[Margin: Exposition of the Tychonic system.]

[I.] The Tychonic System is proposed and expounded by Tycho himself (vol. 1 of the Progymnasmata, from p. 477, and in the Epistle to Rothmann, given in the year 1589, on the 21st day of February, old style); but more fully [in] vol. 2 of the Progymnasmata, ch. 8, from p. 185. Which system—but with the diurnal motion of the Earth adopted—Longomontanus chose (in the Danish Astronomy, bk. 1 of the Theorics, ch. 1); and Blancanus (in the Sphere), with most of our Society [the Jesuits] in [their] writings on the heaven; and toward it Scheiner inclines (in the Mathematical Disquisitions, num. 22). And afterward Giovanni Antonio Magini commended it (in the Epistle to Tycho, given in 1590, on the Ides of September, which is had on p. 52 of Tycho’s own Astronomical Mechanics); and upon it he constructed the tables of the Supplement of Ephemerides. Tycho, therefore—reckoning the assumption of Epicycles with the Ptolemaic Eccentrics [to be] inelegant, nay superfluous, and [reckoning] the Ptolemaic Equants likewise to sin against the first principles of this art (inasmuch as they suppose the Planets to be moved by some physical inequality—that is, not to be moved equally about the center from which they are described, but about an alien center); but, on the other side, offended by the Copernican system—by which the absurdities of the Ptolemaic system are so emended that one falls into a greater absurdity, on account of the diurnal and annual motion of the Earth, against the principles of Physics and the sacred letters [Scripture], and on account of the immense vastness between Saturn and the Fixed [stars]—for these causes, as it were, he turned his mind to another, new system, and set it forth to us in the following diagram.

[II.] In this system the Earth rests by its center in the center of the Universe, wholly immune from the annual motion; and from the same center is described the outermost or supreme sphere of the Fixed [stars], slowly advancing toward the East by an equal proper motion. Moreover, about the center of the Earth are situated the centers of the Orbs of the Sun and Moon, inasmuch as they serve the discrimination of the times; but the centers of the orbs of the five smaller Planets he denies to be situated about the center of the earth, or to regard it per se, but rather to be situated about the Sun, and to measure their Eccentricities from it. For all these five Planets, in this hypothesis, have the Sun, as it were, for the center of their revolutions—so that it [the Sun], like Apollo in the midst of the Muses, moderates the whole harmony of the Planetary choir. Accordingly, hence he hopes that there can be rendered the cause not only of the inequalities, stations, and retrogressions, but also of that admirable connection which the other Planets have, in their motions, with the motion of the Sun; and he promises that he will render [it] in the work On the Restoration of Astronomy. But what is most worthy of note appears in this diagram: that Mars at opposition [acronychal]—namely, when it appears at either extreme of the night, being opposite to the Sun—descends so far toward the earth that it becomes nearer to the earth than the Sun itself; which must happen, both from the hypothesis and observations of Copernicus, and from Tycho’s own observations (according to what was said in bk. 7, sect. 2, ch. 3, schol. 4, and sect. 6, ch. 10, schol. 1). Whence it comes about that the circle through which Mars is carried intersects that orb or circle in which the Sun itself is carried; but no physical absurdity arises hence, since for Tycho the whole heaven is liquid and permeable, as I taught (sect. 1, ch. 7).

System IV — The System of Tycho and Blancanus, and (as to some points) of Longomontanus

[Translator’s note — engraved diagram: The Tychonic geo-heliocentric system. At the center sits the immobile Earth (a dark disc), girt by the ☽ Moon; about the Earth runs also the orbit of the ☉ Sun. The Sun in turn is the common center of the five planets: ☿ Mercury and ♀ Venus on small circles tight about the Sun, then ♂ Mars, ♃ Jupiter, and ♄ Saturn on larger Sun-centered circles. Mars’s circle is drawn crossing the Sun’s circle (the feature noted in ¶II — Mars at opposition coming nearer than the Sun). The outermost band is the starry firmament of the fixed stars.]

[Margin: The theft and error of Nicolaus Dithmarsus [Ursus] concerning the Tychonic system.]

[III.] Now indeed, in the epistle to Rothmann numbered 1 (cited above), he [Tycho] complains that this his system was vended [passed off] by Nicolaus Reimarus Ursus the Dithmarsian as his own; and he convicts him of theft, or plagiarism, from this—that Nicolaus had earlier been a servant of Tycho, and had fled from him, and had copied this system for himself from a certain imperfect diagram, in which, however, through carelessness, the orb of Mars encircled the whole orb of the Sun without any intersection; wherefore, since he could not emend that error, he boasted, as his own, the Tychonic system—but stained by this second [error]—before William, Landgrave of Hesse. And so, by this single indication, Tycho there affirms his imposture to be manifest, and Longomontanus [too] (in the preface to bk. 1 of the Theorics). But he [Tycho] adds that he did not, by these his hypotheses, give occasion to the inverted Copernican hypothesis—for he saw no such inversion by himself, but judged [his system established] both by the approach of Mars at opposition [acronychal] toward the earth, and by the Phenomena of the Comets, which (the annual motion of the Earth being excluded) he judged could not otherwise be explained. Granted Rothmann objected this to him—namely, that his hypothesis is Copernican, but inverted—as appears from the Tychonic Epistles, p. 128.

[Margin: The concordance and discordance of the Tychonic and Copernican systems.]

[IV.] But that Scheiner affirms (in the Mathematical Disquisitions, num. 22) that the Tychonic system shares nothing with the Copernican, must be taken with a grain of salt; for that is true as to the annual motion of the Earth, and the rest [quiet] of the Fixed [stars] and their interval, and the other [things] which depend on these; otherwise many [things] are common to both systems: namely, the Sun [is] the center of the Planetary system, the Earth the center of the Lunar motion; Mars, in opposition with the Sun, [becomes nearer to the—]

[…continues on p. 288 (PDF 323): “…lands than the Sun.” Then ¶IV closes (whether Tycho admitted the Earth’s diurnal motion — Tycho’s Epistles to Rothmann, the falling-leaden-globe and cannonball arguments); ¶V (Rothmann’s critique of the “confusion of the spheres”); ¶VI (Longomontanus’s Semi-Tychonic variant with a rotating Earth); then Chapter IX opens — Riccioli’s own system.]

(printed p. 288 — Chapter VIII concludes, asking whether Tycho admitted the Earth’s diurnal motion in his Epistles to Rothmann, then treating Rothmann’s “confusion of the spheres” objection with Tycho’s reply and Longomontanus’s Semi-Tychonic system. Chapter IX then opens, on Riccioli’s own system.)

…[Mars, in opposition with the Sun, becomes nearer to the] lands than the Sun.

[Margin: Tycho admits neither a diurnal nor an annual motion of the earth.]

But whether Tycho admitted the diurnal motion of the Earth is wont to be doubted. For nowhere did he teach by what reasoning the Fixed [stars] and Planets are moved by the diurnal motion; and (vol. 2, p. 187) he seemed to repudiate only the annual motion of the earth, in these words: “That the Earth which we inhabit occupies the center of the universe, and is not rolled by any annual motion (as Copernicus would have it), I judge must be established beyond all doubt—with the ancient Astronomers and the received opinions of the Physicists, the sacred letters moreover attesting the same.” And Kepler thought that he did not shrink from this [diurnal] motion. But if those [things] be attentively read which he himself, in the Epistles to Rothmann, contrives against the hypothesis of Copernicus, it will doubtless be judged that all motion was denied to the Earth by Tycho—nay, that he brought a peculiar argument against the diurnal motion, both from the opinion of St. Augustine, and from the perpendicular fall of a leaden globe. For in the epistle of the year 1589, Nov. 24, old style, p. 156, he says: “A question was being moved, whether the mobility of the terrestrial globe—and that threefold [mobility] asserted by Copernicus—can really stand, and whether it ought to be preferred to our [own] invention, and whether the sacred letters are contrary to that imagination, or not. If, therefore, you have anything from the sacred oracles, or from their interpreters—say Augustine or other Fathers—making for this Copernican assertion and your agreement, cite it from their writings. Provided the reasons be just, I will not gainsay [it]. This I know well enough: that Augustine—whom alone you name—never granted the motion of the earth, neither annual nor diurnal; from which [it follows] that, as [being] less of a mathematician, by denying the Antipodes, he detracted from its roundness—which, however, must be pardoned him. Wherefore, since he did not perceive [the earth] to be round, far less could he admit a motion befitting [its] roundness.” And at the end of the same epistle he adds: “But since I see that the Copernican opinion about the threefold motion of the Earth quite pleases you, I will propose at least one of any of these [arguments]—although several can be given, [and] the doubt [is] not so laborious. First, as regards the diurnal motion about its axis, by which the Earth is feigned to be revolved in 24 hours, and so the universal course from East to West is excused: Tell me how it can come about that a leaden globe, let down in due manner from a very high tower, should perpendicularly touch exactly the point of the earth placed beneath it; for that this can by no means happen—the earth being meanwhile carried around, since its course is most swift—a Geometrical computation will teach you: since, in a single second of time, the Earth must be revolved—even in these Northern regions—by very nearly 150 paces and a half. Hence reason out the rest. For the fall of the lead does not accompany the air, but violently passes through it.” To whom, when Rothmann had replied (epistle of the year 1589, April 18) that, according to Copernicus’s opinion, heavy and light [bodies] are endowed with two motions—one by which they follow the motion of the whole into a gyre, the other by which they tend up or down—Tycho again pressed against [him], bringing the other argument concerning the globes [cannonballs] fired from a bombard, one toward the East, the other toward the West, as may be seen in his epistles (from p. 190). Again, in vol. 1 of the Progymnasmata, when he had confirmed that the New Star of the year 1572 was celestial from its diurnal motion (by which it complied with the motion of the prime mobile), he says: “Unless perhaps I should wish to assent that that universal motion takes place in the Earth (as it pleased Copernicus and some of the ancients)—which, however, in the truth of the matter, must by no means be conceded, [otherwise] we shall render [it] abundantly manifest.”

[Margin: The Tychonic system [is] defective as to the diurnal motion.]

It must be concluded, therefore, that neither the annual nor the diurnal motion of the Earth ever pleased Tycho. Yet hence it is gathered that his hypothesis is defective, since he never taught how, in a liquid heaven, the stars could accomplish both motions which appear to us, without physical repugnance; which imperfection Galileo too noted (in his Assayer [Trutinator], p. 25); nor did Kepler sufficiently wash away this stain (in the Hyperaspistes, p. 190).

[Margin: The censure of Rothmann and others on the Tychonic system.]

[V.] Rothmann also detected another imperfection in Tycho’s system, as he himself relates (in the Epistle of the year 1588, on the 13th of the Kalends of October [Sept. 19])—namely, the confusion of the spheres, especially because Venus, Mercury, and Mars are posited to wander up and down through the heaven of the Sun; for he says: “Moreover, this inverted reasoning of Copernicus introduces confusion into the spheres of the Planets. For although no collision of the celestial bodies can follow from it (as you strive to excuse [it]), nevertheless no true or determinate distinction of the spheres remains, but all are confounded among themselves. But the Copernican hypothesis attributes to each Planet its own and determinate space, out of which it cannot depart by its motion. And you know that God is the author not of confusion but of order, and that He so founded Nature that it abhors confusion.” The same is objected against it by Malapertius, Tanner, and Amici (in the places cited, bk. 7, sect. 6, ch. 4, schol. 4), and by Hérigone (vol. 5, p. 548); and moreover [they object] that it is not probable that the larger circles of the 5 Planets are carried around by the smaller circle of the Sun. But to the first objection it is answered by Tycho (p. 149, in the epistle of the year 1589, Feb. 21), in these words: “Nor is any confusion committed in my hypotheses, for the heaven is single and similar to itself from the Moon to the eighth sphere, in which the Planets freely ascend and descend, according as they go around the Sun walking in the middle with a most beautiful harmony. For I do not believe that you wish, again, to introduce some real distinction of the celestial orbs—contrary to which it was long since agreed between us.” The second objection too ceases; because the circle of the Sun does not carry the other circles effectively, but objectively, and is the center which the motions of those [planets] regard. Therefore Longomontanus (bk. 1 of the Theorics, ch. 1) extols Tycho’s system and hypotheses with wonderful praises—because, in the three superior Planets, the orbs described around the Sun perform the function of the Ptolemaic Epicycles (namely, because the single annual orb of the Sun serves them for a single and great epicycle); but, on the contrary, the Epicycles of Venus and Mercury, described around the Sun, serve them for orbs [deferents]; and so all and each of the smaller Planets have their orbs Eccentric to the Sun.

[Margin: Longomontanus’s system, in what it differs from the Tychonic.]

[VI.] But Longomontanus himself judged that the diurnal motion of the Earth should be introduced into the Tychonic system (as Origanus had done): both that, by this single and uniform motion, the apparent motion of the stars toward the West may be represented—while in reality their motion toward the East is single and simple; and that the incredible swiftness of the diurnal motion may be removed from the Fixed [stars]. Nay, he attributes no real proper motion at all to the Fixed [stars] toward the East—for he fears lest hence follow a pulling-apart of them from one another, and a variation of distance, which, however, has never been found to vary; which fear would be vain, and would wholly vanish, if he posited the heaven of the Fixed [stars] solid, and the stars fixed in it. But he himself posits that heaven—not to mention [that] of the Planets—[as] flowing and most limpid, and the individual globes of the stars hanging by libration in the free ether, in that manner in which the earth, balanced, hangs in the air. Accordingly, he attributes the apparent motion of the Fixed [stars] to the precession of the Equinoxes, made [taking place] in the earth. Thus has Longomontanus (bk. 1 of the Theorics, partly ch. 1, p. 161 in my [copy], partly ch. 4, p. 220 in my [copy]). Moreover, since on the same p. 161 he says that the center of the Earth is the center of the Sun and Moon—nay, that their orbs are homocentric to the earth—he alludes to his [own] hypothesis of the Sun and Moon; for he explains the motions not by Eccentric orbs (as Tycho did, at least in [the case of] the Sun), but by a single Epicycle of the Sun carried by a Concentric, and the Moon’s motions by twin Epicycles—yet so that the center of the Lunar orb is carried around the earth by a little-circle concentric to the earth, as we have sufficiently set forth (bk. 3 On the Sun, ch. 19, & bk. 4, ch. 26, num. 8, On the Moon). Although, therefore, Longomontanus follows Tycho in the fluidity of the heaven, and in carrying the five smaller Planets around the Sun, but the Sun and Moon around the Earth, and in the very order of the Planets—he nevertheless differs from him, both because he attributes a diurnal motion to the Earth, and transfers to it the apparent motion of the Fixed [stars] toward the East, and because, in [the case of] the Sun, he uses an Epicycle rather than an Eccentric. And therefore it is manifest that Longomontanus’s system ought to be called Semi-Tychonic, and not Tychonic.