Library / Almagestum Novum, Book IX: On the System of the World

Section II — On the Movers and Motions of the Heavens

Chapter II, On the Instruments of the Celestial Motions: whether they are solid Orbs, or mere Circles describable in the fluid ether; and [whether] these [are] Eccentrics with Epicycles, or mere Concentrics

[Margin: Who [is] the Eccentrist and [who] the Concentrist?]

[I.] Although the admirable variety of motions in the Planets has been detected by observation, and indeed [is] as manifold as we indicated in bk. 7, sect. 1, ch. 7; nevertheless [this variety], according to the threefold dimension of bodies, was more manifest to the ancient Physicists and Astronomers—namely, according to longitude, latitude, and depth or altitude. But because, out of these very [dimensions], the diversity as to altitude was not patent to all, or was not seen [to be] real but apparent (arisen from some deception of our sight, or from the diversity of the interposed medium), hence two most ancient sects took their origin. One [was that] of the Eccentrists, who, namely, said that the motions of the Planets are accomplished by orbs having their center diverse from and distant from the center of the World, together with smaller orbs—which, fixed in the larger, they called Epicycles—by whose aid they explained the inequality in motion both of longitude and latitude, and of altitude. The other [was that] of the Homocentrists or Concentrists, who, namely, affirmed that these motions are accomplished by orbs concentric with the center of the World, in such a way that the Planets really always preserve the same distance from the center of the World which each once had; but [they held] that, since their orbs were moved upon diverse poles, some orbs hastening, others retarding, it came about that the motion of the Planet, which in itself was equal [uniform], appeared unequal. But what Eccentrics are, what Epicycles, what Concentrics, “Trepicycles,” etc., and by what reasoning they are imagined to be interwoven with one another, we have declared abundantly—by an appended diagram—for the Sun indeed in bk. 3, ch. 19 and 21, for the Moon in bk. 4, from ch. 25, and for the rest of the Planets in bk. 7, sect. 2, ch. 1; and therefore we refer the Reader thither.

[II.] The Authors of each sect, however, are further subdivided into two classes. For some thought that all these motions are accomplished by solid orbs; others without solid orbs—namely, in the liquid ether—whether by an intrinsic faculty and principle implanted in the Planet, or by an informing soul, or by an Intelligence merely presiding over [them] and leading the Planets around through circles [that are] designable and describable only by imagination or intellect. But this part of the controversy—about the solidity and fluidity of the heavens, abstracting from the concentricity and eccentricity of the orbs—we have already sufficiently weighed in Section 1, ch. 7, where, among the asserters of solid orbs, we placed not only Alfraganus with many of the Arabs, Sacrobosco, and Peurbach with [their] followers, but also, of the Ancients, Eudoxus, Callippus, and Aristotle—inasmuch as they attributed the inequality of the motions to diverse orbs revolved about diverse poles—

[…continues on p. 252 (PDF 287): “…and to an orb in which the Planet was fixed, [these orbs] pushing forward or rolling back; nay even [the view] of Anaximander, of whom Plutarch (bk. 2, On the Opinions of the Philosophers, ch. 16) says: ‘Anaximander carries [the stars] around by circles and orbs, in which each star is placed.’ For neither Peurbach nor the Arabs first introduced that solidity of the orbs…”]


(printed p. 252 — continuing [II.], on who first asserted solid orbs: the doctrine of stars carried in circles and orbs is traced back as far as Anaximander, on Plutarch’s testimony. Neither Peurbach nor the Arabs first introduced the solidity of the orbs; Peurbach merely stuffed Ptolemy’s eccentrics and epicycles into solid material, so that he and Alfraganus were authors of solid Eccentrics and Epicycles, not of solid orbs as such.)

[Margin: Ptolemy does not support the solidity of the orbs, but rather [their] fluidity.]

[III.] For Ptolemy and Hipparchus—nay even the Pythagoreans, who introduced the Eccentrics and Epicycles, or [who] more perfectly delineated [them once] introduced into Astronomy—by no means consigned them to the solidity of orbs, but, either abstracting from solidity, or rather supposing fluidity, set forth the motions of the Planets by mere circular lines, and explained their hypotheses by bare circles, or by the peripheries of circles. And so concerning them—or at least concerning Ptolemy—judged St. Thomas (lect. 10 on 12 Metaphysics), Piccolomineus (in the Theorics of the Planets), Vielmius (lect. 21 on Genesis), Martinengus (in the Gloss, p. 1023), Kepler (on Mars, ch. 2; and in the Epitome of Copernican Astronomy, bk. 4, part 2), Cabeus (on 1 Meteorology, text 38, q. 2), [and] Blancanus (in the Sphere). But what need is there of a gloss, since Ptolemy’s own meaning is sufficiently plain and clear? For thus Ptolemy (bk. 13 of the Great Work, or Great Construction [the Almagest], ch. 2), speaking of the manifold motion of the Planets, especially in latitude, says:

“But let no one think hypotheses of this kind too laborious, when he considers the manifold artifice which is required in carrying them out; for it is not fair to equate human [things] with divine, or to seek assurance about sublime things from the examples of things most dissimilar. For what is more dissimilar than the things which always behave in the same way [compared] to the things which never are constant with themselves, and [than] the things which can be hindered by any cause whatever [compared] to the things which cannot be hindered even by themselves? Rather, one ought to strive that the hypotheses be made as simple as possible and adapted to the celestial motions; and, if this does not succeed, that they be at least such as are possible for us. For if, by such hypotheses, it follows that all the things which appear in the heaven are accounted for, what wonder is it if this variety can befall the celestial motions? Especially since there [in the heaven] there is no nature which would hinder the motions, but [a nature] which is apt by birth to yield to the natural motions of each globe, even if they seem to be contrary; so that all things can permeate through those simple bodies—widely and liquidly diffused—and be transparent or seen through, equally [in every direction]. Nor only in circles can this rightly proceed, but also in the very spheres and axes of the revolutions, whose variety and alternating diversity of motions it is so laborious and difficult for us to represent in constructed figures and in the examples of [planetary] Theorics, that the motions seem to hinder one another. In the heaven, however, that variety of motions least hinders itself. One ought not, therefore, to judge the simplicity of celestial things from those things which can appear simple to us, since there is nothing with us which would appear equally simple to all men. For if anyone should wish so to estimate, he will think nothing in the heaven [to be] simple—not even the stable and simple nature of the prime mobile itself; because something similar [to it] among men is not only difficult to find, but even altogether impossible. Not, therefore, from these [things], but from the very nature and immutability of the celestial motions, must judgment be made. For thus it will come about that all those motions appear simple, and indeed far simpler than the things which seem to us most simple, since we can devise nothing of difficulty, and nothing of labor, in their periods.”

Since, therefore, Ptolemy names spheres and axes, while nevertheless he acknowledges the very greatest simplicity of the motions—and that too through a single continuous line—and posits the Planets as going through the substance of the ether [which] yields and in no way hinders [them], who does not see that he favors the fluidity of the heavens rather than [their] solidity? And so St. Thomas understood him (1 p., q. 70, art. 1, ad 3), the Carthusian (art. 12 on Genesis), [and] Kepler (in the Epitome, p. 504)—granted that [Kepler] in that [place] reprehends [Ptolemy’s] motion [as] from an intrinsic and natural [principle in] the Planets, and the divinity attributed to them, and the exclusion of every figure or image or example of our [terrestrial] things; for Kepler thinks that, by means of the Ellipse, and by examples of the balance and the Magnet and things like these, the motions of the Planets can best be represented. But below there will again be discourse for us about this simplicity of the motions, according to Ptolemy’s mind. Now we must come to the other part of the proposed question: namely, whether—whether in a solid or in a liquid ether—the Motions of the Planets can be accomplished in the heaven and explained on earth by concentric orbs or circles alone; or whether Eccentrics, or [things] equivalent to Eccentrics, are required.

[Margin: 1. Opinion — asserting Concentrics.]

[IV.] The first opinion was that of the Homocentrists, some of whom thought the motions of the Planets equal [uniform], others indeed unequal, but [thought] their intervals from the center of the world equal. About them that [text] of Plutarch (bk. 2 On the Opinions [of the Philosophers], ch. 16) can be understood: “Anaximenes [held] that the stars, both around the earth and above the earth, are turned in the same way. Plato and the Mathematicians [held] that the Sun, Venus, and Mercury are moved with equal motions.”

[Margin: Anaximenes. — Eudoxus. Callippus. Aristotle.]

But chiefly Eudoxus of Cnidus and Callippus of Cyzicus, who, since with Plato’s opinion they judged the celestial motions to be circular, uniform, and perpetual, attempted to explain every real variety of the motions by orbs concentric with the center of the universe—which very [thing] Aristotle confessed [could be done only] by adding other orbs, as is plain from Simplicius (on bk. 1 and 2 On the Heavens) and from Aristotle himself there and [in bk.] 12 of the Metaphysics. Whom Averroes followed there, and Achillinus (in the book On the Orbs), and the Conciliator [Pietro d’Abano] (diff. 1). Which opinion, when Sosigenes, Hipparchus, and Ptolemy had repudiated it (Eccentrics and Epicycles being called in), and when all the Astronomers thereafter had followed Ptolemy—nevertheless a very few called [it] forth again into the light from the rubble: namely John Baptist Amicus of Cosenza (in the opusculum On the Motions of the Celestial Bodies, published in the year 1537), John Baptist Turrianus, and his heir in this [matter] Hieronymus Fracastorius (in the Homocentrics, [published] in the following year, that is, 1538), Lucillus Philalthæus (on 2 On the Heavens, text 51), Andreas Cæsalpinus (bk. 3 of the Peripatetic Questions, q. 4), and at last John Anthony Delphinus, a Franciscan of Casale Maggiore (in the book On the Celestial Globes and Orbs)—whom Alpetragius [al-Bitrūjī] favors in many things in his celestial physics. Our [own] Bartholomew Amicus, however, is mistaken (tract. 5, On the Heavens, q. 5, dub. 2, art. 2) when, among these authors, he reckons all the Astronomers who posit the heaven [to be] fluid, and the stars in it [to be] going like birds in the air or fishes in the sea; since neither Tycho, nor Kepler, nor Bullialdus, nor finally any of the more recent Astronomers who assert the heavens of the Planets [to be] fluid, has used mere concentric circles in his hypotheses.

[Margin: A lapse of Bartholomew Amicus.]

[Margin: 2. Opinion — positing Eccentrics.]

[V.] The second opinion was that of the Eccentrists, that is, of those who, in setting forth the motions of the Planets, used circles, or Ellipses, or as it were circular spirals, but having a center diverse from the center of the world; or [used] concentrics indeed, but bearing various Epicycles equivalent to eccentrics. The inventors of this opinion were the Pythagoreans, as Simplicius reports from Nicomachus (on bk. 2 On the Heavens); who also reports that Aristotle’s opinion about Concentric orbs was rejected by Sosigenes, on the ground that it could not safeguard the greatest part of the motions—especially the stations, retrogradations, [and] elevations from and depressions toward the earth—where, nevertheless, [Sosigenes] describes no determinate hypothesis [of his own]. Hipparchus, however, and Ptolemy everywhere in the Almagest, and thereafter Albategnius, Alfraganus, Geber, Thebit, Peurbach with his expositors, Copernicus (in the work On the Revolutions), Maginus and Piccolomineus (in [their] Theorics), and from Tycho onward all the Astronomers, persisted in the same opinion. But [some] disputed on its behalf and, with distinct arguments, asserted it—chiefly Maior (on 2, dist. 14, q. 4), Peter of Ailly [Alliacensis] (q. 13 on the Sphere), Christopher Clavius (on ch. 4 of the Sphere of Sacrobosco), and Bartholomew Amicus (tract. 5, On the Heavens, q. 5, dub. 2); and these very [men] of old were confirmed by many indications [by] Pliny (bk. 2, from ch. 15 to 17) and Martianus Capella (bk. 8, On the Nuptials of Philology and Mercury, in the chapter [showing] that the Earth is not the center for all the Planets).

THE SINGLE CONCLUSION

The motions of the Planets are not made through circles Concentric with the center of the World, but through Eccentric circles, or quasi-circles, or through [things] equivalent to Eccentrics.

[VI.] The first argument could be drawn from the Authority of all—

[…continues on p. 253 (PDF 288): the first argument from authority — the great multitude of Astronomers, both ancient and modern, who used Eccentrics and Epicycles…]


(printed p. 253 — completing [VI.], the first argument, from authority:)

[Margin: 1st argument, from the inequality of the intervals.]

[VI.] [The first argument could be drawn from the Authority] of nearly all the Astronomers from Hipparchus down to this our age, who through seventeen centuries held this method of setting forth the celestial motions, with very few resisting—and those (if you except Fracastorius) unskilled in celestial observations. But in an Astronomical question it is better to confirm our assertion by reasons. The first reason, then, is taken from the unequal distance of each Planet from the center of the earth: for within one [and the same] period they are now farther from the earth, now nearer, now at a certain middling interval. For we proved the Moon’s unequal distance from the earth, from the diversity of the Lunar parallaxes, in bk. 4, ch. 14. And, diverse distances of it being posited, there follows necessarily a varying distance of the Sun from the earth, on account of the Astronomical connection which the Sun’s distance has with the phase of the dichotomous [half] Moon, as is established from the problem of Aristarchus, and from our careful and legitimate use of it, often reduced to practice and set forth in bk. 3, ch. 7. Wherefore, although from the diversity of the Solar parallaxes the diversity of distances cannot be shown so evidently, yet from the Moon’s distances, and from the time between the appearance of the half-Moon and the moment of Quadrature, it can be gathered. And, the varying distance of the Sun from the earth being acquired, the distances of the remaining Planets become known, because they have no less a connection with the Sun’s distance than their motions have with the motion of the Sun, as can be established from what was said in bk. 7, sect. 2 and 3, and sect. 6, ch. 2. For equations congruent with the true motions and observed places of the Planets cannot be deduced, except by supposing in their hypothesis a diverse distance from the Sun and from the earth.

Moreover, in all seven planets a diverse apparent magnitude is observed—and in the Luminaries indeed both outside Eclipses and in Eclipses, whose magnitude is varied according to their varying recession from or approach to the earth. But in Mercury, Venus, and Mars, that variety too has been observed with Telescopes, so that they appear sometimes full of light, sometimes gibbous, sometimes crescent [falcate], as we showed in bk. 7, sect. 1, ch. 2. Finally, how much larger Mars and Venus appear at perigee than at apogee, we taught clearly in bk. 7, sect. 2, ch. 3 (in the scholia), and sect. 6, ch. 4 (likewise in the scholia), and ch. 10 (likewise in the scholia). If the Reader has well understood these [things], there will hardly remain to him any doubt about that variety of apparent magnitude.

[Margin: The true cause of the diverse apparent magnitude.]

But now the aforesaid variety cannot be referred either to vapors of the air now thicker, now thinner, nor to parts of the heaven now denser, now rarer—as Fracastorius, Amicus, and Delphinus dared to refer it. For there both stands in the way the most invincible argument drawn from the parallaxes, which shows the diversity of distance (from which necessarily follows the diversity of apparent magnitude); and besides, the same planets appear frequently larger when either there are no thick vapors in the air, or [the vapors] are far from them; and finally [there is] the wonderful agreement in the proportion of the increase and decrease of this apparent magnitude with a determinate situation with respect to the Sun—for the three superior Planets always appear very large in opposition with the Sun, and in the acronychal [midnight] position [when] made retrograde; and very small around conjunction with it; and Venus and Mercury always appear largest when crescent—and these Phenomena are discerned whatever, in the end, be the season of the year, and in whatever part of the Zodiac. Besides, if a diverse density of the heaven running underneath were the cause of this variety, the magnitude of the Fixed [stars] too, and the brightness and splendor of the Planets, would also be changed from time to time—for [their light] would either be blunted by the density, or, the rays converging, would appear more intense by the force of refraction. Finally, it would be necessary to multiply so many heavens or celestial Zones slipping beneath the seven Planets, with denser and rarer parts—and indeed one heaven below the Moon—which would happen by no necessity, nay by scarcely the slightest probability, since the same could be done far more naturally and more simply through the alternating elongation of the Planets from the earth, and [their] approach—that is, through that [same cause] by which the inequality of motion in longitude is also said to come about. But if anyone be unwilling, in this matter, to use Eccentrics or Concentro-epicycles, but [will use] concentric circles now larger now smaller—yet, in order to make them continuous, as the observations demand—it will be necessary that these circles, becoming ever wider and wider, follow rather the form of a spiral gyration than of perfect circles returning into themselves, concentric with the world.

[Margin: 2nd argument, from the unequal motion.]

[VII.] The second argument is taken from the inequality of the motions in longitude and latitude, which we have already described in bk. 3, ch. 19 (where [we treat] of the Sun), and bk. 4, ch. 18 (where of the Moon), and bk. 7, sect. 1, ch. 7 (where of the remaining Planets), but chiefly from the inequality of the Stations and Retrogradations, about which [we treat in] bk. 7, sect. 5, ch. 2. But although this argument makes our conclusion more probable, and although the aforesaid varieties are better and—according to the laws of Geometry—more elegantly and more beautifully set forth by Eccentrics and Epicycles (or [by] line-tracings equivalent to them), and the physical cause of such inequalities is in a manner set before the eyes; yet, to profess frankly what I think, it is not an evident argument; and, if the varieties of the parallaxes and the vicissitudes of the apparent magnitudes did not stand in the way, we could set forth all that interchange of speed and slowness through mere concentric circles, and through laws of motion rhythmic and logistic rather than geometric, as we shall say below.

[Margin: 1st objection resolved.]

[VIII.] It remains that we dissolve the arguments of the Homocentrists. First, it is objected against Eccentrics and Epicycles [that the center of the earth would not be at the center of the heaven, or the center] of the heaven would not be at the center of the World; but that this is absurd. It is answered by denying the Major as regards the supreme heaven of the Fixed [stars], and so as regards the whole heaven of the Planets, which is single and fluid, and whose convexity is bounded by the concavity of the Firmament. But if there be solid orbs, the Minor, taken of any [particular] heaven [you please], is denied, and conceded only of the supreme.

[Margin: 2nd objection.]

Secondly: to the elements of the Sun [the sublunary world] there belongs simple motion upward and downward; but to the celestial bodies straight motion does not belong, but simple circular [motion]. Yet if they were moved by the force of Eccentrics and Epicycles, upward motion would belong to the celestial [bodies]. Therefore. It is answered by conceding the Major concerning motion upward and downward along a straight line perpendicular to the globe of the earth—in which sense the Minor is denied.

[Margin: 3rd objection.]

Thirdly: every heaven, according to Aristotle, is perfectly spherical; but it would not be, Eccentrics being posited. It is answered, the Major being granted, by denying the Minor: for if the heaven of the Planets is fluid, it is really one and spherical with respect to the center of the universe; but if it consists of solid orbs, every Eccentric orb (as to its outermost surface), and every Epicycle (with respect to [its] proper centers), are spherical.

[Margin: 4th objection.]

Fourthly: if Eccentrics and Epicycles were granted, they could not be moved without penetration or splitting of the heavens, nor without [their] rarefaction and condensation, so that a less deep part should enter a deeper one: but this is unfitting. It is answered by denying the Major; for in the hypothesis of a fluid heaven the objection ceases; and in the hypothesis of a solid heaven too, the two Eccentrics are not moved in such a way (in a certain respect) that the less deep part of the one should succeed into the place of the thicker and deeper [part], as the Averroists imagine out of inexperience; but they are revolved proportionally in such a way that perpetually the thicker part of the lower Eccentric lies beneath the less deep [part] of the higher, and the narrower part beneath the deeper—so that the Eccentric simply has no other motion than the whole heaven of the Planet.

[Margin: 5th objection.]

Fifthly: according to Aristotle, the more a Planet is distant from the supreme heaven (which has simple motion), the more motions it needs in order to obtain its perfection; but in the hypothesis of Eccentrics and Epicycles the Sun has fewer motions than the three superior Planets. It is answered by denying the Major; for even according to the opinion of the Homocentrists, if they wish to safeguard the Sun’s phenomena, fewer motions are to be assigned to it.

[Margin: 6th objection.]

Sixthly: all the phenomena [φαινόμενα] of the heaven can be defended by concentrics and a plurality of motions, as Aristotle affirms (bk. 2 On the Heavens); therefore Eccentrics and Epicycles are multiplied in vain—especially since the two Eccentrics carrying the apogee of the Planet seem superfluous, and a single one seems to suffice, as Augustinus Niphus says. It is answered by denying the Antecedent; for upward and downward motion cannot be defended through mere concentrics; but, solid orbs being posited, each Eccentric is necessary in the Ptolemaic hypothesis—not for carrying the apogee precisely (as Niphus thinks), but for this: that the whole heaven of the Planet should have a proper motion about the center of the world; for in other hy—

[…continues on p. 254 (PDF 289): “…potheses these motions are ordered otherwise. Seventhly Fracastorius objects: If the Sun is farthest (or most) distant when it is at the beginning of Cancer, and least when at the beginning of Capricorn, [either] it will describe on both sides parallels equally distant from the Equator (and so the Sun’s maximum declination will not be equal on both sides…)…” — Riccioli answers the 7th–9th objections (of Fracastorius, and of Averroes), then turns to Aristotle’s own modesty, and opens Chapter III on the motion of the Prime Mobile.]


(printed p. 254 — continuing [VIII.], the resolution of the Homocentrists’ objections: the page opens mid-sentence, completing the remark that in other hypotheses these motions are ordered otherwise.)

[Margin: 7th objection, of Fracastorius.]

Seventhly, Fracastorius objects: If the Sun is more (or most) distant when it is at the beginning of Cancer, and least when at the beginning of Capricorn, [then] either it will describe on both sides parallels equally distant from the Equator—and so the Sun’s maximum declination will not be equal on both sides, [namely] 23½ degrees, which is contrary to the observations (for the angle made at the center of the world, or at the surface of the earth, by two lines—the one terminated at the periphery of the Equator, the other at the center of the solar globe—will be narrower when the Sun is higher than when [it is] lower, as the laws of Geometry and Optics require); or, if the maximum declination of the Sun is on both sides equal, it will be necessary that the Sun, at the beginning of Cancer, describe a parallel more distant from the Equator than when it is at the beginning of Capricorn, and so that the diurnal arc of the longest day, in an oblique sphere, be not equal to the nocturnal arc of the longest night—which likewise is contrary to Astronomical experience and observations. It is answered: the maximum declination of the Sun is indeed equal on both sides, and the diurnal arc of the longest day [is] unequal, compared with the nocturnal arc of the longest night in the same oblique horizon; but that inequality is not perceived, on account of the immense distance of the Sun from the earth in each case, and the insensible parallax, which for us does not exceed 30″ [seconds]—besides that the varied refractions, accelerating the rising of the Sun and retarding its setting, not rarely compensate that inequality. You should remember, nevertheless, that the Sun’s Apogee is not always situated at the beginning of Cancer.

[Margin: 8th objection, of Fracastorius.]

Eighthly: it would follow, from Ptolemy’s opinion, that the Epicycle of Venus is of such magnitude that it would reach almost to the earth; for its semidiameter contains 43 degrees, and if it contained 45 degrees it would pass through the center of the earth. It is answered by denying the antecedent: for the semidiameter of Venus’s Epicycle does not contain 43 degrees of the heaven of Venus (as Fracastorius falsely assumes), but 43 such parts as 60 of which are contained in the semidiameter of its Eccentric. Then, if you consult the Ptolemaic and Alphonsine least distance of Venus from the earth—which we set down in bk. 7, sect. 3, ch. 1, and sect. 6, ch. 2—you will see it to be 179 terrestrial semidiameters [and] 2′, according to Fernel, but 167 [semidiameters] 57′ according to Maurolyco and Clavius. But in our hypothesis, which we think truer, the least distance of Venus is at least 1917 terrestrial semidiameters.

[Margin: 9th objection, of Averroes and Fracastorius.]

Ninthly: if the Moon were revolved in an Epicycle, we would not always see the same face of the Moon, but one [face] at the apogee of the Epicycle, another at the perigee. But we always see the same. Therefore. I answer: Unless any other motion were attributed to the Moon, I concede the Major; but I deny [it] if there be attributed to it either a turning [vertigo] about its proper center toward the part contrary to the motion of the Epicycle (as Fernel attributes [it], in his Cosmotheoria), or [if] you transform the Epicycle into another Eccentric (as Maginus does), or [if] you use other equivalent hypotheses—about which [there is] enough in bk. 4, from ch. 26.

The remaining objections rest either on false observations, or on the mere authority of Aristotle defending concentrics—who, however, just as in this he subscribed to Eudoxus and Callippus, certainly, if he had lived after Ptolemy and had learned Astronomy from him, would have accepted other hypotheses; since he himself professed that in these matters the more skilled Astronomers are to be consulted. For in bk. 2 On the Heavens, ch. 7, text 34, he says:

“When, therefore, anyone has attained the more certain necessities, then he ought to be grateful to those who find them out; but for now, what seems [probable] must be said.”

And in 12 Metaphysics, text 45, on the motions [lations] of the Planets, he says:

“But how many these are, we now say—for the sake of understanding—those things which certain of the Mathematicians assert, that we may perceive in the mind some determinate plurality. But for the rest, it befits us in part to inquire ourselves, in part to ascertain from the investigators of these matters, if anything beyond what has hitherto been handed down should appear, to those who occupy themselves about these things, to be so; and [it befits us] to esteem both indeed, but to adhere to the more certain.”

[Margin: The modesty of Aristotle’s genius.]

And a little after he confesses that he has spoken only probably about these [things], and that the necessary demonstrations must be sought from those more skilled in these matters, when he says:

“Wherefore the substances also, and the principles—both the immovable and the sensible—are so to be reckoned [to be], rationally (in Greek λογικῶς [logikōs]), that is, topically and probably: for what is necessary, let it be left to be said by [those] more powerful [than I].”

Let those Peripatetics hear [this] who contend that Aristotle—even against his will—always utters infallible oracles, and who try to carve him out for posterity, not as one walking in the Peripatos and ready to follow better [things], but as a stone statue immovably fixed to opinions once conceived.