[Margin: Plato’s opinion.]
[I.] What Plato thought in this matter will become manifest from his Epinomis; for there he calls those who were occupied about the mere observations of risings and settings, and the prognostics to be deduced therefrom, τοὺς ἀστρονομοῦντας [the “star-gazers”]; but he calls ἀστρονόμους [Astronomers] those who investigate the celestial motions themselves; and he says: “You are ignorant of Astronomy; because he who is truly an Astronomer must be the wisest—I do not mean him who practices Astronomy according to Hesiod and all like him, inasmuch as he contemplates the risings and settings of the stars, but him who beholds the seven periods of the eight periods, of which each one traverses the same circle in such a way that universal nature is scarcely, scarcely equal to contemplating them, unless it be a partaker of that wonderful nature.” But I believe that, by “the seven periods of the eight periods” (for thus the Greek codex has, τῶν ὀκτὼ περιόδων τὰς ἑπτὰ περιόδους), he understands not the simple revolutions of the Fixed [stars] and Planets separately, but the revolutions of all these together to the same point—which they are wont to call the Platonic Year, according to that [saying] of Cicero in the Dream of Scipio: “But when all the stars shall have returned to that [point] from which they once set out, and shall have brought back the same configuration of the whole heaven after long intervals, then can it truly be called the ‘turning year’ [annus vertens], in which I scarcely dare to say how many ages of men are contained.” Of this year, therefore, and of the proportions and commensurations of the celestial periods, no one can perfectly attain—in Plato’s opinion—unless he have obtained a celestial and admirable genius. But Aristotle (bk. 1 On the Parts of Animals, ch. 5), notwithstanding this difficulty which he confesses to be found, says that even a modest knowledge of these things is more delightful than the [full] science of certain other [things].
[Margin: Delphinus’s opinion.]
Nay, John Anthony Delphinus (in the book On the celestial globes and motions, ch. 23) contends that no one, while he remains enclosed in the workhouse [ergastulum] of this mortality, can naturally have an undoubted science of the proportions and measures which are precisely in the celestial motions—because those proportions consist in an indivisible [point], and the least difference varies them; but [that], on account of the distance of the stars, differences of this kind become insensible in the life of one man, though afterward, by the lapse of ages, they become sensible.
[Margin: Clavius’s opinion.]
Our Clavius too, toward the end of the Commentaries on the Sphere of Sacrobosco (speaking of Copernicus’s attempt at emending the celestial motions, p. 452), concludes thus: “It is exceedingly difficult so to define the periods of the motions, that they do not deviate from the truth for many ages of years; since no mortal has ever been able so to determine the period of [even] one Planet, that there do not remain over, or be lacking, some tiny amounts which, in a great interval of years, induce a notable error. So that it is indeed wonderful that God, Best and Greatest, willed to obstruct the motions of the planets with such great difficulties, that no one of men can perfectly attain them, but always finds [something] which he may admire in so great an artifice of such noble bodies, and in so great a harmony and concord of their motions—celebrating their Creator and Mover with perpetual praises. So that, especially on account of the constitution of the heavens and their motions—in which there always seems to remain [something] which may be inquired into, with the highest diligence, by the most skilful searchers of celestial things—it seems to have been written by Ecclesiastes (ch. 3): ‘And He has delivered the world to their disputation’—lest, namely, at some time, if men had perfectly understood the number, order, constitution, and motion of the heavens, they should cease to inquire into and admire the works of God; and [their] minds, the cause of exercising [them] being removed, should grow torpid in idleness.”
[Margin: Job 38.]
[II.] But from the divine Scriptures, and the sacred writers, we have long since learned how arduous this Astronomical business is. For what else does that thunder of the divine voice to Job, from the whirlwind, signify, speaking thus: “Dost thou know the order of heaven, and wilt thou set down its reason on the earth?” and again, in the same chapter 38: “Who shall declare the reason of the heavens, and who shall make the harmony of heaven to sleep [be silent]?”—That is, if I am not mistaken: who will so perfectly describe and explain the motions of the heavens, that men, now secure about their course, may cease from observing the motions of the stars in the future, and so sleep [be at rest]? For just as the heavens are said to praise the Lord, because they rouse men to the praises of the Lord, and are an object moving [one] to praise Him, so too they would be said to “sleep,” if they were so [perfectly] known that they now invited men to sleep.
[Margin: Solomon’s knowledge divinely infused.]
But although Solomon proclaimed the wisdom of these things divinely infused into him (Wisdom 7), saying: “For He gave me the true knowledge of the things which are, that I might know the disposition of the globe of the lands, and the powers of the elements, the beginning and end and middle of times, the changes of vicissitudes, and the conversions of the seasons; the courses of the year and the dispositions of the stars”—yet the same [Solomon], in Wisdom 9, considering the merely natural powers of the human genius, thus professes: “And we estimate with difficulty the things which are on earth, and the things which are in [our] view we find out with labor: but the things which are in heaven, who shall investigate?”
[Margin: Philo’s opinion.]
And indeed hence the Fathers press [against] the judicial Astrologers, [arguing] that it is impossible to know exactly the course and aspect of the stars—especially Sts. Basil (homily 6 of the Hexaemeron), Ambrose (bk. 4 of the Hexaemeron, ch. 4), Augustine (bk. 5 On the City of God, ch. 3), [and] Gregory (homily 10 on the Gospels); to whom add Origen (in Eusebius, bk. 6 of the Preparation of the Gospel, ch. 9), and Philo (in the book On Dreams), who, after relating diverse opinions about the stars, concludes: “The [things] which are circulated about them and the heavens are uncertain and incomprehensible, [and] rest on probable conjectures rather than on certain and true reasons—so that it is lawful to swear that no mortal can ever rightly perceive anything of these.”
[Margin: Martinengus’s opinion.]
[III.] But whether the periods of the celestial motions are commensurable with one another, and consist of rational proportions, or rather of irrational [ones]—Astronomy has not yet so advanced that it is permitted to settle this controversy with certainty; and it will be enough to have indicated the opinions. For, as Ascanius Martinengus says (in the Great Gloss on Genesis, p. 1045): “Certain most learned Mathematicians, by the best reasons, thought that the conversions [revolutions] of the heaven are incommensurable among themselves; and therefore that the same face of the heaven, and position of the stars, can never return; and they strive to affirm this by no weak reasons.”
[Margin: John Anthony Delphinus.]
Certain [others] thought that only after thirty-six thousand years—or, according to others, forty-nine thousand, in which the supreme and slowest sphere will complete [its] revolution—the positions of the Stars return to the same. So John Anthony Delphinus (in the book On the celestial globes and motions, ch. 24 and 25) problematically defends each side; and adds that from this it is not sufficiently proved the asymmetry [incommensurability] of these mo—
[…continues on p. 270 (PDF 305): “…tions, [merely] because the Astronomers have hitherto disagreed among themselves about the measure of the Solar Year and the Lunations — for this happened on account of the brevity of life, and the unobserved (or badly-observed) returns of these periods; and on account of this, the Astronomical tables must be reformed every two-hundredth year…” — then the Lunisolar-cycle problem (Vieta, Clavius, Bullialdus), and Kepler’s case that the period-ratios are irrational and the Platonic Year impossible.]
(printed p. 270 — completing [III.], on the commensurability of the periods: astronomers’ disagreement over the measure of the Solar year and the lunations does not prove these motions incommensurable, since it arose from the brevity of life and defective observations. Yet no luni-solar cycle has been found that exactly restores the Luminaries to the same point of conjunction; even Vieta’s 3400-year period falls short, according to Kepler and Clavius.)
[Margin: Bullialdus’s opinion.]
Nay, Bullialdus too (bk. 2 of the Philolaic Astronomy, ch. 3), when he had said, “But that measure is false; for the motion of the Sun does not depend on the Lunar; nor did the ancients, with happier auspices, make the annual motion of the Sun commensurable with the Lunar synods,” a little after says: “For who hitherto has asserted and demonstrated that the annual motion of the Sun is commensurable with the Lunar cycles?” To these, Amicus (tract. 5 On the Heavens, q. 6, dub. 10) teaches that these proportions cannot be known; but [also] that, even if they be irrational, there is no imperfection in the heaven, because they are commensurate to the end fixed by God.
[Margin: Kepler’s opinion.]
But Kepler, contemplating these things with a deeper effort of mind (in the Epitome of Copernican Astronomy, bk. 4, p. 512), distinguished thus: “The ratio, indeed, of the extreme motions—the slowest and the swiftest—contemplated in any one Planet, [being] most exquisitely harmonic, is the supreme and adorable work of the Creative Mind. But the lengths of the periodic times, if they were the work of mind, would have something of beauty, such as the effable [expressible] proportions are—double, triple, and the like. But now the proportions of the periodic times are ineffable (commonly, irrational), and so partakers of infinity, in which there is no mental beauty, because no finition [bound].” And he confirms that these times cannot be the work of mind, in these words: “Secondly, these times cannot be the work of mind, because the times of one period are gathered from unequal delays in diverse parts of the circle; but those unequal delays (as will be said below) arise from material necessity, as it were from the principle of a balance [steelyard].” Thus he [Kepler], wholly bent on showing that the Planets are not moved by Intelligences, but by the Sun, according to the principles of the balance and lever, and magnetic attractions; and the Sun, [moved] by a certain material soul.
[Margin: The Platonic Year [is] impossible, according to Kepler.]
But the same [Kepler], in the Mysterium Cosmographicum (ch. 23), investigating the end [purpose] of the Astronomical World and the Platonic Year, concludes in these very words: “That no terminus can be set for the motion rationally, and that there will be no Platonic Year, I will prove from one postulate. For let it be granted that the Eccentricity is to the orb in a rational proportion: then the radii of the orbs will be mutually irrational, because they are related as [figures] inscribed and circumscribed to bodies, which are irrational—because they follow from the ratio of the subtense [chord] in the square, and of the section according to the extreme and mean ratio [the golden section]—which two are examples of irrationals in Geometry. But now the motions are in proportion to the Radii: therefore the motions too [are] mutually irrational; and so they will never return to the same beginning, even if they should last for infinite ages—because never, in [any] infinite section of time, would there occur a common measure by which, repeated often enough, one terminus of all the motions, and goal of the Platonic Year, might be constituted.” Which being so established, he exclaims, with Pliny (bk. 2, ch. 1): “The World is sacred, immense, whole in [its] whole—nay rather, itself the whole—finite and like to the infinite”; and with Copernicus (bk. 1, ch. 10): “So great, indeed, is this divine fabric of the Best and Greatest [God].”
[Margin: A judgment on Kepler’s opinion.]
[IV.] But the aforesaid argument of Kepler, drawn from the comparison of the orbs and the eccentricities, holds indeed in a hypothesis employing the figure of an Eccentric orb, or in [one] equivalent to it as to Geometry; but not in every [hypothesis] which is equivalent only as to numbers—say, in a motion made spirally through helices, or if the Angels move the heaven and Planets using merely Logistic rules, and not regarding circles, ellipses, or similar figures. Nor is it evident that the proportions which are ineffable to us—or at least, because they tend toward infinity—are devoid of all beauty; since the Divine Immensity and Eternity has all the perfection of the infinite, and yet does not lack its [own] beauty. Just as neither is it evident that it is not more beautiful that, in the celestial motions, there be proportions of each kind [rational and irrational]. Finally, it does not please [me] that he [Kepler] makes God the author of the effable proportions, but denies [Him to be the author] of the ineffable.