[I.] No motion among the celestial [motions] is better known than the motion of the prime Mobile, by which, namely, we see all the stars—but especially the Fixed [stars]—daily, in 24 hours, revolved from the same point to the same point of the heaven toward the West; and yet nothing is more obscure, whether [we ask] about the subject of this motion, or about its difference from the remaining motions of the stars, and about the manner of composing them among themselves without any physical repugnance. I touched on this controversy in bk. 6, ch. 18, in setting forth the Theoric of the Eighth sphere and of the Fixed [stars]; but because afterward I obtained other authors, and a repeated contemplation of this motion brought forth certain considerations not unworthy of being known—and because here at last is its proper place, where we treat of the universals common to all the stars—it pleases [me] to call the same [matter] back to the anvil.

[Margin: 1st opinion, placing the Prime Mobile in the single motion of the Fixed [stars].]

[II.] The first and most ancient opinion was that the Fixed Stars are set in motion by no other motion than the diurnal and common [one] toward the West—the [motion] peculiar to them upon the poles of the Zodiac, with the change of declination, not having yet been detected by certain observation, inasmuch as [it is] sensible only after many years, nor evidently demonstrable within the ordinary lifetime of one observer. This being posited, the first motion was nothing other than the very motion of the Fixed [stars], or of the Eighth sphere, about the axis of the Equator and upon its [the Equator’s] own poles; and the eighth sphere itself was the Prime Mobile and the supreme Astronomical heaven, and the universal time was visible, and a most well-known measure, inasmuch as [it is] nothing other than the revolution of any one Fixed star—say, the Dog-star [Sirius]—to the same point of the same fixed Meridian. And that the Babylonians, and some of the Egyptians and Greeks—but especially Eudoxus and Callippus, and so too Aristotle—were of this opinion, is gathered from Aristotle himself (bk. 2 On the Heavens, from ch. 9, or from text 57 to 70; and 12 Metaphysics, from text 42 to 51), where, together with Eudoxus and Callippus, he attributes a single and most simple lation to the sphere of the non-wandering [fixed] stars; and among the other causes for which that [sphere] is filled with innumerable stars, he adduces this:

[Margin: Authors of this opinion: the Babylonians, the Egyptians, Eudoxus, Callippus, Aristotle.]

that by the multitude of stars the simplicity of the motion may be compensated, and—just as the spheres of the wandering [stars] have a single star but several motions—so the sphere of the non-wandering [stars] should have a single motion, but several stars: for thus [says] he (2 On the Heavens, text 67). And that this method of Astronomy flowed from the Egyptians and Babylonians to the Greeks, he relates (2 On the Heavens, text 60). Therefore the most ancient Babylonians and the Egyptians (as Albategnius relates, ch. 27, On the Science of the Stars), defining the Year, said that it is the Revolution of the Sun to the same Fixed star—just as if the Fixed stars were fixed points, and movable by no other motion than the diurnal. And Nimrod [Nembroth] the Chaldean, in his Astronomical work (in [the citation of] Augustinus Riccius, in the treatise On the motion of the Eighth sphere), ascribes to the signs of the heaven only a single motion. But neither were Hesiod and the other most ancient Poets of the Greeks of a different opinion, when they placed nine Muses in the heaven; for to the supreme [Muse], namely Calliope, they ascribed no peculiar voice, nor any motion, as Glareanus notes (bk. 2 of the Dodecachordon, ch. 8 and 13)—but the supreme, sharpest voice (on account of the greatest velocity of motion), which to Glareanus himself is the Mese [μέσον]—

[…continues on p. 255 (PDF 290): “…they gave to Urania, [as] moderating the sphere of the Fixed [stars]: wherefore Calliope, as the mistress of the celestial harmony, presided over the rest of the Muses and over keeping the motions of all eight heavens together in concord, and contained the voices of all, as Macrobius (bk. 2, on the Dream of Scipio) teaches expressly from Hesiod. But about Plato’s opinion there are [some] who doubt…”]

(printed p. 255 — continuing [II.], the first opinion, mid-digression on the Muses-as-spheres: the highest and sharpest voice, answering to the swiftest motion, was given to Urania as moderating the sphere of the Fixed stars, while Calliope, mistress of the celestial harmony, presided over the other Muses and over the concord of all eight heavens, as Macrobius teaches from Hesiod.)

[Margin: Cicero’s opinion.]

But about Plato’s opinion there are [some] who doubt; yet he, in book 10 On the Republic, introduces a certain Pamphilius [Er]—slain in battle and reviving from the dead, and asserting that he had seen the traces of eight celestial motions, of which the eighth was driven with a most rapid course—and in the Epinomis he says: “The Philosopher ought not to be ignorant how the seven circuits are turned beneath the first.” Nor indeed would Aristotle, his disciple, have kept silent about it, if Plato had taught another motion in the Fixed [stars] besides the diurnal; nor [would] Cicero, in the Dream of Scipio (translating much into Latium from Plato’s books On the Republic)—for there he mentions Nine globes, among which the lowest he assigns to the immobile earth, but the highest [to] the heaven of the fixed [stars] with a single motion. For he says:

“Nine orbs, or rather globes, are all things connected, of which one is the celestial, the outermost, which embraces all the rest—the supreme God himself, confining and containing the others—in which are fixed those everlasting revolving courses of the stars; to which are subject the seven, which are turned backward by a motion contrary to the heaven.”

And, the seven globes of the Planets being enumerated, he adds: “for that which is the middle and ninth, the earth, is neither moved, and is the lowest.” And a little after: “but those eight courses, in which there is the same force of two, produce seven sounds distinct by intervals.” Nay, a little before he had said: “and nature brings it about that the extremes sound, on the one side, low [grave], on the other, high [acute]. For which cause that highest course of the star-bearing heaven, whose revolution is swifter, is moved with a high and rapid sound, but this lowest and Lunar [one with the] gravest.”

[Margin: Macrobius’s opinion about Cicero’s opinion.]

Granted that Macrobius (bk. 1, on the Dream of Scipio, ch. 17) thought that the proper motion of the Fixed [stars] was known to Cicero and indicated by him; for he says: “Besides the two Luminaries and the five stars which are called wandering, some [held] all the rest fixed in the heaven and moved only with the heaven; but others (whose assertion is nearer the truth) said that these too, by their own motion—besides that they are carried along with the revolution of the heaven—advance [precess]: but, on account of the immensity of the outermost globe, they consume ages exceeding a believable number in one circuit of their course, and therefore no motion of them is perceived by man, since human life does not suffice to detect even a brief point of so slow an advance.” Hence Tully [Cicero], not ignorant of any school approved by the ancients, touched at once

[Margin: Philo’s opinion.]

upon both views, by saying (“in which are fixed those revolving everlasting courses of the stars”): for he both called them fixed, and did not keep silent that they have courses. But who would not recognize that Cicero is violently dragged hither, since from that whole context of words it is plain that no other course was understood by him in the Fixed [stars] than the course of the supreme heaven, by whose running they run? Philo too (in the book On the Cherubim), a Platonist certainly, says: “The celestial orbs have motions contrary among themselves; of which the one carries the fixed stars to the right [dextrorsum], the other the wandering [stars] to the left [sinistrorsum]. But that outermost orb of the fixed stars is single, which is rolled from East to West: but the inner seven, namely of the wandering [stars], whose course—at once compelled and voluntary—has two motions contrary among themselves: but the compelled [one is] such as [the motion] of the fixed stars, etc.”

[Margin: The opinion of St. Ambrose and St. Damascene.]

This opinion St. Ambrose too expressed (bk. 2 of the Hexaemeron, ch. 2, whose words we shall report in sect. 3, ch. 1, num. 9); and [St. John] Damascene, when (bk. 2 On the Orthodox Faith) he conceded a motion toward the East to the seven Planets alone, saying: “For they assert there are seven Planets—the Sun, the Moon, Jupiter, etc. But they called these the Planets, that is, the wandering [stars], because they accomplish their motion opposite to the heaven: for the heaven and the rest of the stars are moved from East to West; but these alone have a motion from West to East.” Which opinion some of the Scholastics seem to have held—chiefly St. Bonaventure (on [Sentences] 2, dist. 14, art. 1, q. 1) and Aegidius [Giles of Rome] (part 2 of the Hexaemeron, ch. 26), in these words: “Therefore the orbs of the Planets, [because they] abound in motions, are deficient in stars; but the Eighth sphere, because it abounds in stars, is deficient (so to speak) in motions, because it has only one motion.” Rubius too (2 On the Heavens, ch. 5, q. 1) and Hurtado (disp. 1 On the Heavens, sect. 1) called into doubt the proper motion of the Fixed [stars]. There is also extant a little book of Aben-Ezra [Ibn Ezra] entitled Mishpetei ha-Mazzalot [מִשְׁפְּטֵי הַמַּזָּלוֹת], that is, On the Judgments of the Stars, where it is said: “The great and glorious orb, where are the glorious armies of God, is called the heaven of heavens, because beneath it are the orbs of the seven Planets.” Wherefore this author does not seem to recognize any other heaven above the seven Planets than the single [heaven] of the Fixed [stars]—which, however, he wrongly confounds with the Empyrean. But neither Pliny (bk. 2, ch. 8) recognized any motion of the Fixed [stars] other than this, nor Vitruvius (bk. 9, ch. 4). But as for the fact that Joseph Scaliger (in the book On the Emendation of Times, p. 283, and in the Diatribe on the Equinoxes, ch. 1) contends that Thales of Miletus, Meton, Euctemon, Aristyllus (or Aristarchus) and Timocharis, from the difference between the Tropical Year and the Sidereal [Year] of the Fixed [stars], came into the suspicion of some proper motion of the Fixed [stars]—by which they would gradually recede from the equinoctial points in consequentia [eastward]—that is rather Scaliger’s suspicion than a proven assertion. For that first conjecture and recognition of the proper motion of the Fixed [stars]—indeed from their places observed by Aristyllus and Timocharis, but [from] Hipparchus comparing his own [observations] with the observations of those [men]—Ptolemy attributes [to Hipparchus] (bk. 3 of the Great Syntax [Almagest], ch. 2; and bk. 7, ch. 2 and 3); which [recognition] Ptolemy himself afterward made more certain, his observations being collated with Hipparchus’s.

[Margin: 2nd opinion, distinguishing really two motions, and heavens for them.]

[III.] The second opinion was of those who thus recognized in the Fixed [stars] two apparent motions (Hipparchus and Ptolemy leading the way): one upon the poles of the Equator, from East to West, most rapid, and revolved in the space of 24 hours; the other upon the poles of the Ecliptic, from West to East, very slow—so that, for the diurnal motion, they thought a heaven really distinct from the heaven of the Fixed stars (that is, the Eighth sphere) [to be] necessary, by which all the inferior spheres would be carried toward the West—which motion accordingly they called [the motion] of Rapture [Raptus]. But in this opinion three classes of authors are to be subdistinguished.

[Margin: 1st class, positing 9 movable spheres.]

The authors of the first class posited only nine celestial spheres, and so recognized a Ninth [sphere] for the prime Mobile: Rabbi Moses [Maimonides], Rabbi Joshua (in the Book of Demonstrations), Haly (in the Quadripartite, ch. 11), and many Jews—nay, Aben-Ezra himself (in the book Te’amim, or of Reasons, as Augustinus Riccius relates, ch. 4, On the motion of the eighth Sphere); Sacrobosco (on ch. 1 of the Sphere), Scotus (on [Sentences] 2, dist. 4, q. 2; and 12 Metaphysics, comm. 44), Cajetan (on 2 Corinthians [12]), Delphinus (On the Celestial Globes, ch. 30). Finally Mastrius and Bellutus (disp. 2 On the Heavens, q. 1, art. 2) distinguish the Prime Mobile from the starry heaven, but posit a single starry [heaven]. Of whom Cajetan and Delphinus say the Prime Mobile is the crystalline heaven.

[Margin: 2nd class, [positing] 10 spheres.]

The second class posited ten movable spheres—namely, a tenth for the prime Mobile; a ninth for the motion from West to East to be imparted to the Fixed stars and to the Apogees of the Planets (the Moon excepted); but an eighth for the motion of access and recess from the equinoctial points, that is, [for] the libration or trepidation in longitude. In which class were many Arabs, Moors, and Jews, but especially Alfonso King of Spain, Georg Peurbach with his followers, John Regiomontanus (in the theoric of the Eighth sphere, and bk. 7 of the Epitome of the Almagest, prop. 6), Peter Apian (in the Caesarean Work [Astronomicum Caesareum]), John Baptist Amicus (On the celestial motions), and Peter of Ailly (q. 2 on the Sphere, who reports the opinion of 10 movable spheres and does not reject it), Maurolyco (dialogue 1 and 3 [of the] Cosmography, p. 24, and [p.] 29), Fernel (bk. 2 of the Cosmotheoria, ch. 1 and 7), Joseph Lang (in the Astronomical Elements, ch. 4), Clavius (in the earlier editions of the Sphere, p. 44 and 72), the Conimbricenses (2 On the Heavens, ch. 5, q. 1). To which class can be recalled Thebit, Arzachel [al-Zarqālī], and Isaac the Israelite (in the second treatise On the Foundation of the World), inasmuch as they admitted a motion of trepidation of the Fixed [stars] in longitude—granted that they ascribed its cause to the ninth heaven rather than the eighth, or left this disposition of the orbs in doubt.

[Margin: 3rd class, [positing] 11 spheres.]

The third class posits eleven movable spheres: the eleventh indeed for the prime Mobile; the tenth for the trepidation or libration in latitude, to be imparted to all the inferior spheres, that they may follow the variation of the obliquity of the Ecliptic; the ninth for the trepidation or libration in latitude, by force of which the anomaly of the motion of the Fixed [stars], and of the precession of the Equinoxes, is effected; the eighth, finally, for the equal or mean motion of the Fixed [stars] toward the East. So indeed John Werner (in [the work] of Erasmus Oswald [Schreckenfuchs] on the Peurbachian Theoric of the eighth sphere), John Anthony Maginus (in the Theorics, bk. 1, and in the Secondary Mobiles,

[…continues on p. 256 (PDF 291): “…canon 18); Leupold of Austria (in his Compilation); Clavius (in the last edition of the Sphere, p. 36) — which system Scheiner accordingly calls the Clavian system (in the Mathematical Disquisitions, num. 22); and the same number of movable spheres, of the ancient opinion, Antonius Deusing and Peter Gassendi set forth in their Astronomical Institutions. Some, however, of the authors of the second class — chiefly Clavius and the Conimbricenses — admit an eleventh heaven [as] immobile, that is, the Empyrean…”]

(printed p. 256 — continuing [III.], the third class of the second opinion: the enumeration of its adherents concludes with Maginus, Leupold of Austria, and Clavius — whence Scheiner calls it the Clavian system — while Deusing and Gassendi set forth the same number of movable spheres in their Astronomical Institutions.)

Some, however, of the authors of the second class—chiefly Clavius and the Conimbricenses—admit an eleventh heaven [as] immobile, that is, the Empyrean; nay, Clavius thinks the aggregate of the 9th and 10th heavens to be the glacial and crystalline heaven, which would have merited the name of “the waters above the heavens” in Sacred Scripture, on account of its transparency, and because in it there are no parts denser than others.

[Margin: 3rd opinion, of Turriano and Fracastorius, on 14 movable heavens.]

[IV.] The third Opinion was that of John Baptist Turriano and Hieronymus Fracastorius (in the Homocentrics, section 2, from ch. 1 to 17), where he posits, above the Aplanes (or sphere of the non-wandering [stars]), other movable orbs really distinct, but diverse in number and order and office from those which the authors of the second opinion posited; and he hands down diverse hypotheses of these motions, according as each one shall wish to acknowledge the motion of Trepidation, and [the motion] of the Fixed [stars, as] direct and retrograde, or direct only. But because he himself at last had thought it more probable that the motion of the Fixed [stars] is always retrograde, yet unequal, therefore in ch. 17 he concludes that above the Aplanes there are 14 orbs. The first or supreme is the Prime Mobile, with wonderful velocity in 24 hours carrying with itself, from East through West to the same East, all the orbs enclosed within it. The second is the Circumducens [Carrier-around]; which, cutting the Equator of the prime mobile orthogonally, and carried around through the upper colure from North to South in 3600 years in latitude, bears all the inferior orbs with itself—except insofar as some [orbs], contravected, hinder it. The third is the Circitor, proceeding through the lower colure of the Equinoxes; it is moved by the Circumducens per accidens in 3600 years from South to North, but per se it is moved toward the opposite region. The fourth orb is the Contravectus [Counter-carried], both to the Circitor and to the Circumducens; and through the upper colure it is borne from South to North with a doubly swifter motion, that is, in 1800 years. The fifth is the Anticircitor, which is carried around by the Contravectus always toward the part opposite to the Circitor. The sixth is the Contravectus to the Anticircitor, yielding to it imperceptibly, lest the Aplanes be carried around by a sensible motion in latitude. And beneath it, finally, is the Aplanes, the orb bright with so many lights and distinguished by the Milky circle, which per se completes one degree in 100 years, and in 36,000 years completes its revolution—but within that [revolution] it is now slower, now swifter. Wherefore above the eighth sphere these authors posit six movable orbs, so that they are 14 in all.

[Margin: 4th opinion, of a Prime Mobile distinct but not carrying [the rest].]

[V.] The fourth Opinion admits indeed a Ninth heaven really separated from the eighth sphere, which would be the prime Mobile; but it denies that the inferior orbs are carried [rapi] by it—that is, physically dragged or borne—nor does it absolutely concede that the participation of the first motion is composed of two motions really distinct and contrary; but it does not explain in the same way how the sphere of the Fixed [stars] and the spheres of the seven Planets are moved by that prime mobile.

[Margin: First class of this opinion.]

For Alpetragius [al-Bitrūjī] (in his Physical Theoric of the celestial motions) and—nearly—Achillinus (in the book On the orbs) deny that the prime Mobile carries the inferior orbs by identity, continuation, or immediate contact; but they say that the first Mover, or first Intelligence, impresses upon the separated orbs a turning motion from East to West, just as an impetus is impressed by one throwing a stone or hurling an arrow—which impetus becomes weaker and weaker the farther the spheres of the secondary mobiles are distant from the Prime Mobile. Hence all are indeed carried per se from East to West by a simple motion in longitude, but do not attain by their motion the velocity of the prime Mobile, and so per accidens the Fixed [stars] and Planets seem to retrocede toward the East, and to strive against the prime Mobile; but in reality this motion is single, toward the West—slower, however, in the Fixed [stars], and still slower in Saturn, and slowest in the Moon. But because he knew this motion to be oblique, and [to proceed] through helices, or a gyrating line (which the Arabs call Lacalabinum), and [knew] that the Fixed [stars] change their declinations, therefore he said this motion is made upon diverse poles going around the poles of the World by the force of little circles; and because, with Hermes, Theon, and Arzachel, he suspected the motion of the Fixed [stars] to be sometimes retrograde, or at least unequal, he posited the motion of the poles of the eighth sphere in circles about the poles of the world [to be] unequal. By which means he proportionally explains the anomalies and the directions, stations, and retrogradations of the Planets, without Epicycles and Eccentrics. But against him rise up Augustinus Riccius (On the motion of the eighth sphere, ch. 10), Fracastorius (in the Homocentrics, sect. 2, ch. 3), and Clavius (on the Sphere, p. 48), and other more recent Astronomers—but in that Alpetragius, by this hypothesis, does not explain or safeguard the motion of the Planets in altitude (thinking, I believe, that [the altitude motion] is apparent, not true), he is deservedly reprehended; whereas in that he safeguards the oblique motion of the Fixed [stars], or the anomalies of the Planets in longitude and latitude, he is undeservedly reprehended, as if he had explained that motion upon the same poles and through the same line.

[Margin: Second class of this opinion.]

The other mode of this opinion is that of Peter of Ailly, Cardinal and Bishop of Cambrai, who (in questions 2 and 9 on the Sphere) posits a tenth orb [as] immobile, [serving] to safeguard, from its influxes, the diverse properties of the terrestrial regions ([which are] immobile); but a ninth heaven he posits for the prime Mobile—and that in question 4. Yet he too denies that the inferior orbs are carried or dragged by it, or carried properly and physically by the prime mobile; for he says that the individual orbs have their own Intelligences, and that from the prime Mobile (or mover) there flows into the inferior [orbs] a certain power, which inclines them to a motion similar to the motion of the prime Mobile—just as nature inclines heavy things to upward motion, that a vacuum may be avoided—and so that such motion is neither purely natural nor violent; but that it would be violent and impossible if they were carried [rapt] by the prime Mobile. He concedes, moreover, that this motion is made upon diverse poles and axes; and (q. 13) he admits Epicycles and Eccentrics, or a motion equivalent to them, on account of the elevation and depression of the Planets. Wherefore in this opinion the Fixed [stars] and Planets are really moved by a single motion toward the West, and try to imitate the Prime Mobile; but because they do not imitate [it] perfectly, they seem by their slowness to go back toward the East.

[Margin: 5th opinion, positing a Prime Mobile [as] a ninth heaven, but crystalline, and without rapture.]

[VI.] The fifth Opinion is that of John Anthony Delphinus, of the Franciscan family, who in his book On the globes and celestial motions (ch. 19, 29, 30) affirms, with Alpetragius, that there is a Prime Mobile, and that it is the ninth heaven; but that this is the crystalline or watery heaven (which Sacred Scripture names by the name of “the waters above the heavens”); and that all the orbs are concentric with the world; but he says that the individual [orbs] are moved by their proper Intelligence, or by the Angels, always from East to West—yet in such a way that they move [them] more slowly than the first Intelligence [moves] the Ninth heaven, and besides now toward the South, now toward the North; and indeed not by natural necessity, but by free will, because they willingly serve the Creator commanding such a motion. Finally, he calls the denomination “Ninth mobile” metaphorical, inasmuch as it does not physically move the inferior spheres or globes, but [is] only, as it were, the first exemplar of the swiftest motion toward the West; and that the apparent motion toward the East comes from this, that they are abandoned by the swifter motion of the prime Mobile. Hither can be recalled Claramontius [Chiaramonti] (bk. 2 On the Universe, ch. 18; and bk. 6, ch. 1), inasmuch as he posits for the prime mobile a ninth heaven, which the other spheres—moved by the Intelligences with the diurnal motion alone—do not attain, and so seem to be retarded toward the East.

[Margin: 6th opinion, denying a Prime Mobile distinct from the 8 spheres, but positing two motions.]

[VII.] The sixth Opinion denies that there is a Prime Mobile really distinct, by an adequate distinction, from the eighth sphere and the remaining seven; but it says [the Prime Mobile] is distinguished only as a whole from the parts taken individually; yet it admits two motions. For [it holds] that the whole World, except the globe of the earth, is moved from East to West—that is, the eighth sphere, the seven orbs of the Planets, and the Element of fire and of air; and that the prime Mobile, under one aspect, is the aggregate of all eight spheres, which by priority of nature is so moved before [its] parts; under another aspect, it is the eighth sphere, inasmuch as the Intelligence moves it principally, as the nobler heaven—just as the soul is said to move first and principally the heart, then the other members. Yet, just as the heart does not move the other members, so neither does the sphere of the Fixed [stars] carry [rapit] the other spheres, but is moved together with the whole by the same Intelligence, as the whole body [is moved] by the same soul. And [it holds] that in the individual heavens there is a double appetite—one for the motion of the whole toward the West, the other for the proper motion—

[…continues on p. 257 (PDF 292): ”…[the other] for the proper motion toward the East; and that these motions do not conflict with each other, just as the proper motion of the hand toward the opposite part does not conflict with the motion of the whole animal body toward one part. So Augustinus Riccius (in the treatise On the motion of the eighth sphere, ch. 1, 13, 14, etc.) and Orontius Finaeus [Finé] (bk. 1 of the Sphere, ch. 5), saying: ‘The Prime Mobile, therefore, must be called the World itself, and not some particular heaven…’”]

(printed p. 257 — completing [VII.], the sixth opinion, on the double appetite: Riccius and Orontius Finé hold that the Prime Mobile is the World itself, the particular orbs striving eastward by their own motion without conflict, as a hand may move against the motion of the whole body. Related unnamed views in Fracastorius posit one or two Intelligences per orb. Clavius refutes the opinion as impossible, and Fracastorius objects that the Intelligences would perpetually resist and impede one another, which is violent and unfitting.)

[Margin: 7th opinion, denying two motions and a prime Mobile above the 8th sphere.]

[VIII.] The seventh Opinion is similar to the opinion of Alpetragius set forth at num. 5, but differing in this, that it denies that there is, above the eighth sphere, another heaven which would be the prime mobile; for it says that the prime Mobile is the eighth sphere, inasmuch as it revolves the swiftest of all toward the West, and in the space of 24 hours restores the same stars to the same point of the same Meridian or Horizon, from which that motion began on the first day of the World. But this [eighth sphere] does not carry [rapit] the other inferior spheres, as the Authors of the first opinion (set forth at num. 2) posited; for it says that the remaining inferior spheres—whether moved by their own power, or by an Intelligence—are borne per se toward the West, and strive after the same kind of motion which the eighth sphere accomplishes, but cannot attain its velocity, and arrive somewhat more slowly than it, each day, at the same point of the same Meridian or Horizon—and the more slowly, the more [each] is distant from the eighth sphere. Whence it comes about that, because daily the slower Planets are left behind by the swifter Fixed [stars], and ever more separated, the Planets seem to retrocede toward the East—granted that in reality they do not retrocede, nor are moved by a double motion, but by a single [motion] toward the West, slower however; and which is said to be a motion toward the East not absolutely nor truly, but comparatively to the swifter [one], and apparently.

[Margin: Anaxagoras, Democritus, Cleanthes.]

The authors of this opinion Plutarch indicates [to be] sufficiently ancient (bk. 2 On the Opinions, ch. 16), subjoining however the contrary opinion, when he says: “Anaxagoras, Democritus, [and] Cleanthes think all the stars are borne from East to West; Alcmaeon and the Mathematicians [held] the wandering [stars] to be turned by a motion contrary to the non-wandering [fixed] stars, namely from West to East.”

[Margin: Ptolemy’s judgment on this opinion.]

And at the same time, but somewhat younger than Plutarch, Ptolemy (bk. 1 of the Almagest, ch. 8) indicates that the same opinion can stand, if the apparent motion of the Planets were always made in circles parallel to the Equator, without change of declination; but that, since it happens otherwise, [it] cannot. For Ptolemy [says]: “And so, if the advance of the wandering stars were made, in equal instants, in circles [parallel] to the Equinoctial—that is, around those poles around which the first revolution is made—anyone could rightly enough think that there is one and the same revolution of all, which would follow the first. For it would seem credible that their advance comes about not on account of an opposite motion, but because [each] is left behind by the first. But now, together with the advance toward the East, they also approach toward the North or toward the South, in such a way that not even an equal quantity of this approach is observed—so that this accident seems to come about in them by certain pulsions, etc.” From which he concludes that two greatest and distinct circles are necessary: namely, the Equator, for the prime Mobile carrying the Fixed [stars] and Planets around toward the West; and the Zodiac, within which the Planets proceed obliquely toward the East. Wherefore, since (in bk. 7, ch. 2 and 3) he acknowledged that the Fixed [stars] too slowly advance toward the East upon the poles of the Ecliptic, he seemed to some to suppose a ninth heaven for the prime mobile, but to others [to put] both motions in the eighth heaven. But these [things] about Ptolemy [are said] in passing. The same opinion Martianus Capella attributes to the Peripatetics (bk. 8 On the Nuptials of Philology, in the chapter on the orbs of the Planets), saying: “Finally, the doctrine of the Peripatetics too contends that these stars are not moved forward against the world, but are outrun by the swiftness of the world, which they could not follow.”

[Margin: Fracastorius’s judgment on the same.]

Furthermore, Fracastorius mentions this seventh opinion (no one being named) in the Homocentrics, sect. 2, ch. 3, and from this he refutes [it]: that, if all the orbs are borne per se toward the West according to longitude, they would per accidens be moved in latitude, and so by the force of some higher orb or Intelligence—but this is unfitting, because it would follow, he says, that the Planets are so bent by that orb which moves [them] sideways, that on the same day the Sun, which rises in the summer northern East on this side of the Equator, would set beyond the Equator in the winter southern West—which is against the observations. But this inference is not necessary; for they can, by the same motive force, be borne per se toward the West, and at the same time obliquely—through spirals or helices gradually deflecting from the parallels to the Equator—in such a way that they seem to rise and set in nearly the same parallel, by so much the less difference as the bending sideways is less, by which they vary the declination from the Equinoctial and the latitude from the Ecliptic. Wherefore neither Fracastorius’s, nor Ptolemy’s, nor Clavius’s refutation of this opinion (which is partly that of Alpetragius and Achillinus, [Clavius] impugning it on p. 49 of the Sphere) is solid, as to the oblique motion of the Planets; yet there remains a difficulty on account of the proper and oblique motion of the Fixed [stars], which appears to us. For if they too seem to advance toward the East, because they are moved somewhat slowly, then their motion is not the first motion, but another swifter motion toward the West seems to be assignable, in comparison with which the Fixed [stars] are slower. About which matter our discourse will recur below.

[Margin: 8th opinion, of Joseph Scaliger, denying the motion of the Eighth sphere.]

[IX.] The eighth Opinion was that of Joseph Scaliger (in his Diatribe on the Anticipation of the Equinoxes, and bk. 4 On the Emendation of Times, from p. 284), who says that the motion of the eighth sphere toward the East upon the poles of the Ecliptic is a certain monster, and an old-wives’ and trifling fable; for [he holds] that the Fixed [stars] are neither moved by a motion in longitude—εἰς τὰ ἑπόμενα [eis ta hepomena, “toward the following”], that is, not in consequentia [eastward]—nor change their declinations or distances from the Poles of the World (which he posited [as] immobile); but [that] the equinoctial and solstitial points are moved εἰς τὰ προηγούμενα [eis ta proegoumena, “toward the leading”], that is, in praecedentia toward the West; and [that] not the stars recede from the Sun, but the Sun [recedes] from the Stars, and the Equinoxes and Solstices are celebrated each year in more and more western points of the Equator; and so [that] to Hipparchus and Ptolemy the Fixed [stars] seemed to be moved toward the East, and that they persuaded credulous posterity of this. Then he says that the poles of the E—

[…continues on p. 258 (PDF 293): “…quator are distant from the Poles of the World, and are moved toward the West through little circles described about the poles of the world… The foundation of this opinion is that the pole star, which shines in the tail of Ursa Minor, was seen to be equally distant from the Pole of the world — that is, 12° 24′ — both in the time of Eudoxus (Olympiad 103, the year 367 before Christ) and of Eratosthenes (227 before Christ), [and in the] time of Marinus of Tyre and Ptolemy, who flourished in the year 130…”]

(printed p. 258 — continuing [IX.], Scaliger’s eighth opinion and its refutation: Scaliger’s arguments from the unchanged distances of stars from the pole and from Hipparchus’s risings and settings are recounted, along with his appeal to the mathematicians for help. No one adopted his offspring; rather four Jesuits — Petavius, Guldin, Furnerius, and Clavius — with Bullialdus smothered it, and Riccioli himself subverted its foundation, adding that Scaliger’s account of precession through westward-moving equinoctial points is almost impossible to maintain.)

[Margin: 9th opinion, attributing the Prime Mobile and all motion of the Fixed [stars] to the Earth.]

[X.] The ninth Opinion denies to the Fixed stars all motion—both the diurnal toward the West and the proper [motion] toward the East; but to the Planets it attributes a proper motion toward the East, while it denies to them too the diurnal [motion] toward the West. For the diurnal motion, which appears in the Fixed [stars] and in the Planets, it says is really the motion of the Earth about its own center and axis, by which, in a 24-hour turn, it is revolved toward the East; and so [it says] that it is we who go to meet the stars toward the East, and that rather we rise to them than they to us. But the proper motion of the Fixed [stars] it attributes to the equinoctial points on the terrestrial Equator, preceding toward the West, by force of a certain libration about the earth’s axis (indicated in bk. 3, ch. 28). But the authors of this opinion went off into two Classes.

[Margin: 1st class, attributing the annual motion to the Earth.]

For the first attributes the annual motion (which makes for us the vicissitude of the four seasons) not to the Sun, but to the Earth, which not only daily revolves about its own center, but yearly is carried, together with its center, along [the line of] the Ecliptic toward the East around the Sun resting in the middle of the world, or not displaced.

[Margin: Philolaus. Aristarchus. Copernicus and [his] followers.]

So once Philolaus (in Plutarch, bk. 3 On the Opinions of the Philosophers, ch. 13), then also Aristarchus of Samos (as Archimedes relates in the Sand-Reckoner); which opinion Nicolaus Copernicus revived—not from hypothesis (as some excuse him), but absolutely, as is plain from the preface to Paul III prefixed to the books of the Revolutions, and from bk. 1, ch. 8, 10, and 11, and bk. 5, ch. 2; to whom adhered Maestlin, Rheticus, Caelius Calcagninus, Rothmann, Galileo, Diego de Zúñiga [Didacus a Stunica], Paul Anton. Foscarini, Antonius Laurentius Politianus—but most zealously of all John Kepler (in his Mars, and in the Epitome of Copernican Astronomy, and in the Mysterium Cosmographicum, and in the Harmonica).

[Margin: 2nd class, denying the annual motion of the earth.]

But the second Class attributes to the Sun—as well as to the other Planets—its proper motion (and to the Sun indeed the annual [one]); but to the earth it leaves the diurnal turning of [24] hours about its immobile center, nor does it transfer the Earth from place to place.

[Margin: Heraclides, Ecphantus. Nicetas.]

So once Ecphantus and Heraclides (in Plutarch, bk. 3 On the Opinions, ch. 13), [and] Nicetas [Hicetas] of Syracuse (in Cicero, Academica 2, and Tusculans 1). Whom afterward followed Longomontanus (in his Danish Astronomy, bk. 1 of the Theorics, ch. 2 and 4), William Gilbert (bk. 6 of the Magnetic Philosophy, ch. 3), Origanus (vol. 1 of the Ephemerides, in the dedicatory Epistle), and Andreas Argolus (in the Pandosion Sphaericum, ch. 3). The same opinion Aristotle ascribes to Plato in the Timaeus (bk. 2 On the Heavens, text 75), [as do] Cicero (Academica 2) and [Diogenes] Laertius (in the Life of Plato). But we, from the Platonic Timaeus itself, shall make [it] plain (sect. 4, ch. 2, num. 2) that Plato stood for the immobility of the earth.

[Margin: 10th opinion, leaving the proper motion to the Fixed [stars], but attributing the diurnal [motion] to the Earth.]

[XI.] The tenth Opinion attributes to the Earth both the diurnal and the annual motion, but nevertheless does not take away the proper motion from the Fixed [stars] toward the East—much less from the Planets. So at last Philip Lansberge (in the Tables, precept 11), Jacob Lansberge the Physician (in the Apology for Philip, against Fromondus and Morin), and Ismael Bullialdus (bk. 1 of the Philolaic Astronomy, ch. 2), for the reasons which I adduced in bk. 6, ch. 18, num. 14. They differ, however, in that Lansberge posits the motion of the Fixed [stars] upon the poles of the Ecliptic [as] unequal, on account of the unequal motion of the equinoctial points; but Bullialdus posits it [as] equal. But neither this [tenth opinion], nor the ninth, is it permitted us to follow, by reason of the divine Scriptures or the Ecclesiastical decrees.

[Margin: 11th opinion, explaining all things by a simple motion through gyres and spirals.]

[XII.] The eleventh Opinion is very similar to the seventh, but it does not posit that the prime Mobile is the eighth sphere; rather it says that all the proper motions which appear toward the East—both in the Fixed [stars] and in the Planets—can be reconciled with their diurnal motion toward the West, through a single oblique motion made toward the West, screw-wise [cochleatim], through helices and spirals, or through helicoid spirals, by which the stars do not exactly complete the same diurnal circle, nor return to the same point of the Meridian or Horizon today in which they were yesterday, but bend somewhat toward the sides of the World toward the poles—yet in such a way that the Fixed stars revolve to the same Meridian more quickly than Saturn, and Saturn more quickly than Jupiter, and so of the rest (understand [this] when the Planets are direct; for if they become stationary, then they appear equally swift as the Fixed [stars]; but when they are commonly called Retrograde, then they are swifter than the Fixed [stars]; and only slower when direct). Again, the Planets are borne along this gyrating line so that now higher, now lower they proceed. So teach—but in other words—Scotus (on [Sentences] 2, dist. 14, q. 2), Hurtado (disp. 2 On the Heavens, sect. 3), Mastrius and Bellutus (disp. 2 On the Heavens, q. 4, art. 1), Cabeus (on 1 Meteorology, text 38, q. 2), Amicus (tract. 5 On the Heavens, q. 6, dub. 9, art. 3; who, at num. 2, had adduced for this [view] Philoponus, Alexander, Vimercatus, Galtius, [William of] Auvergne, [and John] Maior), Arriaga (the single disputation On the Heavens, sect. 4 and 5), Oviedo (the single controversy On the Heavens, point 4), John Punch (disp. 22 Physics, q. 9, conclusion 3), [and] Balthasar Téllez (disp. 45 Physics, sect. 3, num. 6). And in the same opinion were, for the most part, Alpetragius, Achillinus, [Peter of] Ailly, and Delphinus (adduced at num. 5 and 6); and before these, Anaxagoras, Democritus, and Cleanthes (about whom at num. 7). But Scotus, Mastrius and Bellutus speak in such a way that they seem to admit a Prime Mobile distinct from the eighth sphere, with Alpetragius; whereas Téllez does not acknowledge that first motion to be made really in any body, but [says] it is only imaginary, and that to its measure neither the Fixed [stars] exactly nor the Planets come up. But others do not sufficiently explain whether any motion of the prime Mobile—true or imaginary—is given, which the Fixed stars emulate but do not attain by their diurnal motion; and those who retain solid heavens, like Amicus and Mastrius, can scarcely safeguard the aforesaid spirals.

[Margin: 12th opinion, on imperceptible little pauses.]

[XIII.] The twelfth Opinion, which I handed down as devised by me (bk. 6, ch. 18, num. 16)—but which, after many months, I found indicated by Amicus (tract. 5 On the Heavens, q. 6, dub. 9, art. 3), in these words: “Fourthly, others, thinking those motions to be two, say [they] are not exercised at the same time, but by an alternating vicissitude—

[…continues on p. 259 (PDF 294): “…while the Intelligence moves the heaven toward the Poles of the Zodiac, it does not move [it] from East to West; and because that lateral motion happens in the twinkling of an eye, the orb does not appear to cease from the diurnal motion.” But this way of speaking, as it lacks a suitable author, so it cannot be probable… yet if that interruption through imperceptible little pauses cannot be refuted by any observation, it is not altogether improbable — and Punch touched on the same, saying it is manifest that something can be moved at once by two motions, one E→W and the other W→E, without any intermission perceptible to our senses.]

(printed p. 259 — completing [XIII.], the twelfth opinion: the alternating-vicissitude view is judged not altogether improbable, Punch conceding that a body can be moved at once, without perceptible intermission, by two motions from East to West and from West to East; the manner of this was explained in bk. 6, ch. 18.)

By so many, then, and so wonderful modes—partly worthy, partly unworthy of the human genius—has the reconciliation of these two motions been attempted. But what our opinion is—although it was indicated in bk. 6, ch. 18, from num. 15—must nevertheless be set forth more fully in this place through the following Conclusions.

FIRST CONCLUSION

[Margin: 1st Conclusion.]

Both the wandering and the non-wandering stars can be moved toward the West by [or: toward] the motion of the Prime Mobile—[a Prime Mobile] really distinct from their own proper heaven, or from the stars—and meanwhile can at the same time be moved, truly or apparently, by a proper motion toward the East, without any physical repugnance.

[XIV.] For if there were any repugnance, it would be either between the moving and the movable bodies themselves (which could not be, or be conjoined or assigned together to that [task]), or it would be in the very mode of effecting each motion. But that repugnance arises from neither head; therefore what is asserted in the conclusion can come about. For as to the first: diverse celestial bodies can be assigned which would discharge the office of the prime Mobile.

[Margin: 1st body for the prime Mobile.]

First, indeed, this can be the watery heaven, [made] of the waters which (according to the more probable opinion of many Fathers, consonant with the letter of the divine codices) we showed to be above the heavens (sect. 1, ch. 2, q. 3; and ch. 3, conclusion 3). Which heaven does not flow apart hither and thither, on account of [its] equal distance from the center of heavy [bodies], or because there it is outside the place of heavy and light [bodies]; and yet the whole is moved, in the space of 24 hours, by one or several Intelligences, if need be.

[Margin: 2nd body.]

Secondly, this can be the glacial or crystalline heaven, which is above the sphere of the Fixed [stars], as Delphinus and Clavius posit; and [it] is conformable to those Doctors and Fathers who believed the waters above the heaven of the Fixed [stars] to have been solidified by God in the manner of ice or crystal (per what was said in sect. 1, ch. 2, num. 8)—of which sort were Josephus the Hebrew, Pope Clement, Severianus, Anselm of Laon, [Walafrid] Strabo, Bede, [and] Peter Comestor. That this heaven could equally be revolved toward the West, by one or several Intelligences, in the space of 24 hours.

[Margin: 3rd body. — 4th body. — 5th body.]

Thirdly, it could be the heaven of the Fixed [stars] itself, but fluid, which would move the Fixed [stars] toward the West immediately, but the Planets by means of the heaven of the Planets (fluid or solid). Fourthly, it could be the heaven of the Planets itself (fluid or solid), which would itself move the Planets immediately—nay, even the Fixed [stars], which it would immediately touch by its convexity—or [move] these and all the rest, by moving the heaven of the Fixed [stars] (fluid or solid). Fifthly, some body could be assumed [taken up] by one Intelligence, or carried around (granted [it be] not properly an assumed body), which would not be a heaven; and [the Intelligence] would carry this around about the Firmament in the space of 24 hours, as a sensible exemplar of the universal time, in imitation of which the Fixed [stars] and Planets would have to be moved by the Intelligences—either immediately, or by means of the orbs. Just as, in the first three days, some say that bright cloud was that primigenial light, which made the three natural days.

[Margin: 6th body. — 7th body.]

Sixthly, without the motion of any body about the heaven, there could be various clocks measuring the time of 24 hours—and far more excellent than ours—which likewise would have to be imitated by the movers of the Fixed [stars] and of the heavens in the motion toward the West. Seventhly, there could be, above the heaven of the Fixed [stars] or in it, a certain Equator, or belt of the World, made of solid material, and really distinct from it, which would be moved by an Intelligence toward the West in the space of 24 hours. For in these enumerated bodies there is nothing which could not have come about physically; but the immediate conjunction of the first two [bodies] with the heaven of the Fixed [stars] neither is repugnant nor absurd in Astronomy. For no sphere is required between it and the prime Mobile for the trepidation or libration in longitude or latitude—for we have already taught (much more truly) that the obliquity of the Ecliptic is not varied (namely bk. 3, ch. 27), nor that the Equinoctial or Tropical Year is unequal (namely bk. 3, ch. 28), nor that the precession of the Equinoxes, or the motion of the Fixed [stars], is either retrograde or anomalous (namely bk. 3, ch. 28; and bk. 6, ch. 17).

[XV.] But as to the mode of moving the other heavens or the stars toward the West, in such a way that nevertheless they seem—truly or apparently—to be moved somewhat toward the East:

[Margin: 1st mode.]

the first could be through imperceptible little pauses [morulae], already set forth in bk. 6, ch. 18, num. 16, and indicated in this chapter at num. 13.

[Margin: 2nd mode. — 3rd mode.]

The second could be through continuous rapture—whether it be called traction, pulsion, conveyance [vectatio], or circumduction—which, however, on account of the resistance of the heaven or star being carried, would not move toward the West so swiftly as it would have moved if nothing resisted it; and therefore could not, within the space of precisely 24 hours (in which the prime Mobile itself completes its entire revolution), equally revolve the inferior globes to the same Meridian or Horizon. The third [mode] is, if the movers of the sphere of the Fixed [stars] and of the Planets try to imitate the motion of the watery or crystalline heaven, or of a body or clock equivalent to them, but in the space of 24 hours do not revolve [them] to the same Meridian [as] their globe, but daily arrive at it somewhat more slowly—and this through spiral helices, as we said at num. 12 in explaining the 11th opinion.

[Margin: 4th mode.]

The fourth [mode] is, if the heaven—both of the Planets and of the Fixed [stars]—be fluid, and be moved by one or several Intelligences in the space of 24 hours; and in imitation of it, other Intelligences move the Planets and Fixed [stars] toward the West indeed, but daily by degrees, and always falling short toward the East. But lest as many Intelligences had to be multiplied as there are Fixed stars, the Fixed [stars] could be bound together among themselves, as in a certain solid net [reticulum] invisible to us (as we said in bk. 6, ch. 18, num. 17, in the 2nd mode). For in none of these four modes is there any repugnance, nor [are there] two motions contrary to each other; but a single motion, slower however, or less swift, than the motion of the prime Mobile.

SECOND CONCLUSION

[Margin: 2nd Conclusion.]

Nevertheless, that double motion which appears in all the stars—one toward the West, the other toward the East—can come about and be explained without any movable body really distinct from the star-bearing heavens, or from the stars themselves, the other motions of the stars also being saved, without any physical repugnance.

[XVI.] This is proved by the modes [already] indicated, of which the First is:

[Margin: 1st mode.]

if one or several Intelligences moving the sphere of the Fixed [stars] from East to West have, in [their] impressed and divinely-infused species [ideas], a perfect idea of a time of 24 hours—not [hours] of which the days consist (which we are wont to measure from the revolution of the Sun or of the Fixed [stars]), but somewhat shorter, and such as they would be if there really were a prime Mobile distinct from the star-bearing heavens and from the stars. But [if], in moving the orb of the Fixed [stars], they exceed the perfect quantity of that intellectual measure, and so revolve it more slowly to the same Meridian—that is, in a time somewhat longer than that intellectual 24 hours (and such as perhaps was the time of the first three days). But the Intelligences of the remaining orbs or globes would have, as the measure of the motion to be accomplished by them, not that intellectual day, but the day made by the single revolution of the Fixed [stars]—yet so that they too revolve their globes somewhat later, and the later, the more they are distant from the Fixed [stars]; and accordingly the sphere of the Fixed [stars] would be, with respect to the Planets, a prime Mobile [that is] not physical, but [operating] in the manner of a moral cause, or as it were exemplary. But all these motions would have to be made through spirals and gyres (about which I spoke at num. 12), so that the variety of declinations and latitudes be saved; and when the Planets are called Stationary, they would have to be moved equally swiftly as the Fixed [stars]; but when Retrograde, they would have to be hastened by the Intelligences somewhat more swiftly than the Fixed [stars].

[Margin: 2nd mode.]

The second mode would be, if all the Intelligences, in the aforesaid motion of both the Fixed [stars] and the Planets toward the West (through spirals, however, etc.), looked to that single time—imaginary to us, but mental or intellectual to them, and shining in their impressed species, divinely infused from the beginning of the world.

[Margin: To imitate the motion of the Fixed [stars] by a mechanical experiment.]

[XVII.] But since to some the motion of the Planets in a Fluid heaven, through the aforesaid spirals, seems easy, but [that] of the Fixed [stars] difficult—because they are accustomed to their me—

[…continues on p. 260 (PDF 295): “…mechanical [globe], resting on poles fixed to the Meridian: let them take any star-bearing globe or Aratean sphere, not fixed by its vertices or any axle to the Horizon or Meridian, but supported by some concave vessel or resting on water or sand; and let them fix a little peg into any one point of it, or of a star depicted on the globe, by which, grasped as a handle, they carry the globe around toward the East, bending it spirally and imperceptibly toward the poles…”]

(printed p. 260 — completing [XVII.], the mechanical-globe demonstration: a star-bearing globe resting free on a vessel, water, or sand, carried around by a peg fixed at one point, shows that all the stars move together with their declinations changing. From this one learns how easily one or several Intelligences could move all the Fixed stars spirally by a single motion, whether they are affixed to a solid firmament or bound together in a fluid one.)

THIRD CONCLUSION

[Margin: 3rd Conclusion.]

It is more probable that there is no body which is the Prime Mobile, nor two motions in the stars made at once toward opposite regions of the World, but a single [motion] toward the West through helicoid spirals—those of the Fixed [stars] indeed in a solid heaven, but those of the Planets in a fluid [one]; and that the place of the prime Mobile is supplied by an intelligible time, that is, an idea of the diurnal motion infused into the mind of each moving Intelligence.

[XVIII.] The first part is proved, because—as is trite in the schools—“what can be done by fewer is done in vain by more,” as Ptolemy advised (bk. 13 of the Almagest, ch. 2), whose words I recited [in] ch. 2, num. 3: that motion is to be attributed to the celestial bodies which so answers to the Phenomena that it is as simple as possible, and exposed to the fewest impediments. And such is [the motion] we stated in the conclusion; for it is made through a single spiral line, accommodable to all the motions of the stars, and describable by Intelligences having the highest skill about the path and leading [ductus] by which they must revolve the stars at God’s prescript; nor can any violence from rapture, or any resistance from the middle or surrounding body, be feared—since the fluid heaven of the Planets yields both to the Planets and to the concave surface of the heaven of the Fixed [stars], above which the watery heaven is fluid. Whence also, even if some body were posited for the prime Mobile, whose motion at least the Intelligence would have to imitate—yet it would be necessary that its motion be understood by [the Intelligence], and so that [the Intelligence] have at least expressed species of it in its mind, which, if it beheld [them] by another, as it were reflex, act, it could use as the impressed species and Idea of that motion. Therefore, through these species (which we cannot avoid), whatever would be done by them with those [bodies] and with that movable body can be supplied by the Angels; and so the motion of that distinct orb or body is multiplied in vain. Nay, not only in vain, but even against the dignity of the Angelic nature. For that Musician is more excellent who knows how to sing, or to strike the strings, according to the harmonic number, using the time which he has in [his] mind, and needs no sensible percussion of the hand, nor an extrinsic sign, for the regulation of the voice. So too more excellent is the mode which we have ascribed to the Intelligences, since they need no corporeal—as it were—clepsydra [water-clock] in order to move skilfully and harmonically the stars or globes committed to them, and to accomplish their dances (so to speak), or this hidden harmony [concentus] of the World.

[Margin: 2nd part of the Conclusion.]

But the second part—about the distinction of the solid heaven from the fluid—has already been proved (sect. 2, ch. 7, num. 21), and is confirmed, because thus it is much easier for the Fixed Stars to preserve their distances among themselves perpetually, and to be moved uniformly, at the motion of one or a few [stars], by one or a few Intelligences, than if they were moved in a fluid heaven.

[Margin: 3rd part of the Conclusion.]

The third part—about the intellectual time, known by each Intelligence and used as the immediate measure of the motion to be accomplished—is proved, because it cannot be denied that that time is known by them; therefore it would be posited in vain [if] it needed that sensible time by which the heaven of the Fixed [stars] is moved; and it is better that there be one common measure to all of them, to which they may attemper [adjust] their motions and revolutions. For thus they also know that time which was not from the World itself, but could have been; thus they know that diurnal time, by which the ninth heaven would be moved, if it were the prime mobile, and how much faster it would arrive at the Meridian than the Fixed [stars] or Planets. This, therefore, they can use immediately; and it is more worthy that they need no other sensible motion and time, even though they must move sensible bodies. Nor is it absurd that the first and most universal time, with respect to an intellectual nature, be really only intellectual—that is (as they say), to exist intentionally, and not to exist except objectively, in the Angelic mind or in ours. For this happens in very many other ideas, which we use in artifacts and sensible works. “For the house which is outside the soul comes to be from the house which is within the soul,” says the Philosopher (7 Metaphysics, text 23)—namely, from the Idea, and the impressed species, which shines objectively in our mind, and is the image of the house to be made. Therefore, if there were a more perfect Architect, who—without a mechanical and external model or exemplar—knew how, and was able, to direct the workmen, or himself to build with his own hands: more perfect too will be the motion of an Intelligence, if it needs no external and sensible exemplar for accomplishing the diurnal motion.

[Margin: What if the Prime Mobile be some sensible body?]

[XIX.] But if nevertheless someone should require that that time—which is the universal measure of all motions, and as it were the norm of the rest—be still, or at least once was, the motion of some sensible body, or its number or measure: I would persuade [him] of those three more probable modes.

[Margin: 1st mode, through a simple Equator.]

The first is the [one] which I indicated at num. 14, in the seventh place: namely, through a certain Equator—in, or above, a celestial globe—divided into 360 Degrees and subdivided into minutes [scrupula], or rather immediately into minutes (not such as ours, but far more subtly, into [tiny] particles), [with] all the points and tiny differences of the motions in the Fixed [stars] and Planets, [reckoned] from the Meridian, suitable for discerning—from the beginning of the World to the end—the [motions] to be carried out; which [divisions], nevertheless, on account of the vastness of that belt, would be very large, if compared with the minutes, or even the degrees, of our spheres or astronomical instruments. For if that 24-hour motion could be represented by the motion of this belt, made of solid material, the whole machine of some ninth, tenth, or eleventh heaven would be posited in vain to be moved, in order to supply this single motion. This motion, therefore, being posited [as] made by a single Intelligence, and revolving that Equator to the same meridian, the remaining Intelligences would have so to move the Fixed [stars] and Planets spirally, or screw-wise, toward the West, that—when the beginning of the Equator arrives at one Meridian, say, of Jerusalem—a Fixed star, which yesterday had been beneath the initial point of the Equator, would on the following day not yet be brought by its center to the same Meridian, and much less Saturn [when] direct, etc.

[Margin: 2nd mode, through the crystalline Heaven.]

The second mode is, that we choose that Watery or crystalline heaven, which is above the Firmament, as that body which, by its motion (made by an Intelligence), would represent the motion of the Prime Mobile; for thus it will be confirmed that those waters were not placed above the Firmament by God in vain—[but] as a second [end], just as others have assigned several other ends [purposes], about which [in] sect. 1, ch. 2, num. 10. The third mode could be through the mere memory of the primigenial light made by God on the first day of the World, and of its motion or successive production—just as the first three days of the World were completed. For there were not lacking [those] who said that that [light], or even the Sun (made on the first day), had no other motion than [that] of the prime Mobile, but that on the fourth day a proper motion was added to the Sun and the rest of the stars (per what was said in sect. 1, partly ch. 1, num. 34—to be referred to Aegidius’s opinion—partly ch. 4, num. 3). For thus that first natural day, or even the first three days, would have been the most perfect and shortest of all, inasmuch as that light was revolved most swiftly—no less swiftly than the Equator of the Prime Mobile is now said to be moved in the spherical treatises; therefore the memory of that day, or of those days, would suffice for the Angels, so that they could revolve their spheres or stars to the same Meridian in a not so [short], but a slightly longer, time. But the rest, which seem to need to be added to this subtlety, I shall indicate soon in the Scholia.

[…continues on p. 261 (PDF 296) with the SCHOLIA to this chapter.]

(printed p. 261:)

SCHOLIA

[Margin: Whether two contrary motions can be given.]

[I.] On the occasion of reconciling the motion of the Prime Mobile with the proper motion of the stars toward the East, it is wont to be disputed by the Physicists whether two continuous and contrary local motions can be given—that is, [motions] by which the same movable, to be carried according to the same part of itself, is carried toward one region of the World and at the same time toward the opposite [region]—if not per se and by force of the same moving principle, at least by diverse acts, and by force of diverse moving principles. Which controversy is touched by Maior (on [Sentences] 2, dist. 24, q. 1), Mayronis (ibid., q. 3), Fracastorius (in the Homocentrics, sect. 1, ch. 8), Clavius (on the Sphere, p. 52), Rubius and the Conimbricenses (bk. 2 On the Heavens, ch. 5, q. 4, art. 2), Mastrius and Bellutus (disp. 2 On the Heavens, q. 4, art. 1, num. 129 and 130), Amicus (tract. 5 On the Heavens, q. 6, dub. 7, art. 3), Hurtado (disp. 2 On the Heavens, sect. 3, paragraph 22), Arriaga (the single disputation On the Heavens, sect. 5, num. 56), Oviedo (the single controversy On the Heavens, point 4, num. 6), Punch (disp. 22 Physics, q. 9, num. 94), and Téllez (disp. 44 Physics, sect. 2, num. 4 and 5). Among whom Punch and Téllez seem to concede two contrary motions—one per se or from within, the other per accidens and from without; and they use the now-trite example of an ant or weasel creeping upon a wheel turned around to the contrary part, or of a man walking in a ship toward the East, from prow to stern, while the prow of the ship is borne toward the West. For what Téllez adds, about a stone naturally about to descend downward along a straight line, but carried crosswise by an external impulse, and so moved by two motions, does not make for the matter, since they are not two contrary motions, or [motions] toward contrary termini. More to the matter is a stone [drawn] from prow to stern, spontaneously drawn by someone sitting on the bank of the river, meanwhile while the ship is borne to the opposite part by the river.

[Margin: Resolution.]

The rest of the aforesaid Authors, however—and at last Punch himself—answer that it is naturally impossible for the same part of a subject to be moved by two simply contrary motions; that is, so that at the same time it approaches the same Fixed point of the World, and at the same time recedes from it. For although metaphysically the contradiction may seem to be removed by distinguishing two diverse moving principles, yet physically this is repugnant to the nature of local motion: for [local motion] is an action, by force of which either the whole movable, or a part of it, recedes from one place as the terminus a quo [terminus from which], and approaches another as the terminus ad quem [terminus to which] along the same line, and acquires another “where” [ubi] distinct from the prior—so that it is naturally impossible for the same movable to be also in two adequate places at the same time, and to approach, actually and really, that terminus from which it recedes; because recession includes (with the motion) the privation of approach and of local presence, but a privation and the form opposite to it cannot physically be founded in the same instant of time. (Although, if by divine omnipotence a body were replicated [bilocated], the [body] thus replicated could be moved into opposite parts.) Yet the same [body], according to the same part of the subject, can be moved by a double impetus—of which one is, by its nature, impulsive of one motion toward the East, the other toward the West—but in such a way that only one prevails, and moves [the body] toward one part, more slowly however than if it were not retarded by the other impetus; for if neither prevailed, the movable would be moved toward neither part. And so they deny that there are two motions, but [say there is] a single, slower [one]. But in the motions of animals, which raise their legs in walking, there is intermixed an up-and-down motion, which is not contrary, nor directly opposite, to the motion of the ship or the wheel. Which response, although it is good, and admitted by me elsewhere, can nevertheless be explained by a still more perfect distinction, as will be done presently in the following scholium.

[Margin: Explanation of two opposite [yet] compossible motions.]

[II.] Two [things], therefore, are to be noted and distinguished, in the motion—whether of animals from within, or of inanimate [things] from without—which are moved not upon an immobile place, but upon a mobile place, that is, within it as a vessel. For in such a motion a double terminus ad quem can be regarded: one fixed and immobile in a determinate part or point of the World; the other mobile in the vessel and place itself—which terminus is moved at the motion of the vessel, as a part [is moved] at the motion of the whole. Secondly, a motion to some terminus (that is, relative, or respective, or comparative, or even hypothetical, toward it) is to be distinguished from an absolute motion, by which that terminus is approached. Therefore, if some body resting within some vessel be carried, at the motion of the vessel, toward the West, and meanwhile that body be carried by another moving principle toward the Eastern part of the vessel: if each impetus be equal, [the body] will indeed approach the mobile eastern terminus by an absolute motion, but from the immobile eastern terminus it will neither recede nor approach, but will remain there, absolutely. But if the impetus by which the vessel is carried toward the West prevails, that body will absolutely recede from the fixed eastern terminus, and will absolutely approach the mobile eastern terminus; but to the immobile eastern [one] it will not approach except respectively (inasmuch as its proper motion is directed toward the East), or comparatively (because you recede less from it than if it were moved by no proper motion within the vessel, or upon that vessel), or finally hypothetically (inasmuch as it would have approached it, if it had used its motion alone, and the vessel had stood still). If, finally, the impetus of that body prevails, it will either approach, or pass beyond, the fixed eastern terminus absolutely; but it will recede from it only respectively, or comparatively, or hypothetically.

Which, for the sake of aiding the imagination, it pleases [me] to set forth by an appended diagram. In it, let there be a portion of a river AEB, bisected at E; of which the half AE is equal to the length of the ship CCDC, and the other half EB [equal] to the length of the same ship DCDD—[the ship] now translated from the place beneath the fixed points of the World CQH, to the place beneath the fixed points HLK. But when [the ship] has completed [traversed], with the middle of its hull, the half of the space AE—namely the space ME—let the same ship be under the fixed points QHL; and let G be the eastern terminus, K the western.

[Figure (river/ship diagram): a horizontal river-line marked, left to right, A · M · E · I · B. Above it the ship is drawn in five successive positions as nested arcs, the stern/prow points labelled (top row) G, Q, H/O, L, K and (below them) C, C, DC, D, D, with dotted verticals dropping to the baseline. It shows the ship gliding westward while a man walks prow-to-stern (eastward), so the curves trace the combined (resultant) path.]

[Margin: 1st case.]

Now, at the beginning of the whole motion, let, First, the man O be in the prow D, under H, and let him begin to walk toward the stern C, toward G; so that in one clock-minute—in which the ship, carried by the river, has traversed the whole space equal to its [own] length, and has come under the points HLK—he himself has arrived at the stern C. For he will still be under the same fixed point H, under which he was at the beginning of the motion, because under it is the stern of the ship, to which he has come. Wherefore, although he has been moved absolutely, and has approached the mobile terminus (the stern), yet to the immobile terminus G he has approached no further absolutely—to which, however, he was going to approach, if the ship had not been moved.

[Margin: 2nd case.]

Secondly, imagine the man O—while the whole ship, in one clock-minute, traverses the whole space AE (which is under the fixed space GQH)—to be moved twice as slowly, and so in one minute to arrive from the prow to the middle of the ship; for he will be in D, under the point L. Wherefore, although he has approached the stern DC absolutely—nay, respectively his walking has been directed toward G—yet absolutely he has receded from G, the fixed eastern point, and has approached K, the western terminus, since at the beginning of the motion he was under it. But if the ship had meanwhile not been advanced at all, he would have come from DC to C, under Q; but this motion is only hypothetical. On the contrary, if the ship alone had been advanced, he himself walking not at all, he would have been, at the end of the motion, in the prow D, under K; wherefore, since on account of the aforesaid walking he is in D, under L, he has indeed receded from G absolutely, but comparatively to the recession which was going to be [had he been] in D, under K, he has approached, because he has receded less.

[Margin: 3rd case.]

Thirdly, while the man O, in one clock-minute, runs through the whole ship from prow to stern, [and] the ship, twice slower, completes half the space ME of its [own] length—so that, when the prow was under H and the stern under G, at the end of the motion the prow is under L and the stern under Q—then that man will be under Q; and so he has indeed approached absolutely both termini, the mobile [stern] and the immobile G; but from the immobile G he has receded only comparatively or hypothetically.

And proportionally are to be understood the motions of an ant on a wheel turned around to the contrary part, and of water stirred by a finger toward the left in a vessel revolved toward the right, and so of similar [cases]; for in reality, in the ant and in the water there are two motions conflated into one, which are not contrary, since the termini-to-which are not the same (since one is fixed, the other mobile), nor is there, to the fixed [terminus], absolutely an approach and recession of the same part, etc.

[Margin: Whether we have any example of the First Motion?]

[III.] You will ask whether, of the motion of the Prime Mobile—which in our Idea we attributed to a rational [conceptual] Equator, and which we said above shines in the minds of the Intelligences moving the heaven of the Fixed [stars] and the Planets—we can have any sensible specimen [example];

[…continues on p. 262 (PDF 297): “…for commonly we have no other exemplar than the motion of one Fixed star revolved once from the same to the same Meridian; and still more commonly we use the revolution of the Sun. I answer: since any Fixed star completes one degree of its proper apparent motion in 72 years (bk. 6, ch. 16)… [Riccioli computes the daily increment, ~8 thirds of arc, and concludes that no pendulum is precise enough to measure the difference between the sidereal day and the “rational Prime Mobile” day — so in practice one uses the sidereal day].”]

(printed p. 262 — completing [III.], the Scholium on a sensible specimen of the First Motion: since a Fixed star’s apparent proper motion amounts daily to only a few thirds of a degree, a pendulum fine enough to distinguish the ideal day from the star’s revolution to the same Meridian is impossible to construct. The differences can be gathered by calculation, and for astronomical practice the day exhibited by a Fixed star’s revolution more than suffices, as treated in bk. 3, ch. 21.)