[Margin: Which System Eudoxus and Calippus followed.]

[I.] The first controversy is about the order of the Planets—namely of Mercury, Venus, and the Sun (for about the three superior [planets], and about the lowest, the Moon, there is no doubt)—as asserted by Eudoxus, Calippus, and Aristotle. And at first, indeed, Eudoxus—as being a Cnidian—seems to have followed the Platonic system, Laërtius attesting this (bk. 8, in the life of Eudoxus); especially since he chose the same opinion about concentric orbs, as we shall presently see. But since Calippus indeed corrected the system of Eudoxus, yet retaining the concentrics, and only adding certain other starless orbs—and the same Aristotle did, adding other revolving [spheres] above the Calippic number, and was moreover a disciple of Plato—it seems consonant that Calippus, equally with Aristotle, retained the Platonic system as to the order of the Planets.

[Margin: The System of the author of the De Mundo ad Alexandrum.]

To this is added that Aristotle, in the book On the World, to Alexander (ch. 2), has these [words]: “Next to this [sphere]—that is, to the globe of the non-wandering [stars]—the so-called circle of Phænon [φαίνων] together with Saturn always has [its] position contiguous; nearest to which is [that] of Phaethon [φαέθων], which is also called Jupiter’s. After this follows Pyroeis [πυρόεις], called also Hercules’s and Mars’s. From this, again, is Stilbon [στίλβων], which is believed sacred to Mercury, by some also to Apollo; after which is the orb of Lucifer, which some call the orb of Venus, some of Juno. From it is the orb of the Sun; and finally the Moon, nearest to us, extending its bounds even to the earth.” But if the author of this booklet be called into doubt, certainly these are the words of Aristotle (bk. 1 of the Meteorology, ch. 4), saying: “Moreover, as is shown in the Astrological theorems, the magnitude of the Sun is greater than the earth, and the distance of the stars from the earth much greater than [that] of the Sun—as [the distance] of the Sun from the earth [is greater] than [that of] the Moon; therefore the cone which it [the earth] casts from the Sun’s rays is not raised very far from the earth, nor will the shadow of the earth (which is called night) reach to the stars; but it is necessary that the Sun look around upon all the stars, and that the earth obstruct none of them.” He supposes, therefore, that no stars can fall into the shadow of the earth, because they are much more remote from the earth than the Sun—granted such a great distance is not necessary, but he supposed it from the hypothesis of certain Astronomers placing all the Planets above the Sun. Finally, that Aristotle supposed Venus and Mercury to be situated above the Sun, affirm Hamerus (ch. 1 on Genesis), Valentin Naibod (bk. 1 of the Astronomical Institutions, ch. 16), Clavius (on the Sphere, p. 64), Ba—

[…continues on p. 284 (PDF 319): “…rozzi (bk. 1 of the Cosmography*, ch. 2), Longomontanus, Argoli…” — then ¶II (whether Eudoxus, Calippus, and Aristotle followed the Egyptian or the Chaldean order), ¶III (Eudoxus’s 27 homocentric spheres and the hippopede), ¶IV (Calippus’s added spheres), and ¶V (Aristotle’s own counter-revolving spheres — 55 or 47).]*

(printed p. 284 — Chapter V continues, completing the list of authors and asking whether Eudoxus, Calippus, and Aristotle followed the Egyptian or the Chaldean order. The page treats Eudoxus’s homocentric spheres and Calippus, and opens the account of Aristotle’s own counter-revolving spheres.)

…[Ba]rozzi (bk. 1 of the Cosmography, ch. 2), Longomontanus (in the Danish Astronomy, bk. 1 of the Theorics, ch. 1), Argoli (in the Pandosion Sphæricum, ch. 3); nor can it be denied that the opinion of these [authors] is probable.

[Margin: Eudoxus’s order called into doubt.]

[II.] These [things] notwithstanding, it seems at first that Eudoxus—as being a Cnidian, and pertaining to the Assyrians rather than the Greeks—ought to have followed the opinion of the Barbarians, namely of the Assyrians and Egyptians; the more so because, as Laërtius relates in his life, he heard Plato at Athens for only two months (being both pressed by poverty and cast out by Plato), and was thence compelled to return to [his] fatherland; and afterward, supported by the largess of friends, he set out to Egypt, where, having tarried 16 months, [and] at last having many disciples, he returned to Athens, so as to vex Plato, who from the beginning had dismissed him. Wherefore, although he chose concentrics, it is nevertheless not certain which part of the Egyptian system he chose—that which set Mercury and Venus [above] the Sun, or that which set the Sun above them.

[Margin: And Calippus’s [order]; and Aristotle’s.]

And I say the same of Calippus, who—as being an Asiatic—is believed to have been addicted to the Chaldean hypotheses, and whose writings were known to Ptolemy (and indeed those of Eudoxus too, it is believed), as is clear from the Almagest (bk. 2, ch. 2); and yet (bk. 9, ch. 1) [Ptolemy] places, according to the opinion of the ancients, Venus and Mercury below the Sun, and attributes the opposite only to the younger [moderns]. As regards Aristotle: since he himself says (On the Heaven, ch. 10): “But now the contrary happens; for the Sun and Moon are moved by fewer motions than some of the stars, although they are farther from the middle and nearer to the first body than these very [stars]“—he seems to have spoken not of all, but only of some Planets, as being higher than the Sun and Moon and yet having more motions; then, since in the same place he had related that Mars was seen by [him] occulted by the Moon (in order to show that the Moon is the lowest of all, although having fewer motions than certain Planets nearer to the Fixed [stars]), he subjoins: “Similarly also they speak about the other stars—the Egyptians and Babylonians, who long ago observed these things through very many years, to whom we attribute much faith concerning each of the stars.” Therefore it is more credible that Aristotle, as to the order of the Planets, followed either the system of the Egyptians; or—because he chose concentrics, and placed no Planets now above, now below the Sun—rather adhered to the Babylonian, or Chaldean, system, which placed Venus and Mercury below the Sun (as we learned from Bede in the preceding chapter, num. 4). For now Alexander the Great, having taken Babylon, had transmitted into Greece the observations made there and recorded for very many years, as may be gathered from Quintus Curtius. And as Pliny relates (bk. 7, ch. 56): “Epigenes teaches that among the Babylonians [there were] observations of the stars of 720 years, inscribed on baked tiles—a weighty author among the first; [those] who [reckon] least, Berosus and Critodemus, [give] 480 years of observations, I understand.” Moved, therefore, by these conjectures, and by the authority of certain Peripatetics [commenting] on the books of Aristotle On the Heaven and Metaphysics 12, I elsewhere opined that Eudoxus and Calippus and Aristotle, retaining concentrics, placed the Sun above Venus and Mercury—though now I confess the opposite to be probable. Now let us come to the other part of this system—namely, to the number and office of the orbs by which the motion of the Planets was set forth by them, the distance of them from the earth being retained always of the same interval [i.e., concentric].

[Margin: Eudoxus’s concentrics.]

[III.] Concerning the Orbs of Eudoxus, Aristotle (Metaphysics 12, ch. 7, or text 45 & 46) relates thus, with wonderful brevity: “Eudoxus, then, posited that the motion of each—I mean of the Sun and of the Moon—is made by three spheres each: the first being that which would accomplish the motion of the non-wandering [stars]—that is, of the Prime Mobile; the second, for the motion which is made through the circle which is through the middle of the Signs—namely, through the Ecliptic, in longitude; the third, for the motion oblique to the Zodiac, in latitude—and [that] the [sphere] by which the Moon is carried is made oblique by a greater latitude than that by which the Sun is carried.” As if indeed the Sun changed somewhat in latitude. “But the motion of the remaining Wandering stars he posited to be made by four spheres each: the first and second [having] the same motion which those [the Sun and Moon] undergo; for both that [sphere] which [has] a motion similar to the motion of the Fixed stars and common to all, and that which is placed below this (and whose motion is through the circle which is through the middle of the Signs), is common to all; but the third sphere of each has its poles in that circle which passes through the middle of the Signs [the Ecliptic]; while the motion of the fourth cuts this circle obliquely and in two ways. And the poles of the third sphere are proper indeed to the other stars, but for Venus and Mercury [they are] the same.” From which it appears that one sphere was attributed by Eudoxus to the Fixed [stars], three to the Sun, three to the Moon, and four to each of the smaller Planets [the five]—that is, in all 27; nor [does it appear] that he thought the lower spheres are carried along by the sphere of the Fixed [stars], but [that] the individual Planets [are moved] by their own sphere with a diurnal motion through the Meridian to the West. Moreover, [it appears] that the variation of the obliquity of the Ecliptic and of the maximum declination of the Sun—asserted by some [to occur] at the Solstices—he attributed to a motion of the Sun in latitude: for he did not think (says Simplicius, 2 On the Heaven) that the Sun perpetually proceeds under the Ecliptic. Each Planet, therefore, had one orb for the common motion from East to West; and another for [its] proper motion under the Zodiac toward the East; and a third for the motion of latitude, from South to North—which (as G. B. Amici gathers from Simplicius and Theophrastus, in the opusculum On the motions of the celestial bodies, ch. 1) completed its motion in that time in which each Planet accomplishes its Metabasis (Μετάβασις, “transit/passage”) through [its] aspects to the Sun: which time, according to Eudoxus, was—for Venus, 18 months; for Mercury, 110 days; for Mars, 8 months and 20 days; for Jupiter and Saturn, 3 months and 10 days. But the fourth orb—as the same [authors], and Delphinus (ch. 5 On the celestial globes), expound—carried the body of the Planet, and, by resisting the third orb, prevented [it], lest the Planet should reach to the poles of the Zodiac; and therefore the Planet described, by its center, a certain line called by Eudoxus the hippopede (ὑπποπέδη, “horse-fetter” [a figure-eight curve]). And Eudoxus wrote a booklet On Velocities (περὶ ταχυτήτων), and several other [things], which have not reached us. Yet otherwise—from mere conjectures—Fracastoro interpreted Eudoxus and Calippus (in the Homocentrica, sect. 3, ch. 25), whom let [him] consult who delights to amuse himself [with it].

[Margin: Calippus’s homocentrics.]

[IV.] But Calippus of Cyzicus, contemporary with Aristotle, added to the homocentrics of Eudoxus some other orbs, likewise concentric to the world. For Aristotle (Metaphysics 12, text 47), where he had set forth the orbs of Eudoxus, writes thus about him: “But Calippus posited the same position of the spheres as Eudoxus—that is, the order of the intervals; and also the same number for Saturn and Jupiter. But he judged that two spheres besides should be added to the Sun and the Moon, if one wished to assign the causes of the [things] which appear to the senses; and to each of the remaining wandering [stars], one [more].” Alas, how meagerly Aristotle [speaks]! But now Eudemus (as Simplicius relates) said this was done by Calippus because he wished to safeguard, in the Sun, the “delay” [dilatio, the inequality] of the Equinoxes and Solstices observed by Almeon and Meton; but others devised other causes (says Delphinus, above)—and in the Moon indeed a certain new inequality, but in Mars, Venus, and Mercury, single [spheres] on account of the stations and retrogressions. Further, from what was said by Aristotle, it becomes manifest that Calippus’s spheres were 33—and, with [that] of the Fixed [stars], 34: namely one of the fixed [stars]; four each for Saturn and Jupiter; five each for Mars, Venus, and Mercury; and five each, finally, for the Sun and the Moon. Yet Aristotle reckons 8 star-bearing [spheres] and 25 starless, that is 33, as we shall presently see.

[Margin: Aristotle’s counter-revolving [spheres].]

[V.] But at last Aristotle himself, in the same Metaphysics 12, text 47, after the indicated opinion of Calippus about the number of the concentric spheres, involved [enveloped] rather than developed his own opinion too, in these words—and the common translator infused not a little cuttlefish-ink [loligo, i.e., obscurity]; but thus we have more clearly rendered that text: “But it is necessary, if the aforesaid spheres, [being] composed together, must restore each Planet to its pristine place, that to each of them there be subjoined just as many other spheres, one being subtracted, which may revolve [back] and constitute, at the same situation, the first sphere of that star which is ordered below [it]. For only in this way will it come about that [the spheres] accomplish all the motion of the Wandering [stars]. Since, therefore, the spheres in which the stars are carried are eight, but the remaining [are] twenty-five, of these the only ones that do not need a [counter-]revolution are those which carry the body of the Planet, or which are lowest in their order. [The spheres] which revolve back the spheres of the first two [planets] will be six; but [those] which [revolve back the spheres] of the four after them, sixteen; and the number of all—both of those which carry [the planets] and of those which revolve them back—[is] fifty-five. But if to the Moon and the Sun one does not add those motions which we mentioned, all the spheres will be forty-seven.” Which words still seem similar to an enigma; but we shall solve this enigma, if [we grasp] Aristotle’s—

[…continues on p. 285 (PDF 320): “…meaning…” — Riccioli’s unravelling of Aristotle’s count of 55 (or 47) homocentric and counter-revolving spheres, with its accompanying diagram.]

(printed p. 285 — The account of Aristotle’s sphere-count concludes with a table of spheres, followed by others’ errors in the count and Sosigenes’s critique, ending Chapter V. Chapter VI then opens, on the systems of Averroes, Alpetragius, Delphinus, and Amici, beginning with Averroes and Alpetragius.)

…[we shall solve this enigma, if we have opened up Aristotle’s] meaning point by point. First, then, Aristotle, among the partial spheres whose number he inquires, does not number the first—although he supposes it, because, being endowed with a single simple motion, it needs no other orb; and hence it is that he reckons the orbs of Eudoxus endowed with stars [to be] eight indeed, but the anastrous (ἄναστροι, “starless”), that is, lacking a star, or not carrying the body of a star, he numbers [as] 25—whose sum is 33. Secondly, Aristotle adds no counter-revolving [spheres] to the Moon; for although at the end he seems to say that he has added counter-revolving [spheres] to the Moon and the Sun, he by no means says this, but [says] that, if there be not added to the Moon and the Sun [those] counter-revolving [spheres] such as he had added to the first two Planets and to the four remaining, the number of spheres is 47. But why he did not fear, for the Moon, lest it be snatched along by the higher orbs—and therefore [why] it had no need of counter-revolving [spheres]—was perhaps the wonderful velocity of the Moon in its proper motion; or rather because the Moon does not have orbs below it, to which it might communicate its motion. Thirdly, to all the other spheres of the Planets, but [only the] starless [ones], he thinks single counter-revolving [spheres] must be added, which may prevent or compensate the snatching of the higher [spheres]; but to the spheres carrying the body of the Planet, he adds no counter-revolving [sphere]. Fourthly, reckoning the Calippic number of starless spheres, he counts in just as many counter-revolving [spheres] for them: namely 6 spheres for Saturn and Jupiter together; but four each for Mars, Venus, Mercury, and the Sun—and so 16 together; and none for the Moon. Now the Lunar spheres were 5 in Calippus, and the Sun’s 5, and Mercury’s 5, and Venus’s 5, and Mars’s 5, and Jupiter’s 4, and Saturn’s 4. These, then, being reduced to a sum, the Planetary spheres come to 55. Fifthly: because the stations and retrogradations of Mars, Mercury, and Venus were more evident in that age than those motions on account of which Calippus added two spheres each to the Sun and Moon—if one wished to mix the Eudoxan with the Calippic number, and, as to the Sun and Moon, to follow Eudoxus (who gave three spheres to the Luminaries, six taken together), but, as to the remaining Planets, to follow the Calippic number increased by the counter-revolving [spheres], the Planetary spheres come out [to] 47. That this reckoning may appear more evident, we will append the numbers of the spheres according to these three authors.

THE NUMBER OF SPHERES

[Margin: Errors of others in the Aristotelian number of spheres.]

[VI.] Hence you now see how great in reality was the number of spheres for Eudoxus, Calippus, and Aristotle, and how various—according as the sphere of the Fixed [stars] was, or was not, counted in; and according as the Calippic [hypothesis] alone, or [one] mixed from the Calippic and Eudoxan, was employed. Wherefore the numbers of certain [writers] in no way stand, nor can they rest on the Aristotelian text. As when Kepler (in the Commentary on Mars, ch. 2) says of Eudoxus, Calippus, and Aristotle: “For since those authors employed 25 orbs to demonstrate the whole inequality of the Planets, Aristotle—believing the heaven filled with solid orbs—judged that 24 other counter-revolving [orbs] must be interposed, namely that each lower orb might be freed from that snatching which, on account of the contiguity of the surfaces, it was going to suffer from the higher [orb]. Therefore, when he had accumulated in all 49 orbs (or, according to Calippus, 53 or 55), he added single movers to the single [orbs].” But neither John Anthony Delphinus (in the book On the celestial globes and motions, ch. 8), nor Fracastoro (sect. 3, ch. 25)—where they most diligently expound this Aristotelian passage—nevertheless put the correct number. For Delphinus says that for Aristotle there are 55 [spheres] Calippically, but 49 Eudoxanly; yet he correctly numbers the Calippic [ones as] 34 separately, and the Eudoxan [as] 27 with the Fixed [stars]. But Fracastoro does not number 47—rather he omits the second computation of Aristotle. Hevelius too (ch. 7 of the Selenography) badly numbers the Aristotelian orbs [as] 53 or 54. But the Conimbricenses (bk. 2 On the Heaven, ch. 3, q. 8, art. 2) put 47 or 50; and Mastrius and Bellutus (disp. 2 On the Heaven, q. 1, num. 35) put 55 or 57; but all err in something from the true number: for there are, for Aristotle, 55, and with the sphere of the Fixed [stars], 56; but if he should subscribe to Eudoxus as to the Sun and Moon, and to Calippus in the rest, there are 47, and with the sphere of the Fixed [stars], 48.

[VII.] Furthermore, Sosigenes detected many imperfections of this system (as Simplicius narrates), inasmuch as it did not safeguard many Phenomena of the Planets. But certainly in this it most errs—that it uses homocentrics, since, from the diversity of the Lunar parallaxes and of the apparent magnitude of the Planets, it has now become evident, physically and optically, that they are now higher, now lower. Deservedly, therefore—the homocentrics being rejected—it took refuge in the Pythagorean Eccentrics and Epicycles.