[Margin: Pliny, bk. 2, ch. 23.]
[I.] It pleases [me] in this place to make use of that Plinian [saying] (Pliny bk. 2, ch. 23): “It is wonderful whither the wickedness of the human heart proceeds, [once] enticed by some tiny, unaccustomed success.” The Pythagoreans had seen someone of their own sect—namely Ecphantus—happily represent, by the diurnal motion of the earth, the same phenomena which others had furnished by the diurnal revolution of the stars; hence, therefore, a step being taken with greater daring, they added to it the annual translation also, which is commonly ascribed to the Sun—placing the Sun, as the fountain of heat and light, immovable in the center of the Universe. Of whom the first I find to have been Philolaus, about whom Plutarch (bk. 3 of the Placita Philosophorum, ch. 11) reports these [things]: “The emulators of Thales said the Earth [is] in the middle. Xenophanes [said it was] first rooted into the infinite. Philolaus the Pythagorean [said] the middle [is] fire—namely the hearth of the universe; the second [he called] the antichthon, that is, the earth of the Antipodes [counter-earth]; the third [is that] which we inhabit, situated both over against the antichthon and turning about it; which is the cause why those who inhabit that [earth] are not seen by us.” And (ch. 13): “The rest said the earth remains [at rest]; but Philolaus the Pythagorean [said] it is turned about the fire in an oblique circle, in like manner as the Sun and Moon.” But with Plutarch agrees Diogenes Laërtius (in the Life of Philolaus), [though] he indicates only the motion of the prime mobile [as belonging to it]. He thinks all things come about by harmony and necessity; he says the Earth is moved according to the first circle: others affirm that Niceta of Syracuse felt this. From which [authors] is better understood that which Aristotle (bk. 2 On the Heaven, text 72) narrates in these words: “Whereas most [of those] who say that the whole heaven is finite assert that the earth lies in the middle, those, on the contrary, who dwell about Italy, and are called Pythagoreans, say [otherwise]. For they say that in the middle there is fire, and that the earth is one of the stars, and, being carried circularly about the middle, makes night and day. Moreover, they construct yet another earth opposite to this, which they name the antichthon [counter-earth]—not accommodating their reasons and causes to the phenomena, but rather drawing the phenomena themselves toward certain opinions and reasons of their own.”
[Margin: Philolaus’s opinions about the Earth.]
Among these reasons, [Aristotle] mentions in the first place (text 73) that one which was drawn from the dignity of place: namely, that to the most honorable of bodies belongs the most honorable region, and that fire, or the Sun, is nobler than the earth; and he subjoins: “Moreover the Pythagoreans indeed, because it most befits that that which is most principal in the Universe be preserved [in the chief place], and the middle is such [a place]—[therefore] they said that the fire holds this region, which they name the ‘prison of Jupiter,’ or his ‘guard-house.’”
[Margin: The opinion of Aristarchus of Samos.]
[II.] Nor indeed in Italy only, but in the island of Samos also—from which we know Pythagoras to have sprung—did Aristarchus, himself too a Samian, teach the same opinion about the motion of the Earth, more than a hundred years after Philolaus: for that this Aristarchus flourished in the year 44 from the death of Alexander the Great, or about the year 280 before Christ, is gathered from Ptolemy (bk. 3, ch. 2). Now concerning Aristarchus, Archimedes in the Sand-Reckoner speaks thus: “These [are the things] which, in those [writings] that have been written by the Astronomers—namely about the Earth resting in the middle of the world—Aristarchus of Samos, refuting [them], set forth [as] certain hypotheses, from which it follows that the World is manifold compared with the World as [commonly] set forth. For he supposes the non-wandering stars and the Sun to remain immovable, but the earth to be carried about the Sun according to the circumference of a circle which is established in the mid-course [of the heaven]. And [he supposes] the sphere of the non-wandering stars, situated about the same center as the Sun, to be of so great a magnitude that the circle in which he supposes the earth to be carried round has the same proportion to the distance of the non-wandering stars
[Margin: Archimedes’ censure of Aristarchus.]
as the center of a sphere has to its surface.” But this Archimedes at once disapproves, saying: “This, however, is impossible: for since the center of a sphere has no magnitude, it must not be supposed to have any ratio at all to the surface of the sphere.” With these sayings of Archimedes those things excellently agree which Plutarch, under the person of Lucius, speaks in the little work On the Face in the Orb of the Moon, thus:
[Margin: Cleanthes’ censure of Aristarchus.]
“Ho there—[do not let us] make ourselves guilty of impiety, in that manner whereby Cleanthes thought that Aristarchus of Samos ought to be arraigned by the Greeks for [the crime of] violated religion, as though he had moved the Hearth of the Universe [Vesta] from its place: because that man, attempting to defend the phenomena of the heaven by certain reasonings, had supposed the heaven to rest, and the earth to be rolled along an oblique circle, while at the same time it is turned about its own axis.” From which passage of Plutarch it came about that
[Margin: What and where Vesta is.]
Kepler, fearing for himself from the Ecclesiastical censure cast at him by Chiaramonti on account of his asserting the motion of the earth, said (in the Hyperaspistes, bk. 3, ch. 22, p. 183): “The hypotheses which I follow, if it shall have thundered upon [me] with the snatched-up dart of Jupiter—if it shall write that I am to be charged, as Cleanthes once [charged] Aristarchus, with violated religions, the sacred Hearth [Vesta] being moved from its place—[the doctrine] will abundantly satisfy the Astronomers, the equivalence [of the hypotheses] having been demonstrated in the Commentaries on Mars, inculcated in the Harmonics, [and] employed in this very little book.”
[III.] But now Plutarch invites me, that on this occasion I should inquire what divinity Vesta was among the Heathen, and in what place she stood—certain [matters] in favor of this Pythagorean fiction about the place or motion of the Earth: in which very question we shall find certain opinions, sprung (if I am not mistaken) from the opinion of the Pythagorean about the place of the earth. For all [the ancients] willed Vesta to be at rest in the center of the world; therefore those who thought the earth to settle in this center, supposed the Earth too to be that same Vesta; but those who believed the center of the Universe to be held by Fire, or by the Sun, they likewise took Vesta for the perpetual and immovable fire. Of the first opinion were those who said her to be the sister of Ceres and Juno, born of Rhea (Ops) and Saturn; as Apollodorus (bk. 1 of the Library), with whom Ovid agrees in the Fasti: “From Ops they record that Juno and Ceres were created / by the seed of Saturn; the third was Vesta.”
[Margin: Plato’s opinion about Vesta.]
[He] who also in Metamorphoses 1 sings: “The earth stands by its own force; by standing [vi stando] it is called Vesta.” But before him Plato, in the Phaedrus, when he had said that the eleven Gods, with Jove as choir-leader and fore-dancer, advance and follow his chariot, subjoined, excepting Vesta: μένει μὲν Ἑστία ἐν θεῶν οἴκῳ [menei men Hestia en theōn oikō]—“for Vesta alone remains and stands fast in the house of the Gods”: and again (bk. 12 On Laws), “The Earth and Vesta is a sacred dwelling-place to all the Gods.” To which point [look] those words of Arnobius (bk. 3 Against the Heathen): “Some pronounce the Earth [to be] Vesta, because it alone stands in the world, the other parts of it being established in perpetual mobility.” Servius too (on Aeneid 1) thinks she was called Vesta because she is clothed [vestita] with various things; “she herself, I say,” says he, “is said to be the Earth.” Some of the Greeks also,
[Margin: (continued)]
as Lipsius notes (in the book On Vesta, ch. 1), think she was called Vesta παρὰ τὸ ἑστάναι ὅ ἐστιν ἐν ἑνὶ τόπῳ [para to hestanai, i.e. “from standing in one place”], because she subsists in one place. And in Festus certain [authors] call her, for this cause, Stata Mater [the “Standing Mother”]. Lipsius also adduces those verses of Pindar: “And Mother Earth, and Vesta, by the wise / art thou surnamed, and a seat in the very air.” Nor does it stand in the way that Fire too is attributed to Vesta; for this can be understood of the subterranean and perpetual fire, although exhaling through various chasms, or of the fire [kept] in the earth and preserved by the earth—as Servius notes, saying: “For Vesta is said to be the Earth, which there is no doubt has fire, as is given to be understood from Aetna and Vulcano [the volcanic isle].” To this make also the words of Phurnutus [Cornutus] to [the same effect as] Lipsius: “That the divine fire which is in the world is nourished from this [Earth], and subsists through it; or that the fertile Earth is the mother also of animals, to which the fiery force is the cause of life”: or certainly—as Dionysius of Halicarnassus reports (bk. 2 of the Antiquities)—“The sacred fire belongs to Vesta, because, since Vesta is the Earth, [and] she holds the middle place of the world, she kindles from herself the up-
[…continues on p. 294 (PDF 329): “…the upper [regions]…” — the rest of the Dionysius/Vesta excursus, then (presumably) Riccioli’s return to the catalogue of authors who ascribed the annual motion to the Earth.]
(printed p. 294 — continuing Chapter III: the Vesta excursus concludes, with Riccioli’s verdict that Plato always held the Earth immovable. The chapter then treats the revival of the moving-Earth doctrine by Cusanus and especially Copernicus — who, Riccioli insists, asserted it absolutely, not merely hypothetically — and begins the catalogue of authors who gave the Earth the annual motion.)
[Header: BOOK IX. SECTION IV. — 294]
—those upper fires. Hence arose the opinion which Martianus Capella indicates (bk. 1, On the Marriage of Philology), that Vesta is the nurse of Jupiter. Others, however, understand Vesta absolutely as the living and perpetual Fire, according to that [verse] of Ovid: “Nor understand Vesta to be anything other than the living flame.” And [that] of Virgil in the Moretum: “And while Vulcan and Vesta perform their parts.” And Cicero (bk. 3 On Laws): “And since Vesta has embraced, as it were, the hearth of the city—as she is called by [her] Greek name”; and (bk. 2 On the Nature of the Gods): “The name Vesta is taken from the Greeks, for she is that [goddess] who by them is called Ἑστία [Hestia]; and her power pertains to altars and hearths.” For just as, by the addition of the letter V, Er was said Ver, and the Eneti [became] Veneti, so Esta was called Vesta, as Servius notes (on Aeneid 1). But more to our purpose [is] Plutarch (in [the Life of] Numa): “Numa is said to have thrown around the temple of Vesta, [built] in an orbicular shape, [a watch] for the perpetual fire, as a guard—not that he might liken [it] to the shape of the Earth, as though Vesta were the Earth, but [to the shape] of this whole universe, whose middle the Pythagoreans hold to be Fire; and this they call Vesta, and Unity. But [they hold] the Earth to be neither immovable, nor situated in the middle of the [world’s] circumgyration; but suspended in an orbit about the fire, nor to be reckoned among the chief or first parts [of the world].”
[Margin: The opinion of the aged Plato about the place and motion of the world/earth.]
Some will have it that Plato too, when now an old man, felt this about the Earth—as situated in another place, while the middle and most worthy region befits some other and more excellent [body]. But so long as no passage from Plato is adduced [for it], I, from his own words (already cited above, in the Phaedrus and Republic 12) and from the words of the Timaeus (adduced in the preceding chapter, num. 2), persist in this opinion: that Plato always thought the earth immovable. Granted that he came into Italy that he might see Pythagoras and Philolaus, and got to know there Timaeus of Locri and Archytas of Tarentum (as we have learned from Cicero, bk. 1 of the Tusculans, and from Laërtius): on behalf of which opinion I appeal from Plutarch to Plutarch, who (On the Opinions of the Philosophers, bk. 2, ch. 6) says that Plato, with Pythagoras, assigned the cube to the Earth on account of its immobility; and (ch. 15) that he did not number it among the Planets; and (bk. 3, ch. 13)—Heraclides and Philolaus excepted—says, “The rest said that the earth remains [at rest].” And so I do not assent to Gassendi (Epistle 2, On impressed motion), who asserts, from Plutarch, that the elder Plato conceded both motions to the Earth: for Plutarch does not assert that, but reports the conjecture of others, when he says, “Some will have it [so].”
[IV.] But the opinion of Philolaus and Aristarchus about this motion of the Earth had slumbered, and—lulled into deepest silence through many ages back—had lain in the oblivion of almost all, when Nicolaus Cusanus, as I noted (ch. 2, num. 3), [roused it] with subdued voice; but the other Nicolaus—namely Copernicus—roused it with a great voice. Nor indeed did Copernicus (as some suppose, especially Scipione Chiaramonti in the preface of his Antiphilolaus, and before him the unnamed Author who prefixed the “Admonition to the Reader” to Copernicus’s works) reckon this motion of the Earth [merely] from a bare hypothesis; rather he asserted it absolutely, either as more probable, or even as demonstrated.
[Margin: Copernicus asserts the Earth’s motion absolutely, and not merely under a hypothesis.]
For this is what the words of Copernicus himself sound, in the preface to Paul III, when he says: “And so, when I myself considered with myself how absurd a discourse [ἀκρόαμα] those would think it who know that this opinion—that the Earth is set immovable in the middle of the heaven, as its center—has been confirmed by the judgments of many ages; if I, on the contrary, should assert that the Earth is moved: I long hesitated with myself whether I should bring into the light my commentaries written in demonstration of its motion; or whether it were better to follow the example of the Pythagoreans and of certain others, who were wont to hand down the mysteries of philosophy not by letters, but by hand[-to-hand], to kinsmen and friends only—as the Epistle of Lysis to Hipparchus testifies.” And not much after, again using the word “demonstration,” he says: “It will come to pass that, the more absurd this my doctrine about the Earth’s motion now seems to most people, the more admiration and favor it will obtain, after, by the publication of my commentaries, they shall see the fog of absurdity removed by the clearest demonstrations.” And again, repeating the same word, he says: “Nor do I doubt that ingenious and learned Mathematicians will agree with me, if—as this philosophy especially demands—they shall be willing to know and weigh, not cursorily but thoroughly, those [things] which are brought forward by me in this work for the demonstration of these matters.” And so greatly did he steel his mind in this opinion about both motions of the Earth, that he even contrived a mark of rashness and ca-
[…right column, p. 294 (PDF 329) — running head “LIBRI IX. SECTIO IV.” — continues:]
—lumny against those who should try to assert the Earth’s immobility from the sacred letters: for, having said that he had dedicated his work to Paul III (as one imbued with Mathematics) precisely lest he should seem to shun anyone’s judgment, he added: “That by your authority and judgment you may easily restrain the bites of the slanderers: although it is in the proverb that there is no remedy against the bite of a sycophant.” And presently: “If perhaps there shall be idle-talkers [ματαιόλογοι] who, although ignorant of all mathematics, nevertheless take upon themselves a judgment about these [things]—on account of some passage of Scripture badly twisted to their purpose—and shall dare to reprehend and assail this undertaking of mine: I heed them not at all, so far that I even despise their judgment as rash.”
[Margin: Copernicus’s arrogant opinion.]
With so great a haughtiness, forsooth, did that man dare to rise up, who but lately seemed almost to dread the judgment of men. But it must now be shown, from his own words, by what reasoning he distributed the annual translation to the Earth—as to one of the Planets—rather than to the Sun. Therefore (ch. 9 of bk. 1 of the Revolutions) thus beginning: “Since, then, nothing forbids the mobility of the earth, I think it must now be seen whether several motions too befit it, so that it can be reckoned one of the wandering stars”; he at length concludes: “If, therefore, the earth also makes other circuits—as, for instance, [the one] according to the center—it will be necessary that they be [the same as] those which likewise appear externally in many [bodies], among which we find the annual circuit. For if [the motion] be transferred from the solar to the terrestrial, the Sun’s immobility being granted, the risings and settings of the signs and stars, by which the morning and evening [phenomena] come about, will appear in the same way. The stations too, retrogradations, and progressions of the wandering [stars] will be seen to be motions not of them, but of the earth, which they borrow for their appearances. Finally, the Sun itself will be thought to possess the middle of the world: all which the order [of the spheres]—in which they succeed one another—and the harmony of the whole world teaches us, if only we examine the matter itself with both eyes (as they say).”
[Margin: Copernicus places the Sun not in the very center of the World, but about it or near it.]
Concerning which order, when he had related many [things] pertaining to the various world-system (ch. 10), he added: “Accordingly we are not ashamed to confess this whole [region] which the Moon encircles, together with the center of the earth, to pass through that great orb among the other wandering stars by an annual revolution about the Sun; and that about it—namely the Sun—is the center of the world: so that, the Sun also remaining immovable, whatever appears as a motion of the Sun is rather verified in the mobility of the earth.” But by what reasoning the annual motion of the Earth’s center about the world’s center is conjoined with its diurnal revolution about its own center—nay, with a certain third motion of the terrestrial axis, preserving its parallelism to the axis of the Equator—he declares more fully, with a diagram appended, in ch. 11; which we shall set forth in the following chapter. And in the fifth book (ch. 1, 2, & 3) he teaches how the annual motion of the earth’s center, referred to the motion of the five lesser Planets, can be called the “motion of commutation”—because it either exceeds the mean motion of Saturn, Jupiter, and Mars, or is exceeded by the mean motion of Venus and Mercury; and by what reasoning their stations and retrogradations are explained through that motion of the earth.
[Margin: They assert the annual motion of the earth: Rheticus, Maestlin, Kepler, Galileo, Bullialdus, Jac. Lansberge, Hérigone, Gemma, Naibod, Reinhold, Calcagnini, Zúñiga, Foscarini, Baranzano, Politiano, Bruno, René Descartes, Philip Lansberge, Schickard, Hevelius.]
[V.] At length there adhered to Copernicus, and made the Earth revolve by a threefold (or at least twofold) motion: his pupil Georg Joachim Rheticus (who, in the very long Narration usually subjoined to Copernicus’s works, expounded them and commended [them] greatly); and Michael Maestlin; and Maestlin’s disciple John Kepler; Galileo; Bullialdus, Jacob Lansberge, and Hérigone (in the passages cited, ch. 1, num. 4); and besides: Gemma Frisius (in the Epistle to Johannes Stadius); Valentin Naibod (bk. 1 of the Astronomical Institutions, ch. 16); Erasmus Reinhold (in the Prutenic Tables, and in his exposition of the Copernican hypothesis); Celio Calcagnini; Diego de Zúñiga (in the Commentary on Job); Paolo Antonio Foscarini the Carmelite (in the Epistle on the mobility of the earth and the stability of the Sun, to Sebastiano Fantoni, General of the Carmelites); Redento Baranzano (part 2 of the Uranoscopia, p. 42), and, in him, Antonio Lorenzo Politiano; and also Giordano Bruno (bk. 3 On the Vast and the Immense, last chapter); René Descartes (in the Principles of Philosophy, part 3, from num. 26 to 34); Philip Lansberge (in his Uranometria, bk. 3, and in the Controversies on the annual motion of the earth); Schickard; and Johannes Hevelius (bks. 5 & 7 of the Selenographia)—but among these, Lansberge and Bullialdus do not admit that third motion of the earth by which Copernicus excuses the proper motion that ap-
[…continues on p. 295 (PDF 330): “…appearing in the Fixed [stars]” — the close of the author-catalogue (the Fixed stars truly move slowly eastward; Bruno’s variant; Rothmann’s recantation to Tycho), then the SCHOLIA on still other motions ascribed to the Earth (trepidation; Pena’s rectilinear up-down motion, refuted geometrically; the meridian/pole-altitude motion).]
(printed p. 295 — completing Chapter III with the rest of the annual-motion catalogue and Rothmann’s recantation to Tycho; then the Scholia on other motions feigned for the Earth: trepidation, Jean Pena’s rectilinear up-and-down motion (which Riccioli refutes geometrically), and the meridian/pole-altitude motion. The chapter ends here, leading into Chapter IV.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 295]
—pearing in the Fixed [stars]; for they say that the Fixed Stars really do move slowly toward the East. But neither does Giordano Bruno, besides the diurnal and annual motion of the earth, admit any other; in the third place, however, he substitutes a motion of the Sun in a circle bounded by the Tropics, from which arise the annual inequality and the variation of the Eccentricity and of the [apparent] magnitude. Rothmann, moreover—who once clung to Copernicus tooth and nail—afterward “gave his hands” [submitted] to Tycho, if we are to believe Tycho himself
[Margin: Rothmann’s recantation against Copernicus.]
(in the Epistles, p. 192); whose words we shall report below (ch. 29, num. 19, & ch. 30, num. 7).
SCHOLIA
Where [it treats] of certain other Motions feigned for the Earth
[Margin: The motion of Trepidation.]
[I.] Among the motions attributed to the Earth, the most celebrated are the three already indicated, after the opinion of Copernicus; and besides those, the motion of trepidation, about which Pierre d’Ailly [treats] problematically (q. 3 On the Sphere), and others adduced and rejected by us (bk. 2, ch. 3, num. 1)—a motion which, however, is favored by Athanasius Kircher (bk. 2 of the Magnet, p. 489). And further, Andreas Cisalpino (bk. 3 of the Peripatetic Questions, q. 4) feigned in the Earth a certain very slow motion toward the East, such as others acknowledge in the Fixed [stars] as proper [to them]—about which there is no need to say more.
[Margin: An up-and-down motion of the Earth, asserted by Jean Pena and Stadius.]
[II.] But Jean Pena also introduced a certain new rectilinear motion of the Earth, upward and downward, in the preface (prefixed to Euclid’s Optics, translated by himself from Greek into Latin) addressed to Charles of Lorraine the Cardinal, On the Use of Optics; and Johannes Stadius [did the same] in the History of Astronomy before the Bergen Tables, p. 23. The foundation of this motion with these [authors] is the apparent inequality in the motion of the Fixed [stars], which Pena refers back to optical causes and to the approach of the Earth toward the Fixed [stars] and its recession from them. But it will be better to draw out this opinion from his very own words; he says, then:
[Margin: Jean Pena’s first foundation.]
“It is an optical law [sanctio], as true as it is brief, that of [bodies] borne with equable speed, those which seem to be carried more slowly are farther distant. Now the non-wandering stars are borne with equable speed (for that the celestial motions are equable, although they appear unequal to us, the hypotheses of Astronomy teach); yet they seem to advance unequally, as the observation of times teaches. For at the beginning of the periods of Callippus—that is, in the times of Alexander the Great—the non-wandering stars traversed one degree of the heaven in seventy-two years; but in Ptolemy’s age, in a hundred years; in the time of Mahomet of Aracta [al-Battānī], in sixty-six years; in this age they advance with nearly the same progress as in those first times of Callippus. From which it is plain that the globe of the Earth was, in Ptolemy’s age, farthest from the heaven; but in Mahomet’s times, nearest to the heaven; while in our age it is moderately distant from both extremes. Thus you see it concluded from Optics (most illustrious Prince) that the Earth must be now nearer, now farther from the heaven: that is, that it has some motion by which it changes place. I do not involve the earth in a threefold motion; I do not assign to it the diurnal and annual [motion], nor the motion of the center or of declination; but only from Optics I assert that the Earth advances by some motion from place to place; and that [it does so] with the progress of time
[Margin: Jean Pena’s second foundation.]
very slowly, since scarcely in four hundred years or more can any such inequality of motions be perceived. Whence another question too is solved, concerning the middle of the world: for if the earth changes place, how will it be the center of the world? Thus the old controversy of the wisest men will be illustrated by the light of Optics, and settled with the least trouble.”
[III.] Thus far Pena—who, in the same preface, had a little earlier built up the same motion of the earth from the apparent unequal magnitude of the same Fixed star, supposing that the diameters of the Fixed [stars] are now seen larger, on account of the earth’s approach toward them, than in Ptolemy’s time. But by the same facility of feigning (not to say futility) he could have asserted that the eighth sphere itself is moved up and down along its diameter, and approaches the immovable Earth and in turn recedes from it. But that that inequality of the Fixed [stars’] motion is improbable—or at least that their equality, even [as it] appears, is more probable—we have sufficiently shown (bk. 6, ch. 17). And how falsely it is supposed that the diameters of the Fixed [stars] now appear larger than in Ptolemy’s age, is clear from what was said (bk. 6, ch. 9, & bk. 7, sect. 6, from ch. 9 to 13). It ought also to have been observed by this writer how much greater and more frequent an inequality would appear in the motion and magnitude of the Planets—especially the Moon—if that approach and recession of the Earth were admitted; nay, it would be necessary that either the Earth should ascend above the heaven of the Moon and the Sun, or at least that, together with the center of the earth, the center also of the Planetary system—and so of the heaven of the Planets—should ascend from the world’s center toward the outermost [region], by as much as is about a tenth part of the distance of the Fixed [stars]; which will be demonstrated by the following diagram.
[Margin: How much the Earth would have to ascend, if the inequality of the Fixed [stars’] motion arose from its motion.]
[IV.] Let AB be an arc of one degree of the heaven of the Fixed [stars], described from the world’s center C, in which [center] is likewise the center of the earth in that age when the Fixed [stars], by [their] mean motion, are imagined to complete one degree in 72 years; and let there be assumed AC, or BC, the distance of the Fixed [stars] according to Ptolemy or al-Battānī, [= ] 19000 semidiameters of the earth. Let the earth then be transferred to D, in that age when the Fixed [stars] are imagined to complete one degree in 66 years—for then, by the rule of proportion, they will be seen to complete one degree and besides 5′ 26″ in 72 years.
[Translator’s note — geometry diagram (right column): a tall narrow triangle. At the top, the short arc A — B (one degree of the starry heaven). From A and B two long lines run down to the world-center C at the bottom; the Earth’s displaced position D is marked just above C on the same baseline, so that AB is viewed from C under angle ACB and from D under the slightly larger angle ADB. The figure visualizes Riccioli’s trigonometric refutation of Pena: the parallax needed to make the stars seem to slow would require the Earth (D) to sit ~1900 earth-radii from the true center C.]
Wherefore the arc AB, viewed from C under the angle ACB, will appear [of] 60 minutes; but viewed from D, under the angle ADB, will appear 65′ 26″. Wherefore, by [Elements] 1.32, the angle CDB in the triangle BCD will be 178° 54′ 34″, and the angle CBD will be 5′ 26″. Since, then, in it all the angles are given, and besides the side BC [= ] 19000 semidiameters of the earth, the side DC will also become known by the help of Trigonometry; and it will be found, by the second [case] of Oblique-angled Triangles, that DC is 1900-and-more terrestrial semidiameters: which measure exceeds the Ptolemaic distance of the Sun—let alone of the Moon—from the world’s center. Therefore it would be necessary that the center of the Earth, from the time of Callippus to the age of al-Battānī, had ascended from the world’s center above the Sun; or at least that the whole system of the Planets, together with the earth, had ascended from the world’s center [by] 1900-and-more earth-semidiameters.
[Margin: Jean Pena’s either error in Geometry, or audacity.]
Let Pena therefore see either how much he has erred in Geometry and in Optics itself, or how much further he would have to dare, and what hypothesis he would have to swallow, if he wished to defend his opinion.
[Margin: The same man’s lapse in the History of Astronomy.]
[V.] But I find yet another lapse of Pena in the history of Astronomy, when, in the same preface to Euclid’s Optics, he says: “Let Aristotle have judged that the Earth rests; let Ptolemy, most experienced in celestial matters, so judge; let Theon so judge; let vulgar credulity have judged the same. But for us, those Pythagoreans judged otherwise, and pronounced that the earth is moved. The same assert Plato’s Timaeus, Philolaus, Ecphantus, Seleucus; the same teach Aristarchus of Samos, Archimedes, and—in this age—the most renowned Copernicus.” But, granted that Timaeus judged the earth to be moved (which, however, is by no means certain, as is plain from what was said in this ch. 3, num. 3)—yet from the same chapter, num. 2, it is plain that Archimedes cannot be numbered among the movers of the Earth, since he disapproved Aristarchus’s opinion, even though, [Aristarchus’s] hypothesis and the immense distance of the Fixed [stars] being granted, he showed in the Sand-Reckoner that the number of grains of sand enclosed within the whole capacity of the World could be reckoned up.
[Margin: Seleucus asserts the motion of the Earth.]
[VI.] But concerning the motion of the Earth in the Meridian—by force of which the altitudes of the northern Pole would be continually increased—which Domenico Maria [Novara] feigned, and Giordano Bruno followed (p. 306), and Magini (Canon 8 of the second mobiles), we shall say more (ch. 11, from num. 7); where (num. 9) [we shall treat] of the motion of libration from the South-west [Africus] toward Caecias [the North-east], asserted by Alessandro Calignone.
[Margin: A motion of the Earth changing the pole-altitudes.]
[End of Chapter III. The page closes with an ornament rule and the catchword “CA-” → Chapter IV (Caput IV) begins on the next printed page (p. 296, PDF 331), presumably expounding the threefold Copernican motion with the promised diagram.]
(printed p. 296 — opening Chapter IV, which expounds the three (or four) Copernican motions of the Earth. After naming them (diurnal, annual, and the motion of declination/parallelism), the chapter explains Copernicus’s substitution of the Earth’s daily whirling for the Prime Mobile and the “sailing-ship” simile by which the geocentric impression is explained away, traced through Cusanus, Buchanan, Kepler, and Gassendi.)
[Header: BOOK IX. SECTION IV. — 296]