[I.] Although in the preceding Chapter, in certain arguments—especially the 2nd and 4th—mention was made of the motion of the Planets; nevertheless the arguments were not deduced from their motion immediately taken, as will be done in this chapter. Let these [remarks] be said for the sufficient distinction of the titles.
First Argument, from the Superfluity of the motions of the three Superior Planets by Epicycles, and of the two Inferior [Planets] by their own Eccentrics—[a superfluity] removed by the single and simple Annual Motion of the Earth
[II.] Here indeed, if anywhere deservedly, the Copernicans seem to triumph, and with an inevitable battering-ram to shake the Ptolemaic system, or others akin to it, and almost to overthrow [it].
[Margin: Commendation of the Earth’s annual orb, from Copernicus.]
And hither likewise look those words of Copernicus (bk. 1, ch. 10): for after he had said, “Whatever appears concerning the motion of the Sun is rather verified in the mobility of the earth,” a little after he added: “Which I think is to be more easily conceded than that the intellect be distracted into an almost infinite multitude of orbs—which they were compelled to do who detained the earth in the middle of the world. But rather the sagacity of nature is to be followed, which, just as it has most of all taken care not to have produced anything superfluous or useless, so has rather often endowed one thing with many effects.”
[Margin: And from Rheticus.]
Adhering to which, Rheticus, in his First Narration, admonishes the Astronomers that—as Galen inculcates (bk. 10 On the use of the parts), namely that nature does not operate superfluous [things], and that what it can attain by one or two means it does not busy itself to inquire through many—so they too, in framing hypotheses, should avoid superfluous [things]; then he infers: “Wherefore, since by this single motion of the earth we should see, as it were, infinite appearances satisfied, should we not attribute to God, the founder of nature, that industry [economy] which we see common clock-makers to have? who most studiously take care not to insert into the instrument any little wheel which is either superfluous, or whose function some other—its position being a little changed—more conveniently supplies.” But explaining in particular the conveniences which arise from the single annual motion of the Earth through its orb, he says: “To these is added, that the motion of the earth in its orb produces the arguments of all the Planets, except the Moon”—that is, the Anomaly of the orb, or second inequality, which the Alphonsines call the “Argument,” and which alone, by itself, seems to be the cause of all the diversity of motion; which [diversity], namely, appears in the three superior [planets] from [in relation to] the Sun, but in Venus and Mercury around the Sun. “And again, from this motion of the earth it follows,” he says, “that all the diversity of the apparent motion of the Planets—which seems to befall in them parà toùs pròs tòn hēlion schēmatismoús [according to their configurations toward the Sun]—comes about because of the annual motion of the earth in the great orb; and that the Planets in reality proceed by only the one other inequality, which is observed in respect of the parts of the Zodiac.” Wherefore, since Ptolemy and almost all the rest, down to Tycho, set forth the first inequality of the motions in the Zodiac, in the five lesser Planets, by Eccentrics, but the second—which arises from the various recession, approach, and configuration toward the Sun—by Epicycles, or orbs equivalent to Epicycles, but multiplied: Copernicus, by the single annual orb of the Earth approaching the Planets and receding from them, sets forth and saves [it], and so performs what in the Ptolemaic system the three Epicycles of the superior, and the two distinct Eccentrics of the Inferior Planets, ought to perform.
[Margin: Commendation of the same orb and motion, from Kepler.]
[III.] This, indeed, is what Kepler so greatly inculcates—both in the Cosmographic Mystery (ch. 1), saying: “This orb, therefore, and motion of the Earth furnishes these conveniences: that we do not need three eccentrics in the usual hypotheses—namely, of the Sun, of Venus, and of Mercury. For because the Earth is carried around about these three Planets, the Earth-dweller thinks that those three, immovable, are carried around about him. But if there were more stars within the orb of the Earth, they too would ascribe this motion to more [stars]. Likewise, this orb being posited, the three great epicycles of Saturn, Jupiter, and Mars, with their motions, fall [away].” But then, more explicitly, in the Epitome of Copernican Astronomy (bk. 4, p. 542), where he confesses indeed that those great Ptolemaic Epicycles were removed by Tycho too, he nevertheless says that [Tycho] left in the world the same thing which was effected by them—namely, that any Planet, besides that motion which is in reality to be conceded to it, is moved even now, over and above, by the very motion of the Sun, mixing both into one; from which measure, since there are no solid orbs, most perplexed spirals are effected in the mundane space. (Of which perplexity I have exhibited a diagram and specimen, from Kepler himself, bk. 7, sect. 1, at the end of the last chapter.) Copernicus, on the contrary, strips the five planets utterly of this extraneous motion of the Sun, by the single simple motion of the center of the earth; and brings it about that the centers of the six primary planets—namely, of the Earth and of the remaining five—each describe a single, simple, and perpetually self-similar orbit in the mundane space, or a line very near to a circle. So he [says] (p. 543), alluding to the Elliptical orbit introduced by him into Astronomy. Moreover Lansberge (tract 4 of the Apology for the motion of the earth), considering the five aforesaid extraneous motions of the Planets removed by the annual motion of the Earth, and the eight diurnal motions of the eight spheres expunged by the diurnal motion of the Earth, says: “By the Earth’s motion is done what ought to have been accomplished by thirteen motions of the stars.” And he urges those physical axioms: that Nature proceeds in an orderly way, abhors superfluities, [and] does nothing in vain.
[Margin: Anticipation of the response, from Kepler.]
[IV.] But since Kepler knew that the aforesaid motions of the Planets, which seem to us manifold, could be attributed to Intelligences leading the Planets around by a single spiral line, [Kepler], meeting this response (bk. 4 of the Epitome of Copernican Astronomy, p. 546), said that the condition of the moving souls would be very hard, and harder [that] of the Intelligences, while they are bidden to look to very many things, so as to carry a planet in order by two motions, distinct in all respects and mixed among themselves; but [that] if the Sun rest and the earth be moved, the motion of each Planet is single, and can be effected by corporeal magnetic powers, by the single rolling of the body of the Sun about its center, and there is plainly nowhere need of the aid of a mind, says he; and he refers the Reader to the Commentaries on Mars, where he teaches by what means the Sun, by a magnetic power diffused and emitted from itself through [its] light, also
[…continues on p. 340 (PDF 375) with the catchword “quo”: “…quo[que]“—the rest of Kepler’s magnetic-light account of how the Sun drives the planets, and Riccioli’s reply to this First Argument.]
(printed p. 340 — within Chapter IX, completing the first argument (superfluity of motions). Finishes Kepler’s magnetic-light account, casts the argument in form, and gives three Responses: the moving-Earth hypothesis destroys what common sense sees without necessity; heliocentrism really multiplies motions rather than economizing; and by retortion, Tycho’s own words show his system dispatches the planetary circuits equally well without making the Earth a thrice-moving star.)
[Header: BOOK IX. SECTION IV. — 340]
[the Sun, by a magnetic power diffused and emitted from itself through its light, also] in every direction lays hold of the Planets, and twists [them] into a gyre [rotation]. But now let us come to the formula of the argument.
[Margin: The argument in form.]
[V.] “That hypothesis is to be preferred to the others which, by fewer and simpler motions, performs that which the others cannot perform except by more, and more composite, motions: But the Hypothesis in which the Earth is moved through the annual orb is of this kind: Therefore it is to be preferred to the others.” The Major is plain from the axioms so often already adduced: for it is most universally received that God and Nature—nay, also Art—are not wont to effect by more [means] what they can [effect] by fewer; nor are means and instruments to be multiplied—nay, generally [no] entities [whatsoever]—without necessity, or greater utility. The Minor has already been proved, since it has now been shown that from the Earth’s annual motion follows that apparent second motion in the lesser Planets, which represents the second inequality—the annual [one], or [the one] attempered to the apparent motion of the Sun; and [that] thus, by a single annual orb, [there] comes about what otherwise ought to be effected by distinct Epicycles or Eccentrics.
[Margin: First Response.]
I answer, first: if it [the hypothesis] furnishes phenomena previously evident to sense, and not more absurd than is the composition of motions, I concede the Major; if it does otherwise, I deny the Major, and so I deny the Minor: for the hypothesis in which the Earth is moved through the annual orb does not furnish phenomena evident to sense, but—by destroying and inverting [those] which are evident to common sense (of which kind is the motion of the Sun, and the harmony of the Planets attempered to the Sun), and indeed by destroying [them] without any necessity—it introduces a motion from which the intellect, leaning on sense (as is fitting in Physical matters), shrinks more than from the multiplicity of motions.
[Margin: How far the fallacy of the senses is to be admitted.]
Nor is there [reason] why that so-oft-repeated [saying] should be thrust [at us]: that the senses are fallacious, and that this dispute is not to be decided from their estimation. For it is answered that they are neither always nor for the most part fallacious, and that their fallacy is detected by applying reasoning—but [reasoning] leaning on that very [thing], on surer sensations; otherwise, so long as in some special object they are not thus caught erring, one must stand by them, and their estimation is in possession [holds the prior right], to the [degree of] exigency of our assent. For surely, because some eyes are blind, or ours sometimes are full of bleariness, or an animal is sometimes sick, is it to be said that all eyes are blind? or that ours always labor with bleariness, or that no animal is ever healthy? Besides, does not the intellect itself, in many [things] which do not depend immediately on sense, so err that that error cannot be attributed to the fallacy of the senses? You would say so indeed; for concerning the same sensible [object], and the same experiment had through the senses—say concerning the Rainbow, or the tide of the Sea—different [people] think different and contradictory [things], of which opinions some must be false: Is the intellect, then, not even to be trusted? Let those, therefore, who are of this kind, see [to it] lest they undermine the foundations of all the sciences.
To the proof of the Major I answer that those axioms are not to be taken absolutely, or in a purely arithmetical sense—as though, indeed, God and Nature, or even Art, always aimed at unity, or at that number which most of all approaches unity—but relatively to the pre-established end, taken not only as to the substance of the thing to be made, but also as to the accidents congruent to it for its being well or better in its [own] order. Nature, indeed, could have made and conserved Plants and Animals with fewer fibers, little veins, little nerves, cuticles, little membranes, hairs, leaves, little roots, etc., but not so well and congruently. God too could, with fewer stars, with narrower tracts of Seas and Lands, and with a smaller number of insects, reptiles, fishes, birds, [and] quadrupeds, fill this world: but He would not have attained that end, nor in that manner, which—and in which manner—He thus attains [it]. And since Rheticus chose the likeness of Clocks: if someone were to add to some clock more wheels, so that the same hour should be struck not once but twice, or so that, with two distinct bells, [it should sound] the hours with the larger and more sonorous [bell], but the quarter-hours with the smaller; he would employ wheels not superfluous, his end being regarded, but necessary. So in the proposed case: if God willed to exhibit not a mere appearance of the motions of the Sun and of the Planets regarding it [the Sun] in its motion, but the real motion itself of the Sun and of the Planets, and that [motion] now so quickened that [the planets] always become more eastern; now [so] slow that they seem neither to progress nor to regress; now, finally, [so] retrograde into the preceding [signs]—and [if He willed] that on this real variety should depend the variety of many effects: He is not to be judged to have introduced superfluous motions.
I shall give another example. A musical concert could indeed be so instituted that, with fewer voices and instruments, but a polyphonic Echo being employed, more voices and more instruments would seem [to sound]: but if someone proposes to himself not this mere appearance, but a real multiplicity of voices and organs [instruments], that he may in that way effect the concert, he is by no means to be blamed, even if he could with equal ease have used that Echo.
[Margin: Second Response.]
I answer, secondly: If that hypothesis multiplies, in another kind [of motion], more and more composite motions than the other hypotheses, I deny the Major; if it does not multiply [them], let the Major pass: but in this sense the Minor is denied. For although the hypothesis moving the Earth by an annual motion seems not to multiply motions—in so far as by this single motion it performs the five motions of the lesser Planets—nevertheless, in reality, on deeper inspection, it multiplies other motions no less, nay [even] more composite [ones]. For it multiplies the Moon’s motion, since it brings it about that, besides the monthly motion about the Earth, [the Moon] is also moved by an annual motion with the center of the Earth—so that, in this respect, the Moon must perform not only the functions of the Moon, but of the Sun. Then it multiplies that same annual motion in the Earth, and in the Water, and in the whole Elementary sphere; wherefore, if the elements are four, the motions of these and of the Moon are five, and indeed distinct by that [same] distinction by which the mobile bodies themselves [are distinct]. Besides, since not only the animals standing on the Earth, but also the birds flying in the air, and all the meteorological bodies which hang or are moved in the air or fire (if [fire] is given [to exist]), must follow the annual motion of the Earth, or of the center of the Earth: this number of motions is multiplied as many times as there are subjects [things] which are moved by such a motion. Finally, since it is certain that the physical and astronomical phenomena cannot be saved unless to the annual motion of the Earth a diurnal [one] be added—which the Copernicans freely confess—it is necessary to add the diurnal motion not only to the Earth, but to all terrestrial and watery bodies, however much torn away from the water and earth, and—besides the rectilinear motion of the Elementary bodies—to introduce a curvilinear [motion] made through a longer way.
[Margin: Note the economy, or number, of motions in the hypothesis of a resting Earth.]
Wherefore, all [things] considered, that annual motion of the Earth involves with itself far more motions, both in number and in kind, than that hypothesis in which—by a wonderful economy of nature—through the immobility of the Earth and of the Elements (as to their entire bodies), and the simplest rectilinear motion of [their] parts (and that not perpetual, but only in the cases in which the parts of the Elements are outside their natural place); but in the heaven, by a single spiral line in each Planet, always toward the West, but now higher, now lower, now loosened into breadth, now with narrower coils, and led around now more swiftly, now more slowly, by the Intelligences—[by all this] the phenomena and the real effects of these vicissitudes are saved.
[Margin: Third Response.]
It could, therefore, be answered, thirdly, by retorting the argument taken from the multiplicity of motions—which it [will] suffice to have indicated. It pleases [me] to transcribe here the words of Tycho (from tome 1 of the Progymnasmata, p. 661), saying: “I confess, indeed, that the five circuits of the Planets, which the ancients attributed to Epicycles, are thus very neatly dispatched, with less ado, in the single Earth, and that many mathematical absurdities committed by the Ancients, and the enormous incoherence, are guarded against by Copernicus, and the celestial appearances are satisfied a little more accurately: but nevertheless, since this can also be performed by another method—as we have done in our hypothesis—equally well, [if] only not more rightly: to what end is it [needful] to fashion, undeservedly, out of the Earth (an opaque, gross, and sluggish body) a certain Star, revolved even more manifoldly than the rest, as being liable to a triple motion—not only against all Physical truth, but also with the authority of the Sacred letters [Scripture], which ought to be the chief [authority], resisting?”
[…continues on p. 341 (PDF 376) with the catchword “II. Ar”: “II. Argumentum ab Imperfectione motuum cælestium”—the Second Argument, from the Imperfection (retrogradations, stations, unequal epicycles) of the celestial motions.]
(printed p. 341 — within Chapter IX, proposing the Second Argument, from the imperfection of the celestial motions: the planets’ stations and retrogradations are removed by the Earth’s annual motion, which makes them a merely optical, parallactic effect (Copernicus, Kepler, Galileo, Gassendi). Further “imperfections” the annual motion removes are enumerated — the differing progress and regress among the planets, the growth of Ptolemy’s epicycles toward the inner orbs, and the superior planets’ retrogradation at opposition.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 341]
Second Argument, from the Imperfection of the celestial motions—[an imperfection] which, if they were in reality such as they appear, [would obtain]—removed, and a mere appearance attributed [to them], and a cause [thereof] rendered a priori through the annual motion of the Earth
[VI.] The greater [is] the variety and inconstancy in the celestial motions, the greater the imperfection by which they seem to labor: but now, in the five lesser Planets, there appears a manifold variety and inconstancy of motions. For, first, it is established that they sometimes so cling under the same place of the sphere of the Fixed [stars] that, their course being checked, they seem to stand [still]; but sometimes, as if led by a repentance of the direct motion, [they] retrocede into the preceding [signs], and, as if unweaving Penelope’s web, annul or obliterate that motion by which they before proceeded into the consequent [signs]. But all this imperfection Copernicus removed (bk. 5, chh. 3, 35, and 36): for, the Earth’s annual motion being posited, below the orbs of Saturn, Jupiter, and Mars, but above the orbs of Venus and Mercury—and so that, in the periodic motion under the Zodiac, the three superior Planets are slower than the Earth, but Venus and Mercury [are] swifter than the Earth—it is necessary that the Earth so approach to these and recede from them, that they seem sometimes to progress, sometimes to stand [still], and sometimes to retrograde; wherefore the cause of these imperfections is not physically in the motion of those [planets], which always progress, but is a mere appearance, and a merely optical cause, on account of the motion of commutation [parallactic shift], by which the Earth is annually carried around in a gyre. For when the additive [forward] motion of the Planet shall be equal to the subtractive [motion] of the commutation, it will seem to stand [still]; but when the subtractive motion of the Planet shall be greater than the additive motion of the commutation, it will seem to step back; but when, finally, the subtractive [motion] of the Planet shall be less than the motion of commutation, it will seem to progress directly. Which we too explained (bk. 7, sect. 5, ch. 4) with diagrams appended.
[Margin: Kepler’s doctrine on the Retrogradation of the Planets.]
Comparing which hypothesis with the Ptolemaic, Kepler (ch. 1 of the Cosmographic Mystery) says: “For of Ptolemy it could be asked, why the five Planets become Retrograde, [but] the Luminaries not likewise? It is answered, first, concerning the Sun, because it rests: whence it comes about that the motion of the Earth, which is always direct, seems to be in the Sun itself merely and undisturbedly, only through the opposite part of the heaven. But concerning the Moon, because the annual motion of the Earth is truly common to its heaven with the Earth: and two [things] which have the same motion in all respects seem to be at rest among themselves. Whence the motion of the Earth in the Moon is not perceived, as in the other Planets. Concerning the Superior [planets]—Saturn, Jupiter, and Mars—it is answered: because they themselves are slower than the Earth, and because that circle and motion of the earth is thought to be in them. Wherefore, just as to those who should look out from the globe of Saturn the Earth would sometimes seem to progress, while it went through the [one] half of the circle above the Sun, sometimes to regress, while it went through the other half, roughly; but to stand [still] at two points, namely the terminal [points] of the Direct and Retrograde course: So it is necessary that, to us looking out from the Earth, Saturn seem to be turned into the opposite directions, and so to regress just when, to one looking from Saturn, the earth would seem to regress; and Saturn to progress when the Earth [seems] to progress,” etc. And he proceeds, saying: “The inferior [planets], Venus and Mercury, seem to regress for this [reason], because they are swifter; whence [it follows] just as if the Earth stood unmoved, [that] Venus, running in the more remote part of the circle, describes a way plainly contrary to that which it accomplishes in the part of its circle near the Earth.”
[Margin: Galileo’s opinion on the cause of the Retrogradations.]
To this is added Salviati, or rather Galileo, who (in Dialogue 3 On the System of the World, p. 252 of the Latin version), when he had said, “In the Ptolemaic system [there] are diseases, and in the Copernican [there] are medicines,” a little after added: “But what shall we say of the apparent motions of the Planets, so deformed that not only are they now swift, soon slower, but sometimes even become altogether stationary, and even retrograde through a long space? To save which appearance, Ptolemy introduced the greatest Epicycles, adapted to the individual Planets, with certain rules of the anomalies, or of incongruous motions—all of which are removed from the midst by the single, most simple, motion of the earth.” But, some words being interposed, Sagredo answers in the same place that these retrograde and stationary motions had always seemed to him improbable, and that he therefore wished that it be explained by what method the system of Copernicus excuses them; which Salviati does presently, and we [did], as I said (bk. 7, sect. 5, ch. 4, num. 3).
[Margin: Gassendi’s concurrence.]
But the same cause why the Luminaries do not seem to retrograde, while the rest of the Planets do seem [to], Gassendi elegantly pursues (Epistle 2 On impressed motion, p. 145).
[Margin: Second Imperfection, removed by the annual motion of the Earth.]
[VII.] The second imperfection or inequality, which seems to be in the motion of the five lesser Planets, and which is removed by referring the true cause of such a phenomenon back to the annual motion of the Earth, is that which Copernicus (bk. 1, ch. 10, toward the end) thus insinuated: “For hence one may note—the contemplator not [being] sluggish—why a greater progress and a smaller regress appears in Jupiter than in Saturn, and a smaller than in Mars; and again, a greater in Venus than in Mercury. And [why] such a reciprocation [back-and-forth] appears more frequent in Saturn than in Jupiter; rarer still in Mars and in Venus than in Mercury.” For we have already taught (bk. 7, sect. 5, ch. 2) that the arc of direction of Saturn is smaller than that of Jupiter, and [that] of Jupiter than of Mars, and greater in Venus than in Mercury, a twin table of this diversity being added; and in the same place (num. 5, prop. 2) we added the cause why the Stations and Retrogradations of Saturn recur more often than those of Jupiter, and of this [Jupiter] than of Mars, and of Mercury than of Venus.
[Margin: Third Imperfection, removed by the annual motion.]
But since Ptolemy tried to explain these [things] by attributing a greater Epicycle to Mars than to Jupiter, and to Jupiter than to Saturn, and to Venus than to Mercury, he seemed to multiply motions and instruments, and yet not to have rendered the true cause of these inequalities; since a greater Eccentric of Saturn would seem to demand also a greater Epicycle. Whence a Third imperfection arises in the Ptolemaic hypothesis, but [is] removed by Copernicus. Hence that reproach of Kepler (ch. 1 of the Mystery): “Thus it could be asked (but with Ptolemy answering nothing) why in the great orbs there are such tiny Epicycles, and why in the small orbs such huge [ones]“—that is, inquire parà toùs prosgeíous [in respect of the perigees] of Mars, etc.—that is, why, among the superior [planets], Mars is greater than Jupiter, and this [Jupiter] greater than Saturn? And why does not Mercury too have a greater [epicycle] than Venus, since it is inferior to Venus—since, of the four remaining, the inferior always has the greater?
[Margin: Kepler’s second commendation for the annual motion of the Earth.]
Here the answer is easy: namely, in the hypothesis of Copernicus (from which he renders the cause of these vicissitudes), because, namely, as each of the Superior [planets] is nearer to the Earth’s annual orb, so the annual orb has a greater proportion to it, and appears greater: Mars, therefore, nearest to the Earth’s orb, has in its Radius more such parts (of which the Radius of the annual orb is 100000) than Jupiter, and this [Jupiter] than Saturn; and therefore the prosthaphaeresis [parallactic equation] arising hence is greatest in Mars, middling in Jupiter, least in Saturn. But now, [as for] those which the ancients thought to be Epicycles in Mercury and Venus, those, in reality, in the hypothesis of Copernicus, are Eccentric Orbs; and to Mercury, as the swiftest, the smallest orb belongs, and a smaller than to Venus. Thus he; who presently adds a certain Fourth [imperfection]—or [rather] necessity—in these Retrogradations, of which the true cause the hypothesis of Copernicus alone seems to bring [forward].
[Margin: Fourth Imperfection, removed by the motion of the Earth.] [Margin: Kepler’s third commendation for the annual motion.]
“Likewise,” he says, “the ancients wondered, not without reason, why the three superior [planets] are always lowest in their Epicycle (understand: and Retrograde) when in opposition with the Sun, but highest in conjunction: so that, if the Earth and the Sun and Mars are in the same line, why Mars cannot then be in another place of the Epicycle than in the Perigee. In Copernicus the cause is easily rendered. For it is not Mars in [its] Epicycle, but the Earth in [its] orb, that causes this variety,” etc. For Mars could be moved in the Epicycle into the preceding [signs], and thus turn out direct in opposition, and retrograde in conjunction with the Sun; nor can the cause be rendered through the Epicycle why this motion was not made in this manner, but one only has recourse to the effect and experiment a posteriori.
[Margin: Gassendi’s confirmation of the aforesaid causes.]
But since Gassendi has treated these arguments not inelegantly, and it is expedient to inculcate this argument in various ways, that its force may be more clearly set forth, it pleases [me] to repeat from him, in other words, the things which have been said thus far. [VIII.] And so Gassendi (Epistle 2 On motion impressed by a translated mover, p. 145) thus argues for the annual motion of the Earth. “Then, whether, concerning the three more remote than Mars too—namely Jupiter, Saturn—we should say: what is the [reason] why they never appear retrograde except when they have the Earth interposed between themselves and the Sun? Or why [they are] always retrograde when they have [it] interposed? Why is the Epicycle of Mars greater than the Epicycle of Jupiter,
[…continues on p. 342 (PDF 377) with the catchword “Iouis”: ”…[Epicycle of] Jupiter”—the rest of Gassendi’s questions and Riccioli’s reply to the Second Argument.]
(printed p. 342 — within Chapter IX, completing the Second Argument (imperfection of celestial motions): Gassendi’s exposition of the planets’ stations and retrogradations as merely apparent under heliocentrism is cast in syllogistic form. Riccioli gives four responses, denying that retrogradation is an imperfection, noting that every famous system renders an a-priori cause of these phenomena, and retorting that heliocentrism makes all earthly bodies really stationary and retrograde twice daily — a greater absurdity.)
[Header: BOOK IX. SECTION IV. — 342]
[the Epicycle of] Jupiter, and this [of Jupiter] greater than the Epicycle of Saturn? And after a few [words]: Why is Mars, so much swifter through the Eccentric than Jupiter, so much more sluggish through the Epicycle, and in the same proportion Jupiter than Saturn, and so of the rest?” But he answers at once that [these things] necessarily so appear, the Earth advancing between the Sun and them: for, although both they and the Earth always progress toward the East, it is nevertheless brought about that, because the Earth is moved more swiftly than they, while [the Earth], approaching from afar, is about to pass near them, or to interpose itself between them and the Sun, they seem to it [now] to advance more slowly than before; and when it approaches as if in a straight [line], they appear as if to stand [still]; and thereupon also to retrograde—since [the Earth], proceeding more swiftly, gradually leaves them behind, so that the retrogression appears greatest when [the Earth] is nearest [them], and has them directly opposite; and afterward [the retrogression] appears gradually to decrease, until, while [the Earth] departs from them along as it were a straight line, they seem again as if to stand [still]. But after the second station they appear to advance directly and more and more swiftly; because thereafter the Earth, as about to pass beyond the Sun, observes them progressing along the series of the Signs—[they] who, in the opposite situation, seemed to go against the same series. Hence, therefore, it is, why they cannot appear retrograde except in opposition with the Sun, etc. Hence why the Epicycle of Mars seems greater than the Epicycle of Jupiter: namely, because, on account of [Mars’s] greater nearness, the retrogradation in it begins to appear nearer [sooner] and ceases later [farther], etc. Hence why Mars is retrograde only once in a biennium [two years]—inasmuch as the Earth, not advancing except twice as swiftly, cannot overtake it except in double the time in which it completes its [own] period. Hence why Jupiter each year runs through [its course] and is made retrograde, and that only one month later [each time]; because, namely, the Earth is twelve times swifter, and always overtakes it—once left behind—in the thirteenth month. Hence why Saturn too each year is made retrograde, and that scarcely later by half a month—because, namely, the Earth is thirty times swifter, and, having departed from it, overtakes it again in the twelfth month, and scarcely by a half [month] besides. With these foundations, therefore, premised, let us build up the following argument.
[Margin: Second Argument, in Form.] [Margin: Proof of the Major.]
[IX.] “That hypothesis is to be preferred to the others in which alone the imperfections of the Stations and Retrogradations are not real but merely apparent, and through which alone a reason a priori is rendered both of the aforesaid Stations and Retrogradations and of the other diversities annexed to them. But of this kind is the hypothesis of the Earth advancing annually between the three superior and the two inferior Planets: Therefore this hypothesis is to be preferred to the others.” The Major is evident to any well-disposed Intellect; for who would not concede that it is better that, if any imperfection occurs in the celestial motion, it be rather apparent than true and real? Who, likewise, would be so álogos [ἄλογος, irrational], as to prefer to stumble in the darkness of that hypothesis along an ever-blind path—[a hypothesis] which cannot bring forward the causes of such appearances—than [to walk] in the light of that [hypothesis] which can demonstrate them?
[Margin: Proof of the Minor.]
The Minor has already been shown above by an induction made both from the Stations and Retrogradations themselves [taken] in themselves, and from the diversities which are connected with them—of which kind are [these]: that these vicissitudes are more frequent in Saturn than in Jupiter, and in Jupiter than in Mars; likewise that the arc of Direction of Saturn is of more degrees than that of Jupiter, and [that] of Jupiter than of Mars; likewise that of Saturn (whose Eccentric is greatest) the Epicycle—or its proportion with the annual orb—is least, and [that] of Mars (whose Eccentric is least among the three superior [planets]) the Epicycle is greatest, but [that] of Jupiter middling; and [that] the Equation of the second inequality is greatest in Mars (the lowest of the superior [planets]), and yet least in Mercury (the lowest or innermost of the inferior [planets]); likewise why they are always retrograde in the situation nearest the Earth, and direct in the most remote, nor could it have happened otherwise. Finally, why the Luminaries are incapable of Station and Retrogradation. For of all these a simple and open reason is rendered through the annual motion of the Earth compared with the proper motion of each Planet under the Zodiac.
[Margin: First Response.]
I answer, first, by distinguishing the Major, and denying and conceding it under exactly that distinction by which I distinguished the Major of the 1st argument of this chapter (proposed in num. 5); and in the same way [I answer] to the Minor—just as if that response were here inserted verbatim.
[Margin: Second Response.]
I answer, secondly, by conceding the prior part of the Major, if the apparent Station and Retrogradation in the Planets be an imperfection; [but] denying [it], if it be not an imperfection, but a great perfection in their motion—the end to which it is ordained being regarded, and the vicissitude of effects in the sublunary nature depending on them. For who would say that in harmonic concords and in rhythmic dances [there] are imperfections—which they call Pauses [rests]—and the retrocessions or recurrences of the little syllables, of the sounds, of the dance-steps, etc.? or, in Dialectical discourse, the progress from causes to effects, and the regress from effects to demonstrate the causes?
[Margin: Third Response.]
I answer, thirdly, the Major being granted meanwhile, by denying the Minor: for it is one thing that a single and simple cause be brought forward at first sight (and thus to repeat the first argument of this chapter, to which sufficient reply has been made); [it is] another that in this hypothesis alone a cause of such appearances be brought forward. But all the hypotheses hitherto famous—whether Ptolemy’s, or Magini’s, or Tycho’s, or Ours—render a cause a priori of these Phenomena, though not in the same way, nor in that [way] which the Copernicans wish. For what these [Copernicans] perform by the motion of the Earth compared with the motion of the five lesser Planets under the Zodiac, the others perform by the motion of the Sun, compared with the motion of the same Planets (the Earth standing still), but by an Epicycle borne by an Eccentric, or by a Spiral, or by another equivalent orb; and in the Ptolemaic [system] indeed the Planets never really stand [still] or retrocede in their orbs, if you place the eye in the center of those Epicycles, but always progress into the consequent [signs] of the Signs: not otherwise than the Copernican Earth, viewed from the Sun as the center of the annual orb—granted that, if it [the Earth] too were viewed from elsewhere, it would seem sometimes to stand [still] under the Fixed [stars], sometimes to retrograde. But in the Tychonic hypothesis, as Kepler confesses (bk. 4 of the Epitome, pp. 535 and 537), the absurdity of the Retrogradations is avoided, if the Sun be established to be the center of the planetary system and to carry with it the centers of the orbs of the five lesser Planets; and [that] in this same way Astronomy is freed from two superfluous Eccentrics of Mercury and Venus, and the three great Epicycles of Mars, Jupiter, [and] Saturn. And so, if the cause of these appearances is the concurrence of motions, or the comparison—on the one hand of the lesser Planets, on the other of the Sun or of the Earth—then the annual motion of the Sun can equally be received among the causes a priori, as [can that] of the Earth; for either is sufficient to represent them—with this difference, however, that the motion of the Sun, as being evident to sense, has already pre-occupied possession among the judgments of most of the Wise. But the Copernican sect seems to be of too dainty a temper, to which neither the motion of the Sun nor any other, except [that] of the Earth, tastes [of] a genuine cause a priori of such phenomena; which taste the simplicity of the annual motion of the Earth sharpens—[a simplicity] greater at first sight, but in depth far less, on account of the many other motions which it involves with itself, as I have already said (num. 5, in the 2nd response). But in reality the motion of the Sun is much simpler, while it overtakes the superior Planets, or recedes from them, or while it carries with it the Epicycles of Venus and Mercury by the same single motion (for in this the hypothesis of Ptolemy must be corrected).
[Margin: Why the Luminaries are not retrograde.]
But the cause why the Luminaries are not retrograde has been sufficiently assigned by us (bk. 7, sect. 5, ch. 3, Theorems 3 and 4).
[Margin: Fourth Response, very notable.]
I answer, fourthly, by retorting the argument: for from the annual motion of the Earth, mixed with the diurnal, it follows that all points of the Terrestrial globe placed outside the center, and all terrestrial, watery, or semi-aerial bodies which follow the motion of the earth—whether fixed to the earth, or torn away, or hanging—turn out really, each day, twice stationary (as to the diurnal motion), once direct, and once retrograde, and yet this is not perceived; but that the Moon, in each month—as to its monthly motion mixed with the annual [motion] of the earth’s center—turns out, at the quadratures, Stationary; but between the 1st and 2nd quadrature, Direct; between the 2nd [of one lunation] and the 1st of the following Lunation, Retrograde; and at the Full Moons Swiftest, at the New Moons Slowest (as to this motion indeed); and yet not even this itself appears to us: as I have already said (ch. 6, toward the end of num. 18), and shall say (ch. 19, num. 12); and Galileo himself admits [it], according to what is to be said (ch. 14, num. 4). Now if it is absurd to posit in the celestial bodies a real Retrogradation and Station—since the Earth, with its cognate bodies, is placed in the number of the Planets, and they are said to be engaged in their [own] heaven with respect to the center of the Universe—then surely it is a greater absurdity to posit, in innumerable bodies diverse in number and kind, a retrograda-
[…continues on p. 343 (PDF 378) with the catchword “nem”: ”…[retrogradatio]nem ac Stationem”—the close of the Fourth Response and the Third and Fourth Arguments.]
(printed p. 343 — within Chapter IX. Closes the Second Argument, then gives the Third Argument, from other astronomical phenomena explained a priori by the Earth’s annual motion (the equal eccentric revolutions of Sun, Venus, and Mercury; the telescopic phases of Venus and Mercury; the outer planets’ size-variation between opposition and conjunction); Riccioli answers that the reformed-Ptolemaic and Tychonic systems give the same a-priori cause. The Fourth Argument, from the latitude and inclination of the lesser planets, opens with Rheticus’s encomium of Copernicus’s Great Orb.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 343]
[a retrograda]tion and Station, and indeed so frequently that it is daily, and yet [one] which can be perceived by no observations, and proved a posteriori; but in the Moon to assert the same [thing] each month—than to posit, in fewer other Planets, a rarer Retrogradation and Station, and indeed [one] founded on observation. Or, if that [former] is not absurd, neither ought this [latter] to be absurd. There is, therefore, no [reason] why the Copernicans should so often inculcate this argument.
Third Argument, from the Cause which is rendered a priori, of certain other Astronomical things, through the Annual motion of the Earth alone
[Margin: Why do the Eccentrics of the Sun, Venus, and Mercury have the same motion as the Sun?]
[X.] “This single motion of the earth being substituted,” says Kepler (ch. 1 of the Cosmographic Mystery), “the causes of very many things are rendered, which Ptolemy could not render from so many motions of the heaven. For, first, of Ptolemy it could be asked, how it comes about that the three Eccentrics—of the Sun, of Venus, and of Mercury—have equal revolutions? For it is answered that they themselves do not truly revolve, but, in their stead, the single Earth.” Besides, as the same [Kepler] notes (in the Epitome of Astronomy, bk. 4, p. 535), what was guessed by Martianus Capella, Campanus, and others—namely Vitruvius, Macrobius, [and] Bede—Galileo has now demonstrated, in his Sidereal Messenger, from [things] observed through the Telescope in Venus; and Simon Marius in Mercury; and we in both: [namely,] that Venus and Mercury, when they advance direct and become nearer to the morning Conjunction with the Sun, appear small and round; but when they turn out retrograde, and are near to the evening conjunction, appear very large and sickle-shaped, or horned: of which phases we have given the diagrams and proofs (bk. 7, sect. 1, ch. 2). And hence it is evidently gathered that they are thus illuminated by the Sun, so that they go around it. But it seems incongruous that these Planets are borne now above, now below the Sun; which incongruity is removed if the annual motion of the Earth be posited—for then their ascent and descent is merely apparent, according as the Earth becomes more remote from or nearer to them as they go around the Sun.
[Margin: Venus and Mercury appear now below, now above the Sun.]
[XI.] Likewise it seems unfitting to the constancy of the celestial motions that the three superior Planets are sometimes scarcely equaled to little stars of the second magnitude—and that when they come to conjunction with the Sun; sometimes equal or surpass stars of the first magnitude—and that when they come to the Sun’s opposition; of which diversity the cause cannot be brought forward by the ancient hypotheses, but is at once brought forward by the single annual motion of the Earth, which, when it interposes itself between them and the Sun, approaches them, and therefore sees them much larger than when it recedes from them, so that the Sun is interposed between it and the Planets.
[Margin: Copernicus’s opinion on why Saturn, Jupiter, [and] Mars appear larger at opposition.]
“For hence one may note,” says Copernicus (bk. 5, ch. 10), “that Saturn, Jupiter, and Mars, [when] acronychal [rising at sunset], are nearer to the earth than around their occultation and apparition [near the Sun]. But most of all Mars, made [to shine] all night, seems to equal Jupiter in magnitude—distinguished only by [its] ruddy color; but there [near conjunction] it is scarcely found among the stars of the second magnitude,” etc. “All which proceed from the same cause, which is in the motion of the earth.” The same [point] Gemma Frisius pursues, in a certain Epistle given to Johannes Stadius at Louvain, on the day before the Calends of March of the Year 1555, asserting that the hypotheses of Ptolemy do not have such evident causes tōn Phainoménōn [τῶν φαινομένων, of the phenomena] as the Copernican have. “For that the three superior Planets,” so he proceeds, “achrónychoi [ἀχρόνυχοι], or placed diametrically opposite the Sun, are always in the perigee of their Epicycle—Ptolemy assumes [it], and this is the tò hóti [τὸ ὅτι, the ‘that’]. But the hypotheses of Copernicus necessarily infer it, and demonstrate the dióti [διότι, the ‘why’].” And so Ptolemy teaches the mere That, but Copernicus [teaches] the Wherefore itself. Finally, Kepler strikes this same chord, in his Cosmographic Mystery (ch. 1), when he says: “Likewise, not without reason did the ancients wonder why the three superior [planets] are always lowest in their Epicycle when in opposition with the Sun, [and] highest in conjunction,” etc. “In Copernicus the cause is easily rendered. For it is not Mars in [its] Epicycle, but the Earth in its orb, that causes this variety.” Let, therefore, the form of this argument be such:
[Margin: Third Argument, in Form.]
[XII.] “That hypothesis is to be set before the others which, either alone or more evidently, renders a reason a priori why Venus and Mercury have the same motion as the Sun, and appear now round above the Sun, now sickle-shaped below the Sun; but Saturn, Jupiter, and Mars appear, always in opposition with the Sun, nearest to the Earth, and so largest, but in conjunction with the Sun, most remote and smallest. But such is the hypothesis in which the Earth is carried around the Sun by an annual motion: Therefore, etc.” The Major is plain of itself. The Minor too remains sufficiently proved from what was said (nums. 10 and 11).
[Margin: First Response.]
I answer, first, by exactly that distinction which I used in the first response to the first argument of this chapter—which re-read from num. 5, and hold [it] just as if it were transcribed hither.
[Margin: Second Response.]
I answer, secondly, the Major being granted, by denying the Minor. For both in the Ptolemaic (but as reformed by us) and in the Tychonic hypothesis, a reason of the aforesaid Phenomena is rendered no less evidently: for it is certain, both in the Copernican and in our [system] and the Tychonic, that Venus and Mercury go around the Sun and follow it as the center of their motions; and from this, as a true cause a priori, it follows that—whether to the Earth resting (but with the Sun moved annually around the Earth), or [to Venus and Mercury] carried around the resting Sun—they appear now round and slender, now large but sickle-shaped, and why they are moved by the same single eccentric motion: nor is the cause of this phenomenon more the Earth by an annual motion than the Sun by an annual motion: nay, if other things were equal, in this the Sun’s motion is superior, that it is more evident to our sense—so much so that, as long as we are not convinced of the opposite, we ought rather to assert it. Likewise it is false, what is imputed to Ptolemy—namely, that he assumes the three Superior Planets, in the acronychal position (or in opposition with the Sun), always to be perigee [nearest to the earth], and in conjunction apogee [most remote], and brings forward no cause of this antithesis [opposition]: for he confers a cause, in the motion of them through the Epicycle into the consequent [signs], attempered to the annual motion of the Sun. But Tycho confers the cause [upon] the Eccentric orbs, but [ones] carried around by the Sun.
[Margin: Kepler’s confession for the Tychonic hypothesis.]
Which I wish to be confirmed by no other [words] than the very words and confession of Kepler himself: for he, in the Epitome of Copernican Astronomy (bk. 4, p. 537), has thus: “Now, as concerns the three superior [planets], Aristarchus, Copernicus, and Tycho Brahe demonstrate that, if we establish them too [as moving] around the Sun—and the Sun as a kind of common center of the five Planets, so that the motion of the Sun, whether true or apparent, holds [embraces] the whole five orbs of the Planets—we are freed, as before in Venus and Mercury [from] two superfluous Eccentrics, so now in the three superior [planets, from three] Epicycles.” But what he adds—that the consent which the aforesaid planets have with the motion of the Sun is “blind and incredible”—is said gratuitously; and it [that consent] is much more credible than the annual motion of the Earth, or that magnetic attraction by which he [Kepler] wishes it [the Earth] to be led around by the Sun. But if Ptolemy perpetually carried Venus and Mercury below the Sun, this has now, after the use of the Telescope, been removed from his hypothesis.
Fourth Argument, from the Latitude and Inclination of the lesser Planets to the Ecliptic
[Margin: Rheticus’s encomium for the Great Orb.]
[XIII.] This argument I once indicated (bk. 7, sect. 4, ch. 5, schol. 3). But Rheticus extends it much more at length in his First Narration (nearly the third page before the end), where, bringing forward the reason why the annual orb of the Earth was called by Copernicus the GREAT [orb], he says: “It was called the Great Orb for this [reason], because it has, both to the orbs of the superior Planets and to the magnitude of the inferior, a notable [proportion], which is the occasion of the chief appearances”: then he subjoins: “Moreover, in the latitudes of the Planets it is first to be seen how rightly the name of ‘Great’ is attributed to the [orb] carrying the center,” etc. “The motions of the Planets in longitude furnish indeed excellent testimonies that the Earth describes the center [as] the Orb which we call Great: but in the latitudes of the Planets, its uses—as [those] of [something] placed in a certain illustrious place—are more conspicuous; since it [the Great Orb], nowhere departing from the plane of the Ecliptic, is nevertheless the chief cause of all the diversity of the appearances in latitude.” He then pursues the doctrine of the latitudes, and, in the whole two last pages, shows how, through the approach of the Earth to the Planets, the angles of the inclinations are optically augmented—which the Ancients thought [to be]
[…continues on p. 344 (PDF 379) with the catchword “tarunt”: ”…[pu]tarunt”—the rest of Rheticus’s latitude-doctrine and Riccioli’s reply to the Fourth Argument.]
(printed p. 344 — within Chapter IX, the Fourth Argument (latitude and inclination): Kepler’s claim that the planets’ latitude-variations and Ptolemy’s librations vanish if the Earth moves is cast in form. Riccioli replies that the Tychonic hypothesis with parallel planes saves the constant inclination equally, and that Kepler himself showed both Ptolemy and Copernicus erred, the planes being simply parallel to the Ecliptic — provable in the Tychonic and corrected-Ptolemaic systems too.)
[Header: BOOK IX. SECTION IV. — 344]
[the Ancients thought to be] increased on account of the position of the Planet in the perigee of the Epicycle, and many other things connected with these, which it is not necessary to transcribe here.
[Margin: Kepler’s opinion for the latitude of the Planets in the hypothesis of a moving Earth.]
[XIV.] This same [point], by a briefer discourse but not once [only], Kepler urges: for in ch. 1 of the Cosmographic Mystery he said: “Likewise, on account of this same approach of the earth to the planets, and recession, in its orb, the very latitudes of the five Planets seem to us to receive some variety; which libration, that Ptolemy might save [it], it was necessary for him to establish five other motions: all of which fall [away], a single motion of the earth being posited.” Again, in the Epitome of Copernican Astronomy (bk. 4, p. 537), he affirmed that by the annual motion of the earth very many entanglements in the motion of latitude are removed from the Theoretical doctrine; and (p. 543) he did not hesitate to say: “If, with the earth standing [still], the Epicycles go around—whether according to Ptolemy, or according to Brahe—it will be necessary that those Epicycles, especially of the inferior [planets], variously shake both [their] sides and [their] head and feet—that is, librate doubly; but, with the Earth going [moving], all the orbs are most constantly inclined to the Ecliptic.” But in bk. 6 of the same Epitome (p. 771), he inquires whence it is, that Ptolemy made the Epicycles of the Planets librating by a double reciprocation, although nevertheless, from the more recent observations which he had adduced in Mars (ch. 14), the inclination of them is found fixed and constant? And he answers that this came about from the unknown annual motion of the earth: for Ptolemy beheld the limits of the Planetary orbit extended toward certain parts of the Fixed [stars]—which [limits], although in reality they constantly decline from the plane of the Ecliptic, yet, with the Earth going around, the orbit of the Planets seems to extend now its boreal limit, now its austral, now its nodes, toward the Earth. But Ptolemy transcribed the circuit of the Earth to the center of the Epicycles of Venus and Mercury annually running through the Zodiac, and in this Epicycle he called that point which at any time is extended toward the earth the perigee, as though it were unique, although in reality all the parts of this Epicycle in order—(which Copernicus calls the Eccentric)—become perigee successively, by accident. Thus it came about that to Ptolemy the so-named perigee seemed, by a certain libration, to be now in the North, now to be in the Ecliptic itself, now in the South. Which doctrine being handed down, he subjoins this exclamation: “And behold, a most evident argument for the annual motion of the Earth around the Sun. For since the Eccentrics of the Superior [planets] have fixed inclinations to the Ecliptic, why should the Eccentrics of the Inferior alone be established [as] librating, with a double libration—since of itself every libration of orbits is absurd, because it begets a tortuous path of the planet instead of a circular one? As much probability, therefore, as the fixed inclination has, so much does the motion of the earth gain thence; but as much absurdity as the double libration [has], so much also does the immobility of the earth totter.” Gathering, therefore, the argument into its formula, it stands thus:
[Margin: Form of the Fourth Argument.]
[XV.] “That hypothesis is to be set before the others through which the latitudes of the five lesser Planets retain a constant angle of inclination to the Ecliptic, without libration of the orbits and tortuosity of the planetary path. But of this kind is the hypothesis of the Earth alone, annually carried through the great orb. Therefore.” The Major, at least other things being equal, is evident; for motions are not to be multiplied in vain, much less librations and windings of motions, if the celestial phenomena can be saved otherwise, and without those entanglements. The proof of the Minor has been sufficiently insinuated from what was said (nums. 13 and 14); for by the Earth’s approach to the Planets alone, and [its] recession, the variety of the angle occurs by which the orbits of the Planets are inclined to the Plane of the Ecliptic; nor, without this motion of the earth, does it appear how, without other entanglements, that variety can be made and explained.
[Margin: First Response.]
I answer, first, to the Major, by exactly that distinction which I brought forward in the first response to the first argument of this chapter (from num. 5)—which, because it is of great moment, I am neither ashamed nor weary to employ and repeat so often.
[Margin: Second Response.]
I answer, secondly, the Major being granted, by denying the Minor: for both by a single spiral motion toward the sides of the world (made, with looser and tighter coils, by an Intelligence), and in the Tychonic or Danish hypothesis, that constancy of the Inclination can be saved by the aid of the parallelism of the planes, as is plain from the Theory of latitudes of Longomontanus, which we expounded (bk. 7, sect. 4, ch. 4). But that Ptolemy erred in the measure of the inclinations and latitudes, being destitute of suitable observations, this does nothing against the hypothesis of a resting Earth viewed in itself: for the Earth, annually carried through the plane of the Ecliptic—by this very fact, that it is always with its center in the plane of the Ecliptic—cannot vary the latitudes of the Planets, except by optically augmenting the angle of inclination by its approach, and diminishing [it] by its recession; the other [things] which pertain to the latitudes and the regions of latitude, and the motion of the Nodes (deduced from observations), must be saved by some other theory than by the annual motion of the Earth in the Ecliptic. Now if the Planets so attemper their own motion of latitude too to the annual motion of the Sun, that they obtain an equal latitude, and of the same disposition, by this motion as by the motion of the Earth—and so that the inclination of the planetary orbit to the Ecliptic, geometrically derived from such latitude, be perpetually of the same measure (that is, so that the plane of the Epicycle be always parallel to the plane of the Ecliptic)—it will not be necessary that this be performed by the annual motion of the Earth. For Copernicus now confesses that all the Phenomena, in both ways, as to the substance of the truth, can stand saved in either hypothesis. And, that you may see that errors, or the inconstancy of the latitudes and inclinations, do not arise from the hypothesis of a resting Earth in itself, nor [does] the constancy and truth [arise] from the hypothesis of a moving Earth, it pleases [me] to show, from Kepler himself, what, in this matter, not only Ptolemy, but also Copernicus, erred—[and to teach it] through those things which Kepler himself hands down in the Commentaries on Mars (ch. 14), whose title is: “The Planes of the Eccentrics are ATALANTA [ΑΤΑΛΑΝΤΑ]“—that is, Non-librating. First, therefore, he begins thus: “The perplexity of his hypothesis imposed upon Ptolemy [the necessity] that he heaped up many monsters in the doctrine of latitudes. For when he weighed [considered] that the plane of the Epicycle is twisted in all directions, and did not immediately see, through those clouds of his hypothesis, that the plane of the Epicycle is parallel to the plane of the Ecliptic, he feigned a triple latitude, and—that contraries might be propped by contraries—he entirely dislocated his Epicycle from its parallel situation; nor from the credit of observations (which he did not have so frequent), nor from the measure of them where he had [them] (because, distrustful of certainty), he chose the means [middle values], placing the extremes in error.” Hence you may see that, in the customary calculation—say, in Magini’s Ephemerides—no conjunction of Mars and the Sun occurs at all which is not (as they say) “through the body” [central]. But if this be true, in vain would nature have feigned a tempering of the latitudes, lest, by bodily conjunctions frequently occurring, there should be excessive agitations of the sublunary powers. Thus far concerning Ptolemy—nay, also concerning Magini, who, although he uses Copernican numbers, nevertheless adheres to the Ptolemaic hypothesis. But presently, concerning Copernicus, he proceeds thus: “Copernicus, himself ignorant of his [own] riches, took it upon himself to express Ptolemy entirely, not the nature of things—to which, however, he had approached the nearest of all.” On which matter read Rheticus in his narration. For [Copernicus], rejoicing that, by his [posited] approaches of the earth to the stars, the kinds of latitudes are increased, nevertheless did not dare to reject the residual Ptolemaic augmentations of the latitudes (which this approach of the earth would not attain); but, that he might express those too, he feigned librations of the planes of the Eccentrics, by which the angle of inclination (constant and fixed for Ptolemy) would be varied—and that [variation] (which is monstrous-like) not according to the laws of the motions of [the planet’s] own Eccentric, but of the earth’s orb, plainly alien [to it]; see Copernicus (bk. 6, ch. 1). Behold, then, [that] from the mere hypothesis of a moving Earth the librations of these planes are not avoided, unless, from surer observations, the quantity of the latitudes be first emended. Now let us see whether, in the Tychonic too—and the Ptolemaic, but corrected—hypothesis, that constancy of the inclinations can remain saved. Kepler, therefore, proceeds in the same chapter; and when he had said that he, from the Tychonic observations had about Mars, and in the preceding chapters, had demonstrated—and would prove below (part 5 of the Commentaries) by several arguments—that the declination of the orbit of Mars from the Ecliptic is everywhere constant, and that there is no libration of the inclinations of the Eccentric of Mars, from the observations of Mars almost alone, he thus concludes universally: “And so let us most firmly conclude that the inclination of the planes of the Eccentrics to the Ecliptic—(for why should I not conclude in general what has no cause for being in one single planet [alone]? although I have demonstrated the same, both in Venus and in Mercury, from observations)—varies plainly nothing at all.” And let him who follows Ptolemy learn hence that the plane of the Epicycle is perpetually parallel to the plane of the Ecliptic. It suffices, therefore, for removing the entanglements of the librations and conserving the constancy of the inclinations, if [the planes]
[…continues on p. 345 (PDF 380) with the catchword “plano”: ”…[if the planes be parallel] to the plane of the Ecliptic”—the close of the Fourth Argument, then the Fifth Argument (the Equant), the end of Chapter IX, and the opening of Chapter X.]
(printed p. 345 — closes Chapter IX with the Fifth Argument, from the equant removed by the Earth’s annual motion (Rheticus, Copernicus, Galileo), answered: the equant is not absurd, and its incongruity is removed in the Tychonic and Ricciolian systems too. Chapter X then opens, dissolving the first two of five arguments from motions of other heavenly things: the fixed stars’ supposed seasonal variation (an arbitrary fiction) and the satellites of Jupiter (at most proving the Sun centers the Jovian system).)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 345]
[if the planes of the Ptolemaic Epicycles] (or of the orbs substituted for them) be always parallel to the plane of the Ecliptic, whether this be done with the earth moving or resting; nor is the perigee of the Planet, in which a greater latitude appears, made more by the approach of the Earth to the Planet than [by the approach] of the Planet to the Earth.
Fifth Argument, from the Equant removed by the Annual motion of the Earth
[Margin: Rheticus’s opinion against the Ptolemaic Equant.] [Margin: And Copernicus’s.]
[XVI.] This argument is very slight, as will be plain from its solution: and yet Rheticus too called it in [as an advocate], in his First Narration, when, concerning the annual motion of the Earth introduced by Copernicus, he says: “By this single method, the Lord Teacher saw, it could conveniently come about that—what is most proper to circular motion—all the revolutions of the circles in the world should be moved equally and regularly upon their own centers, and not upon alien [ones].” Nay, Copernicus himself (bk. 5, ch. 2), discoursing against the hypotheses of the Ancients, said: “They concede, therefore, here too, that the equality of circular motion can come about around an alien center, and not [its] own,” etc. “These and similar [things] furnished us an occasion of thinking, both about the mobility of the earth and in other ways, by which the equality and the principles of the art [astronomy] might remain, and the account of the apparent inequality be rendered more constant.” Finally, Galileo (Dialogue 3 On the system of the world) introduces Salviati speaking thus (p. 252 of the Latin version): “Will not all the sect of the Philosophers say that this is a great incongruity—that some body, mobile in a gyre, should be moved irregularly upon its own center, and regularly upon some other point? But such deformed motions exist in the Ptolemaic fabric of the world; whereas in Copernicus all the motions are equable around their own center.” Let the argument now be formed in this manner.
[Margin: Fifth Argument, in form.]
[XVII.] “That hypothesis is to be preferred to the others through which alone the absurdity of the Equant circle is removed—that is, of that [circle] in which the Planet is not moved, nor the center of [the orb] carrying the Planet, and yet around its [the equant’s] center the Planet is posited to be moved equally; But of this kind is the hypothesis of the Earth alone, annually moved: Therefore, etc.” The Major is plain from the Equality due to the celestial motions on their own [circles], but not on alien circles; otherwise, if they are moved equally on alien circles, it is necessary that they be moved unequally around their own center, and so have not only an Optical, but also a Physical or real inequality—which is absurd. The Minor is established at least by the authority of Copernicus, Rheticus, and Galileo, adduced a little before.
[Margin: First Response.]
I answer, first: If the Equant circle—that is, some real inequality in the motion of the Planets—be absurd, I concede the Major; if it be not absurd, I deny the Major: but that it is not absurd, but very congruent to them [the planets] with respect to [their] end, I taught in this book (sect. 2, ch. 4).
[Margin: Second Response.]
I answer, secondly, the Major being granted, I deny the Minor. For the incongruity—if any there be—of the Equant circle, or of the bisected Eccentricity, is removed also in the hypothesis of a resting Earth (as in the Tychonic, Danish, and Our [system]); and conversely it is not removed by the annual motion of the Earth [taken] in itself: which is manifest from this, that Kepler and Bullialdus—who most of all defend the annual motion of the Earth—nevertheless, the Eccentricity of the Planets being bisected, retained the equipollence of the Ptolemaic Equant, and, by moving the Planets in an Ellipse around the two foci, or navels [umbilici], of the Ellipse, conceded that the one inequality is Optical with respect to the one focus, the other Physical with respect to the other—as is clearly established from what was said (bk. 3, chh. 22 and 23; and bk. 7, sect. 2, ch. 5, nums. 12 and 13; where also—and bk. 7, sect. 2, ch. 1, scholio 2—I handed down much for the explanation and use of the Equant). Therefore the imperfection of the Equant, if there be any, is not of itself connected with the hypothesis of a resting Earth, nor of itself torn away from the hypothesis of an Earth going around.