obseruationibus cum Veterum collatæ. Nam neglectis, vt vides, aliquot minutis, partem saltem gradus recitant similium, vel tertiam, vel quartam, &c. Hæc autem motibus absidum planetarum non satisfaciunt, proinde de aliquo peculiarem motum eis tribui oportuit, vt patebit ex Solis Theoria.

Ptolemy's precession subtracted from the places of the stars set down in Ptolemy leaves how far the stars are distant from the equinoctial point of Aries. Then Albategnius's precession added shows the true place of the observation. This is done in all the others likewise. But these correspond most exactly to the observations of all astronomers, where even single minutes are noted, or are obtained from the declinations set down, or were reduced to greater precision by the Moon's motion, so that in our age, in teaching observations compared with the ancients', [it is] scarcely [otherwise]. For with some minutes neglected, as you see, they at least state a like part of a degree, whether a third or a fourth, etc. But these do not satisfy the motions of the apsides of the planets; therefore it was necessary that some particular motion be assigned to them, as will be clear from the Theory of the Sun.

Cæterum cum deprehendisset à stellis fixis quoque sumendam inæqualitatem Anni siderei, quem reperit 365. dierum, 15. minutorum, 24. secundorum ferè esse, & perpetuò fuisse, à quo tempore factas obseruationes constat. Nam quod referente Albategnio Babylonij tria secunda plus ponunt, Thebith vnum secundum minus, hæc tria iniuria vel instrumentis, & obseruationibus, quæ vt fieri neutiquam potuere, esse possunt, vel diuersitati motus Solis, vel etiam quòd vetustissimi non habita certa eclipsium ratione, diuersitates aspectus Solis in obseruationibus

But since he had found that the inequality of the sidereal year is also to be taken from the fixed stars, which he found to be about 365 days, 15 minutes, 24 seconds, and to have always been so, from whatever time the observations that are established were made. For as to the fact that, by Albategnius's report, the Babylonians put three seconds more, Thebith one second less — these three [discrepancies] can be by a fault either of the instruments and observations, which could in no way be otherwise, or by the diversity of the Sun's motion, or also because the most ancient [observers], having no fixed account of eclipses, [neglected] the diversities of the Sun's aspect (parallax) in their observations —

[margin: Annus sidereus. Cap. 27. (= The sidereal year. Chapter 27.)]

nibus neglexerunt, imputari potest. Nequaquam tamen comparandus hic error, totius huius temporis à Babylonijs ad nos, cum illo, qui est 22. secundorum diei in terPtolemæum, & Albategnium. Quòd autem necesse fuerit inter Hipparchum, & Ptolemæum, diem mum minus partem vicesimam intercidere, inter hunc & Albategnium 7. ferè deficere, non sine summa voluptate, ex prædicta motuum stellarum ratione, & ipsius D. Præceptoris, De Motu Solis tractatione tibi, Doctissime D. Schonere, collegi, vt paulò pòst videbis.

[these diversities of aspect, which they] neglected, can be imputed [to this]. Yet this error of the whole of this time from the Babylonians to us is by no means to be compared with that which is 22 seconds of a day between Ptolemy and Albategnius. But that it was necessary that between Hipparchus and Ptolemy a day, minus a twentieth part, should drop out, and between him and Albategnius about 7 [days] should be lacking — this I have gathered, not without the greatest pleasure, from the aforesaid account of the motions of the stars and from my Lord Teacher's own treatment On the Motion of the Sun, most learned Lord Schoner, as you will see a little later.

[margin: De mutatione obliquitatis Eclipticæ. Ptol. lib. 1. cap. 11. Almag. Coper. lib. 3. cap. 6. (= On the change of the obliquity of the Ecliptic. Ptolemy, book 1, chapter 11, Almagest. Copernicus, book 3, chapter 6.)]

Mutationem maximæ declinationis hanc rationem habere D. Doctor & Præceptor meus reperit, vt dum motus stellarum fixarum semel completus est, dimidia obliquitatis contingeret. Quare & integram mutationis obliquitatis reuolutionem in 3434. annis Ægyptijs fieri constituit. Timocharis, Aristarchi, & Ptolemæi temporibus mutationem obliquitatis in tardissima variatione fuisse constat, adeò vt mediocrem maximam declinationem crederent, semper 11/30 partes circuli magni. Albategnio post hos, 23. grad. 35. minut. ferè, sua ætate prodidit. Deinde Arzahel post eum 190. ferè annis, 23. grad. 34. minut. Prophatius Iudæus ab hoc iterum 230. annis, 23. grad. 32. minut. Nostra autem ætate non maior 23. grad. 28. minut. cum dimidio apparet. Proinde cum clarum sit, in 300. annis ante Ptolemæum, motum mutationis obliquitatis tardissimum fuisse, ab hoc verò ad Albategnium, per 700. annos, ferè, decreuisse per 17. minut. & ab Albategnio ad nos in 630. annis saltem per 7. minut. sequitur mutationem obliquitatis fieri, quemadmodum motum quolibet libratio nis, qui in lineam rectam, cuius est, in medio velocissimum esse, circa extrema tardissimum. Fuit igitur motus æquinoctialis, seu ecliptica circa Albategnij tempora, in medio ferè huius librationis motu, hoc autem seculo circa alterum terminum tardissimum, quo in loco maxima vinus diei & alterum sit appropinquabit. Sed suprà posuimus, per motum æquinoctialis saluari motus stellarum fixarum, & diuersitatem annui & quantitatis ab æquinoctijs, & huius poli sint vertices terræ, à quibus poli eleuationes sumuntur. Vides igitur, vt te, doctissime D. Schonere, obiter moneam, quales hypo-

My Lord Doctor and Teacher found the change of the greatest declination to have this account: that while the motion of the fixed stars is once completed, half [a revolution] of the obliquity should occur. Wherefore he established that a whole revolution of the change of the obliquity takes place in 3434 Egyptian years. In the times of Timochares, Aristarchus and Ptolemy it is established that the change of the obliquity was in its slowest variation, so much so that they believed the mean greatest declination to be always 11/30 parts of a great circle. Albategnius, after these, reported about 23 degrees 35 minutes in his own age. Then Arzahel, after him by about 190 years, 23 degrees 34 minutes; Prophatius the Jew, again 230 years from this, 23 degrees 32 minutes; but in our age it appears no greater than 23 degrees 28 minutes and a half. Therefore, since it is clear that in the 300 years before Ptolemy the motion of the change of the obliquity was the slowest, but from this to Albategnius, through about 700 years, it had decreased by 17 minutes, and from Albategnius to us in 630 years at least by 7 minutes, it follows that the change of the obliquity comes about just as the motion of any libration, which [moves] in the straight line of which it consists, is fastest in the middle, slowest about the extremes. The motion of the equinox, then, or the ecliptic, about Albategnius's time was nearly in the middle of this libratory motion; but in this century [it is] slowest about the other terminus, in which place it will approach the greatest [value] of one day and another. But we laid down above that by the motion of the equinox are preserved the motions of the fixed stars, and the diversity of the annual quantity from the equinoxes, and these poles are the vertices of the earth from which the elevations of the pole are taken. You see therefore, that I may admonish you in passing, most learned Lord Schoner, what kind of hypotheses —

hypotheses, seu theorias motuum obseruationes exigant, verùm adhuc, clariora testimonia audies. Porrò assumit D. Præceptor minimam obliquitatem 23. grad. 28. min. futuram, cuius ad maximam sit differentia 24. minutorum. Ex his constituit geometricè tabulam minutorum proportionalium, vt maxima ecliplicæ obliquitas ad omnes ætates elici possit. Sic suere minuta proportionalia, tempore Ptolemæi 58, Albategnij 24. Arzahelis 15. nostra ætate his, & 24. minuta. differentia facta parte proportionali, patet mutationis obliquitatis certam regulam esse deprehensam.

[you see what kind of] hypotheses, or theories of the motions, the observations require; but you will yet hear clearer testimonies. Further, my Lord Teacher assumes the least obliquity will be 23 degrees 28 minutes, of which the difference from the greatest is 24 minutes. From these he established geometrically a table of proportional minutes, so that the greatest obliquity of the ecliptic can be elicited for every age. Thus the proportional minutes were, in the time of Ptolemy 58, of Albategnius 24, of Arzahel 15, in our age these and 24 minutes; the difference being made by the proportional part, it is plain that a fixed rule of the change of the obliquity has been discovered.

[margin: De mutatione eccentricitatis Solis. (= On the change of the eccentricity of the Sun.)]

In Solis motu, cum circa anni inæquam fluxam inæquabilitatemque, tum etiam difficultas versetur, prius de apogij & eccentricitatis mutatione dicendum, vt omnes causas inæqualitatis anni adstruamus, quas tamen regulares & certas ostendit D. Præceptor, assumptis theorijs ad hoc accommodatis. Cum Ptolemæus apogium Solis fixum, maluit vulgatam recipere opinionem, quàm suis credere obseruationibus, quæ paruum fortassis à vulgata differebant, sed vt certa tamen coniectura ipsius narratione elicitur, constat etiam obseruationibus circa Hipparchum, nempe per 200. ante ipsum annos, talium partium 417. fuisse, qualium quadrans ex centro eccentrici est 10000. Ptolemæi autem ætate earundem 414. Arzahelis (cui potiorem fidem etiam Regiomontanus noster tribuit) ex maxima æquatione 346. ferè fuisse constat, & sua ætate nostro tempore 323. siquidem maximam æquationem non maiorem 1. grad. 50. min. cum dimidio, se deprehendere D. Præceptor affirmat.

In the motion of the Sun, since the difficulty turns both upon the irregular flux and inequality of the year, and also [upon other matters], one must first speak of the change of the apogee and eccentricity, that we may establish all the causes of the inequality of the year, which nevertheless my Lord Teacher shows to be regular and fixed, having assumed theories accommodated to this. Since Ptolemy [held] the apogee of the Sun fixed, he preferred to accept the common opinion rather than to trust his own observations, which perhaps differed little from the common one, but, as is elicited by a sure conjecture from his own narration, it is established also by observations about Hipparchus's time — namely 200 years before him — that it was of such parts 417, of which a quadrant from the center of the eccentric is 10000; but in Ptolemy's age 414 of the same; in Arzahel's (to whom our Regiomontanus also assigns the greater trust) it is established to have been about 346 from the greatest equation; and in his own age, in our time, 323 — since my Lord Teacher affirms that he found the greatest equation no greater than 1 degree 50 minutes and a half.

[margin: De mutatione eccentricitatis Solis. (= On the change of the eccentricity of the Sun.)]

Deinde cum diligentissimè perpenderet motus absidum Solis, & reliquorum planetarum, primum inuenit, et etiam æ prædictis, neque peculiaribus motibus absidua sub sphæra stellarum fixarii procedere, neq; plus contineri, vt vno motu apparentes motus stellarum fixarum & absidum, nec non mutationis obliquitatis ab vna causa dependere affirmemus, quàm si quis vetustiorum Artificum, qui vix àκριβῶς motus referunt, vna eademq; machinatione singulorum planetarum motus, & apparentias effingere conatur: aut quis pedem, manum, & linguam ab eodem musculo, & vi motrice eadem suas obseruationes perficere, defendendum præsumeret. Attribuit itaque D. Præceptor apogio Solis duos motus, medium scilicet, & differentem, quibus sub octaua sphæra moueatur,

Then when he most carefully weighed the motions of the apsides of the Sun and of the remaining planets, he first found, even from the aforesaid, that the apsides do not proceed beneath the sphere of the fixed stars by peculiar motions, nor [is it] more to be held that we should affirm the apparent motions of the fixed stars and of the apsides, and also of the change of the obliquity, to depend by one motion from one cause, than if some of the older astronomers, who scarcely report the motions ἀκριβῶς (accurately), should try to fashion the motions and appearances of the individual planets by one and the same contrivance; or as if someone should presume to maintain that the foot, the hand, and the tongue perform their operations by the same muscle and the same moving force. Therefore my Lord Teacher assigned to the Sun's apogee two motions, namely the mean and the differing, by which it is moved beneath the eighth sphere.

[margin: De mutatione eccentricitatis Solis. (= On the change of the eccentricity of the Sun.)]

[margin: Demotus Apogij Solis. (= On the motion of the Sun's apogee.)]

tur. Huc accedit, quòd cum æquinoctium verum æquali, & diuersò motu in antecedentia signorum moueatur, Solis, & reliquorum planetarum apogia, quemadmodum stellæ fixæ, postponam. Quare vt omnium ætatum obseruationes consentienti sibi inuicem lege respinderent, tres istos motus à se inuicem discernere coactus est.

[it is moved.] To this is added, that since the true equinox is moved into the preceding [parts] of the signs with an equal and a diverse motion, the apsides of the Sun and of the remaining planets, like the fixed stars, I shall postpone. Wherefore, that the observations of every age might answer to one another by a law consistent with itself, he was compelled to distinguish these three motions from one another.

[margin: Vide infrà in appendice Schema Theoriæ Solis. (= See below in the appendix the Schema of the Theory of the Sun.)]

Hæc vt intelligas, assumas maximam eccentricitatem 417. minimam 321. futuram, & differentia sit 96. partium, diameter scilicet parui circuli, in cuius circumferentia ab ortu ad occupatum centrum eccentrici moueatur, à centro igitur mundi ad centrum huius parui circuli 369. partes erunt. Omnes autem hæ partes sunt illæ, qualium quæ ex centro eccentrici 10000. partium. Habes machinationem, quam ex tribus suprà recitatis eccentricitatibus inuestigauit, simili prorsus ratione, quemadmodum ex tribus Lunæ eclipsibus, æquales ipsius motus, Diuino sibi inuento, corriguntur.

That you may understand these things, you may assume the greatest eccentricity will be 417, the least 321, and the difference is 96 parts — namely the diameter of the little circle, on whose circumference the center of the eccentric is moved from the rising toward the [setting], from the center of the world therefore to the center of this little circle there will be 369 parts. But all these parts are those of which those from the center of the eccentric are of 10000 parts. You have the contrivance which he investigated from the three eccentricities recited above, by an entirely similar method, just as from three eclipses of the Moon his equal motions are corrected by the Divine [device] discovered by him.

[margin: Motus centri eccentrici in circulo paruo. (= The motion of the center of the eccentric in the little circle.)]

Porrò statuit centrum eccentrici reuolutionem conficere, æquali velocitate, quâ & omnis mutationis obliquitatis diuersitas redit. Atque hæc hæc digna profectò est summa admiratione, quòd tanto, & tam mirabili consensu perficiatur.

Further, he established that the center of the eccentric completes a revolution with the same velocity by which also all the diversity of the change of the obliquity returns. And this indeed is worthy of the greatest admiration, that it is accomplished by so great and so wonderful a consensus.

[margin: Ad motum centri eccentrici Monarchias Mundi mutari. (= That the Monarchies of the World change according to the motion of the center of the eccentric.)]

Ante natiuitatem Domini 60. ferè annis erat maxima eccentricitas, atque eodem etiam tempore maxima Solis declinatio, & qua ratione vna, simili & prorsus non alia, reliqua quoq; decreuit, vt sæpius maximam mihi in varia rerum mearum fortuna, hic & item alibi id generis NL-usus rusus mitigationem adferant, ægrumq; animum suauissimè leniant.

About 60 years before the Nativity of the Lord there was the greatest eccentricity, and at that same time also the greatest declination of the Sun, and by the same one method, similar and entirely not other, the rest too decreased — so that often, in the various fortune of my affairs, here and likewise elsewhere [things] of this kind bring me the greatest mitigation, and most sweetly soothe a troubled mind.

[margin: Addam & Vaticinium aliquod. (= I will add also a certain prophecy.)]

Addam & Vaticinium aliquod. Omnes Monarchias incepisse videmus, cum centrum eccentrici in aliquo insigni huius parui circuli loco fuit. Sic cum Solis esset maxima eccentricitas hoc fuit Imperium ad Monarchiam declinauit, & quemadmodum illa decreuit, ita & hoc tanquam consenescens defecit, atque adeò euanuit. Cum perueniret ad quadrantem, terminumq; mediocrem, latæ est Lex Mahometica, incepit itaque aliud magnum Imperium, & velocissimè ad motus rationem creuit. Iam 100. annis, cum minima futura est eccentricitas, hoc quoque Imperium suam conficiet periodum, vt iam circa ista tempora in summo sit fastigio, à quo æquè

I will add also a certain prophecy. We see that all Monarchies have begun when the center of the eccentric was in some notable place of this little circle. Thus when the Sun's eccentricity was greatest, this [the Roman] Empire declined toward Monarchy, and just as that decreased, so this too, as if growing old, failed, and thus vanished away. When it reached the quadrant and the mean terminus, the Mahometan Law was brought forth; and so another great Empire began, and grew most swiftly according to the rate of motion. Now in 100 years, when the eccentricity will be least, this Empire too will complete its period, so that it is even now about these times at its highest peak, from which equally —

[margin: Rota Fortunæ. (= The Wheel of Fortune.)]

æquè velociter, Deo volente, lapsu grauiore ruet. Centro autem eccentricii ad alterum terminum mediocrem perueniente, speramus adfuturum Dominum nostrum Iesum Christum. Nam hoc loco circa creationem mundi fuit. Neque multum discrepat hæc computatio à dicto Eliæ, qui, Diuino instinctu, mundum 6000. tantum annos duraturum vaticinatus est, quo tempore duæ ferè reuolutiones peraguntur. Ita apparet hunc paruum circulum verissimè Rotam illam Fortunæ esse, cuius circumactu, Mundi Monarchiæ initia sumant, atque mutentur. In hunc itaque modum summæ totius historiæ Mundi mutationes, hoc paruo circulo inscriptæ conspiciuntur. Porrò qualia illa Imperia esse debuerint, & quis ne legibus, & Tyrannicis constituta, quomodo ex magnis coniunctionibus, & alijs eruditis coniecturis deprehendantur, à te breui, Deo volente, coràm audiam.

[equally] swiftly, God willing, it will fall with a heavier collapse. But when the center of the eccentric reaches the other mean terminus, we hope our Lord Jesus Christ will be present. For at this place [it was] about the creation of the world. Nor does this computation differ much from the saying of Elijah, who, by Divine inspiration, prophesied that the world would last only 6000 years, in which time about two revolutions are completed. So it appears that this little circle is most truly that Wheel of Fortune, by whose turning the beginnings of the Monarchies of the World are taken and changed. In this way, then, the chief changes of the whole history of the World are seen inscribed on this little circle. Further, what those Empires ought to have been, and whether established by laws or by tyrants, how they may be detected from great conjunctions and other learned conjectures — I shall hear from you in person shortly, God willing.

[margin: Æquatio motus apogij Solis. (= The equation of the motion of the Sun's apogee.)]

Porrò centrum eccentrici descendit versus contrarium vniuersi, contineamur est, centrum parui circuli secundum signorum consequentiam, singulis annulis Ægyptijs per 25. ferè secunda procedere. Et quia centrum eccentrici à summa distantia in antecedentia mouetur, æquato respondens motui anomaliæ temporis propositi, à medio motu subtrahitur, donec semicirculus compleatur: in reliquo verò additur, vt æquatus motus habeatur. Maxima autem æquatio inter apogium verum & medium geometricè vt constituit, vt ex prædictis deducta, est 7. grad. 24. min. reliquâ, vt fieri solet, pro ratione centri eccentrici in hoc paruo circulo tunc constituta. Motum diuersum certum habemus, quò tum tria secunda diei æquinoctialis, quod constituitur. Quia centrum eccentrici à summa distantia in antecedentia mouetur, æquato respondens motui anomaliæ temporis propositi, à medio motu subtrahitur, donec semicirculus compleatur: ita litera loca vera apogij Solis sub ecliptica positionem, idq; propter errores, qui inter Albategnium & Arzahelin incidit, vt refert Regiomontanus noster Lib. 3. Prop. 13. Epitomes.

Further, the center of the eccentric descends toward the opposite of the universe; it is contained that the center of the little circle proceeds, according to the sequence of the signs, by about 25 seconds per single Egyptian year. And because the center of the eccentric is moved from its greatest distance into the preceding [signs], the equation corresponding to the motion of the anomaly of the proposed time is subtracted from the mean motion, until a semicircle is completed; but in the rest it is added, that the equated motion may be had. The greatest equation between the true and the mean apogee, as he established it geometrically, derived from the aforesaid, is 7 degrees 24 minutes, the rest, as is usually done, being determined according to the ratio of the center of the eccentric then constituted in this little circle. We have a fixed diverse motion, whereby then three seconds of the equinoctial day, which is established. Because the center of the eccentric is moved from its greatest distance into the preceding [signs], the equation corresponding to the motion of the anomaly of the proposed time is subtracted from the mean motion until a semicircle is completed; thus the true places of the Sun's apogee under the ecliptic position, and this on account of the errors which fell between Albategnius and Arzahel, as our Regiomontanus reports in Book 3, Proposition 13 of the Epitome.

[margin: Rota Fortunæ. (= The Wheel of Fortune.)]

[margin: Æquatio motus apogij Solis. (= The equation of the motion of the Sun's apogee.)]

[margin: Inter obseruationis apogij Solis ab Albategnio & Arzahele falsa errores, error communis creditur. (= Among the observations of the Sun's apogee by Albategnius and Arzahel a common error is believed [to lie].)]

Albategnius liberè abutitur Astronomiæ, vt multis in locis videre est, si hoc in constitutione apogij Solis quoque fecit, vt demus sanè eum certam tempus æquinoctij habuisse, quia tamen impossibile est, vt etiam Ptolemæus testatur, solstitiorum tempora præcisè instrumentis constituere, siquidem vnum minutum declinationis, quod certè facilè sensum effugit, nos quatuor ferè gradibus hoc loco defraudare potest, quibus quatuor respondent dies.

Albategnius freely misuses Astronomy, as may be seen in many places; if he did this also in the constitution of the Sun's apogee — granting indeed that he had a certain time of the equinox — yet since it is impossible, as Ptolemy too testifies, to fix precisely with instruments the times of the solstices, since one minute of declination, which certainly easily escapes the senses, can here cheat us of nearly four degrees, to which four days correspond.

[Figure: Schema Anomaliae praecessionis Aequinoctiorum — see facsimile p117]

Tantæ molis erat, tali ratione stellarum fixarum, & Solis motus restituere, quò ex motuum eorum colligantia, vera annuæ quantitatis ab æquinoctijs ratio colligi posset. Regnum itaque in astronomia doctus, Viro D. Præceptori meo Deus sine fine dedit, quod Dominus & astronomicæ veritatis restaurationem gubernare, tueri, & augere dignetur, Amen.

So great a task it was, by such a method to restore the motions of the fixed stars and of the Sun, that from the interconnection of their motions the true account of the annual quantity from the equinoxes could be gathered. Therefore God gave without end to my Lord Teacher a kingdom learned in astronomy — which may the Lord deign to govern, protect, and increase, [namely] the restoration of astronomical truth, Amen.

Statui tibi breuiter docliss. D. Schonere integram tractationem motus Lunæ, & reliquorum planetarum, quemadmodum stellarum fixarum, & Solis conscribere, vt quæ vtilitates ex D. Præceptoris Libris ad studiosos mathematicos redirent, totamq; posteritati, veluti ex aliquo fonte promanaturam declarem. Verùm cum viderem mihi Opus in præsentiarum nimis excrescere, peculiarem hac de re Narrationem instituendam duxi. Igitur igitur illa tanquam præcurrere, viamq; præparare necessarium putauerim, hoc loco expediam, & in hypothesib. motus Lunæ, & reliquorum planetarum generalia quædam inspergam, quo & de toto hoc Opere maiorem spem concipias, & quæ cogerit necessitas in principio nostræ Narrationis præmiserim D. Præceptorem suum Opus ad Ptolemæi imitationem instituere, mihi amplius nihil opus relictum esse video, quod de ipsius mendè absoluti motus ratione apud te prædicem.

I have determined, most learned Lord Schoner, to write out for you briefly the whole treatment of the motion of the Moon and of the remaining planets, just as of the fixed stars and of the Sun, in order that I may declare what benefits from my Lord Teacher's Books would return to mathematical students, and to all posterity, as if flowing forth from some fountain. But since I saw the Work growing too large for me at present, I judged that a particular Narration should be set up on this matter. Therefore, since it seemed necessary to me to run ahead, as it were, and prepare the way for these things, I will dispatch [them] in this place, and I will sprinkle in certain general matters in the hypotheses of the motion of the Moon and of the remaining planets, that you may both conceive a greater hope concerning this whole Work, and — since necessity has compelled, in the beginning of our Narration I premised that my Lord Teacher set up his Work in imitation of Ptolemy — I see no further need left for me to proclaim before you concerning the method of his completed motion.

[margin: De reliquorum Planetarum theorijs. (= On the theories of the remaining Planets.)]

[margin: Ptolemæ laudat, Copernico multò maior, incumbit. (= He praises Ptolemy; Copernicus, much greater, devotes himself [to it].)]

Siquidem Ptolemæi indefatigabilem calculandi diligentiam, quasi suprà vires humanas obseruationum certitudinem, & verè diuinam rationem omnes motus, & quærat & inuestiget, & quod præsertim admirandi, exequendijs, ac postremò tam vbiq; ipsius inter se consentientem docendi & demonstrandi methodum nullus, cui quidem Vrania sit propitia, satis admirari, & prædicare potest. In hac autem re D. Præceptor meo maior, quò Ptolemæo labor incumbit, quòd seriem, & ordinem omnium motuum & apparentiarum, quem obseruationes 2000. annorum, tanquam præstantissimi duces in latissimo astronomiæ tanquam pelago, certam sibíq; mutuo consentientem rationem, seu harmoniam colligere cogitur: cum Ptolemæus vix ad quartam tanti temporis partem Veterum obseruationes, quibus tutò committere se, haberet. Et cum ἀπὸ τῷ νῦν verò Deo, & Præceptore legum politicæ cælestis errores astronomiæ nobis aperiantur, siquidem insensibiles, vt etiam neglectus erroris in principio constitutionis hypothesium, præceptorum, & Tabularum astronomicæ, procedente tempore se aperit, autetiam in immensum propagari, D. Doctori Præceptori meo, non tam Instaurandæ est Astronomia, quàm de integro exædificanda. Ptolemæus potuit plerasq; Veterum, vt Timocharis, Hipparchi, & aliorum hypotheses, ad seriem omnis diuersitatis

Inasmuch as no one to whom Urania is propitious can sufficiently admire and proclaim Ptolemy's indefatigable diligence in calculation, the certainty of his observations as if beyond human powers, and the truly divine reasoning by which he both seeks out and investigates all the motions, and — what is especially to be admired in carrying them out — and finally his method of teaching and demonstrating everywhere so consistent with itself. But in this matter a greater labor lies upon my Lord Teacher than upon Ptolemy, because he is compelled to gather the series and order of all the motions and appearances — which the observations of 2000 years, like the most excellent guides upon the vastest ocean, as it were, of astronomy — into a fixed account consistent with itself, or harmony: whereas Ptolemy scarcely had the observations of the ancients for a fourth part of so great a time, to which he might safely commit himself. And since by God ἀπὸ τῷ νῦν (from the present time) and through the Teacher of the laws of the heavenly polity the errors of astronomy are opened to us — since [errors], being imperceptible, like even a neglected error, in the beginning of the constitution of the hypotheses, precepts, and astronomical Tables, reveal themselves as time proceeds, or even are propagated to an immense extent — for my Lord Doctor and Teacher Astronomy is not so much to be Restored as to be built afresh from the whole. Ptolemy was able [to reduce] most of the hypotheses of the ancients, such as Timochares, Hipparchus, and others, to a series of every diversity —

tatis motuum, quæ sibi ex tantillo obseruationum tempore elapso nota erat, satis concinnè accommodare, ideo rectè & prudenter, quod & plausibilius erat, eas elegit hypotheses, quæ & rationi, nostrisq; sensibus magis consonæ esse videbantur, & quibus summi ante eum Artifices vsi fuerant. Cum autem omnium Artificum obseruationes, & cœlum ipsum, ac mathematica ratio nos conuincant, quod Ptolemæi, & communes hypotheses, nequaquam ad perpetuam, sibíq; inuicem consentientem colligantiam, & harmoniam rerum cœlestium demonstrandam, & in tabulas ac præcepta colligendam sufficiant; necesse fuit, vt D. Præceptor meus nouas hypotheses excogitaret, quibus videlicet positis, tales motuum rationes geometricè & arithmeticè bona consequentia deduceret, quales Veteres, & Ptolemæus olim τῷ θείῳ ψυχῆς ὄμματι in altum eleuati deprehenderunt: qualesq; hodie Veterum vestigia colligentibus in cœlo esse, diligentes obseruationes edocent. Sic nempe in posterum videbunt studiosi, quem Ptolemæus, & reliqui veteres Authores vsum habeant, quo eos hactenus tanquam ex scholis exclusos, reuocent, & in pristinum honorem, veluti postliminio reuersos restituant. Poeta inquit, Ignoti nulla cupido: Ideo non mirum, quare Ptolemæus hactenus cum tota Vetustate in tenebris neglectus iacuerit, quemadmodum procul dubio & tu, optime D. Schonere, cum alijs item bonis, doctisq; Viris sæpius dolueris.

[Ptolemy could adapt those hypotheses] quite neatly to the variety of motions known to him from so short a span of observations. He therefore rightly and prudently chose the more plausible hypotheses, which seemed more consonant with reason and our senses and had been used by the greatest astronomers before him. But the observations of all astronomers, heaven itself, and mathematical reasoning convince us that Ptolemy’s and the common hypotheses cannot demonstrate a perpetual, mutually consistent connection and harmony of celestial things, or gather it into tables and precepts. My Lord Teacher therefore had to devise new hypotheses from which he could deduce, by sound geometrical and arithmetical reasoning, accounts of the motions such as the ancients and Ptolemy once discerned, raised aloft “with the divine eye of the soul”; and such as diligent observations now teach those following the ancients’ traces to exist in heaven. Thus students will see henceforth what use Ptolemy and the other ancient authors have, so that they may recall them, hitherto excluded as if from the schools, and restore their former honour as though returning by right of restoration. The poet says, “There is no desire for the unknown.” It is therefore no wonder that Ptolemy, with all antiquity, has until now lain neglected in darkness, as you too, excellent Lord Schöner, together with other good and learned men, have doubtless often lamented.

[margin: Alias hypotheses Copernicæ assumendæ, quia vitiantur perpetuitas motuum non satisfacere vides. (= Other Copernican hypotheses must be assumed, because, being vitiated, the perpetuity of the motions you see does not satisfy.)]

[margin: Liber quartus. De Lunæ motu. (= The fourth Book. On the motion of the Moon.)]

Ratio Eclipsium vel vnica, Astronomiæ honorem apud imperitum vulgus tueri videtur. Hæc autem quàm hodie à communi calculo & in tempore, & prædicenda quantitate discrepet, in dies videmus. Cum verò accuratissimæ Ptolemæi, & aliorum optimorum Authorum obseruationes minimè in constituendis tabulis astronomicis, quòd quosdam facere videmus, tanquam falsas, & reprobas reijcere debeamus, nisi manifestum aliquem, argumentaue notæ, errorem irrepsisse deprehendamus, vix eaq; est humanum, quàm falsi nonnunquam & decipi, vel etiam specie recti, præsertim in difficilimis istis reb. abstrusissimis, in nequaquam obuijs: In Lunæ motu demonstrando assumit D. Præceptor meus huiusmodi theorias, & motuum rationes, quib. veteres excellentissimos Philosophos minimè in obseruationibus suis cæcos fuisse appareat. Quapropter sicut suprà anni ab æquinoctijs sumpti

The account of Eclipses alone seems to protect the honor of Astronomy among the unskilled common crowd. But how much this today differs from the common calculation, both in time and in the quantity to be predicted, we see day by day. But since we ought by no means to reject as false and reprobate the most accurate observations of Ptolemy and of the other best Authors in constructing astronomical tables — which we see some doing — unless we detect that some manifest error, or by tokens a noted [error], has crept in; and it is scarcely human [to avoid being], rather sometimes deceived even under the appearance of the right, especially in those most difficult and most abstruse matters, in no way obvious: in demonstrating the motion of the Moon my Lord Teacher assumes theories of this kind, and accounts of the motions, by which it may appear that the most excellent ancient Philosophers were by no means blind in their observations. Wherefore, just as above [in the case of] the year taken from the equinoxes —

[margin: Aliæ hypotheses Copernicæ assumendæ, quia vitiantur perpetuitas motuum non satisfacere vides. (= Other Copernican hypotheses must be assumed, because, being vitiated, the perpetuity of the motions you see does not satisfy.)]

[margin: Liber quartus. De Lunæ motu. (= The fourth Book. On the motion of the Moon.)]

sumpti augmentum, & decrementum regulare esse ostendimus, ita & diligenti quoque Solis, & Lunæ motuum examinatione deduci poterit, quæ singulis ætatibus veræ Solis, Lunæ, & terræ à se inuicem distantiæ, quaue ratione diametri Solis, Lunæ, & vmbræ diuersis temporibus aliter aliter repertæ fuerint, vt certa inter æquinoctium medio, ipsum æquinoctium verum motu diuersò, & regulari discedere, cuius tamen elongationes semidiameter 70. minuta non multum excedat, eóq; certam & quantitas anni ab æquinoctijs sumpti rationem singulis ætatibus extitisse, & adhuc hodie deprehendi posse, quod hæc ratio exactissimæ obseruationibus respondet. Imo quadratura, Luna in perigeo epicycli existente non tanta appareat, cum tamen suntegra lucret, quadruplum opportet apparere ad magnitudinem, quæ argentea opposita, cum fuerit in apogio epicycli. Senserunt & idem Timochares, & Menelaus, vt semper in obseruationibus stellarum cum Lunæ diametro vtuntur.

[just as above we showed] the increase and decrease [of the year] taken [from the equinoxes] to be regular, so also by a diligent examination of the motions of the Sun and Moon it will be able to be deduced what are, for every age, the true distances of the Sun, Moon, and earth from one another, and by what ratio the diameters of the Sun, Moon, and shadow have been found differently at different times — so that the true equinox departs from the mean equinox with a diverse and regular motion, whose elongations a radius of 70 minutes does not much exceed, and thereby a fixed account also of the quantity of the year taken from the equinoxes has existed for every age, and can still today be detected, since this account corresponds to the most exact observations. Indeed at quadrature, the Moon, being at the perigee of the epicycle, would not appear so great, whereas when it shines full, it ought to appear quadruple in magnitude — [the body] which, set opposite [silvery], when it has been at the apogee of the epicycle. Timochares and Menelaus felt the same, as always in observations of the stars they use the Moon's diameter.

[margin: Vide infrà in appendice Schema Theoriæ Lunæ. (= See below in the appendix the Schema of the Theory of the Moon.)]

[margin: Lib. 4. cap. 8. (= Book 4, chapter 8.)]

Quæ D. Præceptorem meum experientia docuit, diuersitates aspectus, & quantitates corporis Lunæ, in omni ipsius à Sole distantia parum, vel nihil differre abijs, quæ in coniunctione, & oppositione contingunt, vel manifestum sit Lunæ minimè talem, vt receptum, æquinoctium ætate, æquinoctium verum nunc diuersò, & regulari discedere. Ponitur eatq; quòd Lunæ orbis, terram cum adiacentibus elementis complectatur, vt æqualiter centrum eccentrici sit centrum terræ, quæ tum secundum diuersitatem, quam à Sole Luna habere videatur, ita saluat: Assumit Lunæ corpus epicyclo epicycli homocentrici moueri, hoc est primò, qui ferè inter coniunctiones vel oppositiones, & quadraturas medio tempore appareat, epicyclo, alium paruum, Lunæ corpus deferentem epicyclum, affingit, proportionem autem prima ipsi epicyclo, ad diametros secundi, sicut 1097. ad 237. esse demonstrat. Cæterum talis est motuum ratio. Circulus declinis, quæ, vt antehac, motus rationem obtinet, nisi quòd eiusdem æqualitatem à stellis fixis habet. Deferens, suo centro contricus, æquatorem regulariter, & æqualiter super suo centro (scilicet terræ) similiter æqualiter & regulariter à linea media motu Solis discedens. Epicyclus primus etiam super suo centro vniformiter; parui, & secundi epicycli centrum, in superiori parte in antecedentia, in inferiori in consequentia deferendo circumuoluitur. Ponit autem illum motum ab apogio vero, quod in superiori parte epicycli primi Lunæ à centro terræ per centrum eiusdem in circumferentiam eiecta ostendit, æqualem & regularem esse. Luna autem in circum-

What my Lord Teacher's experience taught him [is] that the diversities of aspect (parallax) and the quantities of the Moon's body, at every distance of it from the Sun, differ little or nothing from those which happen at conjunction and opposition, or that it is manifest that the Moon [is] by no means such as [was] received, [and that] in this age the true equinox now departs [from the mean equinox] with a diverse and regular motion. It is laid down, then, that the Moon's orb embraces the earth with the adjacent elements, so that equally the center of the eccentric is the center of the earth, which then preserves [the appearances] according to the diversity which the Moon seems to have from the Sun. He assumes the Moon's body to be moved by an epicycle of a homocentric epicycle — that is, first [the one] which appears nearly between conjunctions or oppositions and the quadratures at a middle time; to that epicycle he attaches another small one carrying the Moon's body, and he demonstrates the proportion of the first epicycle itself to the diameters of the second to be as 1097 to 237. For the rest, such is the account of the motions. The deferent circle, which, as before, holds the account of the motion, except that it has its equality from the fixed stars. The deferent, concentric with its own center, [moves] the equator regularly and equally upon its own center (namely the earth's), likewise equally and regularly departing from the middle line by the motion of the Sun. The first epicycle also [moves] uniformly upon its own center; the center of the little and second epicycle is carried round, in the upper part toward the preceding [signs], in the lower toward the following. He posits that motion to be equal and regular from the true apogee, which he shows to be cast out into the circumference in the upper part of the Moon's first epicycle from the center of the earth through its center. But the Moon in the circum-

…circumferentia parui & secundi epicycli etiam regulariter, & æqualiter mouetur ab apogio vero parui epicycli discedens, quod videlicet à linea exeunte à centro primi epicycli, per centrum secundi in ipsius circumferentia ostenditur. Atque huius motus hæc est regula, vt ipsa Luna bis in suo hoc minore epicyclo, in vna deferentis periodo reuoluatur, quo tamen in omni coniunctione, & oppositione Lunæ in perigio parui epicycli, in quadraturis autem in apogio eiusdem reperiatur. Hæc est machinatio, seu hypothesis, qua D. Præceptor omnia prædicta inconuenientia excludit, & quam omnibus apparentijs satisfacere ad oculos ostendit, quemadmodum etiam ex tabulis ipsius est colligere.

…it is moved regularly and uniformly also along the circumference of the small second epicycle, receding from the true apogee of the small epicycle, which indeed is shown by a line drawn out from the centre of the first epicycle through the centre of the second onto its circumference. And the rule of this motion is this: that the Moon herself revolves twice in this her smaller epicycle within one period of the deferent, yet in such a way that at every conjunction and opposition she is found at the Moon's perigee of the small epicycle, but at the quadratures at its apogee. This is the contrivance, or hypothesis, by which my Teacher excludes all the aforementioned inconveniences, and which he shows to satisfy all the appearances before one's eyes, as may also be gathered from his own tables.

[margin: Liber quintus.]

Porrò, doctissime D. Schonere, quemadmodum nos hîc in Luna ab æquante liberatos esse vides, & tali insuper theoria assumpta, quæ experientiæ & omnibus obseruationibus correspondet: ita etiam in reliquis planetis æquantes tollit, tribuens cuilibet trium superiorum vnum solummodo epicyclum, & eccentricum, quorum vterq́ue super suo centro æqualiter moueatur, & pares planeta in epicyclo cum eccentrico reuolutiones faciat. Veneri autem, & Mercurio eccentricum eccentrici. Docet tamè, quòd illorum motus similiter per eccentrum eccentri, & horum reuolutiones per eccentrepicyclos, tradi possint. Quòd enim planetæ directi, stationarij, retrogradi, propinqui & remoti à terra, &c. singulis annis conspiciuntur, per alium insuper, quàm ex superioribus adstruitur, regularem telluris globi motum fieri posse demonstrat, qui est: Vt Sol vniuersi medium occupet, terra autem loco Solis in eccentrico, quem, Orbem Magnum, appellare placuit, circumferatur. Atque profectò diuini quiddam est, quòd ex vnius terreni globi regularib. & æqualibus motibus certa rerum cœlestium ratio dependere debeat. Primum autem, vt terræ mobilitate apparentias in cœlo plerasq́ue fieri posse, aut certè commodissimè saluari assumeret, eum æquinoctiorum indubitata (sicut audiuisti) præcessio, & eclipticæ obliquitatis mutatio induxit.

Moreover, most learned Lord Schöner, just as you here see us freed from the equant in the case of the Moon, and a theory besides assumed which corresponds to experience and to all observations: so also in the remaining planets he removes the equants, assigning to each of the three superior ones a single epicycle and an eccentric, each of which is moved uniformly about its own centre, and the planet makes equal revolutions in the epicycle together with the eccentric. But to Venus and Mercury [he assigns] an eccentric of the eccentric. He teaches, however, that their motions likewise can be conveyed by an eccentric of the eccentric, and the revolutions of these by epicycles upon the eccentric. For that the planets are seen each year direct, stationary, retrograde, near and far from the Earth, etc., he demonstrates can come about through yet another regular motion of the terrestrial globe besides that established from the superior bodies, which is: that the Sun should occupy the centre of the universe, while the Earth, in place of the Sun, is carried round on an eccentric which it has pleased him to call the Great Orb. And truly there is something divine in this, that upon the regular and uniform motions of one terrestrial globe a sure account of the celestial things should depend. Now first, in order that he might assume that most of the appearances in the heaven can come about through the mobility of the Earth, or at least be most conveniently saved thereby, the undoubted precession of the equinoxes (as you have heard) and the change of the obliquity of the ecliptic led him to it.

[margin: Principales rationes, quare a Veterum Astronomorum hypothesibus recedendum sit.]

Deinde, quòd illa eadem eccentricitatis Solis diminutio, pari ratione & proportionabiliter in eccentricitatibus reliquorum planetarum animaduertitur.

Then, that the same diminution of the eccentricity of the Sun is, by like reasoning and proportionally, observed in the eccentricities of the remaining planets.

Postea, quòd planetas suorum deferentium centra circa Solem,

Afterward, that the planets [have] the centres of their deferents about the Sun,

…lem, tanquam medium vniuersi habere appareat. Sensisse autem & idem Vetustissimos (Pythagoricos interim vt taceam) vel hinc satis liquet, quod Plinius ait, Venerem & Mercurium ideo non longius à Sole, quàm ad certos, & præfinitos terminos discedere, optimos haud dubiè Authores secutus, quia circa Solem conuersas absidas habeant, vnde & medium quoque Solis motum eis accidere oportuit.

…as their middle, so that [the Sun] appears to have [it] as the centre of the universe. And that the most ancient men too perceived the same (to say nothing meanwhile of the Pythagoreans) is clear enough even from this, that Pliny says Venus and Mercury for that reason do not depart farther from the Sun than to certain and predetermined limits — following without doubt the best authorities — because they have their apsides turned about the Sun, whence also the mean motion of the Sun had to befall them.

[margin: Plinius lib. 2. cap. 17.]

Cum verò Martis cursum inobseruabilem ait, atque præter reliquas in motus Martis emendatione difficultates, dubium non sit, quin maiorem nonnunquam quàm ipse Sol diuersitatem aspectus admittat, impossibile esse videtur, terram mundi medium obtinere. Porrò etsi ex Saturni, & Iouis in matutino, vespertinoq́ue ortu ad nos habitudine, id ipsum hoc facilè etiam colligatur, in Martis tamen diuersitate ortuum, præcipuè & maximè animaduertitur. Quia enim Martis sidus obtusum admodum lumen habet, non adeo sicut Venus, aut Iupiter visum decipit: sed pro ratione à terra distantiæ, magnitudinis mutationem refert. Proinde cum Mars in vespertino ortu Iouis sidus magnitudine æquare videatur, vt non nisi igneo fulgore discernatur: in apparitione autem, & occultatione vix à secundæ magnitudinis stellis discerni possit, sequitur ipsum proximè ad terram vespertino in ortu accedere, contrà in matutino quàm maximè procul abesse, quod certè ratione epicycli nullo modo contigere potest. Terræ igitur ad Martis, & aliorum planetarum motus restituendos, alium locum deputandum esse patet.

But when he says that the course of Mars is not [easily] to be observed, and since, besides the other difficulties in the correction of the motion of Mars, there is no doubt that it sometimes admits a greater diversity of aspect than the Sun himself, it seems impossible that the Earth should hold the centre of the world. Further, although this same thing may also easily be gathered from the relation of Saturn and Jupiter to us at their morning and evening risings, yet it is chiefly and especially observed in the diversity of the risings of Mars. For since the star of Mars has a rather dull light, it does not so deceive the sight as Venus or Jupiter, but reports a change of magnitude in proportion to its distance from the earth. Accordingly, since Mars at its evening rising seems to equal the star of Jupiter in magnitude, so that it is distinguished only by its fiery glow, while at its appearance and occultation it can scarcely be told apart from stars of the second magnitude, it follows that it itself comes nearest to the earth at its evening rising, and on the contrary is as far off as possible in the morning, which certainly can in no way happen by reason of an epicycle. It is therefore plain that another place must be assigned to the Earth in order to restore the motions of Mars and of the other planets.

Quartò, hac vnica ratione commodè fieri posse D. Præceptor videbat, vt quod proprium circularis motus est, omnes reuolutiones circulorum in mûdo æqualiter, & regulariter super suis centris, & non alienis mouerentur.

Fourth, my Teacher saw that by this single device it could conveniently come about that — as is proper to circular motion — all the revolutions of the circles in the world should be moved uniformly and regularly about their own centres, and not about foreign ones.

Quintò, cum non minus Mathematicis, quàm Medicis statuendum, quod passim Galenus inculcat, Μηδὲν εἰκῇ τὴν φύσιν ἐργάζεσθαι: Et, οὗτος εἴσει τὸν δημιουργὸν, ὃς μὴ μίαν ἕνεκα ἕκαστον αὐτῶν γεγονότων ἔχειν τὴν χρείαν, ἀλλὰ καὶ δύο, καὶ τρεῖς, ἢ πλείους πολλάκις: quare cum hoc vnico terræ motu, infinitis quasi apparitijs satisfaciuerimus, Deo naturæ conditori eam industriam non tribueremus, quam communes horologiorum Artifices habere cernimus?

Fifth, since it must be laid down by mathematicians no less than by physicians — what Galen everywhere inculcates — that "Nature does nothing in vain"; and, "He will know the Maker who [grants] that each of the things that have come into being has its use not for one purpose only, but for two and three, or oftentimes more": wherefore, since by this single motion of the Earth we have satisfied as it were infinite appearances, should we not attribute to God the founder of nature that industry which we discern even common makers of clocks to have?

[margin: Hæc verba sunt in libro 10. de usu partium.]

qui

[catchword: qui]

…qui studiosissimè cauent, ne vllam instrumento rotulam inserant, quæ aut superuacanea sit, aut cuius alia paululum mutato situ, commodiùs vicem suppleat. Et quid D. Præceptorem moueret, vt tanquam Mathematicus aptam motus terreni globi rationem non assumeret? cum videret tali assumpta hypothesi ad certam rerum cœlestium doctrinam constituendam, nobis vnicam octauam sphæram, eamq́ue: immotam: Solem in medio vniuersi immoto: in motib. verò reliquorum planetarum eccentrepicyclos aut eccentrecentricos, vel epicycli eccentros sufficere.

…who most carefully take care not to insert into the instrument any little wheel that is either superfluous, or whose place some other might more conveniently fill with its situation slightly changed. And what should move my Teacher, as a mathematician, not to assume a fitting account of the motion of the terrestrial globe? — since he saw that, such a hypothesis being assumed for establishing a sure doctrine of the celestial things, a single eighth sphere, and that motionless, suffices for us; the Sun motionless in the middle of the universe; while in the motions of the remaining planets eccentric-epicycles or eccentric-on-eccentrics, or eccentrics of an epicycle, suffice.

His accedit, quòd motus terræ in suo orbe, omnium planetarum, excepta Luna, argumenta conficiat, quòdq́ue: vnus solus, causa omnis diuersitatis motus esse videatur, quæ videlicet in tribus quidem superioribus à Sole, in Venere autem, & Mercurio circa Solem apparet. Atq́ue, vt vnica saltem in latitudine deferentis planetæ deuiatione quilibet planetarum sit contentus, sicq́ue: principaliter planetarum motus tales etiam hypotheses exigere.

To this is added that the motion of the Earth in its orb produces the arguments of all the planets except the Moon, and that one single [motion] seems to be the cause of all the diversity of motion — that namely which in the three superior ones appears from the Sun, but in Venus and Mercury about the Sun. And so that each of the planets may be content with a single deviation in the latitude of the planet's deferent, and thus that principally the motions of the planets require such hypotheses also.

Sextò, & postremò, hoc maximè D. Doctorem Præceptorem meum mouit, quòd præcipuam omnis incertitudinis in Astronomia causam esse videbat, quòd huius doctrinæ Artifices (quòd venia diuini Ptolemæi Astronomiæ parentis dictum volo) suas Theorias, & rationes motus corporum cœlestium emendandi, parum seuerè ad illam regulam reuocauerunt, quæ ordinem, & motus orbium cœlestium absolutissimo systemate constare admonet. Vt enim amplissimè suum honorem illis (quemadmodum par est) tribuamus, tamen optandum næ erat, vt in harmonia motuum constituenda Musicos fuissent imitati, qui chorda vna, vel extensa, vel remissa, cæterarum omnium sonos tamdiu summa cura, & diligentia adhibita formant, & attemperant, donec omnes simul exoptatum referant concentum, neq́ue; in vlla dissoni quicquam annotetur. Hoc, vt de Albategnio interim dicam, si in suo Opere secutus esset, haud dubiè & hodie omnium motium rationem certiorem haberemus. Est enim verisimile Alfonsinos plurimum ex eo desumpsisse, atq́ue; hac vnica re neglecta, aliquando (si modo vera fateri animus est) totius Astronomiæ ruina metuenda fuisset. In cômunibus Astronomiæ principijs erat quidem videre, ad medium Solis motum omnes apparentias

Sixth and last, this most of all moved my Lord Doctor and Teacher: that he saw the chief cause of all the uncertainty in Astronomy to be that the practitioners of this discipline (which, by leave of the divine Ptolemy, parent of Astronomy, I wish to be said) too little severely recalled their Theories and methods of correcting the motion of the celestial bodies to that rule which admonishes that the order and the motions of the celestial orbs consist in a most perfect system. For though we should grant to them their honor most amply (as is fitting), yet it were truly to be wished that, in establishing the harmony of the motions, they had imitated the musicians, who, with one string either stretched or slackened, with the greatest care and diligence applied, so long shape and tune the sounds of all the rest, until all together render the desired concord, and nothing dissonant be noted anywhere. Had he followed this in his own Work (to speak meanwhile of al-Battānī), without doubt we should today have a surer account of all the motions. For it is likely that the Alfonsines took much from him, and, this one thing being neglected, at some time (if the mind is willing to confess the truth) the ruin of the whole of Astronomy was to be feared. In the common principles of Astronomy it was indeed [the practice] to see all the appearances [referred] to the mean motion of the Sun,

cœlestes

[catchword: cœlestes]

…cœlestes se dirigere, totamq́ue: motuum cœlestium harmoniam pro ipsius moderamine constitui, & conseruari. Vnde & à Veteribus Sol χαγηγὸς, naturæ gubernator, & Rex dictus est. Sed quomodo hanc administrationem gereret: an quemadmodum Deus totum hoc vniuersum gubernat? vt pulcherrimè Aristoteles περὶ κόσμου depingit; an verò ipse totum cœlum toties peragrando, nulloq́ue; in loco quietus Dei in natura administratorem ageret, nondum videtur omnino explicatum, atq́ue: dubitatumq́ue; sic. Vtrum autem horum potiùs assumendum sit, Geometris, & Philosophis (qui mathematicâ quidem tincti sint) determinandum relinquo. Siquidem in huiusmodi æstimandis, dijudicandisq́ue: controuersijs, non ex plausibilibus opinionibus, sed legibus mathematicis (in quorum foro causa hæc dicitur) sereda est sententia. Priorgubernationis modus est reiectus, posterior receptus. D. Doctor autem Præceptor meus, damnatam rationem gubernationis in rerum natura Solis, reuocandam statuit, ita tamen, vt receptæ etiam & approbatæ suus locus relinquatur. Videt namq́ue, neque in humanis rebus esse opus, vt Imperator singulas vrbes ipse percurrat, quo suo denique munere, à Deo sibi imposito, defungatur: neque cor in caput, aut pedes, aliasq́ue: corporis partes propter animantis conseruationem transmigrare, sed per alia ὄργανα à Deo in hoc destinata, officio suo præesse.

…the celestial appearances to direct themselves, and that the whole harmony of the celestial motions is established and preserved according to its governance. Whence by the ancients the Sun was called chagēgos [the leader/guide], governor of nature, and King. But how he should carry on this administration — whether as God governs this whole universe, as Aristotle most beautifully depicts in On the World; or whether [the Sun] itself, by traversing the whole heaven so many times and resting in no place, should act as God's administrator in nature — does not yet seem altogether explained, and was thus left in doubt. Which of these two ought rather to be assumed I leave to geometers and philosophers (those at least who are imbued with mathematics) to determine. For in weighing and judging controversies of this kind, the verdict is to be reached not from plausible opinions but by mathematical laws (in whose court this case is pleaded). The former mode of governance is rejected, the latter received. But my Lord Doctor and Teacher determined that the condemned account of governance in the nature of things should be recalled to the Sun, yet in such a way that the received and approved one also keeps its own place. For he sees that, even in human affairs, there is no need for the Emperor himself to run through the several cities, in order to discharge his office laid upon him by God; nor for the heart to migrate into the head, or feet, or other parts of the body for the preservation of the living thing, but through other organs destined by God for this it presides over its office.

Deinde, cum statueret medium motum Solis, talem motum esse oportere, qui non tantùm imaginatione constaret, vt in reliquis quidem planetis, sed haberet causam per se, cum ipsum verisimè χορδωτὸν ὄψει καὶ χορουαρίαν esse appareret, factum est, vt suam sententiam firmam, nec à vero abhorrentem comprobaret. Nam per suas hypotheses causam efficientem æqualis motus Solis geometricè deduci posse sentiebat, & demonstrari, quare iste medius Solis motus, in omnibus reliquorum planetarum motibus, & apparentijs, certa ratione, vt in singulis apparet, necessariò deprehendetur: atq́ue: exinde positò telluris motu in eccentrico, in promptu esse certam rerum cœlestium doctrinam, in qua nihil mutandum, quin simul totum systema, vt consentaneum erat, de nouo in debitas rationes restitueretur. Huiusmodi Solis in rerû natura gubernatione cum ex cômunibus nostris theorijs ne suspicari quidè poteramus, pleraque Veterum Solis ὀργώματα, tanquam Poetica negligebamus.

Then, when he laid it down that the mean motion of the Sun ought to be such a motion as should consist not in imagination only, as indeed in the other planets, but should have a cause through itself — since it truly appeared to be a stringing and a choir-leading to the sight — it came about that he proved his judgment firm, and not abhorrent from truth. For through his hypotheses he perceived that the efficient cause of the equal motion of the Sun could be geometrically deduced and demonstrated, wherefore this mean motion of the Sun will necessarily be detected, in all the motions and appearances of the remaining planets, by a sure reason, as appears in each. And from this, the motion of the Earth being posited on the eccentric, there is at hand a sure doctrine of the celestial things, in which nothing is to be changed but that at the same time the whole system, as was fitting, should be restored anew to its due reasons. Of such a governance of the Sun in the nature of things, since from our common theories we could not even suspect it, we used to neglect most of the Sun's [workings] as though Poetic.

P 2 Vides

[signature: P 2] [catchword: Vides]

…Vides itaque, quales ad saluandos motus hypotheses, D. Preceptorem his ita constitutis assumere oportuerit.

…You see therefore what hypotheses my Teacher, these things being thus established, had to assume for saving the motions.

[margin: Transitio ad enumerationem nouarum hypothesium totius Astronomiæ.]

Interrumpo cogitationes tuas, clarissime Vir, video enim tedum causas renouandarum hypothesium Astronomiæ, à D. Doctore meo excellenti doctrina, summóq́ue: studio indagatas audis, animo tecum cogitare, quænam tandem apta, & renascentis Astronomiæ hypothesium futura sit ratio. Illud autem hominum genus, quod omnes simul stellas pro suo arbitratu, haud secus ac iniectis vinculis, in æthere circumducere conatur, commiseratione potiùs, quàm odio esse dignum, te iuxta cum alijs veris Mathematicis, omnibusq́ue; Viris doctis iudicare. Cumq́ue; haud ignores, quem locum hypotheses, seu theoriæ apud Astronomos habeant, & in quantum Mathematicus à Physico differat: sentio te hoc quoque statuere, quòd obseruationes, ipsiusq́ue; cœli testimonia trahunt, retrahuntq́ue; sequendum, omnemq́ue; difficultatem ferendo, Deo duce, Mathematica, & indefatigabili studio omnino, superandam esse. Proinde si quispiam ad summum, principalemq́ue: finem Astronomiæ sibi respiciendum statuerit, vna nobiscum D. Doctori Præceptori meo, gratias habebit, cogitabitq́ue: & ad se Aristotelis illud pertinere, Τᾶς μὲν γὰρ ἀκριβεστέρας ἀνάγκας, ὅταν τις ἐπιτύχῃ, τότε χάρις ἔχειν δεῖ τοῖς εὑρίσκουσι: Et cum nos Aristotelem Calippi, & suo exemplo

…I interrupt your thoughts, illustrious Sir, for I see that you, while you hear the causes for renewing the hypotheses of Astronomy searched out by my Lord Doctor with excellent learning and the greatest zeal, are thinking within yourself what at last will be the fitting account of the hypotheses of a reborn Astronomy. But that kind of men who try to lead all the stars at once around in the aether at their own pleasure, no otherwise than as if chains were cast over them — you, together with other true mathematicians and all learned men, judge them worthy rather of pity than of hatred. And since you are not unaware what place hypotheses or theories hold among astronomers, and how far the mathematician differs from the physicist, I feel that you too lay down this: that whatever the observations and the testimonies of the heaven itself draw and draw back, must be followed, and that every difficulty, by enduring it, with God as guide, by mathematics and by indefatigable study, must be wholly overcome. Accordingly, if anyone shall determine that he must look to the highest and principal end of Astronomy, he will, together with us, give thanks to my Lord Doctor and Teacher, and will think that this saying of Aristotle pertains also to himself: "For when one attains the more exact necessities, then one must give thanks to the discoverers"; and when [we see] Aristotle, after the example of Calippus

[margin: Lib. 2. De cœlo.]

confirmat ad caussas τῶν φαινομένων assignandas, Astronomiam, pro vt se diuersi corporum cœlestium motus obtulerint, instaurandam: neque Auerroem, non satis clementem Ptolemæi Aristarchum, si modò ad physiologiâ æquis oculis respicere velit, acerbius D. Præceptoris hypotheses exceptium speraverim. Tantum abest, vt Ptolemæum adeo hypothesibus suis, si ei in vitam redire daretur, addictum & adiuratum putarim, vt ad certam rerum cœlestium doctrinam exædificandam, vbi regiam viam tot seculorum ruinis impeditam, & inuiam factam deprehenderet, non aliud insuper iter per terras mariáq́ue: inquisiturus speraverim. Quid namq́ue; de isto aliud, cuius hæc sunt verba, statuerem? οὗτε τὰ ἀναποδείκτως ὑποτιθέμενα. ἐὰν ἅπαξ σύμφωνα τοῖς φαινομένοις καταλαμβάνηται, χωρὶς δὲ τιν' ἐφ', καὶ ἐπίτασσος εὑρήσεται δύνηται, κἂν δυσέκδετ' ᾗ ὃ τρόπος αὐτῶν τῇ καταλήψεως. ἐπειδὴ καὶ καθόλου τῶν πρώτων ἀρχῶν, ἤ οὐδὲν, ἢ δυσερμηνευτὸν φύσι

confirms that Astronomy is to be restored, for the assigning of the causes of the appearances, according as the diverse motions of the celestial bodies have presented themselves: nor would I have hoped that Averroes — Ptolemy's not sufficiently merciful Aristarchus, if only he were willing to look upon natural philosophy with fair eyes — would more harshly take exception to my Teacher's hypotheses. So far is it from this, that I should think Ptolemy so addicted to and sworn upon his own hypotheses, were it granted him to return to life, that for building up a sure doctrine of the celestial things, where he found the royal road blocked by the ruins of so many ages and made impassable, I should hope he would seek out yet another way through lands and seas. For what else should I lay down concerning that man, whose words are these: "Neither are things hypothesized without demonstration — once they are grasped as in agreement with the appearances — [to be rejected], even if the manner of their being grasped be hard to unravel; since indeed concerning the universal first principles there is either nothing, or what is hard to interpret in nature…"

[margin: Lib. 21. Metaphy.]

[margin: Lib. 9. Eth.]

[margin: Hæc satisfaceunt, quibus altius inq́ue: domos superas scandere cura fuit.]

φύσι

[catchword: φύσι]

…φυσι/τατον: Quàm verecundè autem, & prudentet Aristoteles de motuum cœlestium doctrina loquatur, passim in eius Libris videre est. Et ait alibi, τετραδεμένην γὰρ ἔστιν ἐπὶ τοσοῦτον. ἄχρι ἕως ἐπιζητεῖν καθ' ἕκαστον γίνεσθαι. ἐφ' ὅσον ἡ τὸ πρᾶγμα φύσις ἐπιδέχηται. Cum autem tùm in Physicis, tùm in Astronomicis ab effectibus, & obseruationibus vt plurimum ad principia sit processus, ego quidem statuo Aristotelem, auditis nouarum hypothesium rationibus, vt disputationes de graui, leui, circulari latione, motu & quiete terræ diligentissimè excusauerit, ita dubio procul candidè confessurum, quid à se in his demonstratum sit, & quid tanquam principium sine demonstratione assumendum, quare & D. Doctori Præceptori meo suffragaturum crediderim, vtpote cum constet rectissimè, vt fertur, à Platone dictum, τὸν Ἀριστοτέλεα τῆς ἀληθείας εἶναι φιλόσοφον: contrà, si in durissima quædam verba prorupturus esset, aliter verò mihi persuadere non possum, quin exclamans pulcherrimæ huius philosophiæ partis conditionem his verbis deploraturus esset, πάνυ

…most natural [in nature]: But how modestly and prudently Aristotle speaks concerning the doctrine of the celestial motions may everywhere be seen in his Books. And he says elsewhere, "for it is settled only so far, until one inquires how each thing comes to be, as far as the nature of the matter admits." But since both in Physics and in Astronomy the procedure is for the most part from effects and observations to principles, I for my part lay it down that Aristotle, having heard the reasons for the new hypotheses — just as he most diligently excused the disputations about the heavy, the light, circular motion, the motion and rest of the Earth — would thus without doubt candidly confess what has been demonstrated by him in these matters, and what is to be assumed as a principle without demonstration; wherefore I should believe he would side also with my Lord Doctor and Teacher, since it stands most rightly, as it is said, that Plato said "that Aristotle is the philosopher of truth": on the contrary, if he were to break out into certain very harsh words — though I cannot persuade myself otherwise — than that, crying out, he would lament the condition of this most beautiful part of philosophy in these words, "altogether…"

[margin: Lib. 1. Ethi.]

[margin: Lib. 7. Polit.]

ἐμμελῶς ἀπὸ Πλάτωνος λέλεκται, γεωμετρίαν τε καὶ τὰς ταύτη ἑπομένας ὑπερορῶντι μὲν περὶ τὸν, ὑπὲρ ᾗ ἀδύνατον αὐταῖς ἰδεῖν, ὡς ἂν ὑπόθεσι ἐστὶ χρώμεναι ταύταις ἀκινήτοις οὖσι, μὴ δυναμένας λόγον διδόναι αὐτῶν: & adderet, πολλὴν τοῖς ἀθανάλοις. θεοῖς χάριν ἔχειν δεῖ, ἐπὶ τῷ τὸν ἴσον λόγον τῶν φαινομένων εἰδέναι:

"it has been fittingly said by Plato — to one who despises geometry and the [sciences] following upon it concerning that for which it is impossible for them to see, inasmuch as they use these as hypotheses while they are unmoved, not being able to give an account of them": and he would add, "one must give much thanks to the immortal gods, that one knows the equal account of the appearances":

Verùm enimuero, cum hæc non tam huius loci sint, quàm alterius cuiusdam disputationis, quæ porrò restant D. Doctoris Præceptoris mei hypotheses, libere, & vt his, quæ suprà diximus aliquid lucis accedat, narrare ordine pergam. Aristoteles, inquit, Verissimum est id, quod posterioribus yt vera sint, causa est, Sic cum D. Præceptor meus, sibi tales hypotheses assumendas esse statueret, quæ superiorum seculorum obseruationes, vt veræ esse confirmarentur, causas continerent: & quemadmodum sperandum, causæ essent, vt in posterum omnes astronomicæ τῶν φαινομένων prædictiones veræ deprehenderentur: Principio non mediocribus laboribus superatis per hypothesim constituit, Orbem stellatum, quem octauum vulgò appellamus, ideo à Deo conditum, vt esset domicilium illud, quod suo complexu totam rerum naturam complecteretur: quare vt vniuersi locum, fixum immobilémq́ue: condidisse. Et quoniam non percipitur motus, nisi per collationem ad aliquod fixum, sicut

But indeed, since these things belong not so much to this place as to some other disputation, the hypotheses of my Lord Doctor and Teacher that further remain I shall proceed to narrate in order, freely, and so that some light may be added to those things which we said above. "Aristotle says: That is most true which is the cause that the things posterior to it are true." So when my Teacher determined that such hypotheses must be assumed by him as should contain the causes whereby the observations of former ages might be confirmed to be true, and (as is to be hoped) should be the causes whereby in the future all astronomical predictions of the appearances might be found true: at the outset, no ordinary labors being overcome, he established by hypothesis that the starry Orb, which we commonly call the eighth, was for that reason founded by God, that it should be that dwelling-place which by its embrace should embrace the whole nature of things; wherefore he founded it as the place of the universe, fixed and immovable. And since motion is not perceived except by comparison with something fixed, just as

[margin: Vniuersi distributio.]

[margin: * μεταφυ. α. τὸ ἐλάττον:]

[margin: Ordo sphærarum Mundi.]

[margin: Orbis stellatus supremus, fixus & immobilis.]

P 3 naui-

[signature: P 3] [catchword: naui-]

…nauigantes in mari, quibus nec ampliùs vllæ apparent terræ, cœlum vndíq́ue:, & vndíq́ue: pôtus, tranquillo à ventis mari nullum motum sentiunt, tametsi tanta ferantur celeritate, vt in hora etiam, aliquot milliaria magna emetiantur: ideo Deum tot eum orbem, nostra quippe causa, insigniuisse globulis stellantibus, vt penes eos, loco nimirum fixos, aliorum orbium, & planetarum contentorum animaduertemus positus ac motus.

…men sailing on the sea, to whom no lands any longer appear, the sky on every side and the deep on every side, in a sea calm from the winds perceive no motion, although they be carried with such speed that in an hour they measure off several great miles: for that reason God, for our sake indeed, marked out that great orb with little glittering globes, that by them — fixed, that is, in place — we might observe the positions and motions of the other orbs and of the planets contained [within].

[margin: Quare orbem octauum tot stellis insignium Creator voluerit.]

Deinde, quòd his quidem consentaneum est, Deum, in huius theatri medium Solem, suum in natura administratorem, totiusq́ue: vniuersi Regem, Diuina maiestate conspicuum collocasse,

Then, that this indeed is consonant: that God placed in the midst of this theatre the Sun, his administrator in nature and King of the whole universe, conspicuous in divine majesty,

[margin: Sol in medio Mundi, immobilis.]

[margin: Pontanus 1. Vrania.]

Ad cuius numeros & Dij moueantur, & orbis Accipiat leges, præscriptaq́ue: fœdera seruet.

"To whose numbers both the gods may move, and the world may receive its laws, and keep the appointed covenants."

Reliquos autem orbes in hunc modum distributos esse, primum locum infra firmamentum, seu orbem stellatum, Saturni orbem fortium, intra quem Iouis, deinde Martis contineatur: Solem verò Mercurij. deinde Veneris orbe circumdari, quo orbium quinque planetarum centra, circa Solem reperirentur. Sed intra concauam superficiem orbis Martis, & conuexam Veneris, cum satis amplum relictum sit spacium, globum telluris cum adiacentibus elementis, orbe Lunari circundatum, à Magno quodam Orbe, intra Mercurij, & Veneris orbes, item Solem complectente, circumferri, vt non aliter, ac vna ex stellis inter planetas, suos motus habeat.

But that the remaining orbs are distributed in this manner: the first place beneath the firmament or starry orb, the orb of Saturn the powerful, within which is contained that of Jupiter, then of Mars: but the Sun [is encompassed] by the orb of Mercury, then surrounded by that of Venus, whereby the centres of the orbs of the five planets are found about the Sun. But within the concave surface of the orb of Mars and the convex of Venus, since a sufficiently ample space is left, the globe of the earth with the adjacent elements, surrounded by the lunar orb, is carried round by a certain Great Orb encompassing the orbs of Mercury and Venus, likewise the Sun, so that it has its motions no otherwise than as one of the stars among the planets.

[margin: Infra Orbem stellarum, Saturnus, Iupiter, Mars.]

[margin: Circa Solem, Mercurius, Venus.]

[margin: Intra Martem & Venerem, Orbis Magnus obtinens Terram cum elementis, & orbe Luna.]

Hunc Sphærarum Mundi ordinem & dispositionem non à Copernico primùm excogitatam, sed ab antiquis Philosophis traditam esse, testis ille Archimedes libello de Arenæ numero, quo de Aristarcho sic scribit. Hæc inq;, qua ab Astrologis (de vtilitatis hypothesibus, quibus Terra Mundi centrum ponitur) scripta sunt, redarguens Aristarchus Samius, positiones quasdam edidit, ex quibus sequitur, Mundum modò dicti Mundi multiplicem esse. Ponit enim Stellas inerrantes, atq;, Solem immobiles permanere: terram verò circumferri circa Solem, secundùm circumferentiam circuli, qui est in medio cursu constitutus: Spheram autem inerrantium stellarum circa idem centrum cum Sole sitam, tantæ esse magnitudinis, vt circulus, in quo ponit terram circumferri, eam habeat proportionem ad distantiam stellarum inerrantium, quam centrum sphæræ habet ad eius superficiem, (id est, quæ nequaquam sit sensibilis) &c. Floruisse autem Aristarchum circa 44. annum post mortem Alexandri Magni, h. e. circa 280. annum ante Christum natum, ante hæc nostra secula, 1876. annis, ex Ptolemæo lib. 3. cap. 2. manifestum est.

That this order and disposition of the Spheres of the World was not first devised by Copernicus, but handed down by the ancient Philosophers, that man Archimedes is witness, in the little book On the Number of the Sand, where he writes thus of Aristarchus: "These things," he says, "which were written by the astrologers (concerning the useful hypotheses by which the Earth is set as the centre of the World), Aristarchus of Samos, refuting them, published certain positions, from which it follows that the World of the World just spoken of is manifold. For he supposes the fixed stars and the Sun to remain immovable; but the earth to be carried round about the Sun along the circumference of a circle which is set in the middle of its course; and that the sphere of the fixed stars, set about the same centre as the Sun, is of such magnitude that the circle in which he sets the earth carried round has that proportion to the distance of the fixed stars which the centre of a sphere has to its surface (that is, which is by no means sensible), etc." And that Aristarchus flourished about the 44th year after the death of Alexander the Great, that is, about the 280th year before Christ was born — 1876 years before these our times — is plain from Ptolemy, book 3, chapter 2.

Ordo

[catchword: Ordo]

[Plate: ORDO SPHAERARVM MVNDI — Copernican heliocentric ordering, SOL at centre — see facsimile (this leaf)]

PRIMA. Ordo Sphærarum Mundi.

PRIMA. The Order of the Spheres of the World.

SPHÆRA STELLARVM FIXARVM. Interstitium inter Saturnum & Stellas fixas, immensum, adeóq́ infinito simile. I. Sphæra SATVRNI. II. Sphæra IOVIS. III. Sphæra MARTIS. IIII. Orbis MAGNVS, vel Orbis TERRÆ vná cum Sphæra LVNÆ. V. Sphæra VENERIS. VI. Sphæra MERCVRII. SOL.

THE SPHERE OF THE FIXED STARS. The interval between Saturn and the fixed stars, immense, and so like to the infinite. I. The Sphere of SATURN. II. The Sphere of JUPITER. III. The Sphere of MARS. IIII. The GREAT Orb, or the Orb of the EARTH together with the Sphere of the MOON. V. The Sphere of VENUS. VI. The Sphere of MERCURY. THE SUN.

Hanc totius vniuersi distributionem ex D. Præceptoris mei sententia mihi perpendenti diligentius, præclarè simul, ac rectè Plinius sensisse video, cum inquit, Mundi, seu cœli, cuius circumflexu reguntur cuncta, exteraindagare, nec interesse hominum, nec capere humanæ coniecturam mentis. Et subdit, Sacer est, immensus, totus in toto, imò verò ipse totum, finitus & infinito similis, &c. Nam vbi D. Præceptorem meum sequemur, nihil extra concauum orbis stellati, quod inquiramus.

Weighing this distribution of the whole universe according to my Lord Teacher's judgment more diligently, I see that Pliny perceived it both excellently and rightly, when he says that to search out the outer things of the World, or heaven, by whose revolution all things are governed, neither concerns men nor falls within the grasp of the human conjecturing mind. And he adds: "It is sacred, immense, whole in the whole, nay rather itself the whole, finite and like to the infinite," etc. For where we shall follow my Lord Teacher, there is nothing beyond the concave of the starry orb that we should inquire into.

[margin: Lib. 2. cap. 1.]

…mus, erit, nisi quantum nos sacræ literæ de his scire voluerunt, tum etiâ quicquam extra hoc concauum constituendi præclusa erit via. Quare totam reliquam hanc Naturam, ceu sacrosanctam, à Deo cœlo stellato inclusam cum gratiarum actione admirabimur, & contemplabimur, ad quam perscrutandam, & cognoscendam multis modis, infinitis instrumenti, & donis nos lucupletauit, & idoneos nos effecit; & quidem eò vsque progrediemur, quò ipse voluit, neque ab ipso constitutos limites transgredi tentabimus. Immensum præterea mundum esse, & verè infinito similem, quantum etiam ad eius concauum, ex eo quidem in confesso est, quòd stellas omnes scintillare videamus, planetis exceptis, etiam Saturno, qui ad cœlum cœlo citimus, maximo fertur circulo. Sed idem longè manifestiùs ex D. Præceptoris hypothesibus per ἀποδείξεις patet. Cum enim Orbis Magnus Terram deferens, ad quinq; planetarum orbes perceptibilem rationem habeat, vnde videlicet omnem apparentiarum diuersitatem in his planetis, per eorum ab Solem habitudinem prouenire demonstratur:ac omnis in terra horizon orbe stellarum in æqualia, vt vniuersi citculus magnus intersecet, & orbes reuolutionum suarum à stellis fixis æqualitatem habere comprobetur: satis clarum est, orbem stellarum maximè infinito similem esse, quoniam quidem orbis magnus ad eum collationem euanescat, omniaq́; τὰ φαινόμενα non aliter conspiciantur, ac si terra in medio vniuersi consedisset.

…it will be, save in so far as the sacred writings have willed us to know of these things; then too the way to establishing anything beyond this concave will be barred. Wherefore we shall admire and contemplate with thanksgiving all this remaining Nature, as sacrosanct, enclosed by God in the starry heaven, to the searching out and knowing of which in many ways he has enriched us with infinite instruments and gifts, and made us fit; and indeed we shall proceed as far as he himself willed, nor shall we attempt to transgress the limits established by him. That moreover the world is immense and truly like to the infinite, even as regards its concave, is admitted from this at least, that we see all the stars twinkle, the planets excepted — even Saturn, which, nearest of all to the heaven, is borne in the greatest circle. But the same is far more manifestly clear from my Teacher's hypotheses by demonstrations. For since the Great Orb carrying the Earth has a perceptible ratio to the orbs of the five planets, whence it is demonstrated that all the diversity of appearances in these planets comes from their relation to the Sun; and [since] every horizon on earth cuts the orb of the stars into equal parts, as the great circle of the universe [does], and it is proved that the orbs of their revolutions have equality from the fixed stars: it is clear enough that the orb of the stars is most like to the infinite, since indeed the great orb vanishes by comparison with it, and all the appearances are beheld no otherwise than if the earth had settled in the midst of the universe.

[margin: Tota Natura inclusa est cœlo Stellato.]

[margin: Mundus immensus, & infinito similis.]

Porrò quanquam admiranda, & haud indigna tum opifice Deo, tum quoq; diuinis his corporibus motuum, & orbium symmetria ac nexus, quæ prædictis hypothesibus assumptis conseruatur, animo citiùs concipi (propter affinitatem, quam ⌐ cœlo habet) quàm vlla voce humana eloqui posse affirmauerim; quemadmodû in demonstrationibus nô tam verbis, quàm perfectis & absolutis, vt ita dicam, ideis harum suauissimarum rerum nostris animis imprimi solent. Tamen & in generali hypothesium contemplatione est videre, quomodo ineffabilis quoq; conuenientia, omniumq́; consensus sese offerat. Nam præterquam quòd nullus in vulgaribus hypothesibus finis erigendarû sphærarum appareat, orbes, quorû immensitas nullo sensu, aut ratione percipi poterat, tardissimis, & velocissimis circumducebantur motibus: alijq́; à supremo mobili omnes

Moreover, although the symmetry and connection of the motions and of the orbs — admirable and not unworthy both of God the workman and also of these divine bodies — which is preserved when the aforesaid hypotheses are assumed, may, I should affirm, be more swiftly conceived in the mind (because of the affinity it has with heaven) than uttered by any human voice; just as in demonstrations [these things] are wont to be impressed on our minds not so much by words as by perfect and absolute, so to speak, ideas of these most delightful things. Yet even in the general contemplation of the hypotheses one may see how an ineffable fitness too, and a consent of all things, presents itself. For besides that no end of raising up spheres appears in the common hypotheses, the orbs — whose immensity could be perceived by no sense or reason — were carried round with the slowest and the swiftest motions; and others all [moved] from the supreme moving thing,

[margin: Quæ in vulgaribus hypothesibus multifariam desiderantur, & quibus]

omnes

[catchword: omnes]

…omnes inferiores sphæras motu diurno rapi constituebant, cum tamen maxima turba disputationum hac de re concitata, qua ratione sphæra superior in inferiorem ius habeat, nec dum constituere potuerint. Alij, vt Eudoxus, & qui eum sunt secuti, cuilibet proprium orbem tribuerent, cuius motu in die naturali circa terram semel circumferretur. Præterea, Dij immortales, quæ digladiatio, quanta vsque adhuc fuit, de orbium Veneris & Mercurij situ, & quomodo sint ad Solem collocandi. Verùm adhuc sub iudice lis est, quamq́; vnquam posse componi, vulgaribus istis hypothesibus constitutis, in difficili admodum esse, atque adeò impossibile, quis porrò est, qui non videt?

…established that all the lower spheres are snatched along by the diurnal motion, although yet, the greatest crowd of disputations being stirred up on this matter, by what reason a higher sphere should have right over a lower, they have not yet been able to establish. Others, such as Eudoxus and those who followed him, assigned to each its proper orb, by whose motion it should be carried once round the earth in a natural day. Moreover — immortal gods! — what a fencing, how great it has been up to now, concerning the situation of the orbs of Venus and Mercury, and how they are to be placed with respect to the Sun! But the case is still before the judge, and that it could ever be composed, with these common hypotheses established, is exceedingly difficult, and even impossible — who, pray, is there who does not see it?

[margin: plurimum litigatur: ea apud Copernicum rectissimè se habet.]

Quid item obstiterit? & si quis Saturnum infra Solem collocet, orbium & epicycli ad se inuicem servata interim ratione: cum in ijsdem hypothesibus communis æqualis orbium inter se in dimensione nondum sit demonstrata, quo per eam quilibet orbis suo in loco geometricè circumscriberetur. Vt sanè hîc silentio præteream, quantas tragœdias calumniatores pulcherrimæ huius partis philosophiæ, & suauissimæ, commouerint, propter epicycli Veris magnitudinem: & quia assumptis æquantibus, lationes orbium cœlestium super proprijs centris, inæquales ponebantur. In D. Præceptoris autem hypothesibus, orbè stellato, vt est dictum, termino constituto, quilibet planetæ orbis suo à natura sibi attributo motu vniformiter incedens, suam periodum conficit, & nullam à superiori orbe vim patitur, vt in diuersum rapiatur. Adde quòd orbes maiores ambitus tardiùs, & propiores Soli, à quo quis principium motus, & lucis esse dixerit, velociùs vt conueniebat, suos circuitus perficiunt. Quare Saturnus sub ecliptica liber viam corripiens in 30. annis reuolutionem complet, Iupiter in 12. Mars in duobus. Centrum autem Terræ anni quantitatem ad stellas fixas determinat. Venus in 7. mensibus cum dimidio zodiacum permeat. Mercurius verò minimo orbe Solem circundans, 88. diebus mundû perlustrat.

What likewise should stand in the way? — even if someone should place Saturn beneath the Sun, the ratio of the orbs and of the epicycle to one another being meanwhile kept: since in those same hypotheses the common equal [proportion] of the orbs among themselves in dimension has not yet been demonstrated, whereby through it any orb might be geometrically circumscribed in its own place. So that I may here pass over in silence what tragedies the calumniators of this most beautiful and most delightful part of philosophy have stirred up, on account of the magnitude of the true epicycle, and because, equants being assumed, the carryings of the celestial orbs about their own centres were set down as unequal. But in my Teacher's hypotheses, the starry orb, as has been said, being established as the boundary, each planet's orb, advancing uniformly by the motion attributed to it by nature, completes its own period, and suffers no force from a higher orb whereby it should be snatched in a contrary direction. Add that the orbs of greater circuit complete their circuits more slowly, and those nearer the Sun — from which one would say is the beginning of motion and of light — more swiftly, as was fitting. Wherefore Saturn, freely seizing its way beneath the ecliptic, completes its revolution in 30 years, Jupiter in 12, Mars in two. But the centre of the Earth determines the quantity of the year with respect to the fixed stars. Venus traverses the zodiac in seven and a half months. Mercury, however, surrounding the Sun with the smallest orb, surveys the world in 88 days.

Suntq́; ita sex tantùm orbes mobiles Solem, vniuersi medium circundantes, quorum orbis magnus terram deferens centrum est mensura: quemadmodum & orbium Lunæ, item Solis à Luna distantiæ, &c. ea quæ ex centro globi terreni.

And so there are only six mobile orbs surrounding the Sun, the middle of the universe, of which the great orb carrying the earth is the centre [and] measure: just as also of the orbs of the Moon, likewise of the distance of the Sun from the Moon, etc., those things [are reckoned] which [proceed] from the centre of the terrestrial globe.

[margin: Sex tantum orbes mobiles.]

[margin: Orbis Magnus est mensura cæterorum orbium.]

Q Et

[signature: Q] [catchword: Et]

…Et quidem senario numero quis commodiorem alterum, & dignionem elegerit? quóue totum hoc vniuersum suos in orbes à Deo Conditore, mundíq́; opifice distinctum, mortalibus faciliùs persuaserit? & is namq; cum in sacris Dei oraculis, tum à Pythagoreis, reliquisq́; Philosophis, vt qui maximè celebratur. Quid autem huic Dei opificio conuenientius, quàm vt primum hoc, & perfectissimum Opus, primo & eodem perfectissimo numero includatur? ad hæc, vt ita à prædictis sex orbibus mobilibus harmonia cœlestis perficiatur, vt orbes omnes sibi eo pacto succedant, vt & nulla ab altero ad alterum interualli immensitas reliquatur; & quisque geometriâ septus suum locum in hunc tueatur modum, vt si quemcunque loco mouere tentes, simul etiam totum systema dissoluas.

…And indeed what other [number] would one choose more convenient and worthier than the senary [six]? or by what would one more easily persuade mortals that this whole universe is distinguished by God the Founder and workman of the world into its orbs? for it is [the number] that is most celebrated both in the sacred oracles of God, and by the Pythagoreans and the other philosophers. But what is more fitting to this workmanship of God, than that this first and most perfect Work should be included by the first and same most perfect number? besides, that thus from the aforesaid six mobile orbs the celestial harmony should be perfected, so that all the orbs succeed one another in such a way that no immensity of interval is left from the one to the other; and each, hedged about by geometry, guards its own place in such a manner that if you should try to move any one from its place, you would at the same time dissolve the whole system.

[margin: De hoc orbiû senario euidentiorem & magis propriam causam habes suprà pag. 24.]

Sed generalibus his prælibatis, accedamus sanè ad lationum circularium, quæ competunt singulis orbibus & sibi adhærentibus ac incumbentibus corporibus, enumerationem. Primò autem dicemus de hypothesibus motuum terreni globi, cui nos inhæremus. Cum D. Præceptor meus Platonem, & Pytagoreos suum diuini illius seculi Mathematicos sequens, sphærico terræ corpori circulares lationes ad τῶν φαινομένων causas assignandas, tribuendas censeret, videretq́ue (quemadmodum Aristoteles quoque testatur) vno attributo terræ motu, & alias item lationes ipsi ad stellarum imitationem competere, tribus eam principio vt maximè præcipuis moueri motibus, assumendum iudicauit. Primò namq́; vniuersali mundi distributione, vt mox dictum est, assumpta, constituit terram intra Lunæ orbem, tanquam sphærulam in torno, diuino ita ordinante numine, ipsius globiab occasu ad ortum motu, diem noctemq́;, atque aliam super aliam cœli faciem mortalibus, prout se Soli obueriat, producere. Secundo loco, centrum terræ cum sibi incumbentibus, elementis scilicet, & orbe lunari ab orbe Magno, de quo semel atque iterum iam meminimus, vniformiter in ecliptiæ plano, secundùm signorum consequentiam circumferri. Tertiò æquinoctialem, & axem terræ ad planum eclipticæ conuertibilem habere inclinationem, & contra motum centri reflecti ita, vt vbicunque sit centrum

But these general matters being tasted beforehand, let us now come to the enumeration of the circular carryings which belong to the several orbs and to the bodies adhering to and resting upon them. But first we shall speak of the hypotheses of the motions of the terrestrial globe, to which we cling. Since my Teacher, following Plato and the Pythagoreans, the mathematicians of that divine age, judged that circular carryings should be attributed to the spherical body of the earth for assigning the causes of the appearances, and saw (as Aristotle also testifies) that, one motion being attributed to the earth, other carryings likewise belong to it in imitation of the stars, he judged that it must be assumed to be moved at the outset by three motions as the chief: First, the universal distribution of the world being assumed, as has just been said, he established that the earth, within the orb of the Moon, like a little sphere on a lathe — the divine power so ordaining — by the motion of its globe from west to east produces day and night, and one face of the heaven after another to mortals, according as it turns toward the Sun. In the second place, that the centre of the earth, with the things resting upon it — namely the elements and the lunar orb — is carried round uniformly by the Great Orb, of which we have already made mention once and again, in the plane of the ecliptic, according to the succession of the signs. Third, that the equinoctial and the axis of the earth have an inclination convertible toward the plane of the ecliptic, and are bent against the motion of the centre in such a way that wherever the centre may be,

[margin: Qui orbi magno, & si adhærentibus motus competant.]

[margin: Terræ motus tres:]

[margin: 1. Diurnus.]

[margin: 2. Annuus.]

[margin: 3. Declinationis.]

centrum

[catchword: centrum]

…centrum terræ, æquinoctialis & poli terræ, propter talem axis terræ inclinationem, & stellati orbis immensitatem ad easdem mundi partes semper fermè respiciant, quod fiet, si quantum terræ centrum ab orbe magno in consequentia ducatur, tantum axis terræ extremitates, qui poli terræ singulis diebus ferè in antecedentia procedere intelligatur, circa axem & polos, axi & polis orbis magni, aut ecliptiæ æquidistantes, circulos paruos describendo. His autem motibus, vbi ex D. Præceptoris mei sententia binas polorum terræ librationes, duos item motus, quibus centrum orbis magni æquali & differenti motu sub ecliptica incedit, adiecerimus, cum'his, quæ superiùs de Lunæ motibus circa terræ centrum dicta sunt, habebimus, doctissime D. Schonere, quæ sit vera hypothesium ratio, ad totam doctrinam, quam Primi motus Recentiores vocant, quamque de omnimodis stellatæ sphæræ motibus habemus, deducendam, & causas eorum assignandas, quæ circa Solis Lunæq́ue motus & passiones in mille annis iam transactis, diligentibus Artificum obseruationibus contigisse est animaduersum, vt sanè, quod postea vberiùs dicendum erit, silentio prætereamus, quòd nimirum Orbis Magni motus apparentias in reliquis quinque planetis ingerat. Tam paucis, & ceu in vno orbe, tanta rerum doctrina comprehenditur. In primi

…the centre of the earth, the equinoctial and the poles of the earth, on account of such an inclination of the earth's axis and the immensity of the starry orb, almost always look toward the same parts of the world — which will happen if, by as much as the earth's centre is led forward in the order [of the signs] by the great orb, by so much the extremities of the earth's axis, that is the poles of the earth, are understood almost daily to proceed in the contrary direction, describing small circles about the axis and poles, equidistant from the axis and poles of the great orb or of the ecliptic. But when to these motions we shall have added, according to my Teacher's judgment, the two librations of the poles of the earth, and likewise two motions by which the centre of the great orb proceeds beneath the ecliptic with an equal and a differing motion, then, together with those things which were said above concerning the motions of the Moon about the centre of the earth, we shall have, most learned Lord Schöner, what the true account of the hypotheses is, for deducing the whole doctrine which the Moderns call that of the First Motions, and which we have concerning every kind of motion of the starry sphere, and for assigning the causes of those things which, regarding the motions and passions of the Sun and Moon over the thousand years now elapsed, have been observed to have happened by the diligent observations of the Practitioners — so that we may pass over in silence (as must afterward be said more fully) that indeed the motion of the Great Orb produces the appearances in the remaining five planets. By so few [motions], and as it were in one orb, so great a doctrine of things is comprehended. In the [doctrine] of the first

[margin: 4. Accedit motus, qui binis polorum librationibus perficitur.]

…motus doctrina nihil venit mutandum, quæ enim est proprietas eorum, quæ sunt ad inuicem, maxima declinatione constituta, eadem ratione inuestigabuntur reliquarum etiam partium eclipticæ declinationes, ascensiones rectæ, in toto terrarum orbe vmbrarum, & gnomonum ratio, dierum quantitates, ascensiones obliquæ, stellarum ortus & occasus, &c. Hoc tamen inter has, & Veterum hypotheses interest, quòd in illis contrà ac à Veteribus præscriptum est, stellato in orbe præter eclipticam, nullus circulus imaginatione propriè describatur. Reliqui verò, vt sunt æquinoctialis, duo tropici, arctici & antractici, Horizontes, meridiani, omnesq́; alij ad doctrinam primi motus pertinentes circuli, verticales, altitudinum, paralleli, coluri, &c. in terræglobo propriè designantur, & per relationem quandam in cœlum referuntur. Eorum autem, quæ circa Solem apparet, præter apparentiam diurnæ circa terram reuolutionis, quam cum omnibus stellis, & planetis reliquis communem habet, & quæ Ptolemæus ac Recentiores proprijs Solis motibus tribuerunt, accidunt ei & ea, quæ circa mutationes punctorum solstitialium, æquinoctialium, & stellarum ab ijsdem elongationes, atque apogij à stellis fixis variationes contingere deprehenduntur.

…of the first motion nothing comes to be changed; for what is the property of those things which are with respect to one another, the maximum declination being established, by the same reason will be investigated also the declinations of the remaining parts of the ecliptic, the right ascensions, the ratio of shadows and of gnomons in the whole orb of the lands, the quantities of days, the oblique ascensions, the risings and settings of the stars, etc. Yet this difference there is between these and the hypotheses of the Ancients, that in the former — contrary to what was prescribed by the Ancients — no circle besides the ecliptic is properly described by imagination in the starry orb. But the rest — such as the equinoctial, the two tropics, the arctic and antarctic, the Horizons, the meridians, and all the other circles pertaining to the doctrine of the first motion, the verticals, [circles] of altitude, the parallels, the colures, etc. — are properly designated on the earth-globe, and are referred to the heaven by a certain relation. But of those things which appear about the Sun, besides the appearance of the diurnal revolution about the earth, which it has in common with all the stars and the other planets, and which Ptolemy and the Moderns attributed to the Sun's own motions, there happen to it also those things which are found to come about regarding the changes of the solstitial and equinoctial points, and the elongations of the stars from them, and the variations of the apogee from the fixed stars.

[margin: Hypotheses Copernici cum vulgaribus, in Motus primi doctrina conueniunt.]

[margin: Præter Eclipticam, reliqui circuli primi motus propriè in terra, secundarii in cœlo describuntur.]

Q 2 com-

[signature: Q 2] [catchword: com-]

…communem habet, & quæ Ptolemæus ac Recentiores proprijs Solis motibus tribuerunt, accidunt ei & ea, quæ circa mutationes punctorum solstitialium, æquinoctialium, & stellarum ab ijsdem elongationes, atque apogij à stellis fixis variationes contingere deprehenduntur. Quæ omnia se nostris oculis offerunt, haud secus, ac si Sol, & stellarum orbis mouerentur: quomodo enim in oriente emergere, seu oriri, & paulatim supra horizontem eleuari, donec meridianum pertingant, à quo pari ratione descendere, deinde inferius hemisphærium permeare, indiesq́; diurnas suas reuolutiones conficere vulgò credantur, ex primo motu, quem terræ D. Præceptor iuxta Platonem tribuit, satis euidentes causas habet.

…it has in common, and which Ptolemy and the Moderns attributed to the Sun's own motions, there happen to it also those things which are found to come about regarding the changes of the solstitial and equinoctial points, and the elongations of the stars from them, and the variations of the apogee from the fixed stars. All of which present themselves to our eyes no otherwise than as if the Sun and the orb of the stars were moved: for how they are commonly believed to emerge or rise in the east, and gradually to be raised above the horizon until they reach the meridian, from which by like reason they descend, then traverse the lower hemisphere, and daily complete their diurnal revolutions — [this] has causes evident enough from the first motion which my Teacher, following Plato, attributes to the earth.

[margin: Altero terræ motu, Sol per zodiacum moueri apparet.]

Quod autem Sol nobis secundùm signorum consequentiam progredi videatur, atque tali motu eclipticam describere, & tempus annuum constituere nobis persuadeamus, per alterum motum, quem D. Præceptor terræ tribuit, fieri potest. Terra enim orbe magno lata, & inter stellas Libræ, & Solem morante, nos, qui quidem terram quiescere putamus, Solem Arietem stellatum habere existimabimus, quippe ex terræ centro linea per Solem in orbem stellarum eiecta in Arietis astrum incidet. Deinde terra progrediente ad Scorpionem, Sol Taurum petere videbitur, & hunc in modum zodiacum permeare, cum tamen ipso quiescente, hunc motum ei competere statuamus. Et annus sidereus erit tempus, quo centrum terræ, seu Solis in apparentia, ab eadem stella ad eandem semel reuoluitur.

But that the Sun seems to us to advance according to the succession of the signs, and by such a motion to describe the ecliptic and to constitute the annual time, can come about through the other motion which my Teacher attributes to the earth. For the earth, carried by the great orb and tarrying between the stars of Libra and the Sun, will make us — who indeed think the earth to be at rest — judge the Sun to have the star Aries, since a line cast from the earth's centre through the Sun into the orb of the stars will fall upon the star of Aries. Then, the earth advancing toward Scorpio, the Sun will seem to make for Taurus, and in this manner to traverse the zodiac, although, [the Sun] itself being at rest, we lay it down that this motion belongs to it [only apparently]. And the sidereal year will be the time in which the centre of the earth, or of the Sun in appearance, is revolved once from the same star to the same.

Tertius terræ motus certas, & ordinatas in toto terrarum orbe temporum vicissitudines producit; per hunc namq́; fit, vt Sol, & reliqui planetæ in circulo ad æquinoctialem oblique ferri videantur; eademq́; sit Solis ad singulos terræ tractus habitudo, quæ futura erat, terra medium vniuersi per hypothesin occupante, & planetis in circulo obliquo motis. Quoniam namq́; æquinoctialis planum, propter polorum suorum, vt dictum, motum ab ecliptiæ plano, in collatione ad Solem reflectitur & declinat, ipsiq́; poli diurnæ reuolutionis semper sub eodem quasi stellatæ sphæræ situ versantur. Deinde in maximis declinationibus æquinoctialis, ab ecliptiæ plano

The third motion of the earth produces sure and ordered vicissitudes of the seasons throughout the whole orb of the lands; for through it it comes about that the Sun and the other planets seem to be carried obliquely in a circle to the equinoctial; and the relation of the Sun to the several tracts of the earth is the same as it would have been had the earth, by hypothesis, occupied the centre of the universe, and the planets been moved in an oblique circle. For since the plane of the equinoctial, on account of the motion (as has been said) of its poles, is bent back and declines from the plane of the ecliptic in its relation to the Sun, and the very poles of the diurnal revolution are always set under as it were the same situation of the starry sphere. Then, at the maximum declinations of the equinoctial from the plane of the ecliptic,

[margin: Tertius terræ motus, vicissitudinum anni partium in terra, causa est.]

[margin: Æquinoctialis ad Eclipticam obliquus: est. Hinc cæteri circuli terræ inscribuntur.]

ad So-

[catchword: ad So-]

…ad Solem linea ex centro Solis exiens, ad terræ centrum, sectione conica terræ globum diurna reuolutione circumuolutum dissecat, tropicosq́; describit. Præterea quando æquinoctialis planum ab eclipticæ plano ad Solem maximè reflectitur, in vniuersa terra æquinoctium contingit, quippe quando à prædicta linea globus terræ in æquinoctiali in duas semiphæras abscindatur. Sed reliqui paralleli dierum in terra, prout reflectio & declinatio (siue, vt verbis vtar Ptolemæi, λόξωσις ἢ ἐγκλισις) æquinoctialis ad Solem sese commiscent, notantur. Arctici verò & antarctici à punctis contingentibus horizontes describuntur. Sed polares D. Præceptoris poli eclipticæ æquidistantes, circa æquinoctialis polos depingunt. Globi terræ autem circulus magnus transiens per æquinoctialis & dictos eclipticæ æquidistantes polos, colurus solstitiorum erit, & alius eundem in æquinoctialis polisad angulos rectos sphærales intersecans colurus æquinoctiorum vicem subibit. Atque in hunc modum, vel cuiuslibet loci proprij circuli, vel alij quotcunque facile terræ inscribi, & exinde ad super extensum cœlum referri intelliguntur.

…a line going out from the centre of the Sun to the centre of the earth cuts, by a conic section, the globe of the earth turned about by its diurnal revolution, and describes the tropics. Moreover, when the plane of the equinoctial is bent back most toward the Sun from the plane of the ecliptic, in the whole earth the equinox occurs, since when by the aforesaid line the globe of the earth is cut at the equinoctial into two hemispheres. But the remaining parallels of the days on the earth are marked according as the reflection and declination (or, to use Ptolemy's words, the obliquity or inclination) of the equinoctial mingle themselves with the Sun. But the arctic and antarctic [circles] are described from the points touching the horizons. And the polar [circles], equidistant from the poles of my Teacher's ecliptic, depict [themselves] about the poles of the equinoctial. But a great circle of the earth's globe passing through the poles of the equinoctial and the said poles equidistant from the ecliptic will be the colure of the solstices; and another, intersecting the same at the poles of the equinoctial at spherical right angles, will take the place of the colure of the equinoxes. And in this manner, either the proper circles of any place, or any number of others, are understood easily to be inscribed on the earth, and thence to be referred to the heaven extended above.

[margin: Tropici.]

[margin: Æquinoctii.]

[margin: Reliqui dierum paralleli.]

[margin: Arctici & Antarctici.]

[margin: Polares circuli.]

[margin: Coluri.]

Porrò cum propter obseruationum imperium terræ globus in eccentrici circumferentiam euoluerit, Sol in medium vniuersi subsederit, & sicut in vulgarib. hypothesib. centrum eccentrici inter centrum totius vniuersi, quod in ijsdem & terræ, ac stellas Geminorum nostra ætate erat, ita contrà in D. Præceptoris hypothesib. centrum orbis magni, quod in principio nostræ Narrationis per centrum eccentrici intelleximus, inter Solem, D. Præceptoris vniuersi medium, & stellas Sagittarij reperiatur, ac diameter orbis magni in centrû terræ incidens medij motus Solis lineam referat: cumq́; linea ex centro terræ per Solem in eccentrico centrum in eclipticam eiecta, verum locum Solis determinet, non est obscurum, quomodo Sol de Ptolemæi, Recentiorumq́; traditione inæqualiter sub ecliptica moueri æstimetur, atqq; angulus diuersitatis à motu medio geometricè inuestigetur. Terra autem in summa absidè orbis magni existente, Sol apogij locum in eccentrico occupare creditur & contrà, illa in ima abside morante, ipse in perigio conspicitur.

Further, since on account of the authority of the observations the earth's globe has rolled into the circumference of an eccentric, [and] the Sun has settled into the midst of the universe, and just as in the common hypotheses the centre of the eccentric [lay] between the centre of the whole universe — which in them was also the centre of the earth, and [near] the stars of Gemini in our age — so on the contrary in my Teacher's hypotheses the centre of the great orb, which at the beginning of our Narration we understood by the centre of the eccentric, is found between the Sun (my Teacher's centre of the universe) and the stars of Sagittarius, and the diameter of the great orb falling on the centre of the earth represents the line of the Sun's mean motion; and since the line cast out from the centre of the earth through the Sun, [from] the centre on the eccentric, into the ecliptic, determines the true place of the Sun, it is not obscure how the Sun is reckoned, according to the tradition of Ptolemy and the Moderns, to be moved unequally beneath the ecliptic, and how the angle of diversity is geometrically investigated from the mean motion. But when the earth is at the highest apsis of the great orb, the Sun is believed to occupy the place of the apogee on the eccentric; and on the contrary, when [the earth] tarries at the lowest apsis, [the Sun] itself is beheld in perigee.

[margin: Qua ratione Solis apparentem motum Copernicus demonstret.]

Verùm enimuerò qua ratione stellæ fixæ à punctis æquinoctialibus, & solstitialibus elongari videantur, & maxima Solis obliquitas variari, &c. quod sub initium Narrationis ex D. Præceptoris

But indeed, by what reason the fixed stars seem to be elongated from the equinoctial and solstitial points, and the maximum obliquity of the Sun to be varied, etc. — which at the beginning of the Narration, from my Teacher's

[margin: Motus apparens in Stellis fixis: & obliquitatis eclipticæ variatio.]

Q 3 ptoris

[signature: Q 3] [catchword: ptoris]

…ptoris Lib. III. deduxi, ex motu declinationis, quem generaliter proposuimus, & binis sibi inuicem occurrentibus librationibus dependere D. Præceptor collegit. A polis, ecliptiæ polis, vt non ita multo antè dictum, æquidistantibus, vtringq; 23. grad. 40. min. circuli magni numerentur, ibíq; duo notentur puncta, quæ polos æquinoctialis medij referant, ac vt conuenit, duo coluri solstitia, & æquinoctia media distinguentes designentur. Hæc sanè discendi gratia concipiantur, & delinientur in orbiculo globum terræ continente, cuius vniformi motu, tertius, qui quidem terræ tribuitur motus, contingat. Centro autem terræ inter Solem, & stellas Virginis commorante, reflectatur, seu obliquetur æquinoctialis medius ad Solem, & linea veri loci Solis per communem sectionem plani eclipticæ, æquinoctialis medij, & coluri distinguentis æquinoctia media transeat. idque ita, vt sit æquinoctium vernale medium, & simul æquinoctium vernale verum, vbi idem, quemadmodum ex sequentibus liquidò constabit, ratio motuum sic exiget. Ab hoc loco terræ centro æquali motu ad stellas fixas singulis diebus 59. min. 8. secun. 11. ter. procedente, punctum vernale medium tantundem in præcedentia super terræ centro conficiat, & paulò velociori gressu incedens 8. ferè ter. angulum maiorem describat. Et hæc est causa, quamobrem paulò antè declinationis motum æqualem fermè, æquali motui centri terræ ad stellas fixas diximus. Sed crescente subinde angulo, qui à puncto vernali æquinoctialis medij super terræ centro (iuxta iam positum canonem) designatur, priusquam centrum terræ ad locum eclipticæ, vnde digressum, reuertatur denuò, linea veri loci Solis in æquinoctium medium incidet; & stellæ videbuntur nobis medio, seu æquali aliquo motu in consequentia, pro anticipationis ratione, progredi. Quæ anticipatio, vt principio dixi, in anno Aegyptio est 50. secund. ferè, & in 25816. annis Aegyptijs in integram reuolutionem excrescit. Patet itaque quid sit æquinoctium medium, quid æqualis præcessio, & quomodo hæc ceu instrumentali fabrica, oculis possint subijci.

…from my Teacher's Book III I deduced — from the motion of declination which we generally proposed, and on two librations meeting one another — my Teacher gathered [that they] depend. From the poles, equidistant (as was said not long ago) from the poles of the ecliptic, let there be numbered on each side 23 degrees 40 minutes of a great circle, and there let two points be marked which represent the poles of the mean equinoctial, and, as is fitting, let two colures distinguishing the mean solstices and equinoxes be designated. Let these indeed, for the sake of learning, be conceived and drawn on a little circle containing the globe of the earth, by whose uniform motion the third motion — that, namely, which is attributed to the earth — comes about. But the centre of the earth tarrying between the Sun and the stars of Virgo, let the mean equinoctial be bent back, or made oblique, toward the Sun, and let the line of the Sun's true place pass through the common section of the plane of the ecliptic, of the mean equinoctial, and of the colure distinguishing the mean equinoxes; and that in such a way that there be the mean vernal equinox, and at the same time the true vernal equinox, where the same — as will plainly appear from what follows — the account of the motions shall thus require. From this place, the earth's centre proceeding by an equal motion with respect to the fixed stars 59 minutes 8 seconds 11 thirds each day, let the mean vernal point complete just as much in the preceding direction over the earth's centre, and, advancing with a slightly swifter pace, let it describe a greater angle by about 8 thirds. And this is the reason why a little before we said the motion of declination [to be] almost equal to the equal motion of the earth's centre with respect to the fixed stars. But the angle thereupon increasing, which is designated from the vernal point of the mean equinoctial over the earth's centre (according to the canon already laid down), before the centre of the earth returns again to the place of the ecliptic whence it departed, the line of the Sun's true place will fall upon the mean equinox; and the stars will seem to us to advance by some mean or equal motion in the order [of the signs], by reason of the anticipation. Which anticipation, as I said at the outset, is almost 50 seconds in an Egyptian year, and in 25816 Egyptian years grows out into a full revolution. It is therefore plain what the mean equinox is, what the equal precession is, and how these can be set before the eyes as it were by an instrumental construction.

[margin: Tertius terræ motus, seu potius quartus.]

[margin: Æquinoctii medium, æqualis præcessio.]

De librationibus. Sit linea recta determinata A B, vt exêpli gratia 24. min. hæc pûcto C in duas æquales parteis deuidatur. Deinde altero circini pede in C collocato, describatur circulus D E, extêsione C D, versus

Concerning the librations. Let there be a given straight line A B, as for example of 24 minutes; let it be divided by the point C into two equal parts. Then, one foot of the compass being placed at C, let a circle D E be described, with the extension C D, toward

[margin: Quomodo Librationes fiant. Cop. lib. 3. cap. 4.]

versus

[catchword: versus]

[Figure: libration/prosthaphaeresis construction — see facsimile (this leaf)]

…versus A, 6. min. (quarta parte scilicet) & eiusdem magnitudinis de alia ab hac materia duo circelli (vt sic interim loqui liceat) fabricentur, & ita componantur, vt alter eorum circumferentiæ alterius applicetur, quo libere circa suum centrum moueri possit. Qui autem alterum in circumferentia sert, primus vocetur, ac centro lineæ A B in pûncto C affigatur; secundi circelli centro nota F, & in circumferentia eiusdem ad placitum pûncto assumpto, nota G adpingatur. Quòd si nota G secundi circelli applicetur A, termino lineæ assumptæ, & F, notæ D eiusdem, ac æquali tempore G in vnam partem super centro F angulum describat, duplum angulo ab F super C in partem diuersam descripto; patet in vna primi circelli reuolutione notam G lineam A B bis describêdo perreptasse, & secundum circellum bis reuolutum. Quia autem tali descriptione lineæ rectæ per duos circulares motus compositos, G punctum circa A & B terminos tardissimè promoueatur, in medio autem circa A concitatiùs, placuit D. Præceptori talem notæ G per A B lineam motum, librationem vocare, cum talis motus ad similitudinem pendentium in aëre fiat. Appellatur etiam hîc motus, motus in diametrum: nam imaginatione assumpto circulo, cuius A B, centro C, sit diameter; ex chordarum doctrina, quo in loco eiusdem diametri A B motu, quem dixi, composito, G punctum sit, recta H G semissis subtendens duplum arcus H A constituitur, secans diametrum A B in G, vnde secundum A G tabula prosthaphæresium fabricatur. Motum primi circelli super G, Præceptor Anomaliam vocat, eo namq́; motu prosthaphæresis deprehenditur. Etenim F centrum secundi circelli in circumferentia primiâ D pûncto in sinistram discedens, describat angulum, qui sub D C F sit v. gr. graduum 30, ibi in circumfetenti-

…toward A, 6 minutes (the fourth part, namely); and of the same magnitude let there be made, out of other material than this, two little circles (so to speak for the moment), and let them be so put together that one of them is applied to the circumference of the other, so that it can move freely about its own centre. But that which carries the other on its circumference, let it be called the first, and let it be fixed at the centre of the line A B at the point C; let the centre of the second little circle be marked F, and a point taken at pleasure on its circumference, let it be marked G. But if the mark G of the second little circle be applied to A, the end of the assumed line, and F to the mark D of the same, and in an equal time G describe an angle on one side about the centre F, double the angle described by F about C on the other side: it is clear that in one revolution of the first little circle the mark G has crept twice over the line A B by describing it, and the second little circle has revolved twice. But since by such a description of the straight line through two combined circular motions the point G is advanced very slowly near the ends A and B, but more rapidly in the middle near the centre, it pleased my Teacher to call such a motion of the mark G along the line A B a libration, since such a motion comes about in the likeness of things suspended in the air. It is also called here a motion into the diameter: for, a circle being assumed by imagination of which A B is the diameter, the centre C — from the doctrine of chords, in whatsoever place of the same diameter A B the point G may be by the combined motion I have spoken of, the straight line H G, half [the chord] subtending double the arc H A, is constituted, cutting the diameter A B in G, whence according to A G the table of prosthaphaereses is constructed. The motion of the first little circle about G my Teacher calls the Anomaly, for by that motion the prosthaphaeresis is detected. For the centre F of the second little circle, departing on the circumference of the first from the point D toward the left, let it describe an angle which under D C F be, for example, of 30 degrees, there on the circumferen-

[margin: Libratio. Motus in diametrum.]

am cir-

[catchword: am cir-]

…am circuli A B, ex centro C, ei circa C F H totidem graduum A H arcum continebit, similem arcui D F primi circelli: & quia secundi circelli pûnctum G ab H, ad dextram ratione dupla processit, à signo H in signum G lineâ rectâ ductâ, patet eandem esse semissem dupli arcus A H, & G C semissem dupli arcus residui A H arcus de quadrante, hoc est, 60. gra. cuius dupli subtensæ semissis est 8660. partium, quare & A G 1340. partium, quarum quæ ex centro 1000. quantum videlicet G distat ab A in diametro A B. Quòd si verò A B præsupponatur 60. G a erit talium 4. & G B 56. vnde facta parte proportionali ad 24. habebitur A G vel B G in quacunq́; parte assumptæ lineæ rectè determinatæ G signum subsistat, in tali casu.

…on the circumference of the circle A B, from the centre C, it will contain about C F H an arc A H of just as many degrees, similar to the arc D F of the first little circle: and since the point G of the second little circle has proceeded from H to the right in double ratio, by a straight line drawn from the sign H to the sign G, it is clear that the same is the half of the double arc A H, and G C the half of the double of the remaining arc A H — an arc of the quadrant, that is, of 60 degrees, of whose double the half of the subtending chord is 8660 parts, wherefore also A G is 1340 parts, of which those from the centre [are] 1000, namely by how much G is distant from A on the diameter A B. But if A B be presupposed [to be] 60, G a will be of such [parts] 4, and G B 56; whence, the proportional part being made to 24, A G or B G will be had, in whatever part of the assumed straight line duly determined the point G subsists, in such a case.

[margin: Priori libratio, qua obliquitas Eclipticæ variatio demonstratur.]

His ita τραχυτέρα sanè Μϋση perceptis, in facili fuerit intelligere, quomodo & maxima æquinoctialis ab eclipticæ plano obliquitas varietur, & vera æquinoctiorum præcessio inæqualis fiat. Principio namq́; (cum breuiores arcus à lineis rectis quoadsensum quidem, nihil differant) æquinoctialis medij polo septentrionali punctum c imaginatione applicetur: Linea autem A B sit arcus coluri, distinguentis solstitia media, inter polum æquinoctialis medij septentrionalem, & adiacentem polum eorû, qui eclipticæ æquidistant. Quare B est terminus minimæ poli diurnæ reuolutionis, seu terræ, ab ecliptiæ, vt dictum, polo distantiæ: A verò inter eundem borealem æquinoctialis medij polum, &ecliptiæ planum, vnde & maximæ poli terræ, à polo ecliptiæ, remotionis. Præterea duobus circellis linea A B, vti conuenit, applicatis, intelligatur quantum ad præsens polus terræ borealis in G pûncto, & motu duorum circellorum composito, lineam A B 24. minu. describere; simili nempe machinatione polo meridionali moto, lege oppositionis seruata, ceu pendente mundo, maximam declinationem mutante.

These things being perceived — by a rather rougher Muse, to be sure — it will be easy to understand how both the maximum obliquity of the equinoctial from the plane of the ecliptic is varied, and the true precession of the equinoxes becomes unequal. For at the outset (since shorter arcs differ in no respect, as to perception at least, from straight lines), let the point c be applied by imagination to the northern pole of the mean equinoctial: but let the line A B be an arc of the colure distinguishing the mean solstices, between the northern pole of the mean equinoctial and the adjacent pole of those [poles] which are equidistant from the ecliptic. Wherefore B is the term of the least distance of the pole of the diurnal revolution, or of the earth, from the pole of the ecliptic (as has been said); but A [is the term] between the same northern pole of the mean equinoctial and the plane of the ecliptic, whence also of the greatest removal of the earth's pole from the pole of the ecliptic. Moreover, the two little circles being applied to the line A B, as is fitting, let it be understood that for the present the northern pole of the earth, at the point G, by the combined motion of the two little circles, describes the line A B of 24 minutes; by a similar contrivance, namely, the southern pole being moved, the law of opposition being kept, as with the world suspended, changing the maximum declination.

Et assumatur, primum circellum in 3434. annis Aegyptijs reuolutionem complere, &terminum, à quo principium motus anomaliæ, esse à punctûm circumferentiæ circuli, cuius diameter libratione prima describitur; Atque cuilibet statim patebit, si præter hanc vnicam poli terræ nullamhaberent librationem, ipsiúsq́; poli terræ à coluro distinguente solstitia media non absciderent, quomodo tali polorum terræ motu tantum, angulus inclinationis plani

And let it be assumed that the first little circle completes its revolution in 3434 Egyptian years, and that the term from which [is] the beginning of the motion of anomaly is from the point of the circumference of the circle whose diameter is described by the first libration; and it will at once be plain to anyone, that if besides this single libration of the earth's pole they had no [other] libration, and the poles of the earth themselves did not cut off from the colure distinguishing the mean solstices, how by such a motion of the earth's poles only the angle of inclination of the plane

[margin: Priori libratione poli terra in coluro Solstitiorum mediorum 24. scrup. ascendentes & descendentes, inclinationem æquinoctialis ad eclipticam 24. scr. variant.]

plani

[catchword: plani]

…plani æquinoctialis veri ad eclipticæ planum, propter polorum suorum progressum, ab A versus G ad B decresceret contra aliam circulationem complendo à B ad C versus A cresceret, nullaque propterea inæqualitas in æquinoctiorum præcessione appareret.

…of the true equinoctial to the plane of the ecliptic, on account of the progress of its poles, would decrease from A toward G to B, [and] on the contrary, completing the other circulation from B to C toward A, would increase, and therefore no inequality would appear in the precession of the equinoxes.

[margin: Altera libratio, qua inæqualis Æquinoctialium punctorum præcessio demonstratur.]

Porrò autem quoniam per obseruationes certo constat, puncta æquinoctialia verâ à punctis æquinoctialibus medijs hinc inde 70. minutis maxima prosthaphæresi elongari, obliquitatisque mutationem ad hanc duplam rationem habere: ad constituendam D. Præceptor & alteram super illam inferendam librationem, animum suum induxit, qua videlicet poli terræ à coluro distinguête solstitia media, in mundi latera permutantibus, vt nempe polus borealis à coluro solstitiorum mediorum sinistrum, australis dextrum latus teneat: verum æquinoctium præcedit medium, citiusq́; Sol cum vero, quàm cum medio æquinoctiali congreditur. Cæterum ab A versus B, polis terræ procurrentibus, quia æquinoctium verum Soli quasi obuiam procedit, annus ad æquinoctia propter hanc causam decrescit à verò versus A, cum Solem quasi fugiat, annus ad æquinoctia crescit. Et polis terræ circa A chærentibus, breuiori annorum spacio notabile anni crementum, aut decrementum percipitur.

But further, since by observations it is certainly established that the true equinoctial points are elongated from the mean equinoctial points on this side and that by 70 minutes at the maximum prosthaphaeresis, and that the change of obliquity has this double ratio: my Teacher set his mind to establishing also another libration to be superimposed upon that [first one], by which namely the poles of the earth, alternating from the colure distinguishing the mean solstices into the [opposite] sides of the world — so that, namely, the northern pole holds the left side of the colure of the mean solstices, the southern the right side — the true equinox precedes the mean, and the Sun meets the true [equinox] sooner than the mean equinoctial. But moreover, from A toward B, the poles of the earth running forward, because the true equinox proceeds as it were to meet the Sun, the year reckoned to the equinoxes decreases for this cause; from the true toward A, since [the equinox] as it were flees the Sun, the year reckoned to the equinoxes increases. And while the poles of the earth cling near A, in a shorter space of years a notable increment or decrement of the year is perceived.

[margin: Altera libratione poli terra à Coluro solstitiorum mediorum vtringq, versus latera mundi deflectentes, veri æquinoctialis cum ecliptica sectionem à media 70. scrup. vtringq, variant.]

Cumq́; apparens stellarum fixarum processus annuæ quantitati ad æquinoctia colligatus sit, eadem prorsus ratione velocior, & tardior punctorum solstitiorum & æquinoctiorum à stellis fixis elongatio in antecedentia animaduertitur.

And since the apparent progress of the fixed stars is bound together with the annual quantity reckoned to the equinoxes, by exactly the same reason a swifter and a slower elongation of the solstitial and equinoctial points from the fixed stars in the preceding direction is observed.

Schema

[catchword: Schema]

…[Figure: large circular diagram of the two librations — the ecliptic, equinoctial and solstitial circles with labelled points B, C, D, E, F, G, H, K, M, X around an inner small circle; lines drawn to a central point — see facsimile p140]

[margin: Schema vtriusque librationis, pro obliquitatis, & veræ æquinoctialis cum ecliptica sectionis mutatione monstranda]

Sit à polo Ecliptica, BCD semicirculus Ecliptica in Coelo ABD solstitiorum medio, E est polus Æquinoctialis FCG medio, mediúmque æquinoctiorum in C, & media obliquitas BF, vel AE, quæ sit 23. gr. 40. scr. Priore libratione, qua vera æquinoctialis polus ab E modo recta, arcus vel recta linea sit HEE, arcus colori solstitiorum, eiúsq́ue quantitas 24. scr. Hæ ergo vera obliquitas mutatur. Nam verò polo in H æstiuæ verus æquinoctialis est KCL: sed eodem polo in F æquinoctialis est MCN, cuius obliquitas vel BK vel ax. gr. 12. scr. hîc 23. gr. 28. scr. Alterius autem librationis recta (vnà quasi recta) sit OEP. Verùm cùm libratio reliqua sit XEZ, partium quantitas 16. scr. Hæ veram veri æquinoctialis & ecliptica sectionem, verúmq́ue Zodiaci initium, à quo signorum, & motus stellarum numeratur, variant. Nam verò polo in H æstiuæ, vera æquinoctialis sectio est in S, sed illo in O, hæc est in T, quasi vere Coperniei est 2. gr. scr. De tantis enim ob obliquitatis congruit O Pleiae. Porrò hæ diuersitates hâ libratione hæc conditione inter se componuntur. 1. Verò polo in X mouebuntur vtriusq́ue librationis polum, sub auribus æquinoctialis cum medio terra in FCG coincidit. 2. Ab E verus polum tam ad H, quàm ad P tendit, in priori quidem libratione enim libratio secundùm OP, dupla est ad librationem obliquitatis secundùm IH, quia illa tota anni 1717. hâc verò 858. complerit, & Copernico asseritur. Vbi ergo verus polus ad P deuenerit, alteraq́ue libratio intra E & H non considera facit. Quare motu composito veram obliquitatem, & auctari, & verum æquinoctialem in KS detegerit, cuius obliquitas quidem maxima est, sed sectio à media remotissima, vt nempe in T, anni 1701. fuerit. Verò polo in P, redeúnte, & simul in EH vlterius ascendente, ipsi vtriusq́ue librationis motu, motuq́ue composito in HK desertur. Ex quo eo verus æquinoctialis KX, & obliquitas eorum facta BK rediit. 4. Pari modo dùm polus verus in K ad E reuertitur, atq́ue X ad O regreditur, libratione obliquitatis composita libratione, vt sit cùm in Q in H peruenerit, ea nunc in à abit. Quo loco verus Æquinoctialis in XYZ, & aduersæ æquinoctialis sectionis RST. 1. Vt enim libratio sub eodem polum in E, atque verùm æquinoctialem in FCG reponit. Hoc igitur tempore æquinoctiorum varietas tua, sed ob-

…[Figure: large circular diagram of the two librations — the ecliptic, equinoctial and solstitial circles with labelled points B, C, D, E, F, G, H, K, M, X around an inner small circle; lines drawn to a central point — see facsimile p140]
[margin: A diagram of both librations, to be shown for the change of the obliquity and of the true equinoctial intersection with the ecliptic]
Let from a pole BCD be the semicircle of the Ecliptic in the heaven, with ABD the mid-point of the solstices, E the pole of the Equinoctial with FCG its mid-point, and the mid-point of the equinoxes at C, and let the mean obliquity BF, or AE, be 23 degrees 40 minutes. By the first libration, by which the true equinoctial pole moves from E now in a straight [arc], let the arc or straight line be HEE, the arc of the colure of the solstices, and let its quantity be 24 minutes. These therefore change the true obliquity. For indeed when the pole is at H, the true summer equinoctial is KCL; but with the same pole at F the equinoctial is MCN, whose obliquity, whether BK or [ax?], here is 23 degrees 28 minutes. But of the other libration let the straight [line] (as it were a single straight) be OEP. But since the remaining libration is XEZ, the quantity being 16 minutes, these vary the true intersection of the true equinoctial [with the ecliptic], and the true beginning of the Zodiac, from which [the count] of the signs and the motion of the stars is reckoned. For indeed when the pole is at H in summer, the true equinoctial intersection is at S, but with it at O this is at T, which by the truly Copernican [reckoning] is 2 degrees [scr.]. For by so great an [amount] of obliquity O agrees with the Pleiades. Furthermore these diversities are compounded among themselves by this libration on this condition. 1. When the pole is at X both poles of the libration will be moved, when [it] coincides with the equinoctial together with the mid-point of the earth in FCG. 2. From E the true pole tends both toward H and toward P, in the first libration indeed; for the libration along OP is double that of the libration of obliquity along IH, since the former completes [its course] in 1717 years, the latter in 858, and so it is asserted by Copernicus. When therefore the true pole has come to P, and the other libration does not occur between E and H, [then] therefore by the compounded motion the true obliquity is both increased, and the true equinoctial is detected in KS, whose obliquity indeed is greatest, but the intersection most remote from the mean, namely in T, as it was in the year 1701. With the true pole returning to P, and at the same time further ascending in EH, by the very motion of both librations, and by the compounded motion, it is carried in HK. Whence the true equinoctial KX, and their obliquity, having been made, return to BK. 4. In like manner while the true pole returns in K to E, and X regresses to O, the libration of obliquity being compounded with the libration, so that when it has come into Q in H, it now passes off into [à]. At which place the true Equinoctial in XYZ, and the adverse equinoctial intersections RST. 1. For as the libration restores the [pole] under the same pole in E, and the true equinoctial in FCG. At this time therefore the variation of the equinoxes [is] yours, but on the other

sed obliquitatis mutatio dimidia complebitur, quia verus polus ex E ad illius vtrumq́ue terminum, P&O, ab huic autem ad alterum tantùm H exijt, & in E reuersus est. Vnde verum æquinoctialem cùm C in S & T translatum in Credit, verúq́ue obliquitas ex F in K deducitur, cum F ternum vinitur. Et verisq́ue via, vt compofito motu fuit dimidia euolla EæIVE peregerit. Et è enim repetritur æquinoctialis verum in XSZ. ex 1. in MCN: ex V in XYZ, donec hæc quoq́ue, periodo confecta in E recurrat. Atq́ue tunc tempore omnis æquinoctiorum varietas C&CIC, obliquitatis autem altera à mediis FMF, completur. Et hic videri vlt. quòd ab K ad M obliquitas minuatur, & ab M K augeatur. Deinde quòd verò æquinoctiali punctò (si modò æquinoctij C præcessio à B versus D scri intelligatur) ab L vsut C ante, vera præcessio retardetur: quare à puncto L vsut H ad B verus punctò tardior appareat, & Anni solaris magnitudo prolongatur. Econtra, eodem ab T ad S tardore, præcessione vera velocior, & Annus solaris vertet minimam abbreuiatur.

…but the change of the obliquity will be half completed, because the true pole has gone out from E to both its terminals, P and O, but from this one to the other only H, and has returned to E. Whence the true equinoctial, when C is transferred into S and T, is credited [reckoned], and the true obliquity is led down from F into K, when F is joined to the third. And on either path, as it had been by the compounded motion, it will have completed the half EæIVE. And for indeed the true equinoctial is found again in XSZ, from 1 in MCN, from V in XYZ, until this too, the period completed, recurs into E. And then at this time all the variation of the equinoxes [is completed by] C&CIC, but the other [variation], that of the obliquity from the means, by FMF. And here it may be seen lastly that from K to M the obliquity is diminished, and from M to K it is increased. Then that at the true equinoctial point (if only the precession of the equinox C from B toward D is understood) from L as before C, the true precession is retarded: wherefore from the point L up to H toward B the true [point] appears slower, and the magnitude of the solar year is prolonged. On the contrary, from T to S with the same slowness, the true precession [being] swifter, and the solar year is shortened to its very least.

[margin: Motus apogæi Solis, & mutatio eccentricitatis eius. De his vide etiam infra duorum Solis.]

DE Solis autem apogio, quæ principio ad observationibus, secundùm D. Præceptoris mei sententiam deduximus, quantum ab æquinoctij verm̃ ab eo, & elongationem deducimus, & nos dictis satis innotuit. Progressus verò ipsius apogij sub ecliptica à motu centri parui circuli & orbis magni centri, in parui circuli circumferentia vnitorum latitudine dependet. Diameter orbis magni, aut ecliptica per Solis patuiq́ue circulu sectionem & ea fines transiens, est linea mediarum absidum Solis: sed diameter per Solis, orbisq́ue magni centra est illa nere arvarum absidum. Quemadmodùm autem centrum orbis magni inter Solem & locum eclipticæ, vbi Sol perigium æstere creditur, repetitur: ita similiter centrum parui circuli inter locum perigij medij, & Solem statuitur. Tempore Ptolemæi linea verarum absidum à prima stella Arietis in 5. grad 50. min. loco apogij apparentis, & 237. grad: 50. min. à punctò opposito 240. grad. 16. min. tum centrum orbis magni, à summa parui circuli à centro Solis distantia 31. grad. cùm intacente fere & remotissima procreabat, æquinoctiale nempe eodem tempore anomalia simplici, æquæ & obliquitatis existente. Vniformiter autem procedente parui circuli motu suprà Solis centro 0. & orbis magni centro in parui circuli circumferentia, visa est summa absis Solis, tempore observationis, quàm habuit D. Præceptor, 69. grad 25. min, à prima stella Arietis tenere; at cùm eodem tempore anomalia simplex 165. grad. ferè esset, prosthaphæresis 2. grad. 10 min. ferè reperta est, centrúmq́ue

…[margin: The motion of the Sun's apogee, and the change of its eccentricity. On these things see also below, of the two [errors?] of the Sun.]
Concerning the apogee of the Sun, which from the beginning we have derived from the observations, according to the opinion of my Teacher [Praeceptor, i.e. Copernicus], how much from the true equinox [it lies] from it, and we derive its elongation, has become sufficiently known to us by the things said. But the progress of its apogee under the ecliptic depends upon the motion of the centre of the small circle and of the centre of the great orb, united in the circumference of the small circle, [and on] their latitude. The diameter of the great orb, or the ecliptic, passing through the section of the Sun and the small circle and crossing those bounds, is the line of the mean apsides of the Sun: but the diameter through the centres of the Sun and of the great orb is that of the true apsides. As moreover the centre of the great orb is found between the Sun and the place of the ecliptic where the Sun is believed to be at perigee: so likewise the centre of the small circle is set between the place of the mean perigee and the Sun. In Ptolemy's time the line of the true apsides held [a place] from the first star of Aries at 5 degrees 50 minutes, at the apparent place of the apogee, and 237 degrees 50 minutes; from the opposite point at 240 degrees 16 minutes the centre of the great orb, at a distance of 31 degrees from the highest [point] of the small circle from the centre of the Sun, when it was producing [it] nearly and most remotely, namely at the same time with simple anomaly equal, and the obliquity existing. But the motion of the small circle proceeding uniformly above the Sun's centre at 0, and the centre of the great orb in the circumference of the small circle, the highest apsis of the Sun, at the time of the observation which my Teacher had, was seen to hold 69 degrees 25 minutes from the first star of Aries; but when at the same time the simple anomaly was about 165 degrees, the prosthaphaeresis was found to be about 2 degrees 10 minutes, and the centre

crúmq́ue parui circuli inter Solem & locum perigij medij constitit. Præterea eccentricitas orbis magni, seu eccentrici Solis, si placet ita loqui, quæ Ptolemæo viginti quarta pars, cuius ex centro orbis magni fuit, nostra ætate trigesimam primam partem ferè attingit: vt observationes ostendunt, & D. Præceptoris hypothesibus constitutis, mathematica adhibita demonstratione facilè deducitur.

…and the centre of the small circle stood between the Sun and the place of the mean perigee. Moreover the eccentricity of the great orb, or of the Sun's eccentric, if one may so speak, which to Ptolemy was a twenty-fourth part, that which was from the centre of the great orb, in our age attains nearly a thirty-first part: as the observations show, and, my Teacher's hypotheses being established, it is easily deduced by applying a mathematical demonstration.

[margin: Coper. lib.3. cap.16.]

Quomodo autem, & propter centri orbis magni in paruo circulo motu, eccentricitates planetarum quinq́ue variantur, in causis renouanda hypothesin propositam, laud magno cum labore intelligi potest: in contemplatione verò quinq́ue planetarum, cum duo positis nem considaranda variant, quomodo, & quanto centri terræ ad deferentium planetas verùs accessus, vel recessus fiat: deinde quàm illud augmentum, vel decrementum ratione, accidat illam quæ ex centro deferentis cuiusubet planetæ habeat, non opus est ire causas longius petere.

…But how, on account of the motion of the centre of the great orb in the small circle, the eccentricities of the five planets are varied — the proposed hypothesis being renewed in the causes — can be understood, not with great labour: but in the contemplation of the five planets, since with two things being posited there must be considered how, and by how much, the true approach or recession of the earth's centre to the deferents of the planets is made: then in what way that increase or decrease happens by reason of that which it has from the centre of the deferent of any planet, there is no need to seek the causes further off.

[margin: In ☉ ista variatio non est sensibilis propter magnitudinem orbi eius.]

In Saturno verò, vel tota dimetiens parui circuli nullum perceptibilem admodum efficit angulum eam, quæ ex centro deferentis eius habeat, propterea quòd primus sub stellato orbe seratur, nullam variationis eccentricitatis Saturni, observationésque proferunt.

…In Saturn however, even the whole diameter of the small circle makes no perceptible angle at all in that [angle] which it has from the centre of its deferent, for the reason that it is borne first under the starred orb; nor do the observations bring forward any variation of Saturn's eccentricity.

[margin: Iste eccentricità in ☿ mutatio partim in anomalia eccentri 3. differentiam prosthaphæresis: 5. per. primorum, quia in anomalia commutationis differentiam prosthaph. parallaxi non omnino directè scrup.]

Deinde quia Iouis apogium per quadrantem ferè à prima stella Arietis distat, hodie propter centri orbis magni processum, nulla sensibilis eccentricitatis eius deprehenditur mutatio, ámentí nec notabilis & perceptibilis ratio diametri parui circuli ad eam, quæ ex centro orbis sui, esset. Atque hæc est causa, quàm Mercurio quoq́ue: nulla eccentricitatis sentiatur mutatio, cùm imbecillior Solis apogij ratio sui ad apogio claudat.

…Then since Jupiter's apogee is distant about a quadrant from the first star of Aries, today on account of the advance of the centre of the great orb no sensible change of its eccentricity is detected, nor is there a notable and perceptible ratio of the diameter of the small circle to that which would be from the centre of its own orb. And this is the cause, as in Mercury too: no change of eccentricity is felt, since the weaker ratio of the Sun's apogee toward its [own] apogee shuts [it] off.

[margin: Ista eccentricità in ♂ mutatio partim in anomalia eccentri 3. differentiam prosthaph. parallaxi non non omnino directè scrup.]

Martis autem apogium distat ab apogio Solis ad sinistram 50. ferè grad. & Veneris ad dextram 42. grad. Sunt itaq́ue centra horum deferentium in idoneis locis constituta, ad percipiendam variationem: & cum diameter parui circuli ad vtriusq́ue orbem, notabilem habitudinem habeat, observationibus de duobus his planetis per triangulorum doctrinam exa-

…But Mars's apogee is distant from the Sun's apogee about 50 degrees to the left, and that of Venus about 42 degrees to the right. And so the centres of these deferents are set in suitable places for perceiving the variation: and since the diameter of the small circle has a notable bearing toward the orb of each, by the doctrine of triangles, from the observations of these two planets, [it is] examined

[margin: Orbes & motus eius ☉ ad Orbis magni eccentricitatem. Vide infrà in Appendice.]

minatis, inuenis D. Præceptor, Martis quidem eccentricitati quadragesimam secundam, Veneris verò quintam partem, propter accessum centri orbis magni ad Solem decessisse. Nec autem vnus aliquis motus terræ attributus parum testimonij videretur habere, industria τῶ τοῖς ἀνερ̃μνῃ-ω̃ factum est, vt quilibet motus pariter & in omnium planetarum apparentibus motibus notabiliter deprehenderetur, adeò paucis motibus τὰ φαινόμενα τοῖς οὐρανίοις in natura necessarijs, satisfieri opportunum fuit. Ideóq́ue & centri orbis magni motus non tantùm ad Solem, & planetas eundem circundantes, sed etiam ad Lunæ passiones pertinet. Quemadmodùm nanq́ue Ptolemæus distantiam Solis à terra maximam constituit esse 1210. partium, qualium est quæ ex centro terræ in A, & axem vmbræ earundem 268, ita D. Præceptor demonstrat nostra ætate eandem Solis à terra maximam elongationem esse 1179. partium, & axem coni vmbræ 265. Cætera verò quo cohærent, ad vtriusq́ue luminaris motus & passiones, propter mutatas hypotheses perpendendas, Secundæ Narrationi huic subsecutura reseruanda putaui.

…examined, you find, D. Teacher [Copernicus], that to Mars's eccentricity a forty-second part, but to Venus's a fifth part, has departed on account of the approach of the centre of the great orb toward the Sun. Nor would one single motion attributed to the earth seem to have little testimony: by the industry of [those who pondered the heavenly things] it has been brought about that any motion alike, and in the apparent motions of all the planets, would be notably detected — so that with few motions [the appearances to the heavenly bodies], necessary in nature, were conveniently satisfied. And therefore the motion of the centre of the great orb pertains not only to the Sun and the planets surrounding the same, but also to the passions of the Moon. For just as Ptolemy set the greatest distance of the Sun from the earth to be 1210 parts, of such as is that which [goes] from the centre of the earth into A, and the axis of their shadow 268, so D. Teacher demonstrates that in our age the same greatest elongation of the Sun from the earth is 1179 parts, and the axis of the shadow-cone 265. But the other things, how they cohere with the motions and passions of each luminary, to be weighed because of the changed hypotheses, I have thought should be reserved to follow in this Second Narration.

[margin: Altera pars hypotheseon de motibus quinq́ue planetarum.]

DVm verò dignum admiratione hanc nouarum hypothesium D. Præceptoris mei fabricam animo mecum reputo, sæpiùs mihi, doctissime D. Schonere, Platonici illius in mentem venit, qui postquam offendit, quid in Astronomo requiratur, subiicit denique, οὐ τῶν εἰ ϕαεινῶν τι, ἀ ϕαεσι ϕῶντι λόγωι ϕιλοσοϕῶν δουριμένος εἶναι χρῆσαι: Cum autem apud te anno superiori essem, atque in emendatione motuum Regiomontani nostri, tuos, & aliorum doctorum Virorum labores viderem, intelligere primùm incipiebam, quale opus, quantúsque labor esset futurus, antequam Reginam Mathematicam Astronomiam, et digna erat, in Regiam suam reduceret, formámque Imperij ipsius restitueret. Verùm cum, Deo ita volente, spectator ac testis talium laborum esse adsim, animo & destinet, & magna ex parte superauisti iam, D. Doctor Præceptori meo sim factus, me nec vmbram quidem tantæ molis laborij somniasse video. Et tantum tam hæc laborum moles , vt non cuiusuis sit Herois, eandem ferre poteris, & superare deniq́;. Quibus de causis, ego quidem Veteres memoriæ prodidisse crediderim, Herculem Ioue summo prognatum, coelum, postquam suis amplius diffideret, & Atlanti iterum imposuisse, qui

…But while I ponder in my mind, again and again, this admirable fabric of my Teacher's new hypotheses, most learned D. Schöner, there comes to my mind that saying of Plato's, who, after he has shown what is required in an Astronomer, finally adds: [Greek: "one must not (be one) of those who philosophize without proof concerning the phenomena, but be made [a knower] of these things"]. But when I was with you last year, and was seeing your labours, and those of other learned Men, in the correction of the motions of our Regiomontanus, I began first to understand what a work, and how great a labour, it was going to be before one might lead back the Queen Mathematic, Astronomy — as she deserved — into her own Royal seat, and restore the form of her own Empire. But since, God so willing, I am present as spectator and witness of such labours, and you both purpose [it] in mind, and have in great part already surpassed [it], D. Doctor, having been made [Teacher] to my Teacher, I see that I have not even dreamed of the shadow of so great a mass of labour. And so great is this mass of labours that it is not for any [common] Hero to be able to bear the same, and at length to surpass it. For which causes, I for my part should believe that the Ancients handed down to memory that Hercules, sprung from highest Jove, when he no longer trusted his own [strength], imposed the heaven again upon Atlas, who

qui ætate longa assuefactus magno animo, infractúsq́ue; virib. vt semel cœperat, hoc onus vsq́ue perferret. Ad hæc Diuinus Plato, sapientiæ, vt inquit Plinius, antistes, haud obscurè in Epinomide pronunciat, ASTRONOMIAM DEO PRÆEVNTE INVENTAM ESSE: Hanc Platonis sententiam alij aliter forsasse interpretentur, ego verò, cum videam D. Doctorem Præceptorum meum observationes omnium ætatum cum suis, ordine ceu in indices collectas, semper in conspectu habere. Deinde cùm aliquid vel constituerit, vel in artem & præcepta conferendum, à primis illis observationibus ad suas vsque progredi, & qua inter se ratione omnia consequentia, perpendere: Porrò quæ inde bona consequentia, Vt utis duæ, collegit, ad Ptolemæi, & Veterum hypotheses reuocare: Et postquam easdem summa cura, perponderans, vrgente astronomicæ δ τις δεσσienda fuerint, neque quidem sine afflatu Diuino, & numine Diuum nouas hypotheses assumere, & mathematica adhibita quidnam ex talibus bona consequentia deduci possit, geometricè constituere: Atq; Veterum denique, hâc bona consequentia, ad astronomiam aptas hypotheses accommodare: Et sic, post istos labores omnes exantlatos, leges Astronomiæ demum constituisse:

…who, accustomed by long age with great spirit, and unbroken in strength, as he had once begun, should bear this burden through to the end. To this the Divine Plato, the high-priest of wisdom, as Pliny says, in the Epinomis announces not obscurely that ASTRONOMY WAS DISCOVERED WITH GOD GOING BEFORE. This sentence of Plato's others may perhaps interpret otherwise; but I, when I see that my Lord Doctor Teacher [Copernicus] keeps ever in view the observations of all ages together with his own, gathered in order as it were into indices: then, when he has either established something, or [something] to be conferred into art and precepts, he proceeds from those first observations down to his own, and weighs by what mutual ratio all the consequences [follow]: furthermore, what good consequences he has thence gathered (so that, as it were, two things) he refers back to the hypotheses of Ptolemy and of the Ancients: and after, weighing the same with the greatest care, the astronomical [things] being pressing — as far as is to be desired — he assumes new hypotheses (and that indeed not without divine inspiration and the will of the gods), and, applying mathematics, establishes geometrically what good consequence can be deduced from such things: and finally accommodates to the astronomy of the Ancients, by this good consequence, fitting hypotheses: and so, after all these labours drawn off [endured], he has at last established the laws of Astronomy:

[margin: Comparatio laborum Astronomicorum: quæ nullus, nisi diuino aditus cæp.: superare valet. Quo ordine Copernicus indaginis suæ rebus progrediendis institutus fuerit.]

Hoc in modum, Platonem intelligendum esse puto, Mathematicum siderum motus perscrutantem, rectissimè, assimulari cæco, cui tantummodò baculo via sit conficienda. Quid fiet? ali quandò in solicitæ incedens, baculo suo viam quæritans, & eidem quandoque desperandus innixus, cœlum, terram, omnésq́; Deos inuocabit, misero sibi auxilio, vt veniant; Hunc permitter quidem eus aliquot annos suas experiri vires, vt intelligat denique, hoc se suo mittimet & instanti periculo se liberari posse, Porrò iamiam animum despondenti, ipsius misertus Deus, manum porrigit, manúq́; ad optatam metam perducet. Baculus Astronomi est ipsa Mathematica, qua viam tentare, & infelicit primùm audet. Quid etenim humani ingenij vires ad diuinas has res, tanquam à nobis dissitas procul, inuestiganda? quid caligantes oculi? Proinde nisi Deus illi pro sua benignitate motus Heroicos indiderit, & tanquam manu, incomprehensibile aliàs rationi humani iter deduxerit, haud crediderim vlla in re Astro-

…In this manner, I think, Plato is to be understood: that the Mathematician scrutinizing the motions of the stars is most rightly likened to a blind man, for whom the way must be made out by a staff alone. What will happen? Sometimes walking in anxiety, seeking his way with his staff, and at times leaning on it as one to be despaired of, he will call upon heaven, earth, and all the Gods, that they may come to wretched himself for help; [Plato] permits him indeed to test his strength for some years, that he may at last understand that he can be freed from this his own and pressing danger; furthermore, when he is now despairing in spirit, God, taking pity on him, stretches out a hand, and with [his] hand will lead him to the wished-for goal. The Astronomer's staff is Mathematics itself, by which he dares to attempt the way, and at first unsuccessfully. For what are the powers of human wit to investigate these divine things, as if set far off from us? what the dimmed eyes? Accordingly, unless God in his kindness has put Heroic motions into him, and, as it were by the hand, has led down the path otherwise incomprehensible to human reason, I should hardly believe that in any matter of Astro-

[margin: Per vnã Orbem magnã apparentia, & planetarum quin alia Sol habent, demonstrá-ria. Catura ipsi propria sunt.]

Astronomum cæco illo præstantiorem esse, & feliciorem esse, præterquam quòd suo ingenio aliquando fidens, & suo illo baculo diuinos exhibens motus, ipsam Vraniam ab Inseris reuocatam sibi congratulabitur; Vbi autem rem secum recta reputarit vis, se non bertiorem Orpheo esse sentiet, qui quidem animo suam sequi cernebat, cum ex Orco satabundus ascenderet, post verò, vt ad ora Auerni fuit peruentum, quam maximè habere se sperabat, ex oculis iterum ad inferos delapsa euanuit.

…the Astronomer is more excellent than that blind man, and more fortunate, except that, trusting sometimes in his own wit, and displaying divine motions with that staff of his, he will congratulate himself that Urania herself has been recalled to him from the Shades; but when he reckons the matter rightly with himself, he will feel that he is no luckier than Orpheus, who indeed saw in his mind [her] following, when from Orcus he was ascending [content], but afterward, when he had come to the mouth of Avernus, [her] whom he most hoped to keep, slipping again to the lower world, vanished from his eyes.

[margin: Occultatio. Eccles. 3. Veterum hypotheses quo modo, & qua occasione.]

Perpendamus itaq́ue, vt incepimus, & in reliquis planetis D. Doctoris Præceptoris mei hypotheses, vt videamus, an constanti animo, & Deo præeunte, Vraniá ad superos perduxerit, suæq́; dignitati restituerit. Posset quispiam fortasse, ea, quæ de motu terræ circa Solis, Lunæq́; apparentes motus dicuntur, eludere, quanquam non video, quomodo præcessionis rationem ad Stellarum transtulerit: reliquorum profecto planetarum apparentes motus, ita aut ad principalem Astronomiæ finem, & systematis orbium rationem ac consensum, aut ad facilitatem suauitatémque vndique causis apparentium elucentibus, respicere quis velit, nullis alijs assumptis hypothesibus, commodiùs, ac rectiùs demonstrauerit: adeò omnia hæc tanquam aureâ catenâ, inter se pulcherrimè colligata esse apparent; & planetarum quilibet sui in positione, & suoq́; ordine, in medij effectu suâ diuersitate semper motum statur, & eos pro diuerso globi terra, vel adhærentus, sitúq́; eredere diuersi modo eius motibus pro propriis diuagari. Et quidem si vis quam alibi & si videre, quomodo Deus mundum nostris disputationibus reliquerit, hoc certè loco, vt quod maximè, est conspicuum. Neq; verò quenquam mouere hoc poste arbitror, quòd Deus Ptolemæum, & alios item præstantes Heroas hac in parte dissentire patiatur, cum non sit hæc ex æquali opinionum genere, quas Socrates in Georgia hominibus perniciosas dicit: neque vllam hinc aut ipsam in inferioribus per librationum motum. Hoc, vt suæ contemplationis quietem teneudum. Hic, vt sane proranum genere, quodam tepidum tribuebant ad Solem habere comprehendebant, propter ipsumque epicyclus tribuebant. Deinde cùm in ijsdem planetis reliquam apparentem inæqualitatem minimè sola eccentrici ratione fieri perspicerent, ad imitationem hypothesium

…that the Astronomer is more excellent and more fortunate than that blind man… Let us therefore weigh, as we have begun, in the rest of the planets also the hypotheses of my Lord Doctor Teacher, that we may see whether with constant mind, and God going before, he has led Urania up to the higher world and restored her to her dignity. Someone perhaps might evade those things which are said about the motion of the earth around the apparent motions of the Sun and the Moon, although I do not see how he transferred the rationale of precession to the [fixed] Stars: as for the apparent motions of the rest of the planets, surely no one would, having assumed no other hypotheses, more conveniently and rightly have demonstrated [them] — whether one wish to look to the principal end of Astronomy and to the rationale and consensus of the system of the orbs, or to the ease and pleasantness, the causes of the appearances shining out on every side: so much do all these things appear bound together among themselves most beautifully, as by a golden chain; and each of the planets, in its position and in its own order, always stands [in] its motion by its own diversity in the mean effect, and [we should] believe them, for the diverse [position] of the earthly globe, or by adhering [to it] and by situation, to wander variously by its motions in their own proper [ways]. And indeed, if you would see, as nowhere else, how God has left the world to our disputations, certainly in this place [it] is, as much as may be, conspicuous. Nor do I think this ought to move anyone, that God allows Ptolemy and other likewise excellent Heroes to dissent in this part, since this is not from that equal kind of opinions which Socrates in the Gorgias calls pernicious to men… [the older astronomers] in the same manner attributed a certain [warmth] to have [a relation] toward the Sun, and on that account assigned epicycles. Then, since in the same planets they perceived the remaining apparent inequality least of all to be produced by the eccentric ratio alone, [they came] to the imitation of [other] hypotheses

thesium Veneris, cum experientia & observationibus consentiret, talem quoq́; secundæ apparentis inæqualitatis rationem assumendam putauerunt, qualem ex demonstrationibus Venerem habere concludebant: vt nempe, quemadmodùm Venerem hîc planetæ æ centrum epicycli, æquidistanter quidem centro eccentrici moueretur, sed æqualitatem motus, respectu centri æquantis puncti, vt quod punctum ipse quoq́ue planeta æ in epicyclo ad apogio modò discedens, perigio in epicyclo motu suas reuolutiones conficeret, ratione autem centri medio Solis motu incederet: ita illâ contrà in epicyclo Solem respicerent, in eccentrico verò peculiaribus ferrentur motibus, ipsæ observationes, vt constituerent, exigebant, dum terram in vniuersi medio collocare quiescentem nitebantur. At præter ea, quæ ad Veneris apparentes motus salvandos competere iudicauerunt, Mercurij theoria aliam insuper æquantis locum, & quod ipsum centrum, à quo ipsius æ esset æquidistantia, in paruo circumuoluetur circulo, recipiendum duxerunt.

…of Venus, since it agreed with experience and observations, they thought such a rationale of the second apparent inequality also was to be assumed as they concluded Venus to have from the demonstrations: namely that, just as here in Venus the centre of the planet's epicycle was moved equidistantly indeed from the centre of the eccentric, but [had] the equality of its motion with respect to the centre of the equant-point — as which point the planet itself also, departing in the epicycle now from the apogee, [and] at perigee, by its motion in the epicycle would complete its revolutions, but by reason of the centre would advance with the mean motion of the Sun — so on the contrary [the others] in the epicycle would look toward the Sun, but in the eccentric would be carried by peculiar motions: the observations themselves required, in order that they might establish [this], while they strove to place the earth at rest in the middle of the universe. But besides those things which they judged sufficient for saving the apparent motions of Venus, the theory of Mercury [required] yet another place of the equant, and that the very centre, from which there was the equidistance of its [epicycle], should be revolved in a small circle, [which] they thought must be admitted.

[margin: Defectus antiquarum hypothesium, in motu longitudinis. Defectus earundem in motu latitudinis.]

Hæc acutè sanè, vt Veterum pleraq́; omnia sunt inuenta, satísq́; concinna mouebat, & apparentijs, si orbes cœlestes inæqualitatem habere super propriis centris, à quo tamen natura abhorret, admittamus, primámq́; & maximè notabilem diuersitatem apparentis motus quinq́; planetarum, ipsis cum eadem in iis per accidens appareret motum, tanquam planetarum tribuamus. In salutaribus autem planetarum & illud quoq́; δ τις λόγος ἀνώμαλος videntur, quòd nempe omnes motus corporum cœlestium sui circulares sint, aut ex circularibus componantur: nisi fortè quòd ipsam Veneris, & Mercurij reflexiones declinationésq́;, quemadmodu paulò antè de motu declinationis terræ est dictu, fieri intelligi velit, & declinationes epicyclorum in tribus superioribus, ac deuiationes in reflexionibus, & declinationibus Veneris & Mercurij, siquidem eorum inclinationum anguli, planorum verò ad epicyclorum in inferioribus per librationem motum. Hoc, vt suæ concedatur in reflexionibus, & declinationibus Veneris & Mercurij, siquidem reflexionibus tamen epicyclorum in tribus superioribus, & deuiationes Veneris, ac Mercurij per librationes fieri communis calculus refutat. Vt namque de Deuiationi-

…These things, very acutely indeed (as nearly all the discoveries of the Ancients are), and elegantly enough, [the matter] moved, [and agreed] with the appearances — if we admit the celestial orbs to have an inequality upon their own centres (from which nevertheless nature shrinks) — and [if] we should attribute, as [belonging] to the planets, the first and most notable diversity of the apparent motion of the five planets, since the same thing appeared in them by accident as a motion. But in the saving [of the motions] of the planets that too [is opposed by] a certain irregular reckoning [Greek: a discordant ratio], namely that all the motions of the celestial bodies should be of themselves circular, or compounded of circulars: unless perhaps he wishes it to be understood that the reflexions and declinations of Venus and Mercury themselves come about (as was said a little before about the declination-motion of the earth), and the declinations of the epicycles in the three superior [planets], and the deviations in the reflexions and declinations of Venus and Mercury — if indeed [there are] angles of their inclinations, but of the planes toward [those] of the epicycles in the lower [ones] through the libration-motion. [But] that the [things] in the reflexions and declinations of Venus and Mercury be conceded — if indeed nevertheless [it be] of the reflexions of the epicycles in the three superior [planets], and that the deviations of Venus and Mercury come about through librations — the common calculus refutes. For as concerning the Deviations

[margin: Lib.13. prop.21. opst. in Almag. Ptol. — Quid Rheticus facturus fuisset, si illa Dei Geometriam fecisset, idum.s. Copera regularia, de quibus M. Keplerum disserit, animaduertisset. — Per vnã Orbem magnã apparentia, & planetarum quin alia Sol habent, demonstrá-ria. Catura ipsi propria sunt.]

tantùm dicã, quia minutâ proportionalia, quibus deuiationes pro locis centri epicycli extra nodos, & absidas ratiocinamur, eadem ratione indagaruis, & constitueruntur, qua in primi motus doctrina partium epicyclice declinatione inuestigantur: hîc, vt in sexagesimo gradu ab aliqua absidum eccentrici, centro quidem epicycli Venere existente, colligamus deuiationem 5. minutorum, Mercurij autem 12. min. cùm dimidio. Quòd si deferens poneretur per librationes deuiare, in tali Veneris epicycli situ vera ratio nõ vltra 2. & semis min. deuiationem, Mercurij verò 11. minu. cum quadrante exposcere. In illius enim centri epicycli situ, angulus inclinationis plani eccentriciâ ecliptica, non maior, ſ. minu. in huius verò ø2. & semis. ex librationum proprietate motus, reperiremur. Atq; ideo fortasse Ioannes de Regiomonte monendos studiosos putauit, æ quæ causæ τῶν φαινομένων sint adstructæ, atque, cum à Cimmerijs tenebris, inuolutæ, quod ipse etiã Ptolemæus nobis cum restatur. Verùm rem plura de Veterum in quinq; planetis hypothesibus, quàm fortè ipsa nouarum (vt sic dicam) hypothesium cum enumeratio, tum ad Veteris collatio requirit, non adducam. Ptolemæum equidem, & qui cum sequuntur, æquè atque D. Præceptorem ex animo amo: Siquidem verò sanctum illud Aristotelis præceptum semper in conspectu, æ memoria habeo φίλος γ' ἀφφότερω, πρὸ τιμᾶ ἢ τῆς ἀληθείας. Et hîc nescio quomodo, me tamen magis ad D. Præceptoris hypotheses inclinari sentio. Id quod fit fortasse partim, quia tam demum verè partim me intelligere animum induco, quasi vltimam hypothesium, quòd Platoni de gravitatem ac veritatem tribuitur, Τὸ Θεὸν δεῖ ϕύσει μετρεῖν partim verò, quòd in D. Præceptoris Astronomiæ instauratione, eo caligine discussa, aperto nunc cœlo, & ambobus, vt dici Solet, oculis, viam sapientissimi dicti illius Socratis in Phædro, intuear. Ἑαντὶ τινα ἄλλον ὑπότοιαι ἥυπικτὰς οἷς ἂν ἢ ἢ ι ϕιλὲλ ἀ μεγαλὰ τὰ μάλιστα ἔρης, τοῦ. τον δίκαιον κατὸ ϕιὸ ἢ μετ' ἥχτερ ἥχειν δέως. His itaque, quæ de terra motu librationes dicta fuit à D. Præceptore meo confirmatis, sequitur (sicut in causis renouandarum hypothesium retulimus) vt omnis diuersitas apparentis motus pla-

…I shall only say this, that by the small proportionals by which we reckon the deviations for the places of the epicycle's centre outside the nodes and the apsides, [these] were investigated and established by the same reasoning by which, in the doctrine of the first motion, the parts are investigated by the epicyclic declination: here, that at the sixtieth degree from some apsis of the eccentric, the centre of the epicycle of Venus existing [there], we gather a deviation of 5 minutes, but of Mercury 12 and a half minutes. But if the deferent were posited to deviate through librations, in such a situation of Venus's epicycle the true reckoning would demand a deviation of not beyond 2½ minutes, but of Mercury 11¼ minutes. For in the situation of that epicycle-centre, the angle of inclination of the plane of the eccentric to the ecliptic [would be] not greater, [some] minutes; but in this latter [case] 2½, from the property of the librations of the motion, we should find. And therefore perhaps John of Königsberg [Regiomontanus] thought the students should be warned what causes of [the appearances] are built up, and, since wrapped in Cimmerian darkness — as even Ptolemy himself attests to us. But I shall not bring forward more about the Ancients' hypotheses in the five planets than perhaps the enumeration of the new (so to speak) hypotheses, and the comparison with the Old, requires. Ptolemy indeed, and those who follow him, I love from my heart equally with my Teacher [Copernicus]: yet since I always have before my eyes and in memory that holy precept of Aristotle, [Greek: "[Plato is] a friend, but truth more so" — friends both, but truth is to be honoured before [them]]. And here, I know not how, I feel myself nevertheless inclined more toward my Teacher's hypotheses. Which happens perhaps partly because at last I induce my mind to understand truly, in part, [it] as the ultimate of hypotheses — which is attributed to Plato concerning weight and truth, [Greek: "God must measure by nature"] — but partly because in my Lord Teacher's restoration of Astronomy, the darkness having been dispelled, with the heaven now open, and (as is commonly said) with both eyes, I behold the way of that most wise saying of Socrates in the Phaedrus: [Greek: "whoever sees some other [man able to look] toward [things], whatsoever are one and many by nature… him [it is] just to follow after, as a god"]. These things therefore, which were said by my Teacher about the librations from the motion of the earth, being confirmed, it follows (as we have related among the causes of the hypotheses to be renewed) that all the diversity of the apparent motion of the pla-

netarum, quæ in eis [Greek: παρὰ τὸν πρὸς τὸν ἥλιον σχηματισμὸν] contingere videatur, propter annuum terræ motum in orbe magno fiat: vtq́; planetæ reuera sola adhuc altera inæqualitate, quæ penes zodiaci partes obseruatur, incedant. Quamobrem eis æ hypotheses tantùm, quibus duæ diuersitates motus demonstrari possunt, opus est. Quemadmodum autem in Luna D. Præceptor maluit epicyclo epicycli vni, ita in tribus quidem superioribus planetis, & ordinem, & motus commensurabilem commodiùs demonstrandam eccentr̃epicyclos elegit, in Venere verò, & Mercurio eccentri eccentricos.

…of the planets, which seems to come about in them [Greek: by reason of the configuration with respect to the Sun], comes about on account of the annual motion of the earth in the great orb: and so that the planets in reality move only by the one [other] inequality still, which is observed throughout the parts of the zodiac. Wherefore for them only such hypotheses are needed by which the two diversities of motion can be demonstrated. But just as in the case of the Moon my Teacher preferred a single epicycle-upon-epicycle, so for the three superior planets he chose eccentric-bearing-epicycles, the more conveniently to demonstrate both the order and the commensurable motion; but for Venus and Mercury, eccentric-upon-eccentrics.

[margin: NB. Hæ triplices hypotheses, & duorum epicyclorum, & eccentrici epicyclorum, tum confer in indifferenter vel duæ commodiores, & in anomalia, simul ac, motus demonstrandi, vis licet.]

Cum autem nos veluti ex terra centro trium superiorum suspicimus, & orbium planetarum centra à terra ferrentur, à quo deinde ad ipsum terræ centrum motus omnésq́ue apparentias, fiat: deinde quàm illud æquidistanter intra nos intueamur, consentanea erat, vt ad orbis magni, orbium planetarum centra à terra rectissimè transferamus. Quare & in quinque planetis eccentricum illum intelligi oportet, cuius centrum à terra centrum orbis magni est.

…But since we, as it were from the earth's centre, look up at the three superior [planets], and the centres of the planets' orbs are borne from the earth — from which then to the earth's very centre the motion and all the appearances come about — then, that we may regard that [centre] equidistantly within us, it was consistent that we transfer the centres of the planets' orbs from the earth to [the centre] of the great orb most rightly. Wherefore in the five planets also that eccentric must be understood whose centre, [reckoned] from the earth, is the centre of the great orb.

[margin: Ratio,quare Copernicus eccentri colligata sit, & Orbis magni eccentricum esse plánetarum eccentrici centrum. Mundi centrum, ad Orbis magni centrum referatur.]

Verùm vt rectiùs intelligatur nouarum hypothesium constituendarum ratio, omnia deniq́ue epicyclos magis magisq́; in aperto sint, ponamus principio quinque planetarum plana eccentricorum esse in ecliptica plano, & centra deferentium, & æquanti ecliptici plano, & centra deferentium æquantium, in partes quatuor æquales diuidantur. Porrò cuiuslibet quidem trium superiorum centri eccentrici à terra magni centro apogii versum eleuetur ad extensione quartæ residuæ, in eccentri ci circumferentia epicyclus describatur, & apparebit fabricæ huius parui circuli ratio prout antedicta. Si itaque ex D. Præceptoris tabulis prosthaphæreseon planetarum habetur.

…But that the rationale of constituting the new hypotheses may be more rightly understood, [and that] all the epicycles at last may be more and more in the open, let us posit at the outset that the planes of the eccentrics of the five planets are in the plane of the ecliptic, and the centres of the deferents, and [those] of the equant in the ecliptic plane; and let the centres of the equant-deferents be divided into four equal parts. Furthermore let the eccentric centre of any of the three superior [planets] be raised from the earth, [reckoned] from the great centre, toward the apogee by the extension of the residual quarter, [and] in the circumference of the eccentric let an epicycle be described, and the rationale of this small circle's fabric will appear as aforesaid. And so, if from my Teacher's tables of the planets' prosthaphaereses [it] is had…

[margin: Orbes & motus suorum planetæ. Vide infrà in Appendice.]

D. Præceptoris tabulis prosthaphæreseon planetarum habetur, planeta à prima stella Arietis in 57. grad 50. min. loco apogij apparentis, & 237. grad: 50. min. ita in loco peculiaris diametri parui circuli eam, quæ ex centro orbis sui, esset. Atque hæc est causa, planeta in huius epicycli circumferentia parte superiori in consequentia procedat, in inferiori in antecedentia ita procedat, vt centro epicycli existente in apogio eccentrici, ipse planeta in perigio sui epicycli reperiatur: & è contrà centro epicycli perigio mota nte, planeta epicy-

…it is had from my Teacher's tables of the planets' prosthaphaereses [that] the planet [is] from the first star of Aries at 57 degrees 50 minutes, at the apparent place of the apogee, and 237 degrees 50 minutes; thus in the place of the peculiar diameter of the small circle, that which would be from the centre of its own orb. And this is the cause [why] the planet, in the upper part of this epicycle's circumference, proceeds in the direction of the [signs]' succession, but in the lower part proceeds in the opposite direction, so that, the epicycle's centre being at the apogee of the eccentric, the planet itself is found at the perigee of its own epicycle: and on the contrary, the centre of the epicycle being moved at perigee, the planet [is at the apogee] of the epicycle…

clo epicycli apogium obtinear: atq; hac motuum similitudine planetæ in epicyclo, cum centro epicycli in eccentrico pati temporis suas periodos absoluat: clarum est, sublatis æquantibus superiorum planetarum, diuersitatem motus, respectu centri orbis magni, regularem esse, & ex æqualibus componi, Epicyclus namq; tali ratione assumptus, in munus æquantis succedit, & eccentricus super suum centrum, ac planeta in epicyclo ad centrum epicycli, cui inhæret, æquali tempore, æquales designat angulos.

…it obtains the apogee of the epicycle: and with this similitude of motions of the planet in the epicycle, while it completes its periods together with the centre of the epicycle in the eccentric in [its] time: it is clear that, the equants of the superior planets being removed, the diversity of motion, with respect to the centre of the great orb, is regular, and is compounded of equal [parts]; for the epicycle assumed by such a reasoning succeeds to the office of the equant, and the eccentric upon its own centre, and the planet in the epicycle toward the centre of the epicycle to which it adheres, in equal time, mark out equal angles.

[margin: Orbis & motus Veneris. Orbis & motus Mercurij.]

Veneris autem motus sic constabit, reiecto deferente, cuius vicem orbis magnus supplet, circa tertiam sectionem, extensione quartæ residuæ describatur paruus circulus. Deinde centrum epicycli Veneris, qui hîc eccentricus eccentrici eccentricus secundus, & mobilis vocabitur, in circumferentia dicti parui circuli tali motu lege, vt quoties terræ centrum in absidum lineam inciderit, ipsum centrum eccentrici in puncto parui circuli, centro orbis magni proximo existat: terra autem mediâ suâ in orbe inter vtranq́; absida, ipsum centrum eccentrici Veneris in puncto parui circuli à centro orbis magni remotissimo subsistat, atque ad easdem partes in signorum consequentiam, quemadmodum & terra moueatur, dúas terram, vt ex his sequitur, reuolutiones in vna terræ circuitione peragens.

…But the motion of Venus will stand thus: the deferent being rejected (whose part the great orb supplies), about the third section, by the extension of the residual quarter let a small circle be described. Then let the centre of Venus's epicycle (which here will be called the second and mobile eccentric of an eccentric) [move] in the circumference of the said small circle by such a law of motion that, as often as the earth's centre falls upon the line of the apsides, the very centre of the eccentric exists at the point of the small circle nearest the centre of the great orb: but the earth, by its mean [motion] in its orb between both apsides, the very centre of Venus's eccentric subsists at the point of the small circle most remote from the centre of the great orb, and moves toward the same parts in the succession of the signs, just as the earth too moves — performing, as follows from these things, two of its revolutions in one circuit of the earth.

Sed Mercurij motuum ratio insenere quidem, cum Veneris theoria conuenit, recepto insuper epicyclo, cuiusipse diametrum per librationem describat, propter diuersitatem reliquam. Cæterùm vt se ad terræ motum accommodet, recipit æqualitatem eius, quæ ex centro deferentis mobilis 3573. partium, quantitatem eius, quæ ex centro parui circuli mobile deferentis centrum continens 211. part. atque diametrum dicti epicycli 380. partium, qualium ea quæ ex centro orbis magni ad centrum terræ est 10000. In mutationem talem hîc accidere, qualem in Venere contingebat, longissimè absidum orbis magni centro distet, terrám absidum planetæ existente: & ad maximam propinquitatem accedat, terrá ad absidibus planetæ remota. Epicyclum, vt patet, fixum habebit, cuius diametrum respicientem centrum

…But the rationale of Mercury's motions, indeed [insofar as it can be], agrees with the theory of Venus, an epicycle being moreover received, whose own diameter [the planet] describes through libration, on account of the remaining diversity. But, that it may accommodate itself to the earth's motion, it takes the equality of that which from the centre of the mobile deferent [is] 3573 parts, the quantity of that which from the centre of the small circle, containing the centre of the mobile deferent, 211 parts; and the diameter of the said epicycle 380 parts, of such as that which from the centre of the great orb to the centre of the earth is 10000. [So that] such a change happens here as was occurring in Venus: [that] it is distant by the longest [interval] of the apsides from the centre of the great orb, with the earth at the apsides of the planet; and that it approaches the greatest nearness, with the earth removed from the apsides of the planet. The epicycle, as is plain, it will have fixed, whose diameter looking toward the centre…

trum deferentis mobilis, ipse planeta motu librationis reptando in lineam rectam describit, hac lege seruata, vt cum centrum eccentrici mobilis in maxima à centro orbis magni distantia fuerit, quod est inferior terminus diametri parui circuli, quam describit: Vice verò reliquum terminum, qui apogium dici poterat, cum idem centrum eccentrici mobilis proximum centro orbis magni fuerit. Motus autem absidum planetarum, quemadmodùm & alia quædam aliis reseruantur Narrationi.

…of the mobile deferent, the planet itself, creeping by the libration-motion, describes in a straight line, this law being preserved: that when the centre of the mobile eccentric is at the greatest distance from the centre of the great orb, which is the lower terminus of the diameter of the small circle which it describes: and contrariwise [at] the remaining terminus, which might be called the apogee, when the same centre of the mobile eccentric is nearest to the centre of the great orb. But the motions of the apsides of the planets, just as certain other things too, are reserved for the [Second] Narration.

[margin: Quomodo veri motus ad centrum absidum referuntur. Vide infrà in Appendice.]

HÆc est tota ferè hypothesium ratio, ad omnem propriam diuersitatem motus planetarum, secundùm longitudinem saluandam. Quapropter si oculus noster in centro orbis magni existeret, radij visuales ex eo per planetas, ceu lineæ verorum motuum in stellarum sphæram erectæ, à prima stella Arietis non aliter in ecliptica circumducerentur, quàm dictorum circulorum, & motuum rationes exigerent, vt propriæ eorum diuersitates motuum in zodiaco osten- derent. Verùm quia nos terræ incolæ, ex ea cœlestium apparentem motus contemplamur, ideo verùm tanquam ad puncta, intimúmq́; domicilij nostri omnes motus, apparentiásq́; referimus, eductis ex eo per planetas lineis, veluti oculo in orbis magni centro, in terræ centrum translato: omnium inde, vt à nobis quidem videntur, verarum & propriarum diuersitates motus planetarum, si esset animus colligere, & ad lineas ex centro orbis magni, si fieri posset, eius causes efficiendum fore.

…This is nearly the whole rationale of the hypotheses, for saving every proper diversity of the planets' motion according to longitude. Wherefore, if our eye were placed at the centre of the great orb, the visual rays from it through the planets, as lines of the true motions erected into the sphere of the [fixed] stars, would be led round in the ecliptic from the first star of Aries no otherwise than the rationale of the said circles and motions would require, so that they would show the proper diversities of their motions in the zodiac. But because we, the earth's inhabitants, contemplate from it the apparent motion of the celestial [bodies], therefore we refer all the motions and appearances, as it were to a point, the innermost [seat] of our dwelling, lines being drawn out from it through the planets, as if the eye, [reckoned] in the centre of the great orb, were translated to the centre of the earth: and thence (as they are seen by us at least) the diversities of the true and proper motion of the planets, if [one] had a mind to gather [them], and [to refer them] to lines from the centre of the great orb, if it could be done, would be its causes to be effected.

[margin: Motus planetarum apparentium ad centrum orbis magni. post ad ipsa planetas.]

Veruntamen quò expeditiùs nos ex ijs, quæ porrò restant enumeranda à τοῖς φαινομένοις planetarum explicemus, totáq́; tractatio facilior, & suauior existat, concipiantur sane animo non tantum lineæ verorum apparentium motuum ex centro terræ per planetas in eclipticam, quas propterea perducens, sed etiam ex centro orbis magni, ideoq́; propriè diuersitatis motus lineæ dictæ. Incedente itaque terra motu diurno, ipsa veri motus lineæ à dictarum vbi eò peruenerint, vt ipsa in eadem linea reciderint Solem, & aliquem ex tribus superioribus planetis interponatur, planeta quidem vespertino eo ortu oriri videbitur: Et quia terræ sic fità ipsâ proximâ via, & Veteres posuerunt planetam vità eccentricorum

…Nevertheless, that we may the more readily explain from those things which further remain to be enumerated [the appearances] of the planets, and the whole treatment may be easier and more pleasant, let there be conceived in the mind not only the lines of the true apparent motions from the centre of the earth through the planets into the ecliptic, which I therefore lead through, but also [the lines] from the centre of the great orb, and thus the lines of the proper diversity of motion. As the earth therefore advances with its diurnal [annual] motion, the very lines of the true motion from the said [ones], when they have come to [the point] where it [the earth] has fallen back upon the same line [as] the Sun, and some one of the three superior planets is interposed, the planet will seem to rise at its evening rising: and because the earth thus [is] by its very nearest path, the Ancients too placed the planet by the [path] of the eccentrics…

propinquante ad lineam veri & apparentis loci planetæ, quod sit terra perueniente ad oppositum iam dicti loci: planeta vespertino occasu disparere incipiet, maximéq́; à terra elongari, quoad linea veri loci planetæ etiam per centrum Solis transeat, atque Sole inter planetam & terram interueniente, planeta occultetur; à quo deinde occultatione propter perpetuum terræ motum, quia linea veri loci Solis, à linea veri loci planetæ discedit, planeta iterum matutino ortu, vbi quantum arcus visionis requirit, iustam à Sole distantiam nactus fuerit, oriri conspicitur.

…approaching the line of the true and apparent place of the planet — which happens when the earth comes to the point opposite the said place: the planet will begin to disappear at its evening setting, and to be most greatly elongated from the earth, until the line of the planet's true place passes also through the centre of the Sun, and with the Sun intervening between the planet and the earth, the planet is occulted; from which occultation thereafter, on account of the perpetual motion of the earth, because the line of the Sun's true place departs from the line of the planet's true place, the planet is again seen to rise at its morning rising, when it has gained a just distance from the Sun, as much as the arc of vision requires.

[margin: Descriptio apogæi medij & veri in epicyclo veterum, & in orbe magno harum hypotheseon. Modus Directionis, Stationis, & Retrogradationis Planetarum. De his vide cap. 18. Prodromi suprà pag. 28. & tabulas pag. 78. vt cum infra in appendice.]

Porrò quoniam orbis magnus in horum trium planetarum hypothesibus, munere epicycli à Veteribus cuilibet planetarum attributi fungitur: in diametro orbis magni, ad planetam vsque continuata, apogium perigiúmq́; planetæ verum respectu orbis magni reperitur. Apogium autem, & perigium medij, in diametro orbis magni, quæ lineæ ex centro eccentrici in centrum epicycli protractæ æquidistanter mouetur, & cum terra in mediastate verius planetam. ipsi planetæ apropinquet in reliqua & opposita remouentur, illic quidem extremitates diametrorum orbis magni perigia referent. hîc verò apogia, cum illa medietas in locum inferioris epicycli partis succedat, hîc autem superioris.

…Furthermore, since the great orb in the hypotheses of these three planets performs the office of the epicycle attributed by the Ancients to each of the planets: in the diameter of the great orb, continued as far as the planet, the true apogee and perigee of the planet with respect to the great orb is found. But the apogee and perigee of the mean [motion], in the diameter of the great orb (which is moved equidistantly [along] the lines drawn from the centre of the eccentric into the centre of the epicycle), and when the earth [is] in [its] midmost [position more toward] the planet, [when] it approaches the planet itself, in the remaining and opposite [position] they are removed: there indeed the extremities of the diameters of the great orb refer the perigees, but here the apogees, since that mid-portion succeeds into the place of the lower part of the epicycle, but here of the upper.

FAcesse haud longè à Solis, & planetæ coniunctione, fit terræ centrum in planetæ apogij loco vero, respectu (scilicet orbis magni, ipsáq́; lineâ propriæ diuersitatis cum apparenti loci lineâ planetæ coincidat. Ab hoc autem loco terra non modo perigium, lineæ propriæ diuersitatis, & lineæ veri loci planetæ, sese in corpore planetæ interiectae incipient, altera regulari suo motu diuersio in signorum consequentiam perget, altera verò ab eadem sese reficitens, reficitens nobis planetam velocius in ecliptica incedens, quoad rursus à terra motu proprio procedat. Verùm terra perueniente ad oppositionem orbis magni planeti proprionem, hæc & vestigio in antecedentia sese conuertit, vt apparens planeta proprionem orbis subinde tardior videatur. Amplius quia terra versus planetam ascendit, ipsa veri motus Solis lineá à planetæ promouebitur; ac planeta ad nos accedere, veluti de parte superiori descendens æstimabitur. Tam diu autem planeta directus videbitur, quousq́; terræ

…Far off (not far from the conjunction of the Sun and the planet), the earth's centre comes to be in the true place of the planet's apogee, with respect (namely) to the great orb, and the line of [its] proper diversity coincides with the line of the planet's apparent place. But from this place the earth, not only [at] perigee, the line of proper diversity and the line of the planet's true place will begin [to be] interposed in the body of the planet; the one by its regular motion will go on diversely in the succession of the signs, but the other, turning itself back from the same, [shows] the planet to us advancing more swiftly in the ecliptic, until again it proceeds from the earth by its proper motion. But when the earth comes to the opposition of the great orb [to] the planet's [advance], this [line] forthwith turns itself into the antecedent [direction], so that the apparent planet seems thereafter slower in [its] proper [motion] of the orb. Further, because the earth ascends toward the planet, the very line of the Sun's true motion is promoted from the planet; and the planet will be reckoned to approach us, as it were descending from the upper part. But so long will the planet seem direct, until the earth's…

terræ centrum ad eum orbis magni & planetam, situm peruenerit, vbi angulus diurnus reflexionis lineæ veri loci planetæ in antecedentia, æqualis exsitat angulo diurno propriæ diuersitatis: Ibi namque duobus sē perimentibus motibus planeta statione prima per aliquot dies, in pro ratione orbis magni ad centrum planetæ propsisi, ipsiusq́; planetæ in suo de situm, propriáq́ue motus sui velocitate stare apparebit. Porrò ab hoc loco terra sic conficiet, vt si fità ipsâ planetæ propinquitatem accedat, vbi planeta veterum proprium motum superare, idq́ue eo vsq́;, vt cum perigium verum diametri respectu orbis magni & terræ proximus consistet. Quo in illo Marte repertus, præter communem, ratione orbis magni, reflexionem, seu diuersitatem aspectus, etiam aliam insuper (propter perceptibilem quantitatem eius, quæ ex centro terræ ad ipsius distantiam) aspectus diuersitatem admittit, quemadmodum diligens testabitur observatio.

…centre comes to that situation of the great orb and the planet where the diurnal angle of the reflexion of the line of the planet's true place into the antecedent [direction] becomes equal to the diurnal angle of [its] proper diversity: for there, with two motions destroying each other, the planet at its first station for some days, in the ratio of the great orb to the centre of the planet posited, and the planet itself in its [station], will appear to stand with the proper velocity of its own motion. Furthermore, from this place the earth so accomplishes [its path] that, if from itself it approaches the nearness of the planet, where the planet [is seen] to surpass the proper motion of the ancients, and that so far that, [at] the true perigee of the diameter with respect to the great orb and the earth, it stands nearest. In which [position], in that Mars, [is] found — besides the common reflexion (by reason of the great orb), or diversity of aspect — yet another diversity of aspect besides (on account of the perceptible quantity of that which [is] from the centre of the earth to its distance): as diligent observation will attest.

[margin: Nota de Marte. Is terra factus proximus parallaxin admittit, propior enim terra fit, quàm Sol fit.]

Pro confirmatione huius, quæ ex Copernici hypothesi sequitur, longissimè contraria vitatis hypothesibus sentenitia, libet apponere, quæ excellentissimus Nobilis Mathematicus Tycho Beate, Danus, suis experimentis observauit, quibus tanquam à primario in Artifice habetis observationibus hac vtique fidem deogan non potest. In Epistola ad D. Peucerum Anno 1572. data, sic scribit. Constituí periculum facere, qua nam earum, qua hactenus inuenta erant (hypothesibus), Ptolemaicam scilicet, vel Copernicanam à Copernico traditam vel eorum quibus mocosticionem figmentum, conuenientior, veritati propius accederet. Idq́; per Martis prosthaphæreseon stellam æ no abest faciem proxime considerabam, quia, & ad ψ μνομένων appropinquaret. Semin nobis propior accederet, quàm ipse Sol. Copernicanam speculationem prænalere : Sin minus, cum Ptolemaico partim standum arbitrabar. Tandemq́; magna diligentia, nec parvis sumptibus, conquisito varijq́; organa & Astronomica, postea facturum mereri sentiebar, vt non saltem inisse seruajui, sed etiam res dimidia vel quarta parte explorari certo possent, hanc subtilem considerationem aggredi non verebar. Idq́; postissimum Anno 1582. cum Mars pernox factus Soli opponeretur in cancro, & insuper in eorum latitudinem facilimor quotidianum circuitu redderetur. Habebitigitur tum pluribus accuratis observationibus, tam circa intumi medium, mum transitum, deprehendi, Martem maiorem cum causa parallaxin, quàm ipsum Solem, ideóq́; etiam terra propinquiorem, qua nobis verior, fuit; ut ergo, asti pulante vis maior virose situatio, cum Copernicantis potius mouenti coniuncta, in quod paulò celerius certe diuersorum interuallo in antecedentia procedat, quàm Aphoshorum communem & Ptolemæo deducta ratiocinatio: Idq́; ob minorem à terra distantiam, qua motuum pauli intentiorens apparere efficiebat. Id cum is Marti dicas, explorari tum habitum, & idem etiam in Venere…

…In confirmation of this, [namely] of that opinion which follows from Copernicus's hypothesis, most contrary to the avoided [older] hypotheses, it pleases me to set down what that most excellent Noble Mathematician Tycho Brahe the Dane observed by his own experiments — from whom, as from a foremost Artificer in observations had, faith on this point cannot be withheld. In a Letter given to D. Peucer in the year 1572, he writes thus: "I resolved to make a trial which of those [hypotheses] which had hitherto been found — namely the Ptolemaic, or the Copernican handed down by Copernicus, or [that] of those by whose [device] a fiction [is made] — were more agreeable [and] should come nearer to the truth. And [I would do] this through [the observation] of Mars by its prosthaphaereses, the star [being] not far off, [which] I was considering closely, because [it would come near] also to [the appearances]. Whether for us it would come nearer than the Sun himself [I judged that] the Copernican speculation prevailed: if not, I thought one must stand partly with Ptolemy. And at length, with great diligence and no small expense, having procured various Astronomical instruments, I afterward judged it worth my while [to find] that not only [the things] I had begun could be preserved, but that matters could be explored with certainty to a half or a quarter part; [and so] I did not fear to undertake this subtle consideration. And [I did this] especially in the year 1582, when Mars, made [visible] all night, was opposed to the Sun in Cancer, and moreover in its latitude was rendered easier by its daily circuit. I shall therefore have then, by several accurate observations — both about the middle of [its] transit — found that Mars admits a greater parallax, with reason, than the Sun itself, and therefore [is] also nearer to the earth — which to us was the truer; so therefore, the greater [authority] supporting [it], combined rather with the Copernican [view], [shows] that it proceeds somewhat more swiftly in the antecedent [direction] over the interval, than the common reasoning deduced [from] Apheliotes and Ptolemy: and that on account of [its] lesser distance from the earth, which made the motions appear somewhat more intense." When he says this of Mars, [it was] then found explored, and the same also in Venus…

[margin: Argumentú planetæ Copernicus Commutationem vocat. Venus & Mercurius propter orbis magni motum, per Zodiacum, sicut Sol, moveri videntur.]

Venere alliquoties à me interdim, atque in 1556 Meridiano observatum, & iuxta eorundem collatione facta, imò etiam alia quadam peculiari ratione Anno 1587. circa diem 24. Febr. quando intra vmam vel alteram fixam cum vespertinam quam observabam (quod aliàs rarissimum est) vidi, motum apparentem cum eis, qua ratione parallaxeos fierent, conferendo, comprobassem, ita quòd Ptolemaicis hypothesibus hac omnia minimè congruent: impeluisse, vt postmodum magis magisq́; Copernicas inuentioni fidem attribuerem.

…Venus [was] sometimes observed by me at intervals, and in 1556 on the Meridian, and according to a collation made of the same — indeed by a certain other peculiar reasoning in the year 1587 about the 24th day of February, when within one or another fixed [star] together with the evening [Venus] which I was observing (which is otherwise most rare) I saw [it] — having proved the apparent motion with these [stars], by which reasoning the parallaxes were produced, by comparing [them], so that with the Ptolemaic hypotheses all these things were least of all agreeing: [this] impelled [me] thereafter to attribute faith more and more to the Copernican invention.

Postremò, vbi terra ab hac centrali cum planetâ, vt ita dicam, coniunctione in consequentia remouebitur, ipsa reflexio in antecedentia eadem ratione, quæ antè creuerat, minuetur, donec facta denuò motum compensatione, planeta statione secunda stationarius fiat. Postea proprio planetæ motu superante reflexionem, terra procedente dirigatur, quo tandem in directionis loco medio planeta apparet, terra iterum apogium planetæ verum vnde eam deduxiimus, obtineat, omnésq́; iam dictas apparentias ordine in singulis planetis nobis introducat.

…Lastly, when the earth shall be removed in the succession [of the signs] from this central conjunction (so to speak) with the planet, the very reflexion into the antecedent [direction], by the same reasoning by which it had before grown, will be diminished, until, the compensation of motion being made anew, the planet at its second station becomes stationary. Afterward, the planet's proper motion surpassing the reflexion, with the earth proceeding, it is directed, [so] that at last in the mid-place of [its] direction the planet appears, [and] the earth again obtains the true apogee of the planet whence we led it, and introduces to us all the now-said appearances in order in each of the planets.

[margin: Argumentú planetæ Copernicus Commutationem vocat.]

Atque hæc est prima orbis magni, in contemplatione motuum planetarum vtilitas, quà à tribus magnis epicyclis in Saturno, Ioue, & Marte liberamur. Quod autem Veteres Argumentum planetæ dixerunt, hoc D. Præceptor motum Commutationis planetæ vocat, quia per eum apparentias ratione motus terræ in orbe magno contingentem ratiocinamur, quas nihil aliud esse constat respectu à prima stella Arietis in 57. grad 50. min. loco apogij apparentis, quàm parallaxes Lunæ: propter habitudinem eius, quæ ex centro terræ ad eiusdem orbes. Cuiuslibet autem planetæ centri epicycli motus, à terræ motu æquali, qui à Solis motus medius est, subtractus, commutationis motum æqualem relinqui: & numerator ab apogio medio, à quo & terra æqualiter eleuatur, vnde & in prompt cuiuslibet verus & apparens planeta motum in ecliptica ex D. Præceptori tabulis prosthaphæreseum planetarum habetur.

…And this is the first usefulness of the great orb in the contemplation of the planets' motions, by which we are freed from the three great epicycles in Saturn, Jupiter, and Mars. But what the Ancients called the Argument of the planet, this D. Teacher [Copernicus] calls the motion of the Commutation of the planet, because through it we reckon the appearances occurring by reason of the earth's motion in the great orb, which [appearances] it is agreed are nothing other (with respect to the first star of Aries at 57 degrees 50 minutes, at the apparent place of the apogee) than the parallaxes of the Moon: on account of the bearing of that which [goes] from the centre of the earth to the orbs of the same. But the motion of the centre of the epicycle of any planet, subtracted from the earth's equal motion (which is the mean of the Sun's motion), leaves the equal motion of commutation: and [it is] numbered from the mean apogee, from which the earth too is equally raised, whence also at hand the true and apparent motion of any planet in the ecliptic is had from D. Teacher's tables of the prosthaphaereses of the planets.

[margin: Venus & Mercurius propter orbis magni motum, per Zodiacum, sicut Sol, moveri videntur.]

Alteram porrò orbis magni vtilitatem partem, haud illa leuiorem, in Veneris, & Mercurij theoria nanciscemur. Cum namq́; nos duos planetas ex terra tanquam à specula observemus: & si ipsi non aliter atque Sol fixi manerent, tamen nos, quia per orbis magni motum circa eos circumducimur, nihilominus ipsos planetas, vt Solem, suis motibus zodiacum peragrare putaremus. Et quia obser-

…Furthermore, we shall obtain another part of the usefulness of the great orb, by no means lighter than that one, in the theory of Venus and Mercury. For since we observe these two planets from the earth as if from a watchtower: even if they themselves remained fixed no otherwise than the Sun, nevertheless we, because through the motion of the great orb we are carried round about them, should none the less think the planets themselves, like the Sun, traverse the zodiac by their own motions. And because [observations]…

observationes testantur Venerem, & Mercurium in suis orbibus etiam proprijs moueri motibus: præter Solis motum medium, quo in succedente feruntur, & alia quoq́ue in iis apparentiæ per accidens, ratione orbis magni conspicientur. Principio enim orbes eorum, epicyclos putabimus, qui tanquam proprijs deferentibus cum Sole æqualibus passibus Zodiacum conficiant. Sic terra existente ad perigium primorum deferentium, totius ipsorum orbes in eccentrici apogio existimabuntur, & contra ad apogium orbes in perigio. Præterea quemadmodum planetis superioribus arces & perigia procedebant ad planetas, ipso in orbe magno determinatur: ita conuersio in Venere & Mercurij orbibus, respectu centri terræ relinquetur fuerit diametri, & pro motu inter alienam apo verò omnia deferentium loca pertrahuntur. Termini diametri deferentis mobilis, quæ lineæ medij motus Solis, scilicet quæ ex centro orbis magni in terræ centrum, æquidistanter mouetur, sunt absides mediæ. Absides quæ in parte deferentis media, opposita terræ, summæ: quæ in propiore, infimæ haud iniuria vocabuntur.

…observations attest that Venus and Mercury are moved in their own orbs also by their proper motions: besides the Sun's mean motion, by which they are borne in succession, other appearances also will be seen in them by accident, by reason of the great orb. For at the outset we shall reckon their orbs epicycles, which, as it were by their own deferents equal with the Sun, complete the Zodiac. Thus, with the earth being at the perigee of the first deferents, the whole of their orbs will be estimated to be at the apogee of the eccentric, and contrariwise [with the earth] at apogee, the orbs at perigee. Moreover, just as for the superior planets the apogees and perigees were proceeding toward the planets, [as] determined in the great orb itself: so a conversion is left in the orbs of Venus and Mercury, with respect to the centre of the earth, [as] the diameter [is], and for the motion among the foreign apogee — but truly all the places of the deferents are drawn through. The termini of the diameter of the mobile deferent, which is moved equidistantly to the lines of the Sun's mean motion (namely those which from the centre of the great orb [go] into the centre of the earth), are the mean apsides. Those apsides which [are] in the part of the deferent midmost, opposite the earth, [will] not unjustly [be called] the highest; those which [are] in the nearer [part], the lowest.

Si autem motus terræ annuus quiesceret, cum Venus in nouem mensibus suam reuolutionem, cum supra dictum peragat, & Mercurius quasi in tribus, quislibet in suo temporis spatio, in subis bis terra cum Sole coniungi, bis stationarius, bisq́; cernens, illis limites in deferentibus suæ reuolutionis: semel autem matutinus, vespertinus, retrogradus, directus, apogius, & perigeus appareret. Porrò oculo verò in orbis magni centro, proprijfa liter motus diuersi Veneris, & Mercurij, quemadmodum & reliquorum sese offerent, nempe totum oculorum suis motibus peragantes fierent ad Solem oppositi, reliquisque cum intueri τὰ φαινόμενα μετίσι cerneremur.

…But if the annual motion of the earth were at rest, since Venus completes its revolution in nine months (as was said above), and Mercury as it were in three, each in its own span of time: it would [be] twice conjoined with the Sun together with the earth, twice stationary, and twice [showing] in the deferents those limits of its revolution; but once it would appear morning, evening, retrograde, direct, at apogee, and at perigee. Furthermore, to an eye [placed] truly in the centre of the great orb, the diverse motions, properly [reckoned], of Venus and Mercury, just as of the rest also, would offer themselves — namely all [of them], performing [their courses] by their own motions, would be made opposite to the Sun, and with the rest we should be discerned to behold [the appearances] [in their] limits.

Verum enimuerò cum neque ex centro orbis magni stellarum motus contemplamur, neque terra motu annuo quiescat, satis perspicuum erit, quare apparentia nobis terram inhabitantibus tanta varietate appareant. Venus, & Mercurius terræ præsalcant, pro suorum orbium magnitudine motu velociore, ipsa terra motu suo annuo eos insequitur. Quare Venus ad terram in 19. ferè mensibus, Mercurius in quatuor reuertitur, atq; in hoc tem-

…But indeed, since we neither contemplate the stars' motion from the centre of the great orb, nor does the earth rest in its annual motion, it will be sufficiently clear why the appearances appear to us inhabiting the earth with such great variety. Venus and Mercury outrun the earth, with a swifter motion in proportion to the magnitude of their orbs, [while] the earth itself by its annual motion follows after them. Wherefore Venus returns to the earth in about 19 months, Mercury in four, and in this time…

[margin: Mercurius diebus 116. h.e. mensib.3. diebus 26. ferè. Commutatio Veneris & Mercurij. Orbis Terræ quare MAGNVS dicatur à Copernico.]

poris spatio omnes apparentias, quas Deus ex terris conspicui voluit, nobis ostendere repetunt. Sicut propriarum diuersitatum motus regulariter incedunt, planeta verò centro orbis magni suas reuolutiones in tempore sibi à Deo præfinito conficiente. Lineæ autem verorum locorum, quæ ex centro terræ per Venerem, & Mercurium trajectæ, longè aliter circumducuntur, tum quia à punctò extra absidum orbes educuntur, tum quia illud ipsum nobis mobile. Nos putamus Venerem, & Mercurium in suis orbibus eo motu procedere, quo Veteres in epicyclo eos moueri statuerunt, cum tamen ille motus superatio tantùm sit, qua velocior planeta, verò in Solis motum medium excedit. Hanc superationem vocat D. Præceptor commutationis motum, qui idem plane de causis, vt huic in tribus superioribus. Fit itaq́ue ratione Veneris epicycli, & Mercurij apparentia: quæ etiam à terra fixa apparuissent, propter terræ motum tardiùs reuertuntur: vtq́ue eædem in omnibus suorum deferentium partibus, & ecliptica locis contingant, omnino omnimodò eorum motus deprehenduntur. Nequaquam enim, terrâ sub Cancro fixâ, Ptolemæus deprehendisset Mercurium breuissimam à Sole circa Libram euagationes, & Venerem circa Taurum habere. Vbicunq́; autem terra fuo in orbe magno fuerit, & ecliptica apogio descendentis nodo esse, & apogium epicycli ad septentrionem perpetuum æ declinare. perigium verò ad meridiem. Pormæ tueluetre tos sublimes terra motu suo annuo verius locum æquantis verum eam deduxiimus, obtinent, omnésq́; iam dictas apparentias ordine in singulis planetis nobis introducat.

…of time they return to show us all the appearances which God willed to be visible from the earth. Just as [their] proper diversities of motion advance regularly, the planet truly completes its revolutions about the centre of the great orb in the time foreordained for it by God. But the lines of the true places, drawn from the centre of the earth through Venus and Mercury, are led round far otherwise, both because they are drawn out from a point outside the apsides of the orbs, and because that very [point] is mobile [for] us. We think Venus and Mercury proceed in their orbs by that motion by which the Ancients established them to be moved in [their] epicycle, although that motion is only [the] surpassing by which the swifter planet exceeds into the mean motion of the Sun. This surpassing D. Teacher [Copernicus] calls the motion of commutation, which [is] plainly the same as to causes [as] this [one] in the three superior [planets]. And so by reason of Venus's epicycle, and Mercury's, the appearances [arise]: which would have appeared even with the earth fixed, [but] on account of the earth's motion return more slowly; and so that the same [appearances] occur in all the parts of their deferents and in the places of the ecliptic, their motions are altogether and in every way detected. For by no means, with the earth fixed under Cancer, would Ptolemy have detected that Mercury has its shortest excursion from the Sun about Libra, and Venus about Taurus. But wherever the earth shall have been in its great orb, [it follows that] the [epicycle is] at the descending node of the ecliptic apogee, and that the apogee of the epicycle perpetually declines toward the north, but the perigee toward the south. [And the earth by its annual motion obtains the true place of the equant whence we led it, and introduces to us in order all the now-said appearances in each of the planets.]

[margin: Mercurius diebus 116. h.e. mensib.3. diebus 26. ferè. Commutatio Veneris & Mercurij. Orbis Terræ quare MAGNVS dicatur à Copernico.]

Cæterùm Solis quoq́; clarius est, orbem terram deferentem verè MAGNVM appellari placuit, & Solis quoq́; sub stellato orbe seratur. Si enim Imperatores propter res feliciter bello gestas, aut gentes deuictas, cui augustissimum attribuerentur nomen, cum ipse quasi solus, legum cælestis politiæ particeps no faciatómenésq́; errores motuum emendet, cumq́; in grandi quodam circulo & ordine sub stellato orbe seratur. Ideo autem est dictus orbis magnus, quia tam ad superiorum planetarum orbes, quàm ad inferiorum magnitudinem notabilem habet, quæ præcipuarum apparentiarum sit occasio.

…But of the Sun too it is clearer that it pleased [Copernicus] to call the orb bearing the earth truly GREAT, and [that] of the Sun too [it] is borne under the starred orb. For if Emperors, on account of affairs happily conducted in war, or nations conquered, had the most august name attributed to whomever, [then] since [the earth] alone, as it were, [is] partaker of the laws of the celestial polity and amends all the errors of the motions, and since it is borne in a certain grand circle and order under the starred orb. And it is therefore called the great orb, because it has a notable magnitude both toward the orbs of the superior planets and toward [those] of the inferior, which is the occasion of the chief appearances.

[margin: Quomodo planeta ab ecliptica discedere, appropinquare possit. De his agit Copernicus libro Sexto. Explicatio latitudinis trium superiorum.]

Porrò in latitudinibus planetarum primùm est videre, quòd recte deferenti centrum terræ Magni nomen tribuatur, quod eò insuper maiorem admiratione meretur, quò Veterum hac de re præcepta perplexiora obscuriorisq́; esse constat. Motus planetarum in longitudinem, egregia quidem testimonia perhibent, quòd in latitudinibus autem planetarum cuius vtilitates, ceu in illustri quodam loco, conspicuâ, magis sunt conspicua, cum ipse nisi quasi planò discedens, præcipua tamen causâ omnis diuersitatis apparentiarum in latitudinem existat. Tu verò doctissimè D. Schonere, ideo summo amore orbem hunc prosequendum & amplectendum vides, quòd totum motum in latitudinem breuiter, tamq́; dilucidè, omnibus propositis causis, ob oculos ponat.

…Furthermore, in the latitudes of the planets it is first to be seen that rightly is the name "Great" attributed to the deferent of the earth's centre, [a thing] which the more deserves admiration the more it is agreed that the Ancients' precepts on this matter are more perplexed and obscurer. The motions of the planets in longitude indeed give excellent testimonies; but in the latitudes of the planets, whose usefulnesses, as in some illustrious place, are more conspicuously conspicuous, since it [the orb], departing as it were only in plane, nevertheless [is] the chief cause of all the diversity of the appearances in latitude. But you, most learned D. Schöner, see that this orb is therefore to be pursued and embraced with the highest love, because it sets before the eyes the whole motion in latitude briefly and so lucidly, all the causes being set forth.

Sint primò trium superiorum planetarum primùm est videre, quòd recte deferenti centrum terræ & eclipticam inclinari, quorum apogia septentrionem versus, perigia autem ad meridiem reperiantur: Vsq́ue hîc ipsi planetæ in suis orbibus, quemadmodum Luna in orbe declinij, extra cuius planum ne egrediatur, circumferantur. Lineæ propriæ diuersitatis, Dracones planetarum, vt vulgò vocant, deferentium ad eclipticæ planum habitudines, & intersectiones æ planetarum motus designabunt: lineæ autem verorum locorum, prædictas lineas in centris planetarum intersecantes, pro centri terræ in orbe magno situ ad planetam, & ipsius planetæ in suo orbe declinij, vera planetarum loca, & remotioris ab eclipticæ planò ablatione, referent, pro angulorum habitudine, quos ad eclipticæ medium constituunt, quemadmodum mathematica ratio explicabit. Quam ob causam planetam quacunque sui deferentis & epicycli, in circulo declinij, portione morante, à centro terræ existente in remotiori à planeta orbis magni mediate, quàm Veteres superiorem epicycli partem dixere, latitudines apparentes minores fieri oportere angulo inclinationis deferentis ad planum eclipticæ, clarum est; quia in tali centri terræ situ ad planetam: angulus apparentis latitu-

…Let first, of the three superior planets, [it] first be seen that rightly [the name "Great" is attributed to] the deferent of the earth's centre, and [that they] are inclined to the ecliptic, whose apogees are found toward the north, [and] perigees toward the south: thus far the planets themselves are carried round in their orbs, just as the Moon in the orb of [its] declination, beyond whose plane it does not go out. The lines of [their] proper diversity, the Dragons of the planets (as they commonly call [them]), will designate the bearings of the deferents toward the plane of the ecliptic, and the intersections, and the motions of the planets: but the lines of the true places, intersecting the aforesaid lines in the centres of the planets, will refer — for the situation of the earth's centre in the great orb relative to the planet, and [for] the planet's own [position] in its orb of declination — the true places of the planets, and the removal of the more remote [planet] from the plane of the ecliptic, according to the bearing of the angles which they constitute toward the middle of the ecliptic, as the mathematical reckoning will explain. For which cause it is clear that, while the planet tarries in any portion whatever of its deferent and epicycle in the circle of declination, with the earth's centre being in the [part of the] great orb more remote from the planet (which the Ancients called the upper part of the epicycle), the apparent latitudes ought to become smaller [than] the angle of inclination of the deferent to the plane of the ecliptic; because in such a situation of the earth's centre toward the planet, the angle of the apparent latitude…

latitudinis acutior est angulo inclinationis, interior videlicet exteriori, & opposito. Porrò centro terræ perueniente ad propiorem meridianam orbis magni ad planetam, contrà latitudo apparens maior angulo inclinationis, iisdem planè de causis, & contrà, conspicietur: quippe quia exterior & oppositus, iam interior. Atq́; hæc est causa, quamobrem Veteres putauerunt, centro epicycli extra nodos consistente, superiorem epicycli partem semper inter deferentis & eclipticæ planum existere, vbi planetam tanquam ad eam partem vergere, ad quam medietas deferentis æquidistanter ecliptico plano incedere: & epicyclo in nodis, planetam latitudinem nullam, in quacunque epicycli fui parte, habere. Quod in his hypothesibusverificatur, plana in aliquo nodorum morante, & terra quacunq́; in parte orbis magni reperta. Si angulus superficiei epicyli ad suum deferentem, in Veterum hypothesibus æqualis perpetuò æqualis inclinationis plani deferentis & eclipticæ æqualis fuisset deprehensum, prædicta latitudinum ratio sufficiens fuisset, verùm cum huius diuersùm sit observationibus testabitur observatio.

…of the latitude is more acute than the angle of inclination — namely the interior [more acute] than the exterior, and the opposite. Furthermore, with the earth's centre coming to the nearer southern [part] of the great orb toward the planet, on the contrary the apparent latitude [will be] greater than the angle of inclination, for the very same causes, and contrariwise, [it] will be seen: since [what was] exterior and opposite [is] now interior. And this is the cause why the Ancients thought that, with the centre of the epicycle remaining outside the nodes, the upper part of the epicycle always existed between the plane of the deferent and the ecliptic, where [they thought] the planet inclined as it were toward that part toward which the mid-part of the deferent advances equidistantly to the ecliptic plane: and [that], with the epicycle in the nodes, the planet has no latitude, in whatever part of its own epicycle. Which is verified in these hypotheses, [with] the plane tarrying in some one of the nodes, and the earth found in any part whatever of the great orb. If the angle of the epicycle's surface to its deferent, in the Ancients' hypotheses, had been found perpetually equal [to] the equal inclination of the plane of the deferent and of the ecliptic, the aforesaid rationale of the latitudes would have been sufficient; but since [it is] otherwise than this, observation will attest by the observations.

[margin: Latitudinis veneris rationes, & modus.]

Veneris autem, & Mercurij apparentiæ in latitudinem, vnica deuiatione excepta, speculationis facilitate superiorum planetarum theorias superant. Sed Veneris latitudines primò perpendantur, intra orbem magnum, primùm Veneris (sphæra) occurrit. Ponit itaque D. Præceptor planum, in quo Venus mouetur, ab ecliptica seu orbis magni planò declinare, super diametro per absidas proprias deferentis primi, ita vt orientalis medietas, à plana ecliptica superficie in septentrionem eleuetur, & inclinationis angulum, quem in Ptolemæi hypothesibus quidem planum cum deferentis plano contineret, occidentalis autem medietas ad meridiem.

…But the appearances in latitude of Venus and Mercury, with the single deviation excepted, surpass the theories of the superior planets in ease of speculation. But let Venus's latitudes first be weighed: within the great orb, first the (sphere) of Venus presents itself. D. Teacher [Copernicus] therefore posits the plane in which Venus moves to decline from the ecliptic, that is, from the plane of the great orb, upon the diameter through the proper apsides of the first deferent, so that the eastern half is raised from the plane ecliptic surface toward the north, [by] the angle of inclination which (in Ptolemy's hypotheses indeed) the plane would contain with the plane of the deferent, but the western half [is depressed] toward the south.

Per orientalem verò medietatem intelligenda æ, quæ est à loco summæ absidis in consequentia, &c. Sola hac & simplici hypothesi omnes declinationum, & reflexionum regulas: cum causis, & sic terra & planetæ planum habitudine facilè erit peruidere. Cum sis dis deferentis quidem æ summa absidisin consequentia, & ab eclipticæ planò in septentrionem eleuata, dixerunt Veteres epicyclum Veneris in descendente nodo esse, & apogium epicycli ad septentrionem perpetuum æ declinare. perigium verò ad meridiem. Pormæ tueluetre tos sublimes terra motu suo annuo verius locum æquantis verum eam deduxiimus, obtinent, omnésq́; iam dictas apparentias ordine in singulis planetis nobis introducat.

…But by the eastern half [is] to be understood that which is from the place of the highest apsis in the succession [of the signs], etc. By this single and simple hypothesis all the rules of the declinations and reflexions, with their causes — and so the bearing of the earth and the planet's plane — it will be easy to perceive thoroughly. When, of the deferent indeed the highest apsis [being] in the succession [of the signs], and raised from the plane of the ecliptic toward the north, the Ancients said the epicycle of Venus was at the descending node, and that the apogee of the epicycle perpetually declines toward the north, but the perigee toward the south. [And the earth by its own annual motion obtains the truer place of the equant whence we led it, and introduces to us in order all the now-said appearances in each of the planets.]

[margin: Declinationum & Reflexionum Latitudines in Venere ab vna causa dependent.]

prias deferentis primi, ita vt orientalis medietas, à plana eclipticæ superficie in septentrionem eleuetur, & inclinationis angulum, quem in Ptolemæi hypothesibus quidem planum cum deferentis plano contineret, occidentalis autem medietas ad meridiem. Per orientalem verò medietatem intelligenda æ, quæ est à loco summæ absidis in consequentia, &c. Sola hac & simplici hypothesi omnes declinationum, & reflexionum regulas: cum causis, & sic terra & planetæ planum habitudine facilè erit peruidere. Cum absidis & planetæ planum habitudine facilè erit peruidere. Cum absidis deferentis quidem æ summa absidisin consequentia, & ab eclipticæ planò in septentrionem eleuata, dixerunt Veteres epicyclum Veneris in descendente nodo esse, & apogium epicycli ad septentrionem perpetuum verò ad meridiem declinare. Porrò euidentius hoc sub limitibus terra in suo annuo motu, quare & latitudinem quoq́; apparens maior in ortu verò matutino minimus, vnde & ipsa apparens latitudo, & ipsa quoque inclinatio, nisi conuenientiam maximus, quare & latitudinem quoq́;.

…[through] the proper [apsides] of the first deferent, so that the eastern half is raised from the plane ecliptic surface toward the north, [by] the angle of inclination which (in Ptolemy's hypotheses indeed) the plane would contain with the plane of the deferent, but the western half [is depressed] toward the south. But by the eastern half [is] to be understood that which is from the place of the highest apsis in the succession [of the signs], etc. By this single and simple hypothesis all the rules of the declinations and reflexions, with their causes — and so the bearing of the earth and the planet's plane — it will be easy to perceive thoroughly. When the highest apsis of the deferent indeed [being] in the succession [of the signs], and raised from the plane of the ecliptic toward the north, the Ancients said the epicycle of Venus was at the descending node, and that the apogee of the epicycle declines perpetually toward the north, but the perigee toward the south. Furthermore more evidently this [appears] under the limits, [with] the earth in its annual motion, wherefore [the] apparent latitude too [is] greater [at evening], but at the morning rising least; whence both the apparent latitude itself, and the inclination itself also, [appear] unless [there be] the greatest agreement, wherefore also the latitude [varies].

infima deferentis sui de Veterum sententia, esse abside creditur. Atque hîc est vt τῶν φαινομένων ordo, dum centrum terræ semicirculationem complet, à loco infimæ absidis Veneris in consequentia signorum, ad locum summæ absidis Veneris ascendens. Eadem autem ratione descendente terra reflexio ad nostrum decrescit paulatim in declinationem mutabitur, & quia medietas plani deferentis à summa abside in antecedentia, nobis tali incessu terræ fit opposita, apogium deferentis Veneris in meridiem à plano eclipticæ declinare incipit, donec terra in nonagesimo gradu à loco absidis constituta, vtique medietas deferentis ab ecliptica planum declinata conspicietur, orbisq́;, eius epicyclus Veneris in nodo alterè dendre ad summam absidem putetur. A quo loco terra recedente declinatio iterum in reflexionem commutetur, ac consecuta locum infima absidis Veneris, eademq́; apparentias latitudinum in Venere, terra iterum producere incipiant. Ex quibus patet, terra ad lineam absidum Veneris posita, planetam reflexionem apparere, in quadratúris verò ab his declinatum, in locis autem intermedijs mixtas latitudines conspici.

…[that the earth] is believed to be at the lowest [apsis] of its deferent, of the Ancients' opinion, [the] abside. And here is, as it were, the order of [the appearances], while the centre of the earth completes a semicircuit, ascending from the place of Venus's lowest apsis in the succession of the signs to the place of Venus's highest apsis. But by the same reasoning, the earth descending, the reflexion toward us decreases [and] little by little will be changed into declination; and because the mid-part of the deferent's plane, from the highest apsis in the antecedent [direction], is made opposite to us by such an advance of the earth, the apogee of Venus's deferent begins to decline toward the south from the plane of the ecliptic, until the earth, set at the ninetieth degree from the place of the apsis, [then] indeed the mid-part of the deferent will be seen declined from the ecliptic plane, and its orb, the epicycle of Venus, [will be] thought to [be] at the other node descending toward the highest apsis. From which place, the earth receding, the declination again is commuted into reflexion, and, having attained the place of Venus's lowest apsis, the same appearances of the latitudes in Venus the earth begins again to produce. From which it is plain that, with the earth placed at the line of Venus's apsides, the planet appears [in] reflexion, but in the quadratures [it appears] declined from these, and in the intermediate places mixed latitudes are discerned.

[margin: Deviationis Veneris latitudo.]

Cum autem præter has latitudines, quas Veteres, epicyclo Veneris tribuerunt, & alia à Veteribus deuiatio, à Ptolemæo τὸν ἐκνεύσιν εἰς τὰ πλάγια dicta, sic permiteat, ac eandem per deferentis centrum epicycli Veneris, quæ iam sublatus est, demonstrant, aliam & cum observationibus magis consonam D. Præceptor rationem ineundam iudicauit. Hanc autem rationem D. Doctoris, Præceptoris mei deuiationem saluandi, vt facilius quoq́;, haud secus, ac reliqua vsq́ue posita, assequamur: Constituamus planum, cuius mox meminimus, esse medium planum, ac ideo fixum, à quo verum, iam huic abside, deuiatione ratione. Ac quia omnes motus, polorum respectu minori labore ac dispendio percipiantur, principio terminum à plano eclipticæ ad inclinationis anguli quantitatem eleuari: alterum verò in oppositò tantùdem in latitudinem deprimi: & quæ ab septentrionali polo, autijs, quæ circa hunc fieri ostensuri sumus, mihi ratione, ratione nimirum oppositionibus habita, de meridionali intelligi oportere. Proinde circa septentrionalem plani medij polum assumamus esse circulum mobilem, cuius ea quæ excen-

…But since, besides these latitudes which the Ancients attributed to Venus's epicycle, [there is] also another deviation [noted] by the Ancients, called by Ptolemy [Greek: "the swerving toward the oblique [directions]"], so [as] to permit [it], and they demonstrate the same [as] through the deferent of the centre of Venus's epicycle (which is now removed), D. Teacher [Copernicus] judged that another rationale, more consonant with the observations, should be entered upon. But this rationale of my Lord Doctor my Teacher, for saving the deviation, that we may attain [it] more easily also, no otherwise than the rest hitherto set down: let us constitute the plane, which we just mentioned, to be a mean plane, and therefore fixed, from which the true [one], now at this apsis, [is reckoned] by reason of the deviation. And since all motions, with respect to the poles, are perceived with less labour and expense, [let] at the outset one terminus be raised from the plane of the ecliptic by the quantity of the angle of inclination; but the other, in the opposite [direction], be depressed just as much in latitude: and [the things] which we are about to show happen about the northern [pole] — [the things] which [happen] about this — must, by the [same] reasoning (the opposition being held, namely), be understood concerning the southern. Accordingly, about the northern pole of the mean plane let us assume there is a mobile circle, whose [property] is that which [is] eccentric…

ex centro maximis obliquitatibus plani medij à plano vero correspondet: ipse autem polus septentrionalis plani veri per librationis motum, dicti circuli diametrum describat. Porrò circulus mobilis insequatur planetæ motum, vt Venus suo motu incedens, relinquat duarum quamlibet in inclinationem intersectionem, ideáq́; hac lege, vt anno exacto ad relictam denique reuertatur. Ducto verò circulo magno per vtriusq́; plani polos, ab huius communi cum plano vero intersectione, vtrinq́; 90. gradibus numeratis, cum poli plani, veri & medij scilicet differunt, nodi cui intersectiones dictæ determinantur. Interim autem dùm Venus à terra ad alterutrum nodorum periodus completur, à polo plani veri per librationis motu, dicti circuli mobilis diameter bis describitur. Hæc autem ita fiant, quo planetam cum terræ centro tale pactum iniisse appareat, vt quoties terra ad deferentis abside iuerit, Venus vbicunque fuit in deferente vero, maximè in septentrionem à plano medio deuiet, hoc est, maximè extra viam mediam consistat. Præterea terra à quadrante ab absidibus deferentis distante, ipse planeta cum suo motu in medij deferentis planum incidat. Sed terra à reliqua loca intermedia peragente. ipse quoque in declinationibus intermedijs suum cursum teneat. Hoc terræ, & planetæ pactum vt esset perpetuum, ordinauit Deus, vt prima nodi intersectionis circellus (vt ita dicam) eodem tempore semel reuolueretur, quo via Veneris ad alterutrum mobilium nodorum periodus est confecta.

…from the centre corresponds to the greatest obliquities of the mean plane from the true plane: but the northern pole of the true plane describes, through the libration-motion, the diameter of the said circle. Furthermore let the mobile circle follow the planet's motion, so that Venus, advancing by its own motion, leaves either of the two [intersections] in inclination at the intersection, and so by this law, that, the year completed, it returns at last to the [intersection] left behind. Then, a great circle being drawn through the poles of each plane, from its common intersection with the true plane, 90 degrees being counted on each side, when the poles of the plane — the true and the mean, namely — differ, the nodes by which the said intersections are determined [are fixed]. Meanwhile, however, while the period of Venus from the earth to one or the other of the nodes is completed, by the pole of the true plane, through the libration-motion, the diameter of the said mobile circle is described twice. But let these things so come about, that the planet may appear to have entered such a pact with the earth's centre, that as often as the earth goes to the apsides of the deferent, Venus, wherever it was in the true deferent, deviates most toward the north from the mean plane — that is, stands most outside the middle way. Moreover, with the earth distant by a quadrant from the apsides of the deferent, the planet itself with its motion falls into the plane of the mean deferent. But with the earth performing the remaining intermediate places, it too keeps its course in the intermediate declinations. That this pact of the earth and the planet might be perpetual, God ordained that the little circle of the first node-intersection (so to speak) should be revolved once in the same time in which the way of Venus to one or the other of the mobile nodes [is] a completed period.

Hæc vt exemplo illustriora fiant, si in aliquo deuiationis motus principio polus septentrionalis plani veri à polo plani medij adiacentis, maximè meridionalis fuerit: Ac Venus tantùm in maximo deuiationis limite, qui est septentrionalis, exiterit; terræ quoque centro in aliqua absidum Veneris commorante, in quartam anni partem, terra motu annuo ad locum inter absidis medium veniet, & eodem tempore planeta ad locum inter absidis medium, seu nodum mobilem. Et quia motus librationis commensuratur cum motu planetæ ad nodos, seu intersectiones, primus librationis circellus quadrantem quoque conficiet, & per reliquum circellü, quù altero sit velocior duplo, polus plani verii sub poli plani medij constituetur, quare & ambo plana coniungentur. Recedente autem planeta ab hoc nodo, terra procedet ad alteram absida eccentrici primi, & po-

…That these things may become clearer by an example: if at some beginning of the deviation-motion the northern pole of the true plane were most southern from the pole of the adjacent mean plane: and Venus stood only in the greatest limit of deviation, which is the northern; with the earth's centre too tarrying in some one of Venus's apsides, in a quarter of the year the earth by its annual motion will come to the place between the mid-apsis, and at the same time the planet [will come] to the place between the mid-apsis, or the mobile node. And because the libration-motion is commensurate with the planet's motion to the nodes or intersections, the first little circle of the libration will also complete a quadrant, and through the remaining little circle (since it is twice swifter than the other) the pole of the true plane will be constituted under the pole of the mean plane, wherefore both planes too will be joined. But with the planet receding from this node, the earth will proceed to the other apsis of the first eccentric, and the pole…

& polus plani veri per librationem à polo plani medij ad septentrionem promouebitur. Sic fiet, vt & si Venus meridiana sit, quemadmodum in nostro exemplo, tamen latitudo meridiana minuatur: si septentrionalis, eadem crescat. Eò loci autem vbi peruentum fuerit, polus plani veri, librationis motu maximè ad septentrionalem limitem attinget, & planeta motu suo annuo ad nodos, in medio inter vtramq́; intersectionem, maximam iterum in septentrionem deuiationem habebit. Apparet itaque motum circulationis assumpti, hunc habere vsum, vt in anno, Veneris ad nodos statu resoluto, semperq́; terra collocata in absidum lineà, planeta vbicunque in suo plano vero fuerit, maximam à plano medio deuiationem habeat, & in medio inter vtranq́; absida eius constituatur. Porrò librationis motu fieri, vt Venere in aliquo nodorum existente, ambo plana coniungantur: & illa pars plani veri, quam ingreditur, ad septentrionem semper à medio discedat: quo, proutconuenit, latitudo hæc perpetuò borealis maneat.

…and the pole of the true plane will be promoted by libration from the pole of the mean plane toward the north. So it will come about that, even if Venus be southern (as in our example), nevertheless the southern latitude is diminished: if [it be] northern, the same grows. But at that place where [the earth] shall have arrived, the pole of the true plane will, by the libration-motion, most reach toward the northern limit, and the planet by its annual motion to the nodes, in the middle between either intersection, will have again the greatest deviation toward the north. It appears therefore that the motion of circulation [thus] assumed has this use, that in the year — the [position] of Venus to the nodes being resolved, and the earth always placed in the line of the apsides — the planet, wherever it shall have been in its true plane, has the greatest deviation from the mean plane, and is constituted in the middle between either of its apsides. Furthermore, [it comes about] by the libration-motion that, with Venus being in some one of the nodes, both planes are joined; and that part of the true plane which it enters always departs toward the north from the middle; whereby, as is fitting, this latitude remains perpetually boreal.

[margin: Latitudinis Mercurij rationes & modus. Declinationum & Reflexionum latitudines in Mercurio. Deviationis eiusdem latitudo.]

Quemadmodum autem Veneris planum, quod medium appellare placuit, in absidum eccentrici primi lineà ab ecliptica intersecatur, & eius plani medietas à summa abside in consequentia ab eclipticæ plano in septentrionem vergente: Ita in Mercurio similiter ab eclipticæ plano medium, quod super suam absidum lineam. Et pariter, ab ecliptice plano verùq́; inclinatur, vt viceuersâ medietas plani medij à summa abside in antecedentia septentrionalis sit. Quare in centri terræ annuâ reuolutione, declinationes, & reflexiones in Mercurio permutatæ ad Veneris scilicet, deprehendentur: Verùm hæc varietas et eo conspicua magis fore, disposuit Deus, & deuiationem plani veri Mercurij à medio, vt ea medietas perpetuò, quam ingreditur, à plano medio ad meridiem discedere: quò fit deniq́ue, vt re-liquæ latitudinum Mercurij varietates facilimè non aliter, atque in Venere colligentur. Cæterùm reliquas latitudinum Mercurij varietates facilimè non aliter, atque in Venere colligentur.

…But just as the plane of Venus, which it has pleased [us] to call the mean [plane], is intersected by the ecliptic in the line of the apsides of the first eccentric, and the mid-part of that plane, from the highest apsis in the succession [of the signs], inclining from the ecliptic plane toward the north: so in Mercury likewise the mean [plane is intersected] by the ecliptic plane, which [lies] upon its own line of apsides. And equally, it is inclined from the ecliptic plane truly, so that conversely the mid-part of the mean plane, from the highest apsis in the antecedent [direction], is northern. Wherefore, in the annual revolution of the earth's centre, the declinations and reflexions in Mercury will be detected permuted with respect to Venus's, namely: but [that] this variety may be the more conspicuous, God disposed also the deviation of Mercury's true plane from the mean, so that the half which it enters perpetually departs from the mean plane toward the south: whence at last it comes about that the remaining varieties of Mercury's latitudes are most easily gathered no otherwise than in Venus. But the remaining varieties of Mercury's latitudes will most easily be gathered no otherwise than in Venus.

[margin: Pars superat cœpti, pars est exhausta laboris: Hic teneat nostra ancora iacta ratés.]

vt primam hanc Narrationem nostram Poetæ verbis siniam. Alteram autem mei promissi partem, quum primùm iusto adhibito studio totum D. Præceptoris Opus euoluero, colligere incipiam. Eò verò gratiorem tibi vtramq́; fore spero, quò clariùs Artificum propositis observationib. nisi D. Præceptoris hypotheses τοῖς φαινομένοις consentire videbis, vt etiam inter se, tanquam bona consequentia cum definito conuenire possint.

…that I may end this our first Narration with the Poet's words. But the other part of my promise, when first, with due study applied, I have unrolled the whole Work of D. Teacher [Copernicus], I shall begin to gather. But I hope each [part] will be the more welcome to you, the more clearly you shall see — by the observations set forth by the Artificers — that D. Teacher's hypotheses do not [fail to] agree with [the appearances], so that they may also accord among themselves, as good consequences with a defined [end].

[margin: Epilogus.]

Clarissime, & doctissime D. Schonere, ac tanquam Pater mihi semper colende, reliquum nunc iam est, vt hanc meam operam qualemcunq́; æqui boníq́; consulas. Nam quanquam non nescio, quid humani mei ferre possint, quidóq́; ferre recusent: tamen tuus in me singularis, & (vt ita dicam) paternus amor fecit, vt omni non non formidarem hoc cælum subire, & quod eius quidditati fortè potuit, omnia ad te referre. Quod Deus Opt. Max. bene vertere dignetur, precor, mihíq́; aspiret, vt iusto tramite ad propositum finem, laborem cœptum perducam. Si quippiam autem ardore quodam iuuenili (qui quidem semper, vt ille inquit, magno magis, quàm vtili spiritu fumus prædit) dictum fit, aut per imprudentiam exciderit, quod liberius contra venerandam, & sanctam Vetustatem dictum videri possit, quàm fortasis fas est rerum magnitudo, & grauitas postulabat, tu certè, quodq́; apud me dubium non sit, in meliorem accipies partem, & potius animum in te meum, quàm quid præstiterim, spectabis.

…Most illustrious and most learned D. Schöner, and as a Father ever to be revered by me, it now remains that you take this work of mine, such as it is, in good and equitable part. For although I am not unaware of what my human [powers] can bear, and what they refuse to bear, nevertheless your singular and (so to speak) paternal love toward me has brought it about that I should not at all dread to undergo this heaven, and to refer all things to you, [as far as] could [be done] toward its essence. Which may God, Best [and] Greatest, deign to turn well, I pray, and may He breathe favour on me, that by a just track I may bring the begun labour to the proposed end. But if anything was said by a certain youthful ardour (by which indeed we are always — as he says — endowed with a spirit more of greatness than of usefulness), or fell out through imprudence, [something] which might seem said too freely against venerable and holy Antiquity — more than perhaps the magnitude and weight of the matters demanded what is right — you certainly, and (let there be no doubt with me) will take [it] in the better part, and will rather regard my mind toward you than what I have performed.

[margin: Excusatio quòd nequaquam nauitatis studio, aut ingenij ostentatione (cuius à me nullus, præter meritum, eiusq́; simulator) sed rebus ipsis necessario perductus, à Philosophandi more, à veterum tritâ ac tentatâ semitâ recesserit.]

Porrò velim te de doctissimo Viro, D. Doctore, meo Præceptore, hoc statuere, tibiq́; persuasissimum habere, apud eum nihil prius, nec antiquius esse quicquam, quàm vestigijs Ptolemæi in insistat, nec saltem; ac ipse Ptolemæus fecit, Veteres, & se antiquiores multò secutus: dum autem τὰ φαινόμενα, quæ Astronomum regunt, & mathematica se cogere intelligeret, quædam præter voluntatem etiam vt sumeret: satis interim esse putauit, vt eadem arte in eundem scopù cum Ptolemæo tela sua dirigeret, etiamsi arcum, & tela ex longè alio materiæ genere, quàm ille assumeret. Ac hoc loco illud arripiendum, [Greek: ὁ τι ἂν εὑρίσκωσι τινα τ' οἷς γνώμη τὸ μᾶλλόν τε φιλόσοϕον] tertia re-q̃ φιλόσοϕον cesserit.

…Furthermore, I should wish you to determine this concerning the most learned Man, D. Doctor, my Teacher [Copernicus], and to hold [it] most persuaded with yourself: that with him nothing [is] prior nor more ancient than anything, [than] that he should tread in the footsteps of Ptolemy — nor [does he depart] at all; even as Ptolemy himself did, having followed the Ancients and those more ancient than himself by much: but while he understood [the appearances], which govern the Astronomer, and mathematics, to compel him to take certain [things] even against [his] will: he thought it enough meanwhile that, by the same art, he directed his weapons toward the same mark with Ptolemy, even if he took a bow and weapons from a far other kind of material than that one [did]. And in this place that [is] to be seized upon: [Greek: "whatever [things] some men may find, by whose judgment the more philosophical [is preferred]"] — [the matter] yields to the more philosophical [judgment] in the third [place].

[Greek: ϕιλοσοϕῶν.] Cæterùm, quod alienũ est ab ingenio boni cuiuslibet, maximè verò à natura philosophica, ab eo vt qui maximè abhorret D. Præceptor meus, tantum abest, vt sibi à Veterum philosophorum sententijs nisi magnis de causis, ac rebus ipsis effiagitantibus, studio quodam nouitatis, temerè discedendum putarit. Alia est ætas, alia morum gravitas, doctrináq́; excellentia, alia denique ingenij celsitudo, animíq́; magnitudo, quàm vt tale quid in eum cadere queat, quod quidem sit vel ætatis iuuenilis, vel τῶν μέγα φρονούντων ἐπὶ διανοίᾳ μειζόν, vt Aristoteli vtar verbis, vel ardenium ingeniorum, quæ à quolibet vento, suísq́; affectibus mouentur, ac reguntur, vt etiam cum [Greek: εὐλόγῳ] excusso, quoduis obuium sibi arripiant, & acerrimè propugnent. Verùm vincat veritas, vincat virtus, Husq́ue honos perpetuò habeatur artibus, & quilibet bonus suæ artis Artifex in lucem prodeat, proferat, atque in hunc tueatur modum, vt veritatem quæ fuisse videatur. Neque verò D. Præceptor bonorum, & doctorum Virorum iudicia vnquam abhorrebit, quæ subire vltrò cogitat.

…[Greek: "philosophizing."] But that which is alien from the disposition of any good man, but most of all from a philosophical nature — from which my Lord Teacher [Copernicus] most shrinks, [and] so far is [he] from [it], that he should think one must rashly depart from the opinions of the ancient philosophers, [except] for great causes, and with the matters themselves demanding [it], out of a certain zeal for novelty. Other is [his] age, other [his] gravity of morals and excellence of doctrine, other finally the loftiness of [his] wit and greatness of [his] mind, than that any such thing could fall upon him as would indeed be [the mark] of youthful age, or of [Greek: those who think greatly upon a too-great mind] (to use Aristotle's words), or of ardent wits which are moved and ruled by every wind and by their own affections, so that even with [Greek: reasonable [judgment]] cast aside, they snatch at whatever [is] obvious to them, and most fiercely defend [it]. But let truth conquer, let virtue conquer, and may honour perpetually be had for the arts, and may every good Artificer of his own art come forth into the light, bring [it] forth, and protect [it] in this manner, that the truth may seem to have been [established]. Nor indeed will D. Teacher [Copernicus] ever shrink from the judgments of good and learned Men, which he willingly purposes to undergo.

[Narratio Prima ends here, on page 163 (printed folio 152), under the "NARRATIO" running head. The text closes with "…quæ subire vltrò cogitat." The large word "BORVS-" appears below as a catchword leading into the BORVSSIÆ ENCOMIVM (page 164 onward — a separate work, not transcribed here.)]

Ioannes Keplerus — Mysterium Cosmographicum