[Margin: Peter Ramus’s opinion about Astronomical hypotheses.]

[I.] The occasion of this controversy was given us by Peter Ramus; about whose opinion it is better to hear Tycho, writing and judging thus in [his] Epistle to Rothmann (of the year 1587, on the 20th day of January): “But that that most celebrated Philosopher of our age, Peter Ramus, thought that Astronomy could stand without Hypotheses, by Logical reasons, lacks foundation. He proposed indeed to me, 16 years ago, when we were together at Augsburg, this opinion; and was at the same time an exhorter [urging] that, after I had reduced the course of the stars into exact order through Hypotheses, I should aim to attempt the same without these. For he wished this to be done”—he says, and added the reason, that he had read that the Egyptians of old had a most easy knowledge of Astronomy; “and, since the method of Hypotheses seems difficult and intricate,” [he reasoned] that they must have known the courses of the stars by another, more compendious and plainer way—that is, without all hypotheses. Thus he [says], p. 60; to which I subjoined my judgment and censure in these words:

[Margin: Tycho’s censure of P. Ramus.]

“But I resisted him, showing that, without Hypotheses, the celestial phenomena cannot be reduced into a certain science, nor be accounted for so as to be understood; but that that Egyptian ‘easiness’ existed only in the Equatories [the planetary-position instruments] of the Planets, by which they freed themselves from tedious computation, when the ready method of Ephemerides was not yet in use. But although this man, otherwise endowed with a perspicacious genius, and a lover of truth if any [other] was, seemed to me not to have thoroughly inspected the inner sanctuaries [penetralia] of this art, and not to have noticed the variety in the motion of the stars, by no means recurring at fixed times of the year—I could neither obtain anything from him in this part, nor [did I] wish [to]. He has still very many followers, who hope that the same can be done; but who do not understand the matter itself, nor will ever bring [it] into effect. For since all things consist of number, weight, and measure, by these too [nothing] can be explained [otherwise] in the invisible world. But Hypotheses show nothing other than the measure of the apparent motion through a circle and other figures, which Arithmetic resolves into numbers: without these, if anyone wish to comprehend the motion of the Stars, let him invoke fortune (as it is wont to be said), and imagine a supramundane reason, beyond human intellect, and plainly incorporeal, and more than Angelic—[which] is necessary.” Thus far Tycho against Peter Ramus.

[Margin: Patrizi’s opinion, and Kepler’s censure.]

And not dissimilar [things are said] against Francesco Patrizi by Kepler (in the commentary on the motion of Mars, ch. 1), where, when he had indicated the ancients’ observation about the double motion in the heaven, he subjoined: “This first adumbration [sketch] of Astronomy—which stands by no explanation of a cause, but only by the slow experience of the eyes, and which can be explained neither by figures nor by numbers, nor be drawn out [predicted] into future times, since it perpetually disagrees with itself (so that no spiral is equal to another by a delay of time, [and] none passes into a neighboring [spiral] by a bending of the same quantity)—this [adumbration], I say, some nevertheless today, the labors of these thousand years being trampled under foot, strive to restore by diligence, erudition, [and] science, forcing upon the crowd an admiration of themselves (by an effort not unsuccessful among the unskilled); whom the more skilled judge—rightly and deservedly—to play the fool, or (if the Philosophers will [have it] otherwise, like that Patrizi) to be mad with method [reason].”

To these is added that God is said (Wisdom 11) to have disposed all things “in measure, and in number, and weight,” and by Plato [is said] “always to Geometrize” [θεὸς ἀεὶ γεωμετρεῖ, God always geometrizes]; and, finally, [that] if it can be done that the Phenomena of the celestial motions be represented by some figure having the beauty of a Geometrical figure, this would be better than to set forth those motions without this appearance.

[Margin: A defense of Ramus and Patrizi.]

[II.] Yet for the opinion of Ramus and Patrizi there occur reasons not to be despised. For, first: out of so many Geometrical figures which the Astronomers have hitherto tried to accommodate to the celestial motions—whatever they boast, and especially Lansberge—none yet plainly satisfies all the legitimately-observed phenomena of [even] one Planet; nay, every year some discrepancies are detected, both in Eclipses and in the other vicissitudes of such motions; and this, not a few refer rather to the hypotheses [being] contrived, than to a defect of the observations. But what has not been done through these hypotheses, scarcely seems able to be done in the future through others; since all the combinations of Eccentrics, Epicycles, and Concentrics, and all forms of hypotheses through circles or ellipses, seem [already] to have been tried (as is plain from what was said in bk. 7, sect. 2 and 3); but the multiplication of little circles is liable to several errors, the more it has been complicated from several differences of motions.

[Margin: 2nd reason.]

Secondly: that necessity of a Geometrical hypothesis seems to have arisen rather from our own weakness or habit, than from the nature of such motions. For because, from adolescence onward, we have been versed in the mathematical dust [trained in geometry], and can ill do without the apparatus of Geometrical demonstrations—or, without it, can only with difficulty imagine the causes and rules of the celestial motions—therefore we seem to need these for understanding and thoroughly teaching their Theory; especially since we do not have all and singular the observations which would manifest to us one whole period, explored day by day through its parts, and exhibit its constant law; and therefore the remaining equations for the calculation of the mean motions (which we ourselves feigned for an easier use of calculation) we are in a manner forced to hunt out, from the necessity of some Geometrical figure, by whose laws the Planets may be bound. And hence, doubtless, it seems to be, that we never attain the subtlety of Astronomical truth; for we hunt the path of the Planets by a way feigned by us. But if we had sufficient observations, held on each [single] day, we could perhaps render the account of these motions without the laws of Geometry, and by purely Logistic [arithmetical] laws—that is, by very recondite ratios and proportions of numbers.

[Margin: 3rd reason.]

Thirdly: the motions of the stars are most probably accomplished through spirals, as we already said in ch. 3; and [they] are per se unequal, as we taught in ch. 4; but these two conditions do not seem easily to cohere with the termini of any Geometrical figure, but rather to connote the motions of the Planets [as] loosed from them, and bound by other laws outside the jurisdiction of Geometry.

[Margin: 4th reason.]

Fourthly: it pertains to the dignity of the Intelligences moving the heavens and stars, that in these [motions] they follow rather the ideas of numbers (which abstract from sensible and imaginable matter) than [the ideas] of continuous quantity (which does not abstract from it); nor [that] they need, for directing those motions, the contemplation of circles, or ellipses, or similar figures. And if perchance they designate any figures in the heaven by those motions, [these are something] posterior, and a consequent effect, but not an exemplary cause or idea of which they have need. Just as neither to singers, nor to cithara-players, nor to dancers to the beat, are there set forth, for imitating, figures of the various motions which they certainly designate by tongue, hand, or feet—like a footprint passing [vanishing] in the air.

[Margin: 5th reason.]

Fifthly: just as the proportions of the motions, by which various pendulums are agitated to and fro, together with their intervals, follow the ratio of the odd numbers taken in order—so that the heights [amplitudes] of any two pendulums are to one another as the squares of the times; and [just as] the increments of velocity in the natural motion of heavy bodies keep a similar proportion (as we taught in bk. 2, ch. 20 and 21)—nor in these is the law of any figure attended to: so it seems probable that similar, or more sublime, reasons are in the minds of the Intelligences, by which they infallibly carry the stars around, and present them in their places at the fixed time, without the aid of any figure.

[Margin: Conclusion.]

[III.] Let us conclude, therefore, that Geometrical figures are indeed to be used, as long as nothing better and more certain occurs; but that they are not to be vended [touted] as the true causes of the anomaly of the celestial motions, nor [is one] to pass, from the name “Hypothesis,” to a real necess—

[…continues on p. 269 (PDF 304): “…ity of such a figure. Yet meanwhile [it is] probable [that] what was said at num. 2 [is true] — namely, that the Intelligences use merely logistic [arithmetical] reasons for the harmony of these motions, without the contemplation of a figure directing them, or [a figure] set before them, by primary intention, for imitating…”]

(printed p. 269 — completing [III.], the Conclusion of Chapter V: one may not pass from the name “Hypothesis” to a real necessity of geometrical figure in the celestial motions; probably the Intelligences use merely logistic, arithmetical reasons, though they may also represent the beauty of some figure fitted to the spiral motion. Whatever geometry or harmony be feigned must agree with the phenomena and with the end divine Providence set for these motions, as the analogy of the human body’s organs shows; and it is not yet established that such figures repugn that end.)