[Margin: The order of examining the Arguments for the annual motion of the Earth.]

[I.] All the arguments which, by a most subtle inquiry, have been devised by the Philolaic [school] and the Copernicans for removing the Earth—if it can be done—from the center of the universe, and for transferring it about that [center] through an annual orbit, seem able to be recalled to four general heads: namely, either to certain conditions of the Earth compared with the conditions of the Planets (not yet, however, involving motion); or to the motion itself of the Planets; or to other motions observed in the heaven; or finally to motions or changes observed in the sphere of the elements. This order, therefore, we ourselves too shall keep in weighing them.

First Argument, from the greater Nobility of the Sun than of the Earth

[Margin: The argument of Philolaus and Kepler.]

[II.] It seems not to be doubted that the center of the Universe is the most noble place in the world, inasmuch as it is equally distant on every side from the extremes, and holds the middle position. Hence it came about that certain Pythagoreans—as Aristotle relates (bk. 2 On the Heaven, texts 72 and 73)—placed in the middle of the Universe not the Earth but Fire, that they might ascribe to the most honorable of bodies the most honorable seat; which Fire they called the guard or prison of Jupiter [Zeus]. That the chief author of this opinion and argument was Philolaus, we have already learned from Plutarch (bk. 3 On the Opinions [of the Philosophers], chh. 11 and 13), and we have already reported his words in ch. 3 of this section, where also (from num. 3) we treated of Vesta, placed by the ancients in the center of the World as a terrestrial Fire: this Fire, however, the Copernicans assert to be the Sun—especially Kepler (bk. 4 of the Epitome of Copernican Astronomy, p. 444).

[…continues on p. 331 (PDF 366) with the catchword “444”: ”…[p.] 444. For thus the Pythagoreans were accustomed to conceal their dogmas under other terms, and by Fire to understand the Sun”—the rest of ¶II and Riccioli’s reply to the First Argument.]

(printed p. 331 — within Chapter VIII. Completes the first argument (the Sun’s nobility) with Aristotle’s rebuttal of the Pythagorean central fire and Kepler’s reply, casts it in form, and answers it: the Earth with its plants, animals, and especially men is the more excellent body. The Second Argument, from the center of the planetary system (Copernicus, Galileo’s telescope, Rheticus, Kepler), is then proposed and cast in form, with Riccioli’s First Response begun — the Sun is not the center of the whole system.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 331]

[p.] 444. For thus the Pythagoreans were accustomed to conceal their dogmas under other terms, and by Fire to understand the Sun, as the most excellent of all bodies, and to which the most fitting place ought [to be given] for guarding and preserving [it]; and this [place to be] the center of the Universe. But since Aristotle had tried to blunt this argument of the Pythagoreans, saying that the center of magnitude and [that] of the nature of a mundane body are not the same—just as in animals the principle of life, which is the heart, is not precisely in the middle of the animate body, if you regard the center of magnitude, but in another, more congruous, place; and that therefore one must seek from elsewhere which is the place fitter for that principle on which the chief operations of the universe depend, than [to seek it] from the center of the mass of the universe itself: Kepler says that there the case [reckoning] of animals is unlike, whose bodies are not round, and [that] of the World, which is spherical and needs no operation outside itself; wherefore there is no cause why its heart should not be in the center of the universe. He adds that Aristotle, while he seeks lowliness for the center, does not do rightly, since it is the principle of the likeness shadowing forth the mystery of the Trinity—for by the center is designated the First Person, the origin of the others. To this argument—poorest [as it is]—how many mysteries [are given] for clothing it! [The argument], constrained to the form of a syllogism, is such:

[Margin: First Argument, in form.] [Margin: Response.]

[III.] “To the most excellent of mundane bodies the most excellent place is owed: But the Sun, and not the Earth, is the most excellent body of the world, and the most excellent place of the Universe is the center; therefore to the Sun, not to the Earth, is the center of the Universe owed.” It is answered by conceding the Major concerning the most excellent place [taken] not from mere Geometrical excellence, but from a physical end and good—[namely] that such a body ought to receive from others, or to communicate to others: but in this sense the latter part of the minor proposition is conceded, with respect to the natural end of which here is the discourse; but the prior part is denied: for the Earth ought not to be taken nakedly as a mere single element out of the four (or three) elements, but together with the living plants and animals, but especially with men, for whose sake all the stars were made and are moved—God attesting this in Deuteronomy; and so taken, it is the most excellent body of all the bodies of the world, if we estimate the magnitude of [its] power and the dignity of [its] end (as is fitting) rather than the magnitude of [its] mass. But I said [this] speaking of the natural order and end; for if [we speak] of the supernatural, the center of the Earth is the lowest and most wretched place, and [the place] of the prison of Hell—which is now no longer the guard of Jupiter, nor of a saving Fire, but of a Fire destined for the eternal burning of the damned; but on the contrary the Empyrean—that is, the earth translated into heaven, or the Earth of the living—is the most excellent place.

Second Argument, from the Center of the Planetary System

[Margin: First reason of Copernicus for [the Sun as] the center of the planetary system.]

[IV.] That the Earth is not the center of the system of the Planets, but the Sun, the Copernicans have affirmed chiefly for two causes. The first Copernicus touched (bk. 1, ch. 5) in those words: “Since, if anyone deny that the earth holds the middle or center of the world, and yet not confess [that] the distance is so great as to be comparable to the sphere of the non-wandering [fixed] stars, but [that it is] notable and evident with respect to the orbs of the Sun and the other stars; and think on that account that the motion of those [planets] appears diverse, as though they were regulated to another center than is the center of the earth: he will perhaps be able to bring forward not an inept reason for the apparent diverse motion. For [the fact] that the wandering stars are seen now nearer the earth, and the same [stars] now farther [off], necessarily argues that the center of the earth is not the center of their circles. [Nor] is it even settled whether the earth nods toward them, or they toward the earth.” Hence, therefore, Galileo (Dialogue 3 On the System of the World, Latin p. 241), to Simplicio asking whence it would be established that the Sun is in the center of the conversion [revolution] of the Planets, answers under the person of Salviati that this is made out by most evident and necessary observations, of which the first is that all the Planets are found now nearer the earth, now farther from it, by differences so enormous that Venus, most remote in her apogee, is found six times farther from us than when she is nearest and at perigee; and Mars, in apogee, has eight times a greater distance from the earth than [when] at perigee:

[Margin: Second reason of Copernicus.]

yet this argument does not hold of the Moon, because it is established from elsewhere that [she] cannot be separated from the earth as the center of her motion. [V.] The second reason the same Copernicus brought forward (bk. 1, ch. 10): namely, that the five lesser Planets perform their circuits about the Sun. Let us hear him, that from the fountain of this teaching we may draw more clearly. “Wherefore,” he says, “I judge it by no means to be despised, what Martianus Capella—who wrote an Encyclopedia—and certain other Latins thoroughly knew. For they think that Venus and Mercury run around the Sun [as it] exists in the midst, etc.” And a little after: “What else, then, do they wish to signify, than that the center of those orbs is around the Sun? So indeed the Mercurial orb, within the Venereal—which it is agreed is more than twice as great—will be enclosed, and will obtain, in that very [Venereal] amplitude, a place sufficient for itself. Hence, occasion being taken, if anyone refer Saturn too, and Jupiter and Mars, to that same center—provided he understand the magnitude of their orbs to be so great that it may contain and surround, together with them, the earth as well [remaining within]—he will not err, [as] the canonical reckoning of their motions declares.” And he at once confirms this by saying: “For it is established that they are always nearer the earth around [their] evening rising—that is, when they are opposed to the Sun, with the earth mediating between them and the Sun—but most remote from the earth at the evening setting, when they are hidden around the Sun; namely, while we have the Sun between them and the earth. Which [things] sufficiently indicate that their center pertains rather to the Sun, and is the same as that to which Venus and Mercury also refer their revolutions.” The very same reasoning Galileo pursues (Dialogue 3 On the System of the World, p. 241 likewise), and Kepler (bk. 4 of the Epitome of Copernican Astronomy, p. 536); but what Copernicus had assumed concerning Venus and Mercury from the mere authority of Capella and of certain Latins, [Galileo] himself affirms much more certainly by the experiment of the Telescope, by which it is now established that these Planets are thus illuminated by the Sun, like Moons going around it. By these conjectures, therefore, partly, [and] partly by sure observations, both these and the rest of the Copernicans—and most of all Rheticus in his First Narration, and Kepler in the introduction to the Commentaries on Mars, and in the Epitome of Astronomy (p. 450), who nevertheless (p. 449) had rightly warned that Copernicus’s hypothesis is not disturbed if the center of the Universe be set [as] the Sun rather than the center of the great orb—try to persuade, and as it were to demonstrate, that the Sun is in the center of the world, and that on that account it was deservedly called by the Ancients the Sun chorēgon [χορηγόν]—that is, the Choragus [chorus-leader] of the Planets, and the moderator of Nature; and [that] those Poetic encomia of the Sun are no more Poetic than Physical. Now, therefore, [let us come] to the argument.

[Margin: Second Argument, in Form.]

[VI.] “That body ought to be in the center of the Universe which is the center of the System of the Planets; But the center of the Planetary System is not the Earth but the Sun: Therefore not the Earth but the Sun ought to be in the center of the Universe.” The Major is not indeed proved by the Copernicans, but rather supposed, as [if] it were certain that the other Planets are moved about the center of the world, on the ground that the system of the Planets seems the chief part of the mundane system. The Minor has already been proved (nums. 4 and 5), from the notable variety of the distance of the lesser Planets from the Earth, and from the circuit of Venus and Mercury about the Sun—from which the same becomes very probable concerning the three remaining Planets.

[Margin: First Response.]

I answer by distinguishing the Major, and denying it if that body be not the center of the whole System of the Planets adequately taken, nor of the Fixed stars, nor of the new Phenomena [novae], nor of the elementary motions, and of the animals dwelling in them [the elements]: for all these, just as they are to be considered for the integrity of the Universe, so also for constituting its center—inasmuch as [the center] includes a relation to all, and not only to some great parts of the world. But if it [the body] be such, I concede the Major; yet in this sense I deny the Minor: for granted that, against Ptolemy, it be now certain that the Sun is the center about which Venus and Mercury revolve, and [that], according to Tycho, the Sun be the Choragus of the five lesser Planets describing their orbs about it; it is nevertheless not the center of the Lunar motion, nor of the motion of the Fixed [stars], nor of the new stars, nor of the Comets, nor of the Elementary motions: nay rather, according to our system—which can probably be maintained with the phenomena saved—it is the center of nothing but the circulations of Mercury, Venus, and Mars, as [being] its satellites; for the reasons indi[cated]

[…continues on p. 332 (PDF 367) with the catchword “tas”: ”…[indica]tas”—the reasons indicated [earlier], and the continuation of the First Response to the Second Argument.]

(printed p. 332 — within Chapter VIII. Finishes the First Response to the second argument and adds a Second by retortion: the Earth, not the Sun, is the center of all motions. The Third Argument, from the source of light and heat (Kepler’s light-encomia and Copernicus’s “lamp in the temple”), is cast in form and answered — the Sun is not the universal cause of light. The Fourth Argument, from the source of motion (Copernicus’s “ruler and governor,” Rheticus), then begins.)

[Header: BOOK IX. SECTION IV. — 332]

[indica]ted in section 3, ch. 9. Nay, if we should wish to pursue all the scruples, not even in the hypothesis of Kepler and Bullialdus is the Sun the center of the Planetary orbit, since they establish that orbit to be not a circle but an Ellipse, and place the Sun not in the center of the Ellipse, but only in one of the navels [umbilici], or foci, of the Ellipse. But on this last subtlety we do not lean, because in every hypothesis of a Planetary orbit, on account of the Eccentricity—required for accounting for the anomaly—the center of it [each orbit] is distant from the center of the Universe, except the orbit of the Earth, whose center, according to the opinion of Copernicus, is in the very center of the Universe, and is distant from the Sun by as much as is the Eccentricity of the Solar orb in the hypothesis of the others.

[Margin: Second Response.]

I answer secondly, by retorting the argument thus: “That body ought to be set in the center of the Universe which is the center of the motion both of the non-wandering [fixed] and of the wandering stars, and both of the old and of the new phenomena, and both of the elementary or sub-celestial and of the celestial bodies. But a body of this kind is not the Sun but the Earth. Therefore not the Sun but the Earth ought to be set in the center of the Universe.” The Major at all events contains a far greater probability than if the center of the Universe be referred to the circulations of some Planets only, all the other parts of the World being neglected. The Minor has no difficulty except as regards the Planets; for the Sun, not the Earth, seems to be the center of the Planetary system. But by this very fact, that the Earth is the center of the motion of the great Luminaries—namely the Moon and the Sun—it is also, through their mediation, the center of the other Planets, if they be set to be borne about the Sun, as Tycho holds. But in our system the difficulty is less; for the Sun is the center of nothing but Mercury, Venus, and Mars—for these are satellites of the Sun, and look to the same heaven—but the Earth is the center of the orbs of Jupiter and Saturn, and, through their mediation, of the Jovian and Saturnian satellites.

Third Argument, from the Source of Light and Heat

[Margin: Kepler’s opinion on the source and place of light.]

[VII.] This argument seemed indeed splendid to Kepler (in the Optical Astronomy, ch. 1, p. 7), where, when he had brought forth many encomia of light—as of the most excellent thing among the visibles in the world, and the matrix [womb] of all the faculties of animals, and the bond of the corporeal and spiritual world (as he thinks), and therefore created by God on the very first day of the world—he added: “The Sun, therefore, is a certain body: in it [is] this faculty of communicating itself to all things, which we call light:

[Margin: The encomia of the Sun and [its] place, from Kepler.]

to which, even for this cause, the middle place in the whole world is owed, that it might equably and perpetually diffuse itself into the whole globe.” But in the same place (ch. 6, from p. 221 to 226) he pours himself wholly out in praises of the Sun, and ascribes to it as great a density and abundance of matter as is in the whole ethereal aura, and yet so great a transparency that our eye may see its depth and center, and [its] soul or vital faculty, and many other things; but to our purpose he says that the office of the Sun in the world is, by the confession of all, what [the office] of the Heart [is] in an animal, and [that] the motions of the Planets are dispensed from the Sun, etc. Then (in the Epitome of Copernican Astronomy, bk. 4, p. 448) he says that if the whole world, which is spherical, needs the light and heat of the Sun equally, the Sun is best placed in the middle, whence, equally situated, it may be distributed into all regions of the world; and [that] this is done more equably and more rightly if it rest in the center of the World than if it go around the center; and—by receding from some and approaching to others—illumine and warm these more, those less: nor is the likeness of a lantern to be derided, in the middle of which we place the light. But quite new are the things which, to this purpose, he there subjoins, saying: “But concerning light a peculiar demonstration is woven, supposing fitness [elegance], not necessity. Imagine the sphere of the Fixed [stars] to be a concave mirror: it is known that an eye placed in the center of such a mirror beholds itself on every side; and if there be a light in the center, it is reflected back from the concave surface on every side at right angles, and the reflected [rays] meet again in the

[Margin: Kepler’s symbol of the Most Holy Trinity.]

center. But this can happen in no other concave point except in the center. Therefore, since the Sun is the source of light, the eye of the world, the center will be owed to it, that (it [the Sun] being, in the divine symbolization, the Father) it may contemplate itself in the whole concave surface (which bears the symbol of the Son of God), and in that image of itself may be pleased with

[Margin: The Encomia of the Sun and [its] place, from Copernicus.]

itself, and by illuminating may illustrate itself, by warming may kindle [itself].” [VIII.] But before Kepler, Copernicus (bk. 1, ch. 10), using another likeness, had assigned this very seat to the Sun in those words: “In the middle of all resides the Sun. For who, in this most beautiful temple, would put this lamp in another or a better place than [that] whence it can illuminate the whole at once? Since not ineptly some call [it] the lamp of the world, others the mind, others call [it] the ruler.

[Margin: And of Pliny.]

Trismegistus [calls it] the visible God; the Electra of Sophocles, [calls it] that-which-beholds-all-things. So indeed, as upon a royal throne, the Sun, residing, governs the surrounding family of the stars.” To which can be referred the things which Pliny most magnificently utters concerning the Sun (bk. 2, ch. 6), and which were recited by us from him (bk. 3, ch. 1). Hence, therefore, the following argument is built up.

[Margin: Third Argument, in Form.]

[IX.] “That body ought to be set in the center of the Universe which is the cause and source of the light and heat diffused through the whole world. But of this kind is the Sun; Therefore the Sun ought to be set in the center of the universe.” The Minor is certain among all. The Major is proved both from the equal communication of heat and light, which ought to be made [but] cannot be unless the source of light and heat be equally distant from all the parts of the world; and from the likeness of a mirror, a lamp, etc., of which [we spoke] in nums. 7 and 8. It is answered by distinguishing the Major, and denying it if [the Sun] be not the universal cause of light, nor those very things which receive light from it receive light equally; but conceding or granting [it] if it be the universal cause, and illumine all things in the same manner: But in this sense the Minor is denied; for the Sun is neither the cause of light in the Fixed stars (as is plain from what was said, bk. 6, ch. 2, even with Kepler himself agreeing), nor does it illuminate the Earth and the Planets equally—both on account of its unequal and ever-variable distance from the Earth, and [that] of the Planets from it, and on account of the manner of illuminating them; for at one time we discern [certain] phases in the Moon, at another in Mercury and Venus, which are sometimes seen sickle-shaped [crescent], at other times in Mars, which sometimes appears gibbous, never sickle-shaped, at other times in Jupiter and Saturn, which to the sense always appear round—granted that they too receive their primary light from the Sun. Feigned, therefore, is that equality, and brought forth with little consideration. But neither is the likeness from a mirror valid, since the sphere of the Fixed [stars] is not a mirror of the Sun—otherwise it would shine all over; nor are the Fixed [stars] images of the Sun—otherwise they would not have light from themselves; and all [stars] which are equally distant from the center of the world would appear of the same magnitude, and [would appear] at any point of the celestial concavity from which the rays could reflectedly reach our eyes. It suffices, therefore, if the Sun be in such a place that it can illuminate round about the Earth and the Planets, but in that manner and measure which the end of divine Providence requires.

Fourth Argument, from the Source of Motion

[Margin: Rheticus’s opinion on the source of motion, and the place of this source.]

[X.] Now this argument too we have heard insinuated by Copernicus (bk. 1, ch. 10), when he calls the Sun the ruler and governor of the Planets driven around [it]. But to this Rheticus added force in his First Narration, where indeed he had said: “In the common principles of Astronomy it was indeed [possible] to see that all the celestial appearances direct themselves to the middle [mean] motion of the Sun, and [that] the whole harmony of the celestial motions is constituted and conserved by its [the Sun’s] governance. Whence also by the ancients the Sun was called chorēgos [χορηγός], the governor and King of nature. But how it would conduct this administration—whether in the way in which God governs this whole universe (as Aristotle most beautifully depicts [in the book] On the Cosmos); or whether it itself, by traversing the whole heaven and being at rest in no place, would act the part of God’s administrator in nature—does not yet seem to be altogether explained and settled.” These things, I say, being premised, a little after he subjoins: “The former mode of governance is rejected, the latter received.” But the Lord Doctor, my Teacher [Copernicus], he [Rheticus] understands [to have] decided that the condemned manner of governance [should] be recalled into the nature of things of the Sun, yet so that to the received and approved [manner] too its own place be left. For he saw that neither in human affairs is there need that the Emperor himself run through the individual cities, that so he may at last discharge his office, imposed on him by God; nor [is there need] that the heart migrate into the head, or the feet, and the other parts of the body, for the conservation of the living thing, but [that] through other organs [organa] destined by God for this it preside over its office. After these things he says, lest the mean motion of the Sun in the other planets [serve] by

[…continues on p. 333 (PDF 368) with the catchword “sola”: “…by mere imagination alone, but should have a true efficient cause”—the rest of Rheticus’s and Kepler’s source-of-motion argument, and Riccioli’s reply.]

(printed p. 333 — within Chapter VIII. Completes the fourth argument (source of motion) with Kepler’s physics and answers it by distinguishing the Major: the Sun is only an exemplar the planets imitate, itself moved by its own Intelligence around the Earth. The Fifth Argument, from the mass of the Sun and Earth (Kepler), and the Sixth, from need and the end of motion (including Kepler’s surveyor-analogy), are then proposed and answered.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 333]

[the mean motion of the Sun in the other planets] should serve by mere imagination alone, but should have a true efficient cause—[he says] that this was brought about through the annual motion of the Earth in the great orb; for hence the cause is ready at hand why the mean motion of the Sun flows into [influences] the theory of all the planets.

[Margin: Kepler’s doctrine on the source of motion, and the place owed to it.]

[XI.] But by other reasons Kepler busies himself to advance this very doctrine (in the introduction to the Commentaries on Mars, p. 4), where, from [the fact] that the Planets are quickened by approach to the Sun, and are checked or retarded by recession—and [that] this same thing happens to the Earth, if the Earth be moved annually—he gathers by a Physical conjecture that the Sun is the source of the motion of the Planets and of the Earth, and says: “It is therefore highly probable that there is the source of the Earth’s motion where there is the source of the motion of the other five Planets: namely, likewise in the Sun. It is therefore probable that the Earth is moved, since the probable cause of its motion appears.” And so, with no delay interposed, he argues conversely thus: “On the contrary, that the Sun stands still in its place in the center of the world is made probable both by other [considerations] and most of all by this: that in it is the source of the motion of at least five Planets; for whether you follow Copernicus or Brahe, for both [systems] the source of the motion of the five Planets is in the Sun; in Copernicus, of the sixth too, namely the Earth. But [that] the source of all motion remain in its place is more probable than [that it] be moved.” But because he saw that the phenomena of the Sun are saved in the Tychonic hypothesis, and [that] the Sun is slow in receding from the Earth, swift in approaching, and that the Sun can be the source of light, and yet be moved about the Earth, a little after he subjoined these words: “Upon this most certain conclusion, therefore, by the Physical conjecture used above, this Physical philosopheme would have to be built up: that the SUN, together with that whole greatest load of five Eccentrics (to speak crudely), is moved by the Earth—or [that] the source of the motion of the Sun and of the five Eccentrics fixed to the Sun is in the Earth. But let both bodies, of the Sun and of the Earth, be inspected, and let judgment be made concerning both, to which the source of the motion of the remaining body more belongs. Whether the Sun should move the earth—[the Sun] which moves the other Planets; or the Earth [should move] the Sun, the mover of the rest, [the Earth being] so many times larger than itself? Lest, therefore, they be forced to concede that the Sun is moved by the Earth—which is absurd: immobility is to be conceded to the Sun, motion to the Earth.” But there is another peculiar reason of Kepler for this hypothesis, because, according to his fictions, the Sun moves the Planets by a magnetic force through diffused light, by which it grasps and leads them around, as I have already explained (bk. 3, ch. 2, num. 7). This argumentation, therefore, being gathered into few [words], thus may someone reason for the Copernicans.

[Margin: Fourth Argument, in form.]

[XII.] “That body ought to rest in the center of the Universe which is the source of the motion of the Planets. But the Sun, and not the Earth, is the source of the motion of the Planets. Therefore the Sun, and not the Earth, ought to rest in the center of the Universe.” The Major rests on probability, which could be augmented from the analogy of a spring: for the spring is not moved, but the river or brook flowing from the spring [is]; and in mechanics the movers are wont to stand in a determined place, that thence they may the more firmly move other bodies. The Minor is proved both from this, that the motion of the Planets, in its second anomaly, is attempered to the mean—or, as the more recent [astronomers] will have it, to the true—motion of the Sun; and from the magnetic faculty of the Sun, by which it leads the Planets around; and finally, because it is more probable that the Sun is the source of the motion both of the Planets and of the Earth, than that the Earth is the source of the motion of the Sun, and, through the Sun’s mediation, of all the Planets.

It is nevertheless answered by distinguishing the Major, and denying it if that body be not the universal source of motions—namely, of all the Planets, the Fixed [stars], the new Phenomena, and the Elements and elementary bodies; or if it be not a source but [only] an objective exemplar or rule of motions; but conceding or granting the Major if it be of this kind—in which sense the Minor is denied: for the Sun is neither the source of the motion of the Elements or of elementary bodies, nor of the Fixed [stars], nor of the satellites of Jupiter and Saturn. But neither is it the source—that is, the efficient cause—of the motion of the Planets (as Kepler gratuitously feigns), but only the exemplar, which by their motion they in part follow or imitate, just as the Standard-bearer moves [leads] the column of soldiers, and the Choragus [leads] the chorus of dancers. Wherefore the burden of carrying the Eccentrics of the Planets does not lie upon the Sun as upon a porter; and too crude is Kepler’s likeness, even by his own confession: nor does the Earth move the Sun effectively, or sustainingly, but objectively and finally, in so far as the Sun, around the Earth and for the sake of those dwelling in it, is moved by its [own] Intelligence—in which [sense of] metaphorical motion, and [this] manner of motion, we deny there to be any absurdity. Nay, on the occasion of the question pointed out by Rheticus, it is probable that, among the other ends intended by God, this was one: that it might be established, from the very agitation and unresting course [of the Sun], that the Sun is not God, but God’s minister, bidden to rise upon the good and the evil, and to carry the torch before all the inhabitants of the Earth. For I remember that I read, in the history of the East Indies, [of] the King of Peru—called the Inca, and a worshipper of the Sun—[so called] even on this ground, that the Sun runs around with so great diligence that it succours all—[who was] refuted by a Spaniard, [saying] that thence it ought rather to be gathered that [the Sun] is not God, since immobility befits God. But what was added by Kepler concerning the magnitude of the Sun with respect to the Earth will be dissolved [answered] by the following argument.

Fifth Argument, from the Mass of the Sun and of the Earth

[Margin: Kepler’s argument for the annual motion of the Earth.]

[XIII.] What for us is the fifth, for Kepler is the sixth argument (bk. 4 of the Epitome of Copernican Astronomy, p. 544), from those words: “For it is more credible that the body is great about which lesser ones go around.” But he supposes it certain that Saturn, Jupiter, Mars, Venus, [and] Mercury are smaller than the Sun, and likewise the Moon smaller than the Earth which it goes around, and the Jovian Satellites [smaller] than Jupiter; then he concludes: “But now, if the Sun is moved, the greatest Sun, and the three superior [planets], each larger than the earth, will go around the smaller earth: it is therefore more credible that the Earth, a small body, goes around the great body of the Sun.”

[Margin: Response.]

It is answered, however, that this is not true unless the rest be equal [other things being equal]: for if what is less in mass be greater in power and in the excellence of [its] end—of which kind is the Earth, taken not nakedly but with its inhabitants—it is more credible that it rest, and [that] the remaining bodies, [being] about to serve it by their motion, be moved around it. Besides which, the sphere of the elements, around which the Sun is moved, is greater in mass than the Sun: and yet the Copernicans move it, together with the whole Lunar heaven, around the Sun [which is] so much smaller. Wherefore the argument, if it were valid, could be retorted against them.

Sixth Argument, from Need, and from the End of Motion

[Margin: Another Argument of Kepler for the annual motion of the Earth.]

[XIV.] “The Sun in no way needs the Earth, but the Earth [needs] the Sun and the rest of the stars: it is therefore consonant that it [the Earth] be moved, and by motion seek for itself those things which it needs.” But this argument has already been sufficiently met (ch. 5, nums. 31 and 32). As for the end of motion, Kepler (in the Epitome of Copernican Astronomy, bk. 4, p. 549) thus philosophizes. “The Earth,” says he in nearly these words, “is the dwelling of the contemplative creature; and indeed it was not fitting that man, the inhabitant and observer of this world, should reside in one place of it, as in a closed chamber; for in this way he would never have arrived at the measurement and contemplation of stars so remote: it was needful, therefore, that—just as surveyors are wont to take different stations—so he, using the annual translation [carrying-about] of the Earth, should walk around as if by a navigation, that he might more rightly behold and measure the individual members of this great house.”

[Margin: Response to the Argument.]

But Kepler does not see that neither was this necessary, since it abundantly suffices that a man go out into the open and contemplate the stars; or, if there be need of some motion, that he walk about the resting earth; and that the motion of the Earth confers nothing on him for this, since through it he approaches the Planets no more than in the hypothesis of a resting Earth; and toward the fixed [stars] he is brought by no sensible approach through the motion of the Earth, since the whole annual orb is, as it were, a point with respect to the sphere of the Fixed [stars], in the opinion of Copernicus. But on the contrary, if, for measuring the motions, diameters, and intervals of the Planets and Fixed [stars], there had been need of an approach to the stars—as though it were necessary to measure them with ten-foot rods or with ropes—this argument would prove too much: namely, that there would also be need that [a man] approach each of the stars as nearly as possible—which is plainly most false. Let Kepler, therefore, cease to press the rest [quiet] of the Earth with arguments so trivial, or to attempt with these little contrivances to move it from its seat; and let him remember [that] man

[…continues on p. 334 (PDF 369) with the catchword “Homi”: ”…[Homi]nes indigere stellis non vt Dominis, sed vt seruis”—“that Men need the stars not as Masters, but as servants”—the close of the reply to the Sixth Argument.]

(printed p. 334 — within Chapter VIII. Closes the reply to the sixth argument, dismisses the Seventh (from the analogy of the microcosm — the Earth as the world’s “feet”), and answers the Eighth, from the congruent thickness of the heavens (Copernicus and Baranzano), with a First Response. The Ninth Argument, from the distinction of the heavens (Mars at perihelion coming nearer than the Sun, urged against the Tychonic system by many), is then proposed and cast in form.)

[Header: BOOK IX. SECTION IV. — 334]

[that] Men need the stars not as Masters, but as servants serving [them] by God’s command.

Seventh Argument, from the Analogy of the Microcosm

[Margin: Another, most trivial, argument, and its solution.]

[XV.] Just as in the Microcosm—that is, the small world, namely man—the feet are moved, but not the head, by a progressive motion; so in the Macrocosm, or great world, the Earth has the character of the feet, and accordingly it, rather than the Sun, ought to be moved. But both parities are denied: for neither is the Earth a foot in the world, but rather the immovable footstool of God’s feet (from the sacred letters [Scripture]), nor, by the Copernicans themselves, is it the lowest part; nor, if it were, ought it to be moved by that progressive motion by which the feet of an animal [are moved], or to the same end, nor to carry the head around with it—otherwise at its motion the Sun too, or the whole heaven as the head, would be moved: and so this argument too would prove too much, if it had any weight in so great a triviality of reasoning.

Eighth Argument, from the Congruent Thickness of the Heavens

[Margin: Copernicus’s reason for placing the Earth between Mars (♂) and Venus (♀).]

[XVI.] Among other things which seem to favor the Copernican system, [there] is first of all the distinction of the heavens—on account of which no Planet enters into the domain of another—and the congruent filling of the space interposed between them. Which Copernicus indicated (bk. 1, ch. 10) when he said: “But indeed, all these [orbs] resting upon one middle [point]—that is, the Sun—it is necessary that the space which is left between the convex orb of Venus and the concave of Mars be discerned also [as] an orb, or sphere, since there is, homocentric to it [the Sun] according to both surfaces, [a space] which receives the Earth with the Moon its attendant, and whatever is contained below the Lunar globe. For we can in no way separate the Moon from the Earth, etc.—especially since in that space we find a sufficiently fitting and abundant place for it.”

[Margin: And of Baranzano.]

Hence, occasion being taken, the Lord Redemptus Baranzano (part 1 of the Uranoscopia, quest. 3, doubt 10, member 2) thus argues for Copernicus from the Thickness of the spheres. Since the thickness of the Lunar heaven is twenty-one terrestrial semidiameters, the thickness of the heaven of Mercury 103, of Venus 933, of the Sun 44, of Mars 7640: it would seem unfitting and far from all proportion that the Sun, chief among the stars and of so great power, should have so tiny a heaven, unless it were in the center of the world, but that Venus, which is smaller than it [the Sun], and Mars should have so great a depth in their heavens: which disproportion is certainly removed if the Sun be placed in the center of the World, and the Earth with the Lunar heaven between Mars and Venus; for thus the thicknesses of the spheres are increased by degrees; for the sphere of Mercury turns out greater than the Sun, and the sphere of Venus greater than the Mercurial, and the thickness of the elementary sphere together with the Moon’s heaven [is] greater than the sphere of Venus. Someone too could, with Philolaus (published at Paris, ch. 7), reason thus against the old hypotheses. The concave of the Sun and the convex of Venus is distant from the center of the earth 1070 terrestrial semidiameters, according to certain Alphonsines; but the concave of Venus and the convex of Mercury, 162⅓; and the concave of Mercury [is distant by a] semidiameter 503; but the Moon, at the apogee of the Eccentric and Epicycle, is distant 64 semidiameters 10′: there are wanting, therefore, 13 semidiameters of the earth, 46′, in the space assigned below the concave of the Sun, that it might contain the entire orbs of Venus, Mercury, and the Moon; which absurdity, however, on this head, is not found in the Ptolemaic hypothesis—it ascribing to the concave of the Sun a distance of 1146 semidiameters of the earth—as Chiaramonti noted in his Anti-Philolaus (part 1, ch. 7). This, therefore, being dismissed, there remains the former argument of Copernicus and Baranzano, reduced into the following formula.

[Margin: “Seventh Argument, in form.” — sic in the 1651 print; this is properly the Eighth Argument (from the Congruent Thickness); the next syllogism (¶XIX) is correctly numbered “9,” so the numeral here is a misprint for “8.”]

[XVII.] “Unless the Sun be constituted in the center of the Universe, and the Earth with the Elements and the Lunar heaven between the convex of Venus and the concave of Mars, the due proportion between the thickness and [the next] thickness of the spheres ascribed to the Planets is not preserved; But it is absurd that the aforesaid proportion be not preserved; Therefore the Sun is to be constituted in the center of the Universe, and the Earth with the Elements and the Moon’s heaven between the convex of Venus and the concave of Mars.” The Minor seems certain from the ordered manner of the supreme Maker in determining the thickness of the heavens. The Major is proved, because to the Sun, the greatest of the planets, the smallest—or least thick—heaven would befit, whereas to Venus and Mars, which are far smaller Planets, a far greater heaven would have been given, and the space between the convex of the Sun and the concave of Mars would be excessive and idle.

[Margin: First Response.]

It is answered by denying the Major: first, because [there] would be a greater disproportion and absurdity that the Sun, which is the greatest of the Planets, should have no heaven, than [that it should have] a small [one], and [that] the Earth, with the other elements—which are bodies commonly sub-celestial, and of most diverse properties—should be placed in [a] heaven; but to the Sun, constituted immovably in the center of the universe, there would be no heaven, but the whole space between it and Mercury would belong to Mercury’s heaven, since a heaven is ascribed to the mobile Planets, that through it they may go around. Then, if Mercury and Venus be assigned to the Sun as satellites, there is now no reason why a distinct heaven should be ascribed to them—just as none is assigned to the companions of Jupiter and Saturn; wherefore for the Sun’s heaven will have to be understood that whole heaven in which Venus too and Mercury are engaged; and thus the heaven will be very thick; but it will be much more ample still, if, according to our system, Mars too looks to the heaven of the Sun as a Satellite; for thus, the greatest of the Planets [the Sun] being thronged with the greatest satellites, a heaven of very great thickness will befit [it]: concerning which thickness, see what was said in section 3, toward the end of chapter 9. The rest of the things which are brought against Ptolemy and Alphonsus—as, namely, [those] always placing Venus and Mercury below the Sun—are not valid against the Tychonic or our system.

Ninth Argument, from the Distinction of the Heavens

[Margin: Kepler’s argument against the Tychonic system, as regards the place of the Sun.]

[XVIII.] Now, by the witness of the Telescope, we are compelled to confess that Venus and Mercury are engaged sometimes below, sometimes above, the Sun: the observations too of Mars and the Sun, and of the parallaxes due to them—so that congruent equations of the motions may follow thence—sufficiently prove that Mars at perigee becomes nearer to the Earth than the Sun; on which matter see what we said (bk. 7, sect. 2, ch. 3, schol. 4; and sect. 6, ch. 4, scholia 3 and 4; and ch. 10, scholio 1). Now, if we attribute to the Sun a motion and a place among the aforesaid Planets, it follows that those Planets, or at least Mars, penetrate the heaven of the Sun—which was objected as absurd to the Tychonic system by Rothmann, Hérigone, Tanner, Malapert, Amico, and Argoli, as we said (sect. 3, ch. 4, num. 5; and ch. 8, num. 5). Nay, Kepler himself (in the Epitome of Copernican Astronomy, bk. 4, p. 544) has thus: “If Brahe’s reckoning holds, so that the orbit of Mars be one-and-a-half-fold the orbit of the Sun, the body of Mars at certain times will succeed into that point of the mundane space in which at other times the Sun was”—which, concerning the primary Planets, is highly incredible, that their regions, which they traverse, should thus be confounded: whereas in Copernicus[‘s system] they are not only distinct, but intercepted by the amplest empty intervals. Of which difference, if anyone desires a specimen, let him consult the figures of the systems set forth by us—the Tychonic indeed and ours (section 3, chh. 8 and 9), but the Copernican (in this section 4, ch. 4, num. 15): for in the Tychonic and ours the circle of Mars intersects the circle of the Sun’s orbit when it approaches perigee; but in the Copernican the whole circle of Mars remains apart from the Sun, among the orbits of the other planets, nor does it intersect the great orb of the Earth; and the great orb [itself] performs that which otherwise the Epicycle of Mars would perform in Ptolemy, and the orb of the Sun in Tycho; and it is the Earth which approaches Mars [when] opposite to the Sun, and therefore [Mars] then appears so much larger than when it is far from perigee, and from the same [cause] it is that it undergoes a greater parallax than the Sun. But this objection has greater force among those who retain solid orbs; for, for two causes, they will not admit this penetration of Mars into the heaven of the Sun—namely, on account of solidity, and on account of the distinction of the heavens.

[Margin: Galileo’s words on the same argument.]

And so Galileo too (Dialogue 3 On the system of the world, p. 253) says: “Would you not, to Simplicio, call it a very great absurdity, if in the system of Ptolemy Mars should so let itself down that, the orb of the Sun being broken through, it should descend below it, and approach the Earth nearer than the solar body itself: and a little after be exalted above that same [Sun] by an enormous interval?” Now to the form of the argument.

[Margin: Ninth Argument, in form.]

[XIX.] “It is absurd that the distinction of the heavens be not preserved, and [that] one primary Planet traverse the heaven of another primary [Planet]:

[…continues on p. 335 (PDF 370) with the catchword “meare”: ”…[per]meare: But unless the Sun rest in the center of the world…”—the rest of syllogism XIX and the five Responses to the Ninth Argument.]

(printed p. 335 — within Chapter VIII. Completes the ninth argument’s syllogism and gives five Responses, Riccioli preferring his own: the Copernican remedy incurs worse absurdities, the Sun is no planet and Mars its outermost satellite, and the fluid heavens make one heaven suffice for all the planets. The Tenth Argument, from the intervals and number of the planets — Kepler’s Cosmographic Mystery with its five nested Platonic solids — then begins.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 335]

to traverse:] But unless the Sun rest in the center of the world, and in its stead the Earth perform an annual motion through the great orb, Mars—which is a primary Planet—sometimes penetrates the heaven of the Sun, which is itself also a primary Planet; Therefore, unless the Sun rest, etc., and the Earth be moved, etc., an absurdity follows.” The Major seems evident from the order due to the nobler parts of the world—of which kind are the elements, which God separated, and the heavens—especially since they are a certain image of that hierarchical order which is found in the intelligible world, or among the nine choirs of Angels. The Minor is proved, because Mars, when opposite to the Sun, in either of its perigees [perihelia] appears, as to [its] disk, sixtyfold larger than itself at apogee, and as to [its] diameter sevenfold or eightfold, if it be inspected with the Telescope; nay, by our observations, its diameter near apogee ought to appear of only 10″ and 6‴, but in either perigee of 92″—that is, of a diameter ninefold greater—concerning which we said more (bk. 7, sect. 6, ch. 10, scholio 1). Besides, if the apparent place of Mars, often observed in the acronychal position—that is, when it rises in the evening and is opposed to the Sun—ought to be reconciled, by just prosthaphaereses [equations], with the mean place of the tables, it is necessary to apply greater parallaxes of Mars than of the Sun, or [to assume] a smaller distance of Mars from the earth in that position than [that] of the Sun, as was said (bk. 7, sect. 2, ch. 3, scholio 4; and sect. 6, ch. 4, scholia 3 and 4; and ch. 7, num. 3). But these appearances cannot be saved, and composed with the due measure of the orbs, unless Mars approach very near to the Earth, and pass from a greater distance—greater than is the distance of the Sun—to a lesser, through a middle or equal distance; and sometimes, devoid of latitude (just when it is equally distant as the Sun), pass through that point of the Ecliptic through which the Sun has passed in that year, or is about to pass, if the Sun be supposed to be moved through its annual orb. Thus it comes about that the Sun pervades the heaven of Mars, and Mars [the heaven] of the Sun, by turns, with their rights and domains confounded.

[Margin: A response—but [that] of the unskilled.]

Someone might perhaps answer, first, by denying the Minor and its proofs, recalling into the suspicion of fallacy the observations of Tycho and of others—as I grieve was done by some, whom I named (bk. 7, sect. 6, ch. 4, scholio 4). But in this matter Kepler, Magini, Bullialdus, Lansberge, and all the most skilled [astronomers] of the more recent Astronomy received them as ratified [reliable]; and that appearance of Mars, sometimes greater than Jupiter appears—of which Copernicus [speaks] (bk. 1, ch. 10), and others like it reported by us (bk. 7, sect. 6, ch. 10, scholio 1)—cannot, with the due commensuration of the orbs of Mars and the Sun (deduced from the motions of both) preserved, be reconciled, unless Mars can sometimes approach the Earth more [nearly] than the Sun. Wherefore the proof of the Minor, as regards this part, can be denied only by [those] less skilled in Astronomical subtleties.

[Margin: A response—but a forced one.]

Others might perhaps answer, secondly, by likewise denying the Minor and its proof, [by] saying that the heaven of the Sun is not an entire sphere, but only a segment, round in the manner of a wheel, and occupies only as much ethereal space as is the body of the Sun carried by its center along the Ecliptic; [and] that thus the heaven of Mars is likewise a round segment, in the manner of a certain wheel, occupying only as much space as is the corpulence [bulk] of Mars itself, and besides as much as its greatest elevation upward and declination in latitude demands: and that it can come about that the smaller wheel of the Sun be so obliquely inserted into the wheel of Mars that Mars at perigee is nearer to the earth than the Sun, and yet never passes through the Sun’s wheel—the latitude of Mars so requiring. But these [things] are arduous, and would be said with little consistency, [when] all the cases are considered which the Theory of the Sun and of Mars by its [own] nature admits, if the small duration of the world does not by accident [fail to] extend to these cases. Nor, for the solution of the proposed argument, is there need of fictions of this kind, forcibly imported into the hypothesis of these Planets.

[Margin: Third Response.]

It is answered, therefore, thirdly, by distinguishing the Major, and denying it if this absurdity cannot be avoided without a greater absurdity; conceding [it] if it can—but in this sense I deny the Minor: that is, [I deny] that, the Sun being placed in the center of the World and the Earth moved through the annual orb, the distinction of the heavens is so preserved that a greater absurdity be avoided: for two far greater incongruities are incurred—one is that the Sun [be] thrust down from [its] heaven into the center of the world, so that it really has no heaven of its own—which is worse than sometimes to admit, within its own heaven, the passage of another Planet; the other is that the Earth, with the whole elementary sphere, [be] transferred into [the] heaven—against the common perception, and against the order due to the World, which demands rather that the Heavens be distinguished from the Elements by separated regions, than the Heavens among themselves, or the Elements among themselves. But if the Copernicans have despised this common opinion of most of the wise, it will not be unfairly borne by them if someone, against their opinion, say that it is not absurd that the heaven of one Planet be intermingled or interwoven with the heaven of another.

[Margin: Fourth Response.]

I answer, fourthly: the Major being granted, and that part of the Minor conceded by which Mars is said to penetrate the heaven of the Sun, I deny that part by which Mars and the Sun are said to be a primary Planet; for the Sun, among the Copernicans, is not even a Planet, since it is in no way moved by a motion of translation, much less by an erratic and wandering motion; but among the others it is indeed a Primary Planet—but Mars, in our system, is not primary if it be compared with the Sun, for it is the greatest satellite of it [the Sun], and is related to the Sun as the outermost Satellite of Jupiter to Jupiter; and accordingly it is no wonder if, together with Venus and Mercury, it has been admitted within the same heaven of the Sun, as into the most ample hall [court] of its King. But if this likewise seem absurd to the Copernicans—namely, that Mars, one of the three superior Planets, [should] from a primary be made, by us, a secondary and satellite of Jupiter—we say [that it] is much more absurd to make the Sun, from a Planet, a non-Planet, and to make the Earth with the sphere of the elements, from a non-Planet, a Planet; and to make the Moon—which is one of the great luminaries—a secondary Planet and companion of the Earth: nor will this altercation be ended unless the one party gratuitously grant to the other what is [itself] supposed by it, although it is [the very thing] in question.

[Margin: Fifth Response.]

It could be answered, fifthly, by denying the Major: for, since it is established that the heaven of the Planets is fluid, and [that] the Planets freely accomplish their passages in the liquid ether, there is no greater necessity of assigning to them distinct regions individually than [of assigning] distinct regions to the birds of the air and the fishes of the ocean; and a single Heaven suffices for all the Planets. If, however, anyone is still tenacious of the distinction of the heavens—at least by [way of] designation—let him use the third or fourth response.

Tenth Argument, from the Intervals and Number of the Planets, taken from the dimension of the Five Regular Bodies, or from Kepler’s Cosmographic Mystery

[Margin: Kepler’s invention and the Cosmographic Mystery.]

[XX.] This is that offspring of the Keplerian genius, conceived by him not long after the year 1589, and first published in the year 1596, and finally polished and reprinted in the year 1621—in which he so pleased himself that, to preserve its structure, he applied almost all the machines [devices] of Astronomy, and from it dispensed almost the whole economy of this Art: this [offspring], in fine, for love of which especially he clung to the sect of the Copernicans, and never ceased to establish it with all his effort. In this place, therefore, those [things] must be gathered into few [words] which are necessary for perceiving the force of the argument, reserving more for another place. He, therefore, while he inquired more deeply into the proportion of the celestial orbs, and into the causes of the number of the heavens, recognized that, if the Earth were received into the heaven between Mars and Venus, and the Sun rested in the center of the Universe, and [if] the Copernican intervals of the Planets—and indeed of the earth—were somewhat corrected, those [intervals] could be distributed according to that proportion which the five Regular bodies (otherwise called Platonic) have, inscribed in order one within another, with orbs mediating [between them].

[Margin: What [are] the Regular bodies?]

Which bodies, since they are only five, and cannot be more or fewer, [it follows] that, for the five intervals of them to be filled, six Planets are required. Hence he judged that a necessary cause of the senary [six-fold] number of the primary Planets could be rendered; for in place of the Sun he counts the Earth, together with the Moon as a secondary Planet. Now the Regular bodies are Solid figures which are contained by plane equilateral and equiangular [figures] equal among themselves: of which kind are the Cube, or Hexahedron—that is, [a body] terminated by six equal square faces; with 12 sides [edges], and [8] soli[d angles]

[…continues on p. 336 (PDF 371) with the catchword “soli”: ”…[soli]dis”—the rest of the definition of the regular solids and Kepler’s nesting of them for the planetary intervals.]

(printed p. 336 — within Chapter VIII, the tenth argument (Kepler’s Cosmographic Mystery). Completes the definition of the five regular Platonic solids, surveys their ancient assignment to the elements, and expounds Kepler’s improvement — the five solids generate the five intervals of the six planetary orbs, with his nesting formula — introducing the engraved nested-solids diagram and its key.)

[Header: BOOK IX. SECTION IV. — 336]

[8] solid [angles]; and the Tetrahedron, or equilateral Pyramid, terminated by four equal equilateral triangles, and six sides [edges], and 4 [solid] angles; and the Octahedron, terminated by eight equal equilateral triangles, and 12 sides, and 6 angles; and the Dodecahedron, terminated by twelve equal Pentagons, and 30 sides, and 20 angles; and finally the Icosahedron, terminated by twenty equilateral and equal triangles, and 30 sides, and 12 angles. But that there cannot be, besides these five, other bodies which are contained or terminated by plane [faces] equal among themselves, and equilateral, the interpreters of Euclid demonstrate—especially Clavius (bk. 13 of the Elements, in the scholia of proposition 18) and Kepler himself (bk. 4 of the Epitome of Copernican Astronomy, p. 467). And (bk. 2 of the Harmonics, proposition 25) he rightly notes that the Cube, Tetrahedron, and Dodecahedron are simple and therefore primary, but the rest secondary, as being composite—the Octahedron and the Icosahedron—because the three former have the simplest angle, that is, a three-lined [trilinear] one, and a proper and distinct plane; but the rest [have] an angle comprehended by more lines than three, and in the plane communicate with the Tetrahedron.

[XXI.] Moreover, this whole doctrine of Kepler is handed down by him, as it were restricted into a compendium, in the preface of the Cosmographic Mystery, and chh. 2 and 14; and in the preface of the Harmonics, and book 2, from proposition 25; and bk. 5, ch. 9; and bk. 4 of the Epitome of Copernican Astronomy, from p. 455. First, therefore, it must be noted, from Aristotle and Plutarch, that of old the five Regular bodies were accommodated by the Platonists and Pythagoreans to the mundane bodies [the elements]; which Proclus also did (on bk. 13 of Euclid), affirming that Euclid proposed to himself the five Regular bodies as [his] ultimate end, and that for their sake he wrote all the things which he handed down in the Elements, except those which lead to the perfect Number; whereas, on the contrary, Petrus Ramus (in the Mathematical Schools) contends that these five bodies are to be removed from the end of Euclid’s elements; and Lazarus Schoner thought them of no use—against whom see Kepler in the preface of the Harmonics. Indeed I read these [things] in Plutarch (bk. 2 On the Opinions, ch. 6): “Pythagoras, since there are five solid figures which are called mathematical, said that the Earth was made from the cubic [one], Fire from the meta or Pyramid, Air from the Octahedron—that is, the body of eight seats [faces]; but Water from the Icosahedron—that is, the body of twenty seats; and from the Dodecahedron—that is, the body of twelve seats—the globe of the universe.” Plato Pythagorizes in all these [matters]; the congruences of which distribution—no mention of Plutarch being made—Kepler investigates (bk. 2 of the Harmonics, prop. 25, and in the Mystery, ch. 2); but there, and in that preface, he suspects that the Pythagoreans concealed symbolically, under the names of the Elements, the names of the Planets: and under the name of Earth, Saturn—nearest to immobility by its slowness; under the name of Water, Venus—who is feigned to have arisen from the foam of the Sea on account of the humors subject to her, and therefore called Aphroditē [Ἀφροδίτη]; under the name of Air, Mercury—on account of the mobility of its swiftness; under the name of Fire, Mars—who accordingly was called from Fire Pyrois. But Proclus too said that this is, among others, the end of Geometry: that it may teach how the heaven received figures congruent to its [own] certain parts—namely from that great Demiurge, who disposed all things in number, weight, and measure. More truly, therefore, Kepler judged that from those five figures arose the five intervals of the celestial orbs mutually including one another; wherefore, if they are five, it was necessary that the primary Planets be six—just as, for terminating four intervals on one hand, five fingers are required. Now the order and distribution of these bodies into the heavens of the Planets is handed down by Kepler, first conceived in this formula (in the preface of the Mystery): “The Earth is the circle, the measurer of all: about it circumscribe a Dodecahedron; the circle comprehending this will be Mars: about Mars circumscribe a Tetrahedron; the circle comprehending this will be Jupiter: about Jupiter circumscribe a Cube; the circle comprehending this will be Saturn: now within the Earth inscribe an Icosahedron; the circle inscribed in it will be Venus: within Venus inscribe an Octahedron; the circle inscribed in it will be Mercury. You have the reason of the number of the Planets.” And so the Moon, as a secondary Planet and companion of the Earth, he counts [it]; but the Sun he does not reckon among the Planets, but places [it] in the center of the planetary system, as the source of light, heat, and motion. But, the intervals having been examined—the intervals by which the Planets are distant from the Sun, according to the Copernican measures (but somewhat emended by himself and by Mästlin)—he gathers that those intervals are capable [receptive] of the aforesaid order and distribution, as he teaches (from ch. 2 of the Cosmographic Mystery to ch. 20, and in the Epitome from p. 468). Yet Kepler concedes that the Copernican intervals approach so nearly to the proportions of the aforesaid figures that they fall short in some very small [amount]; but he says that this comes about because the archetype of this mobile world consists not only of the beauty of the regular bodies, but also of Harmonic proportions, and of the concord of six voices, to whose Idea the swiftest and slowest motions of the Planets had to be attempered—which attempering could not be done unless the Harmost [Tuner] varied somewhat those figural intervals.

[XXII.] Someone might perhaps wish that in this place we should represent this order and symmetry by some diagram; but we cannot [do] it exactly, since those solid figures cannot be so described in a plane that they preserve the number of all the sides, planes, and angles with their quantity; and if in their place we used plane figures, we would furnish the Reader an occasion of manifold error: let, therefore, the diagram written below suffice for him—in which, from A, the center of the annual orb (next to the Sun, according to Copernicus, but the Sun itself [at center], according to Kepler), let there be described, between two circles, the orb of Saturn (♄) with its thickness, and of Jupiter (♃) with its [own]; and of Mars (♂) with its [own]; and the great Orb of the Earth, with the sphere of the Elements and the space of the Lunar excursion—all which we have also marked off above and below by a little black globe; then, between two circles likewise, let there be described from the same center A the orb of Venus (♀) with its thickness, and the orb of Mercury (☿) with its [own]. These [things] done, between the orb of Saturn and [that] of Jupiter let the letter C, C be inscribed on either side, which signifies that a Cube is to be inscribed in the Orb of Saturn, but circumscribed about the orb of Jupiter; but between the orb of Jupiter and [that] of Mars, let the letters T, T be inscribed, indicating that a Tetrahedron is to be inscribed in the orb of Jupiter, but circumscribed about the orb of Mars. Thirdly, in the space, that is, between the orb of Mars and the annual orb of the Earth, let D, D be noted, to signify that in that space a Dodecahedron is to be inscribed in the orb of Mars, but circumscribed about the annual orb of the Earth. In the fourth interval, namely between the annual orb and the orb of Venus, let the letter I be inserted twice, which indicates that an Icosahedron is to be inscribed in the annual orb, but circumscribed about the orb of Venus. Fifthly, at last, in the space which [is] between the orb of Venus and [that] of Mercury, let the letter O be inscribed twice, indicating that an Octahedron is to be inscribed in the orb of Venus, but circumscribed about the orb of Mercury. Or else, with the words written out, let the names be expressed: in the first interval, of the Cube; in the second, of the Tetrahedron; in the 3rd, of the Dodecahedron; in the 4th, of the Icosahedron; in the 5th, of the Octahedron. But also, for the sake of aiding the memory, the following distich [couplet] will not be useless:

Kappa surrounds Jupiter; Tau, Mars; Delta, the Elements [Earth]; Iota surrounds Venus; and Omicron, Mercury.

[Translator’s note — engraved nested-solids diagram (Kepler’s Cosmographic Mystery figure): concentric circles centered on A, the Sun (drawn as a radiant sun-face). Outward from the center: the orb of Mercury (☿); the Octahedron (“oct.”); the orb of Venus (♀); the Icosahedron (“icos.”); the annual orb of the Earth (a small black globe, ●); the Dodecahedron (“Dodec.”); the orb of Mars (♂, with an arrow); the Tetrahedron (“Tetraëdr.”); the orb of Jupiter (♃); the Cube (“Cubus”); the orb of Saturn (♄, outermost). Across the top arc the inscribed solids are labelled by their initials, symmetric about the center: C · T · D · I · O — [A] — O · I · D · T · C (C = Cube, T = Tetrahedron, D = Dodecahedron, I = Icosahedron, O = Octahedron).]

[…continues on p. 337 (PDF 372) with the catchword “Dum”: ”…[Dum]modo memineris Cappa idest C, significare Cubum”—the key to the distich’s letters, then Kepler’s planetary-distance numbers, the comparison table, and Riccioli’s reply.]

(printed p. 337 — within Chapter VIII, the tenth argument (Kepler’s Cosmographic Mystery). Gives Kepler’s Copernican planetary distances with comparison tables of the solids’ ideal sphere-ratios against the actual orb-ratios, and his argument that only the Copernican system leaves inter-orb spaces fitting the regular solids, yielding an a-priori cause of the planets’ number and spacing. The argument is cast in form, and the First Response begins.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 337]

provided you remember that Kappa, that is C, signifies the Cube; and Tau, that is T, the Tetrahedron; and Delta, that is D, the Dodecahedron; and Iota, namely I, the Icosahedron; and Omicron, that is O, the Octahedron.

[Margin: Kepler’s philosopheme on the intervals of the Planets and the Regular bodies.]

[XXIII.] Now Kepler supposes (in the Epitome, p. 455), from Astronomical observations and the demonstrations of Copernicus, that—relative to the distance of the Earth from the Sun, or to the semidiameter of the great orb—the distance of Saturn is nearly tenfold; of Jupiter fivefold; of Mars one-and-a-half-fold; of Venus sub-sesquitertian [¾]; of Mercury about sub-triple [⅓]. And so the diameter of Saturn’s orb has less than double its neighbor the Jovian; but the Jovian has triple the Martian, and the Martian one-and-a-half-fold the terrestrial orb described about the Sun. The terrestrial, in turn, has more than one-and-a-third of the Venereal; and the Venereal, of the Mercurial, five-thirds or eight-fifths; although he adds that the proportions of the distances are not the same in every part of the orbit, but different in different [parts], especially in Mars and in Mercury.

But from p. 468 of the same Epitome, together with ch. 14 of the Cosmographic Mystery, the following numbers are collected—of which the former signify the proportion of the semidiameter of the orb inscribed in some Regular body (the semidiameter of the orb circumscribed about the same Regular body being set at 100000 parts); but the latter signify the proportion of the same semidiameters as arising from the Copernican hypothesis: so that from their parallelism, or comparison, it may appear how nearly the Copernican measures approach to the measures of the required intervals, that the regular bodies may, in the aforesaid order, be inscribed in the concave orb of the upper Planet, or circumscribed about the convex orb of the lower.

Of what kind the semidiameter of the circumscribed Orb is 100000, of that kind the semidiameter of the inscribed Orb:

Of what kind the semidiameter of the Concave [orb] is [100000], of that kind the semidiameter of the Convex [orb] is, by Copernicus — from Copernicus, bk. 5, chapter:

I explain the little table. If a circle, or rather an orb, be made whose semidiameter is of 100000 parts, and to it a Cube be inscribed, and in this cube another orb be inscribed, the semidiameter of this [inner] orb will be of 57735 such parts. Again, if the semidiameter of this second orb be divided into 100000 equal parts, and to it a Tetrahedron be inscribed, and to the Tetrahedron a third orb be inscribed, the semidiameter of this orb will be of 33333 such parts. And so of the rest.

[XXIV.] These [things] being premised, Kepler thus philosophizes. In the Ptolemaic hypothesis the distances of the Planets from the center of the Earth and of the universe are so disposed that between the lowest or least [distance] of Saturn and the highest or greatest of Jupiter there is no interval, but the concavity of the Saturnine heaven immediately touches the convex surface of the heaven of Jupiter, and so of the rest—for no other cause, indeed, than lest there be anything empty between the heavens which does not belong to the domain and right of some Planet, occupied at least by its Epicycle, if not by the body of the star itself; but in this no Geometrical beauty shines forth, to which God may be said to have looked. But in the hypothesis of Copernicus, between the concave of the upper and the convex of the lower Planet there intervenes a space which is not necessarily occupied by the body of the Planet, nor by any Epicycle of it or other orb; and these spaces are so interposed that between the heavens of the three upper Planets three simple or primary Regular bodies can be inscribed—namely the Cube in the concave of Saturn, the Tetrahedron in the concave of Jupiter, the Dodecahedron in the concave of Mars; but the two remaining secondary figures can be inscribed—the Icosahedron indeed in the concave of the Annual orb, and the Octahedron in the concave of Venus, circumscriptible about the convex of Mercury. These [things], I say, can be done exactly indeed as regards Mars and Venus, and nearly exactly as regards the Earth—for the due number is 79465, but Copernicus[‘s is] 79500. Nor does Mercury deviate enormously, if in the middle of the Octahedron you inscribe a square, formed from the four middle edges, to which square the inscribed circle will have a semidiameter of 70711 parts—of which kind the radius of the orb inscribed in the Octahedron is 100000, but the Copernican measures supply 72300 parts. Jupiter alone strongly discrepates from the due [value]: for the radius of the orb inscribed in the cube ought to be 57735, but by Copernicus it is 63500; yet, though it discrepates, it is nearer to no body’s measure than to this. This so great analogy and proximity of the numbers, therefore, cannot be said to have been fortuitous in the mind and Idea of God the Creator; and if those numbers, according to these ideal and archetypal ratios (the ratios being nevertheless preserved which the harmonic proportions of the motions, according to the six musical voices, require), be somewhat corrected, the most beautiful analogies arise, and a cause a priori is rendered why six primary Planets were created by God, and why there is only [such] an interval between the concave of the upper and the convex of the lower heaven; and to the three upper Planets three primary Regular bodies correspond in order. But such analogies and causes a priori cannot be rendered in any hypothesis of an Earth resting in the middle of the universe, and much less in the Ptolemaic. Therefore the Copernican hypothesis (although Copernicus was ignorant of his [own] riches, and did not see these analogies) is to be preferred; and accordingly the Sun, in the center of the Universe, is nowhere translated [moved], but the Earth, annually mobile between Mars and Venus, is to be placed [there]. And behold, now the argument coming of its own accord into its [proper] form, which it pleases [us] to repeat distinctly.

[Margin: Tenth Argument, reduced into Form.]

[XXV.] “That Hypothesis is to be preferred to the rest in which alone, or most of all, a reason a priori is rendered—by Geometric and Harmonic proportions, and those most beautiful—both of the number of the Planets and of the interval between the Planetary heavens. But such is the Hypothesis of Copernicus, and this requires the Sun immovable near the center of the world, and the Earth mobile by an annual motion between the orbs of Mars and Venus; Therefore the Hypothesis of Copernicus is to be preferred to the rest, and the Sun is to be established immovable near the center of the world, but the Earth mobile by an annual motion between the orbs of Mars and Venus.” The Major does not seem able to be called into doubt except by one who would deny what very many wise men have confessed—that God, in the structure of this visible world, looked to the most excellent Ideas of the intelligible world, which He had from eternity in His divine intellect, and expressed by speaking His Word, according to that [verse] of Boethius:

… . the Fairest, Himself bearing the fair World in [His] mind, and forming [it] from a like image:

or [except by one who] would deny what was said by Plato in the Timaeus, in the Epinomis, and in the books On the Republic—nay, before him, by Pythagoras—and received with so great applause of all the ages: namely, that God, in founding and conserving the World, was a Geometer and a Harmost [Tuner]; or who would dare to gainsay what the sacred letters attest concerning God (Wisdom 11): “Thou hast disposed all things in measure, and number, and weight”; but concerning the concord and harmony of the heavens, [it is plain] from the same divine letters (Job 38), and will be plain from the things to be said below in their places. The Minor seems sufficiently proved by Kepler, from the things said from num. 20 to 25.

[Margin: First Response.]

I answer, however, first, by distinguishing the Major, and denying it, if the number of the Planets—commonly received by the wise, and evident to sense itself—be not retained, and [if] those proportions do not, again and again, agree with the certain observations of the celestial motions, nor be fit for the end and effects which Divine providence proposed to itself in the structure and administration of the World; and finally, [denying it] if not even those proportions be found adequately in such a hypothesis

[…continues on p. 338 (PDF 373) with the catchword “nian”: ”…[inuenian]tur”—“…be [adequately] found”—the rest of the First Response, and the further refutation of Kepler’s Cosmographic Mystery.]

(printed p. 338 — within Chapter VIII, refuting the tenth argument. Continues the First Response through four sub-points: the Copernican system demotes the two Luminaries and destroys the septenary of the planets; its tables do not perpetually match observations; geometric proportions are not of themselves fit for nature’s ends; and the proportions are not adequately found even in the Keplerian system. A Second Response then begins — the harmonic proportions hold in the Tychonic system too, as Kepler himself confessed.)

[Header: BOOK IX. SECTION IV. — 338]

[adequately] be found. But I concede the Major, if the four aforesaid conditions are found in that hypothesis: but in that sense I deny the Minor. For, first, in the Copernican hypothesis the Sun—which by all the wise (excepting a few followers of the Copernican opinion) was reckoned to obtain the chief place among the Planets, and by its motion to govern the rest—[is] cast down from heaven into the center of the Universe, and has no heaven, nor is it now a Planet, but [is] outside the number of the Planets; and the Moon, which likewise was always held [to be] among the primary Planets, in this hypothesis is not numbered among the primary Planets, but is the attendant of the Earth: but the Earth itself—nay, the whole sphere of the elements—by a monstrous Uranomorphosis [heaven-transformation] is transferred into [the] heaven, and turns out a primary Planet. Thus it comes about that the two great Luminaries are not numbered in the number of the Planets (the cause of which is here inquired into), and so to that number the two Lights of the world are, as it were, twin eyes, torn out; and that most famous septenary [seven] of the Planets and of the Chords [strings], illustrious by so many other analogies and conditions (as I indicated, bk. 7, sect. 1, ch. 1), perishes in our hands. And so, if Kepler was of so robust a stomach that he could digest the striking of the Moon and the Sun from the roll [register] of the seven Planets, let him not take it ill if someone should say that the analogy of a few regular bodies with the intervals of some Planets was neglected from the primary order of the divine Ideas in the structure of the world. For it is far more evident that the Moon and the Sun are primary Planets—both in the measure of Times and in the effects of nature—and that the Earth is not moved, nor is a Planet, nor merits the name of a star or of a celestial body, than that the intervals of the planetary heavens were taken from the regular bodies.

[Margin: Second Response.]

Secondly: Neither the Prutenic tables, built upon the Copernican hypothesis, nor the Rudolphine [tables], [built upon] the Copernico-Tychonic, are such that they perpetually cohere with the celestial observations; nay, again and again they stray from them, and indeed in the chief Phenomena, namely Eclipses, as is plain from what was said (bk. 5), and is now sufficiently ascertained to the Astronomers of this time: but in those [matters] which concern the apparent magnitude of Mars, and the proportions between its mass and its intervals, that Kepler erred, and conflicts with the manifest observations concerning the diameter of Mars, we have sufficiently shown (bk. 7, sect. 6, ch. 10, scholia 1 and 3 joined together).

[Margin: Third Response.]

Thirdly: those purely Geometrical proportions, derived from the five regular bodies, do not seem of themselves fit for the ends and effects which God willed in nature to depend on the intervals and motions of the Planets; and I say the same of the Harmonic [proportions]: for the excellence of the regular bodies does not consist in the proportions of the diameters of the inscribed or circumscribed circle, but in the very ratio [nature] of bodies terminated by such faces; but the heavens of the Planets do not flow into [influence] these lower things by reason of their corpulence thus terminated—especially since, the fluidity of the heavens being posited, there is in reality one single heaven of the Planets; and so that real distinction of the heavens and of the regular bodies perishes. But [it is] through the mediation of the bodies of the Planets, and their light and the qualities flowing from that light, [that] the bodies which are contained within the Zodiac [act]; nor do they affect the celestial spheres (designable by us by reason alone), nor are affected by them, nor from them, in so far as they are bodies, do they receive their power or the governance of [their] virtue; much less from the bodies which can be inscribed among them. And it is far more probable that a much higher and nobler

[Margin: How the Geometry of God is to be understood.]

Geometry and Harmony of Divine wisdom [was] in the structure of the World, than that it should have followed that material beauty of dimensions, and of a harmony accommodated to our ears. But just as we say metaphorically that some Prince “geometrizes” well, or administers the Republic “musically,” if he chooses and applies means fit for the end of public happiness, and distributes offices, rewards, penalties, and burdens according to the gifts and merits of each, and so attempers himself to the dispositions and characters of [his] subjects that he conserves peace and concord among them and with himself, and likewise the due subordination of the lower with the higher: so too, and much more worthily, must we think of God in the governance of this world, even as regards [its] natural effects. And thus, in Wisdom 11—when there was discourse concerning the governance by which God had so inflicted punishments on certain impious [men] that by the [very things] through which one had sinned, by those he might be punished, and so they might be corrected; whereas otherwise He could by His Omnipotence at once destroy [them] in many ways, as will be plain to one reading that chapter—therefore, after those words: “But Thou hast disposed all things in measure, and number, and weight,” it is at once subjoined: “For to be greatly able is Thine alone always, and who shall resist the strength of Thine arm? Since the whole world before Thee is as the [tiny] weight of a balance, and as a drop of the morning dew that descends upon the earth. But Thou hast mercy on all, O Lord,” etc. So when, in ch. 32 of Ecclesiasticus, it is said: “They have set thee [as] a ruler,” and after a few [words]: “lest thou hinder the music”—what music is there spoken of is expressed, namely, the prudent and congruent rule of subjects.

But if it nevertheless pleases [anyone] to bind God to the compass and rule of material Geometry, I would gladly ask of Kepler: why, in the distribution of the Fixed [stars], and in the Lunar spots, and in the surfaces of the Seas and great continents, did he not preserve the laws of any regular figures? Why, in organizing the body of an animal—especially of man, in whom we so greatly admire the depth of divine Wisdom—did he not conform the magnitudes, figures, [and] intervals of the brain, the heart, the liver, and the other parts according to the properties of the regular bodies? Is it because they are not spherical bodies, nor destined for circular motion? But neither are the orbits or paths of the Planets spheres, or a great part of spheres, except among those who—without any necessity, nay, with the observers of the heavens crying out against [it]—introduced solid orbs (which Kepler disapproves). More truly, without doubt, it will be answered that figures of this kind are not of themselves fit for the duties and effects which God and nature pre-ordained in these works.

[Margin: Fourth Response.]

Fourthly, at last, the proportions taken from the Regular bodies are not found adequately in the Copernican or Keplerian hypothesis; for neither is the quantity of the interval between Saturn and the Fixed [stars], or between Mercury and the Sun, determined from them, nor the thickness of the heaven of Saturn; and of the remaining five intervals there are only two which most nearly or nearly approach to the proportions due to the bodies to be inscribed—namely the intervals of Mars and Venus; the rest discrepate greatly—not only between Jupiter and Saturn, and between Venus and Mercury (which Kepler confesses in the places cited, granted that he begs a remedy for them from afar), but also [that] of the Earth, if the space of the Lunar heaven carried around with it is to be confined within the orbit of the Earth; and therefore in the Cosmographic Mystery (ch. 16) he concedes that the little orb of the Moon projects above the orb of the Earth, like a gem above a ring, or like the orbs of the Satellites of Jupiter above the orbit of Jupiter, and [that it] is not impeded by the spaces of the regular bodies, because the heavens are not adamantine or solid. But concerning Mercury I have already said above that its interval [is to be determined] not from the Octahedron, but from a square inscribed in the octahedron itself—if [the value] is to approach near to the measures of the Copernican hypothesis. And so, unless, by various windings, corrections of the measures be scraped together by a forced inquiry, the analogy of the planetary intervals with the capacity of the regular bodies does not shine forth except in two, or at most in three, intervals.

[Margin: Second Response.]

[XXVI.] I answer, therefore, secondly: the Major being granted, denying the Minor as to both parts; for that in the Copernican hypothesis the proportions of the aforesaid bodies are not found exactly and adequately, nor a reason of the true number of the Planets rendered, is plain from what was said in the first response, paragraphs First and Fourth; but that the Harmonic [proportions] can be found also in the Tychonic or others similar, Kepler confessed (bk. 5 of the Harmonics, ch. 3); and in the same place [he confessed] that the Tychonic observations conflict with that exact configuration of the regular bodies. For when he had said: “That the Earth is one of the Planets, and is borne among the stars, around the immovable Sun,” he nevertheless at once added: “Let those, therefore, who are offended by the unwontedness of this science, know that these harmonic speculations obtain a place even in the hypotheses of Tycho Brahe; because that Author has in common with Copernicus all the rest of the things which pertain to the disposition of the bodies and the contempering of the motions.” And on the following page: “As regards the proportion of the planetary orbits, that, indeed, between each two neighboring orbits is always so great that it easily appears

[…continues on p. 339 (PDF 374) with the catchword “mia”: ”…[Astrono]miam polliceri”—the rest of the Kepler quotation (the solids’ fit is not quite exact, the harmonic ratios prevailing), closing the refutation of Argument 10 and the end of Chapter VIII; then Chapter IX opens.]

(printed p. 339 — closes Chapter VIII and opens Chapter IX. Finishes the reply to Kepler’s Cosmographic Mystery: the five solids do not exactly fit the planetary intervals, and the harmonic ratios Kepler prefers hold in the Tychonic system too. Chapter IX then opens — five arguments for the annual motion from the planets’ motions — beginning the First Argument, from the superfluity of epicyclic and eccentric motions removed by the Earth’s single annual motion (Copernicus, Rheticus, Kepler, Lansberge), with Kepler’s pre-emptive reply to the “Intelligences” objection.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 339]

[a perfect Astrono]my to promise. For after the completed demonstration of the intervals from Brahe’s observations, this is found, etc.” He proceeds, indeed, to explain at greater length the defect or excess of the intervals arising from the Tychonic observations—below or above the measures due to the inscription of the regular bodies—and concludes: “In brief, the Cube and Octahedron, [as] consorts [paired], penetrate their planetary orbs somewhat; the Dodecahedron and Icosahedron, [as] consorts, do not quite attain theirs. The Tetrahedron precisely touches both—there less, here more, here equal—in the intervals of the Planets.” From which it is plain that the very proportions of the planetary intervals from the Sun were not taken from the Regular figures alone. Read the rest in him [Kepler]; who, in the same bk. 5 of the Harmonics, ch. 9, proposition 49, bursts out into that exclamation: “It was good that the solid figures should yield, in the generation of the intervals, to the Harmonic ratios.” Since, therefore, the intervals of the Planets, in neither hypothesis (namely Copernicus’s and Tycho’s), were taken from the Regular bodies exactly taken, and since the Harmonic proportions are chiefly to be regarded (as Kepler indeed judges)—but these obtain a place in the Tychonic too (I add: and in ours, which, as regards these [matters], is sufficiently equipollent to the Tychonic)—we are not compelled, on account of these proportions, to prefer the annual motion of the Earth to the annual motion of the Sun, or the rest of the Sun to the immobility of the Earth.