[I.] The first and chief argument of the Copernican sect—and, as is said proverbially, [its] Achilles—is that which is derived from the incredible velocity of the Fixed stars, if they rather than the Earth were moved. Which velocity, that they may exhibit it [as] incredible, various [men] propose according to the various distance of the Fixed stars from the Earth.
[Margin: Maestlin’s calculation for the velocity of the Fixed stars.]
For Maestlin, in the preface to the First Narration of Rheticus, first assumes from Reinhold (who computes the Ptolemaic measures of the orbs) a distance of the Fixed stars of 25,000 semidiameters of the earth, from which, he says, it follows that a fixed star placed at the Equator of the heaven is, in one single second of an hour (in which little space of time you would scarcely utter three or four words in hurried speech), snatched more than fifteen hundred German miles. Then, assuming from Alfraganus a distance of the Fixed stars from the earth of 20,110 semidiameters of the earth—and so a diameter of 40,220 terrestrial semidiameters, to each of which he assigns 860 German miles—the diameter of the sphere of the Fixed stars comes out for him [as] 34,589,200 German miles; and, according to the proportion of the diameter to the periphery, or 7 to 22, he gathers the circumference of the sphere of the Fixed stars [to be] 108,708,914 German miles. These being divided by 24 hours, it follows that any Fixed star at the Equator runs through, in each hour, 4,529,538—that is, more than four million five hundred thousand German miles; and in each single minute of an hour 75,492—that is, more than seventy-five thousand; and in each single second, 1258—that is, more than twelve hundred German miles, of which 15 make one degree of the greatest circle on earth. Or, if we believe Cardano (bk. 5 On proportions, props. 58 and 218), and—often confirmed by experiments, says Maestlin—who says that in one hour the artery of a man of temperate nature pulses about four thousand times: it follows, he says, that in one beat of the human artery the aforesaid star runs through 1132—that is, more than eleven hundred German miles—and the prime Mobile yet more, if it be placed higher than the eighth sphere; which “exceeds all belief,” concludes Maestlin. Finally, in the Additions, or notes, to the same First Narration of Rheticus, p. 119 (it ought to be 115, but the printers erred), assuming a distance of the Fixed stars not [of] 14,000 [semidiameters, the] Tychonic [figure], but still a little less—namely, 13,500 terrestrial semidiameters—and so a diameter of the sphere of the Fixed stars of 27,000 semidiameters of the earth (that is, 23,220,000 German miles), he gathers the periphery of the celestial Equinoctial [to be] 72,977,143; which divided by 24 he computes, for each hour, 3,040,714 German miles; which again divided by 4000 beats of the human artery, there come out, for each beat, 760 German miles, to be traversed by any one star situated at the Equator of the eighth sphere.
[Margin: Maestlin’s rash opinion.]
“But this is far absurd to believe,” he there concludes; nay, a little after he does not hesitate to say: “Whether this is to be believed of a natural celestial body, and not to be accepted as absurd and simply impossible, anyone—if only he enjoy some use of reason—will judge. But all these and suchlike absurdities are far exiled from Copernicus’s hypotheses.” And so, if we listen to this man, we must either be mad and devoid of the use of reason, or surely we must judge that it was impossible for God, as the author of nature, naturally to concede so great a velocity to the Fixed stars, that in each beat of the human artery they should run through 760 German miles.
[Margin: Kepler’s calculation for the velocity of the Fixed stars or of the Earth.]
[II.] Let the disciple Kepler succeed Maestlin: who, first (in the Epitome of Copernican Astronomy, bk. 1, p. 107), affirms that it is more likely that nature should express a proportioned and small motion in the small Earth, than, in the vastest heaven, a motion incredibly swift, and which in swiftness should surpass [its] vastness by an immense ratio. For motion, no otherwise than magnitude, is a Geometric thing: “to great [things], therefore, slowness, and to small [things] swiftness, answers, not vice versa, as we learn in the Harmonics,” says he; and he goes on [to say] that, if the machine of the World were turned about the Earth, it would accomplish, in one minute of an hour, up to fifty thousand German miles, the Tychonic distance of the Fixed stars being supposed. But if the Earth is turned, those parts which are rotated in the greatest circle of all accomplish, in one minute of an hour, only 3 German miles and three-quarters: which space is not even a thirteen-thousandth, nor a twenty-thousandth, of the space to be run through by the Fixed stars. Again, in the same Epitome (bk. 4, p. 500), from the same swiftness he attempts to establish the diurnal motion of the Earth, saying: “For if the outermost sphere of the Fixed stars has at least 4,000,000 diameters of the Sun in [its] diameter, the long circumference will be 12,566,370 [solar diameters]; which, if the whole be turned within 24 hours, in one [hour], then, 523,600 will be turned; in one minute, 8727; in one second (which nearly equals a man’s pulse) there will pass 145 diameters of the Sun—of which each is not less than 13,000 German miles: and so, in the space of time in which the artery is once dilated and again contracted (the pulse [being] doubled), about seven million five hundred thousand miles of the greatest circle would be turned; and Saturn, with an orbit two thousand times narrower, will still cross nearly 4000 miles.” But here he uses the distance of the Fixed stars owed to the Copernican hypothesis (the annual motion of the Earth being supposed), which [figures] avail nothing against the hypothesis of a standing Earth, in which the distance and swiftness of the Fixed stars is much less. The same Kepler, moreover, in the book On the New Star seen in Serpentarius (ch. 16), had reasoned thus: if the Earth be moved by the diurnal motion, the parts situated at its Equator will accomplish, in one hour, 240 German miles; but because its center, by the annual motion, accomplishes 740 German miles each hour, if these be added to those, there come about 980—or nearly a thousand—German miles, which some city placed under the Equator would have to complete in one hour of midnight; and, a few [things] which do not concern our matter being interpo-
[…continues on p. 321 (PDF 356) with the catchword “sitis”: ”…[a few things] being interposed”—the rest of Kepler’s reckoning, then Galileo’s, Longomontanus’s, Lansberge’s, Mulerius’s, and Gassendi’s versions, Riccioli’s own calculation, and the argument in syllogistic form.]
(printed p. 321 — within Chapter VI, the “Achilles” (velocity) argument. Completes Kepler’s reckoning and surveys the further Copernican calculators — Galileo, Longomontanus, Lansberge, Mulerius, and Gassendi — adding Riccioli’s own figures for the stellar velocity on his hypothesis. The argument is cast in form (motion belongs to the body whose velocity is more credible), and the First Response begins: the Earth’s supposedly slower motion is no motion at all to sense, and velocity grows with the radius in the same species of motion.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 321]
—posed, there follows: “Nor let this passage of a thousand miles in one hour seem to you even now incredible: I bid you consider the proportion of the density of air to the density of aether, which I demonstrated in the Optics, from which it comes about that the passage of a thousand miles in one hour through the aether is, by many parts—by an incredible number—more tranquil than is the passage of one mile in one hour through our air.” These things posited, he passes to the Ptolemaic hypothesis, and affirms that all [things] are found more incredible in it; for he says: “In it the semidiameter of the sphere of the fixed stars possesses twenty thousand semidiameters of the earth: the circuit, therefore, will be sixty-three thousand.”
[Margin: Kepler’s slip.]
This slip is manifest, but pardonable; for he ought to have taken the diameter [as] 40,000 semidiameters of the earth, and, as 7 to 22, so to have made it to a circuit of nearly 126,000. Yet from his own calculation he gathers that in one hour a Fixed star must traverse 2625 terrestrial semidiameters, of which each contains 860 German miles. After these [things] he repeats that [saying] of his: “It is more credible that a great subject be without motion, than [that there be] a great motion in a small subject”; and below: “It is more difficult to intend [stretch] an accident beyond the measure of the subject, than [to have] the subject without the accident” (now velocity is an accident): “Copernicus, therefore, does the more probable [thing], who increases the orb of the fixed stars without motion, than Ptolemy, who increases the motion of the fixed [stars] by an immense velocity.” Yet in that whole discourse he uses the proper motions of the Planets toward the East, showing that they are proportionally slower the more they are distant from the Earth; but, on the contrary, [he argues] that if the diurnal motion were attributed to the Fixed stars, there would be made a passage from the slowest Saturn to the swiftest Fixed stars: in which matter there is a foul—not to say crafty—equivocation; for the Fixed stars and Planets ought to be compared in the same genus of motion, not in a diverse [one], as we shall teach below.
[Margin: Galileo’s defense for Kepler.]
[III.] Galileo, however, cleaving to Kepler (Dialogue 2 On the System of the World, p. 198 of the Latin version), adduces—in order to dissolve Chiaramonti’s objection against Kepler—[an objection] which is of this kind: “Kepler is deceived when he says that in the sphere of the Fixed stars the accident—that is, the velocity—is increased beyond the measure of the subject; for since the circumference of the sphere is increased in [a certain] proportion, by the same [proportion] is increased also the motion, or the space to be traversed by the mobile.” Which Galileo tries to dissolve by saying that Kepler was not so dull of wit as not to see that, but understood, by “the measure of the subject,” the norm and example of the other celestial bodies, which, the more they are removed from the center, the slower they are, as appears in the Planets and in the Medicean stars. But this solution is frivolous, since the comparison is not made in the same species of motions, as will be said in the solution of the second argument.
[Margin: Lansberge’s calculation for the velocity of the Earth and of the Fixed stars.]
[IV.] Longomontanus too (bk. 1 of the Theorics, ch. 1) calls the swiftness of the Fixed stars incredible. But Lansberge, in his 6th argument for the diurnal revolution of the Earth, says that any terrestrial point at the Equator accomplishes 225 German miles in one hour, and in one minute (that is, second) a sixteenth part of a mile; which has a fitting proportion with the motions we experience in nature. For a cannonball traverses, in one minute, a sixteenth part of a German mile.
[Margin: The velocity of a cannonball.]
But if the Eighth sphere were moved, it would have to run, in one minute, 643,848 miles; and Saturn, if it were turned by the diurnal revolution, would complete in one minute 930 miles—which he thinks utterly absurd. Yet Lansberge confesses, from an experiment of the Landgrave of Hesse, that a cannonball traverses half a German mile in one minute of an hour before it strikes the ground; for Kepler affirms (p. 108 of the Epitome) that the Landgrave and Tycho experienced this.
[Margin: Mulerius’s calculation for the velocity of the Fixed stars.]
On the contrary, Nicolaus Mulerius (p. 322 of the Frisian Tables), the Tychonic distance of 14,000 terrestrial semidiameters being supposed (or 12,040,000 miles), says that the great circle in the Firmament is extended over 88,000 terrestrial semidiameters (or 75,680,000 miles), and so that the hourly motion of a Fixed star at the Equator is 3,153,333 miles; but from this velocity he deservedly rises up to the praise of God’s power, exclaiming with the Psalmist, “The heavens declare the glory of God,” etc., and [of God’s] benignity, which for our sake moves the Firmament with so great a velocity—repeating that [verse] from Psalm 8, “What is man, that thou art mindful of him?”—so far is he from gathering thence any absurdity.
[Margin: Gassendi’s calculation for the velocity of the Earth and of the Fixed stars.]
[V.] Lastly, Pierre Gassendi (Epistle 2 On motion impressed by a translated mover, p. 111) rightly indeed admonishes that there is no reason why it should be objected to the Copernicans as absurd, that we, in some part of the earth—namely under the Equator—are moved with so great a velocity that scarcely a cannonball attains so great a velocity: but he adds that there can be retorted by the Copernicans an incomparably more absurd velocity of the Fixed stars. For a point of the Earth, in one second of an hour (or in the interval from one pulsation of the human artery to another), under the Equator, where the motion is swiftest, would run through about two hundred Orgyas, or toises. But since the circuit of the Firmament is (according to the common opinion, says Gassendi) greater than the circuit of the Earth by more than fifty thousand times, it is necessary that, in one second of an hour, a point of the circuit of the Firmament should run through fifty thousand times as many fathoms.
[Margin: Our calculation for the velocity of the Fixed stars.]
[VI.] Thus far the measures of the Copernicans, if you except Mulerius—for [the figures], however, the Reader can consult our Table on the swiftness of the Fixed stars, which we set forth (bk. 6, ch. 7, num. 18), where, from others’ distances of the Fixed stars from the earth, we gathered that velocity; but from our own hypothesis [a velocity] much greater. For in one second of an hour, or in the interval of a human artery’s pulse, any Fixed star at the celestial Equator traverses, on the Ptolemaic [reckoning], at most three semidiameters of the Earth; but on our hypothesis, 152⅔ terrestrial semidiameters—that is, 629,128 Italian Bolognese miles, which are 157,282 German [miles] (according to what was said, bk. 2, ch. 7, on our measures of the terrestrial globe). And so, far from wishing that velocity diminished, we rather, by our hypotheses, make it and confess it about seventy times greater than it is in Tycho’s hypothesis, and fifty times [greater] than in the Ptolemaic. And yet, this notwithstanding, we shall presently show that the Achilles of the Copernicans has feet of clay, and feeble. But first let the argument [be] in form.
[Margin: The syllogistic form of the argument.]
[VII.] “The diurnal motion is to be attributed rather to that [body] whose velocity becomes the more credible, and the more proportioned to the mobile subject. But if the diurnal motion be attributed to the Earth, its velocity becomes more credible and more proportioned to the terrestrial mass, than if it be attributed to the sphere of the Fixed stars. Therefore the diurnal motion is to be attributed to the Earth rather than to the sphere of the Fixed stars.” The Major is plain of itself, and is established even from this, that Nature and God do that which is easier in itself, and more intelligible, and more credible to an intellectual creature. The Minor is proved from this, that the velocity of the Earth comes out many times less than the velocity of the Fixed stars (as was shown from numbers 1 to 6), and is more congruous to the measure of the subject (or to the mass of the Earth), than is the velocity of the Fixed stars [congruous] to the immensity of their sphere (as was shown at numbers 2 and 3).
[Margin: First Response.]
It is answered, first—the Major being granted but not yet conceded (for God and Nature do not always do what is on that account more credible to us, because it is easier)—by denying the Minor as to each of its parts. Just as the consequence of the argument adduced for the first part of the Minor is denied: for it does not follow that a velocity is more credible from this precisely, that it is less, and more incredible from this, that it is in reality greater—unless the excess of the latter over the former be also against sense, or disproportionate to the capacity of the subject and to the motive power, and the deficiency of the lesser be conformable to sense. Which does not happen in our case: for the motion of the Fixed stars is indeed evident to sense, and their velocity is very slight to sense—so much so that in one second of an hour, nay in one minute of an hour, they scarcely seem to be moved. But the motion of the Earth is plainly none to sense; wherefore its velocity is not less, but the utmost slowness—nay, no motion at all—if we stand by the physical evidence which we have from sense; wherefore all its velocity is contrary to sense. But if the comparison were made between two mobiles, of whose motion we had physical evidence, then assuredly that velocity would seem the more credible which was less, or at least so [moderate] as not to offend sense, than that which would offend sense by excessive rapidity, if the eye wished to follow it. For to the intellect it cannot be excessive, since it comprehends a much greater [one].
[Margin: The velocity of the Fixed stars is proportioned to the subject.]
As to the other part of the Minor, concerning the velocity proportioned to the subject, this too is denied (as I said), and its proof. For if the comparison be made (as it ought) in the same genus or in the same species of motion—namely, in the diurnal motion—by as much as the semidiameter of any sphere grows, by so much also [grows] the circumference, which is the space traversable by the diurnal motion. Wherefore, just as the velocity of the parts [nearer the axis] would not be incongruous—
[…continues on p. 322 (PDF 357) with the catchword “tium”: ”…[the velocity] of the parts”—the completion of Riccioli’s reply (that within one rotating body the outer parts must move faster, so the comparison of “proportion” fails), and the remaining arguments of Chapter VI.]
(printed p. 322 — within Chapter VI. Finishes the reply to the first (velocity) argument with two further Responses, including the retortion that the Copernican annual motion forces an immense idle gap between Saturn and the fixed stars. The Second Argument, from the proportion of motions, intervals, and mobile subjects (Kepler, Galileo, Lansberge), is then proposed and cast in form, and the First Response begins: by the proper eastward motion the fixed-star sphere is actually the slowest.)
[Header: BOOK IX. SECTION IV. — 322]
—of the parts of the terrestrial surface, even if it be four thousand times greater than the velocity of the parts which are distant by one single pace from the center of the earth: so neither is the velocity of the parts of the sphere of the Fixed stars incongruous, even if it be many thousands of times greater than the velocity of the parts of the terrestrial surface. For this happens in [our] case just as if the single pace of some giant were compared with the single pace of an ant; for each [pace] is proportional to the legs of its [own] subject—granted that in one single pace of the giant a thousand paces of the ant be contained, and on account of this number that pace, which to the giant is single and very easy, should seem (by the multiplicity of the little parts) too swift for the ant. But how sophistically the comparison of the diurnal motion of the Fixed stars is transferred to the [proper] motion of the Planets toward the East will be plain from the solution of the second argument, presently to be proposed. And thus far concerning the comparison of the spheres as to surfaces; for if [we compare] as to masses, the excess of the mass or solidity of the greater sphere over the lesser is greater than [the excess] of surface over surface, since that [ratio] is the tripled [ratio] of the diameters. But this will appear more evidently from what will be said (ch. 30, num. 8), where [I treat] of this expressly.
[Margin: Second Response.]
It is answered, secondly, by conceding the Major if that velocity be more credible to the intellect with the evidence of the senses safe, and [with] an authority that constrains us; [but] by denying [it] if it be more credible to the intellect [taken] precisely, but credible not only to [an intellect] abstracting from sense and from constraining authority, but even to [one] judging against both. This distinction being supposed, the Minor is then denied: for the Copernicans, against the evidence of sense, deny motion to the Fixed stars and concede it to the Earth, and are wholly bent on this, that we should follow mere intelligible reasons, sense being neglected or corrected, and the sacred authority being dragged, without necessity, from the literal sense to a tropical and alien [one]. But we are not yet disputing about Authority; nevertheless we ought not always to forget it amid the responses to their arguments.
[Margin: Kircher’s witty saying.]
And not unskillfully did Athanasius Kircher say (in the Magnet, p. 539): “God commends Himself by the velocity of the Sun; canst thou not believe [it]?”—namely by those words [Ps. 18]: “He hath rejoiced as a giant to run the way.”
[Margin: Third Response.]
It is answered, thirdly, by retorting the argument—not indeed against the Semi-Copernicans, who admit only the diurnal revolution of the Earth, but against the Copernicans who add the annual [motion] too. For from that [annual motion] follows the immense distance of the Fixed stars, so that the diameter of the great orb [the Earth’s orbit] comes out [as] a point in respect of it—and indeed a vastest interval, idle and destined for no stars, between Saturn and the Fixed stars. As, therefore, those [Copernicans], in order to soften its incredibility, have recourse to the admirableness of the Power and Majesty of God the Maker, so from the remarkable velocity of the Fixed stars we [shall] suffer the Omnipotence and Majesty of the same God to be commended. Especially since the divine Power and Wisdom shines forth far more in attributing to a sphere of moderate magnitude a remarkable velocity—but one serving some use—than in extending a mass into the immense without any motion, or [without] an action equivalent to motion, and in such a way that it cannot appear to what use that inert mass, void of sensible bodies, serves. To me, surely, he would seem of greater genius and skill who should so construct a certain great ship full of sailors, soldiers, and merchants, that—whether by the contrivance of sails or of wheels—in the space of one hour it should fly across a thousand miles in the Ocean, than he who should raise a crag up beyond the clouds, but a bare one, and (except for its peak) furnished with no herbs, plants, animals, gems, or minerals.
Second Argument, from the Proportion of the Motions and Intervals, and of the Mobile Subjects
[VIII.] I should indeed be ashamed of this argument—as being sophistical and resting on a manifest equivocation—did they not so seriously urge it, on the occasion of the first argument related in this chapter; in the first place Kepler (ch. 16 On the new star in Serpentarius), where he so plainly draws up the reckonings.
[Margin: Kepler’s calculation for the proportion of the celestial motions to the intervals.]
“In Copernicus’s hypothesis,” he says, “the globe of Saturn traverses in one hour nearly 300 German miles; of Jupiter, 400; of Mars, 600; of the Earth, 740; of Venus, 800; of Mercury, 1000.” (But he is speaking of the proper motions toward the East.) And he subjoins: “A fair proportion indeed, where always the swifter is that which is nearer to the resting Sun, and to the dispenser of all motion.” Then, having said that in Ptolemy’s opinion all [things] are found more incredible, he adds that to the Fixed stars, if they move, must be [assigned] in one hour 2625 semidiameters of the earth, of which each contains 860 miles. “Here behold,” he says, “for me an immense difference: Saturn, which with Ptolemy is nearest to the Fixed stars (so that it all but touches them), crosses, with Copernicus, in one hour, 300 miles; with Ptolemy, two million two hundred fifty-seven thousand five hundred miles. He must be believed, then, [to be] swifter with Ptolemy than he is with Copernicus seven thousand five hundred and twenty-five times. Whoever shall attempt to comprehend with the mind this incredible velocity will be equally fatigued—and even more vehemently—than he who [attempts to comprehend] the Copernican immensity. Meanwhile weigh, O Philosopher, that here the proportion of the accident to its subject is far more to be demanded than anyone can rightfully demand, with Copernicus, the proportion of [one] part of the World to [another] part.”
[Margin: Galileo’s discourse for the same proportion.]
[IX.] By exactly the same reasoning, Galileo (Dialogue 2 On the System of the World, Latin p. 84) judges Ptolemy’s hypothesis improbable, because, every proportion being taken away, the manifest order of the motions in nature is disturbed: “The order,” says he, “is such, that the greater an orb is, by so much the longer time it finishes its revolution, and the smaller in a shorter [time]. Thus Saturn, etc. Nor less sensibly do we see, in the Medicean stars, that one which is nearer to Jupiter completing its revolution in the shortest time—that is, in about forty-two hours; the next in three and a half days; the third in seven days; and the remotest in seventeen days. And this concordant tenor will not be changed at all, while we assign to the terrestrial globe a motion of 24 hours upon itself. But if we establish the Earth immobile, then it will be necessary to pass from the slowest sphere of Saturn to the incomparably greater sphere of the Fixed stars, and to attribute to it a revolution of 24 hours, etc. But if we assign mobility to the Earth, the order of the periods is in the best agreement with itself, and from the laziest sphere of Saturn there is a passage to the entirely immobile Fixed stars.” Like things he repeats in the same Dialogue, p. 199, where, refuting the responses of the Anti-Tycho—that is, of Chiaramonti—for the Ptolemaic system, he says: “But this conflicts with the architectonic rules of nature itself, which observes this in the measure of the lesser spheres (as we see in the Planets, and most sensibly in the Medicean stars): that it turns the smaller orbs in smaller times too. Wherefore the time of Saturn’s revolution is longer than all the times of the other lesser spheres, inasmuch as it is completed in 30 years. Now to pass from this to another much greater sphere, and to determine its revolution by only 24 hours—that indeed, not without reason might one say [it is] to wander outside the rules of the measure.”
[Margin: Lansberge’s similar discourse.]
Where Galileo plainly Keplerizes—as also Lansberge, in his commentaries on the diurnal and annual motion of the earth, who discourses by the same reasoning of the aforesaid order. But presently we shall detect the equivocation, when we shall have constrained the argument to the laws of the syllogism.
[Margin: The Second Argument reduced into form.]
[X.] “The diurnal motion is to be attributed rather to that sphere which is the least of all, than to that which is the greatest of all. But the sphere of the Earth is the least of all the spheres of the world, and the sphere of the Fixed stars [is] the greatest. Therefore the diurnal motion is to be attributed to the sphere of the Earth rather than to the sphere of the Fixed stars.” The Minor is called into doubt by no one; the Major is proved by induction from the manifest motions of the spheres: for the greater each sphere is (whether of the Planets or of the satellites of Jupiter), the slower, or of longer time, is its motion; and the smaller the sphere, the swifter, or of shorter time, the motion; but on the other side, the shortest revolution among the manifest revolutions of the stars is [that] of 24 hours, and so the least.
[Margin: First Response.]
I answer, first, by denying the Major, and distinguishing the prior part of its proof. For we grant rather than concede it, if the talk be of the proper motion of the Planets and of the Satellites of Jupiter toward the East—yet in such a way that not Saturn’s sphere be admitted to be the laziest of all, but the sphere of the Fixed stars, inasmuch as it cannot naturally complete its revolution toward the East except in about 26,000 years, or, according to Ptolemy, 36,000; nor let that induction be conceded except of the celestial motions, as being manifest to sense, and so [with] the comparison made between the spheres of the world which it is beyond controversy are moved apparently—but not of the sphere of the elements, much less of the terre-
[…continues on p. 323 (PDF 358) with the catchword “terre-”: ”…[much less of] the terrestrial [sphere]“—the completion of the First Response and a Second Response to Argument 2, then the Third Argument (the repugnance of the proper motion with the Prime Mobile’s).]
(printed p. 323 — within Chapter VI. Finishes the reply to the second argument (proportion of motions) with three Responses — the “bigger = slower” rule holds only for the proper eastward motion; the celestial motion may be one helical motion rather than two; and by retortion the diurnal motion should belong to the greatest sphere, with an excursus on the ancient harmony of the spheres. The Third Argument, from the repugnance of the proper motion with the Prime Mobile’s in the same subject (Kepler, Galileo, Lansberge, Gassendi), is then proposed and cast in form.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 323]
—of the terrestrial [sphere], whose immobility, rather than motion, is manifest to sense. But this same prior part of the proof we utterly deny, if the talk be of the apparent and common motion of all the stars—namely, toward the West—which is called the motion of the Prime Mobile, and could be called the common [motion] of the mobile [bodies], if not by snatching, at least by imitation: for the greater the sphere, or the higher the star, that is moved by such a motion, the swifter is its diurnal revolution; and the smaller or lower, the slower—speaking here too of the spheres whose motion appears, and is manifest to sense. Hence it comes about that the sphere of the Fixed stars is revolved in 24 hours to the same Meridian, Saturn a little [more] slowly, and so of the rest—so much so that the Moon, the lowest of all, is revolved [back] to the same Meridian, toward the West, only in 24 hours and about 48 minutes more. But the posterior part of the proof is most true—namely, that the revolution of 24 hours is the shortest of the manifest [ones].
[Margin: Second Response.]
I answer, secondly, by denying the Major, and likewise denying the prior part of its proof, without any distinction. For there are not really two motions in the Fixed stars or in the Planets—one toward the East, the other toward the West—but, as we more probably posited and set forth with many [authors] (sect. 2, ch. 3, nn. 6, 7, 8, and 14), there is a single [motion] along spiral or helical—or quasi-screw-shaped—lines; because [the lower body] does not perfectly attain the idea of the Prime Mobile, but falls short of it in the time of revolution to the same Meridian by so much the more as it is, in place, more distant from it and nearer to the earth. Therefore, by that very slowness of attaining it, there seems [to be] a motion toward the East; nor, for saving this very appearance of this motion and satisfying the senses, is it needful to acknowledge that slowness as a distinct species of motion; but it suffices to imagine a motion toward the West, slower and slower, so much so that, the slownesses of many days being aggregated, the lower spheres or the Planets seem more and more to be left behind by the higher [ones]—but especially by the Fixed stars—and to be left behind backward toward the East. But this common motion toward the West is more manifest than its modification or retardation toward the East—inasmuch as it [the westward motion] is observable daily, whereas that retardation (if you except the Moon) requires several days to be made manifest by observation. Wherefore, in the order and proportion of the motions, the induction must be made either solely or rather according to this motion toward the West; but in it the motion is swifter in the greater spheres or higher stars: therefore with the best right is denied the prior part of that proposition which was adduced for the proof of the Major.
[Margin: Third Response.]
I answer, therefore, thirdly, by retorting the argument thus: “The diurnal motion is to be attributed rather to that sphere which is the greatest of all and the most remote from the center of the World, than to that which is the least and nearest to the center. But the sphere of the Fixed stars—or some [sphere] higher than it—is the greatest and highest; whereas the Earth [is] the least and nearest to the center of the World. Therefore, etc.” The Minor is plain; the Major is proved both from the nature of the sphere and circle (in which, if the motion of all the parts be common, those move most swiftly which are most remote from the center), and especially by an induction made from the motions which in the stars are the most manifest of all—these being the daily motions toward the West, and the revolutions to the same Meridian; for it is established that such motions are swifter, and are completed in a shorter time, by the greater spheres, or by the higher stars, as was said in the second response. Therefore, etc.
And truly, unless this be done, the manifest order in the apparent motions of the mundane bodies is disturbed, and that most ancient Harmony of the heavens is taken away—which, with Plato and Hesiod, Cicero, Macrobius, Ficino, Glarean, [and] Zarlino, and very many of the Harmonic [writers], admired and received; inasmuch as they ascribed to the supreme sphere either the Mese or the Nete (that is, the sharpest [highest] of the notes and strings), on account of [its] swiftest motion, but to the Moon the Hypate (the gravest [lowest]), on account of [its] slowest motion. Granted that a few others, regarding that slowness of the apparent revolution toward the East, attributed the Nete to the Moon and the Hypate to Saturn—namely Nicomachus and Boethius, as I said (bk. 7, sect. 1, ch. 1); but these had fewer followers among the Musicians. But if both opinions are to be received, and the single motion is to be distinguished into two, what more admirable order of divine Providence could shine forth in these [things], than that a compensation should be made from the highest to the lowest, and from the lowest to the highest, in traversing this harmonic system upward and downward—and that the motion toward the West of that sphere should be slower whose motion toward the East is swifter? But this most beautiful compensation and antithesis is taken away, if the common motion—which evidently appears to sense in the stars—be attributed to the Earth, whose immobility is evident to sense. Away with that sophism, by which Kepler, Galileo, and Lansberge—regarding only the appearance of the celestial motion toward the East (as if this were the single or chief motion among those manifest to sense), the evidence of the common motion toward the West being meanwhile dissembled—have tried to block [the truth] from the eyes of the unskilled.
Third Argument, from the Repugnance of the Proper Motion with the Motion of the Prime Mobile in the same subject
[Margin: Kepler’s ineffective argumentation.]
[XI.] “If the first motion,” says Kepler (Epitome of Copernican Astronomy, bk. 1, p. 104), “is in the celestial orbs, then in the same subject there are two motions—one common to all the spheres, the other proper to each sphere. But it is far more likely that the first motion and the second motions are distinct in [their] subjects, so that the second motions, which are several, are each in its own sphere; but the first, which is single, is in the single body of the Earth.” An ineffective argumentation, surely—as if the nature of “animal,” because it is generic and common to every species of living things, must exist in [a] subject and in reality separately, in a single Idea, or in something else; or—to give an example, as in a sensible accident, of which kind is the apparent motion—as if it were needful that the nature of color be in a single subject, but in the rest whiteness, blackness, and the other differences. But you will say: if they are in the same subject, they will fight one another;
[Margin: Galileo’s argumentation.]
and therefore Galileo (Dialogue 2 On the System of the World, Latin p. 83) said: “If that great motion be attributed to the heaven, it must necessarily be made contrary to the particular motions of all the Planets, each of which, without controversy, has its own proper motion from the West toward the East—which then we must make to be snatched into the contrary, that is, from the East into the West, by that most rapid diurnal motion: whereas, on the contrary, the Earth being asserted [to move] by a whirling upon itself, the contrariety of the motions is taken away, and the single motion from the West to the East is accommodated to all the appearances, and exactly satisfies all [of them].”
[Margin: And Lansberge’s.]
The same argument Lansberge inculcates, in his commentary on the motion of the Earth, affirming that it is impossible that the eighth sphere be moved by two contrary motions; and therefore he concedes to the Fixed stars [their] proper [motion] toward the East (in which he differs from Copernicus), but attributes the common [motion] to the Earth.
[Margin: Gassendi’s opinion.]
[XII.] With much weightier formulas Gassendi labors to prove this (Epistle 2 On motion impressed by a translated mover, p. 109), where he speaks thus of the motion of the prime Mobile: “Although the matter might perhaps seem somehow tolerable, if that whole machine were carried round by a single and simple motion toward the West; yet since, on the other hand, so many Planets are carried round also toward the East—what could be made more absurd than to feign, above the Planets and above all the Fixed stars and even the crystalline spheres, a vastest sphere of the Prime Mobile, which, against the lower [spheres] striving toward the East by their own and slow motions, itself strives in the opposite [direction], and toward the West snatches them all away with an incredible velocity? Can there be anything more violent, and yet be thought to be perpetual in the nature of things? Can there be anything more tortuous, and yet be attributed to nature, which, whither it tends, always proceeds by the shortest and most level way?” And, a few [things] being interposed for the simplicity of the terrestrial motion, he teaches that the snatching of the prime Mobile cannot be communicated to the lower orbs, which are not solid; and even if they were solid, [that] it could not [be communicated], because they lack the little handles by which they might be grasped by the higher orb. But these [things] do not militate against so many others, who—as I taught (sect. 2, ch. 3)—do not posit a Prime Mobile as distinct from the sphere of the Fixed stars and the motions of the Planets, and yet attribute the diurnal motion to them. Let the argument now be, in form, of this kind.
[Margin: The Third Argument in form.]
[XIII.] “It is impossible that the same mobile be moved by two contrary motions; or, if they be not really contrary motions, [they are at least] to be avoid-
[…continues on p. 324 (PDF 359) with the catchword “tanda”: “…to be avoided”—the completion of the Third Argument’s syllogistic form, and Riccioli’s reply.]
(printed p. 324 — within Chapter VI. Completes and answers the Third Argument (deny the Minor — there is no real contrariety, the slower body merely lags; and by retortion the Copernican hypothesis has its own contrariety in the oblique fall of heavy bodies). The Fourth Argument, from the simplicity of the motions (Copernicus, Galileo, Gassendi), is then cast in form and met with two Responses, the second denying that the Copernican hypothesis is in fact simpler, since it multiplies motions.)
[Header: BOOK IX. SECTION IV. — 324]
—[are at least] to be avoided, as far as can be, the appearance of contrariety. But if the diurnal motion be attributed to the Fixed stars and Planets rather than to the Earth, the same mobile would be moved by two contrary motions, or at least the appearance of contrariety would not be avoided as far as can be: therefore the diurnal motion is not to be attributed to the Fixed stars and Planets rather than to the Earth. The Major seems sufficiently evident, and to be denied by no one; the Minor has been proved at number 11: for one motion of the same mobile would either be, or appear to be, made toward the East, the other toward the West, which are contrary termini, and accordingly specify contrary motions; and this appearance of contrariety would most easily be avoided by attributing the diurnal motion to the Earth.
[Margin: First Response.]
I answer, first, the Major being conceded, by denying the Minor and both parts of its proof. For there is no apparent contrariety in the aforesaid motions, except in the imagination of those who in reality distinguish this motion into two motions toward contrary regions; but those who conceive it without that fiction—as a single motion toward the West, distinguished only by slowness or velocity from another motion made toward the same region—remove not only the real, but even the apparent contrariety from such a motion. But if you nevertheless urge that, by that very slowness by which they are forsaken by the swifter mobile, they seem to recede toward the East, and the appearance of contrariety cannot be wholly taken away: I answer that not even by the diurnal motion conceded to the Earth is that appearance avoided; for the same [things] would appear which [appear] now. Wherefore, if some cannot correct their fancy, so as not to seem to themselves [to have] two contrary motions, they will not conquer it even in this way, if they wish to cling to the appearances. But what, I pray, is that deception or perversion, that of two mobiles running toward the same part in a circle, the one which is moved more slowly must be said or seem to run in the opposite part? Re-read, I beseech, what was said by us about this apparent contrariety (sect. 2, ch. 3, from num. 6 to 8, and at 14, and in the scholia of the same chapter).
[Margin: Second Response.]
I answer, secondly, by retorting the argument against that contrariety which, in Copernicus’s hypothesis, must be posited among the motions of heavy bodies while they are borne downward, if they have been thrown obliquely toward the West—and in many other mobiles of this kind; which [contrariety], if it is not absurd, then neither will that apparent contrariety in the motions of the stars be absurd.
Fourth Argument, from the Simplicity of the Motions
[Margin: Copernicus’s opinion for the abridgment of the motions.]
[XIV.] But, they say, it cannot be denied that there is a greater simplicity of the motions if to the Planets, or even to the Fixed stars, a single motion toward the East be attributed, without any admixture of the diurnal motion to be represented (by spirals or in another way) toward the West; and [if] the appearance of the other motion be transferred to the single motion of the Earth. Hence that saying of Copernicus (bk. 1, ch. 10): “But the sagacity of nature is rather to be followed, which, as it most of all took care not to have produced anything superfluous or useless, so it has rather often enriched one thing with many effects.” And this indeed is the third reason by which Galileo (Dialogue 2 On the System of the World, p. 84) confirmed the diurnal rolling of the Earth; for he concedes that whether the celestial motions toward East and West be contrary or not is an altercation of words, but he subjoins: “I know that in reality it is much simpler and more agreeable to nature, if we can save all [the appearances] by one single motion, than if we introduce two motions—which, if you will not call contrary, you may call opposite. Nor indeed do I condemn that introduction of opposite motions as impossible; nor do I affirm that a necessary demonstration is made from its negation, but [only] that at least something of weight accrues to the probability.”
[Margin: Gassendi’s opinion for the same abridgment.]
To which those words of Pierre Gassendi accord (Epistle 2 On motion impressed by a translated mover): “The Earth indeed being turned toward the East (than which nothing is more compendious), their own and slow motions toward the East are left to the Planets themselves; and that which appears to be in them, as in the Fixed stars, toward the West, will appear [to result] from the single conversion of the Earth toward the East—so much so that this single and simple conversion is equivalent to that prime Mobile, and meanwhile frees the lower orbs from that so great rapidity, violence, [and] intrication.” But, lest [we say] more of these [things], let the argument be formed in the following manner.
[Margin: The Fourth Argument enclosed in its [own] form.]
[XV.] “Of two motions, that one is to be chosen which is simpler and single, rather than that which is multiple and composite. But the diurnal motion of the Earth is simpler and single, while [that] of the Fixed stars and Planets [is] multiple and composite: therefore the diurnal motion of the Earth is to be chosen rather than the diurnal [motion] of the Fixed stars and Planets.” The Major rests on that most-received axiom of the Peripatetics: “It is done in vain through more [things], which can be done through fewer”—to which Galileo (Dialogue 2 On the System of the World, p. 88), with excessive subtlety, denies that the limitation “equally well” is to be understood, because that which is not done well, or not with entire goodness, is not the same [thing]; but the axiom supposes [that] it is the same [thing] which is done by more or by fewer. The Minor is easily proved: for, the diurnal motion of 24 hours being assigned to the Earth, it is not necessary to compound, with the proper motions of the Fixed stars and Planets, another motion toward the West; and so the single and simple motion of the Earth will represent the appearance of all the diurnal [motions].
[Margin: First Response.]
Someone may answer, first, by distinguishing the Major, and conceding it if all else be equal on both sides—that is, if equal satisfaction be given to the evidence had through the senses, or also to the authority which is superior to all reason; but otherwise, if it be not so, by denying [it]. But in the proposed case, [there stand in the way] both the Authority of Sacred Scripture (which attributes the diurnal motion to the stars, and immobility to the Earth), and—what is of this place—the evidence of the senses concerning the diurnal revolution of the stars, and the rest of the Earth.
[Margin: Second Response.]
I answer, however, secondly, the Major being conceded, by denying the Minor: for more motions, both in number and in species, are multiplied in Copernicus’s hypothesis—the diurnal motion being attributed to the Earth—than if it be attributed to the heaven and the stars; provided that all the conditions of the motions be considered which the diurnal motion given to the Earth necessarily draws with itself, and provided that, on the other side, that hypothesis of the resting Earth be chosen which, by a single spiral line, represents all the varieties of motion in each of the Planets and in the sphere of the Fixed stars (according to what we have said so often, but especially in sect. 2, ch. 3, from num. 14, of this book). For in this hypothesis there is a single motion of the Eighth sphere toward the West, but gradually falling short of the most perfect Idea of the first motion which shines forth in the mind of the Intelligence (or of the Intelligences) moving that sphere along a spiral line—and which motion, perhaps on the first day, or the first three days, before the founding of the Sun and the stars, was accomplished by a most perfect revolution of the light to the same Meridian. In the seven Planets too there is a single motion, likewise toward the West, but slower in the lower ones, and accomplished obliquely by the Intelligences through spirals now looser, now tighter; and so in all there are eight motions, with the little appendages of motions by which the satellites are turned about Saturn and Jupiter—concerning which there is no dispute in this place.
[Margin: How mixed the motion of heavy and light bodies would be, if the Earth move.]
But in the motion of heavy and light bodies a simple motion through the shortest and simplest straight line suffices. But in Copernicus’s hypothesis, besides the motions of the Seven Planets and the eighth (which he attributes to the terrestrial axis, somewhat slowly reclining backward [against the order of the signs]—but the Semi-Copernicans [attribute it] to the Fixed stars), there is need of a ninth motion really distinct, and [need] to attribute it to the earth; which being posited, in order that the innumerable experiments of motions be saved (by which both inanimate and animate [things] are moved in Earth, Water, and the Air nearer to the lands), it is necessary—besides the straight motion of heavy and light bodies, and the peculiar motions of living things, of winds, of clouds, etc.—to posit a circular motion, included in those motions but unknown to us, or not seen [by us]: from which there arises a motion mixed of straight and circular—whether it be parabolic (according to what was said in the scholia of ch. 4), which surely is not the shortest, but must be accomplished by a longer way, or of some other figure (about which matter, below, ch. 17). Nor here [is] the end of the perplexities. For one must feign that a clod of the earth, torn from the earth’s surface near the Poles and thrown there straight upward to the perpendicular, is moved with that slowness with which the circles of the earth parallel to the terrestrial Equator, but near its poles, are moved; but if the same clod be carried in a chest by someone into another parallel, or be thrown upward from North toward South by an oblique cast, [one must feign that it] ascends and descends with the ratio of [its] velocity continually changed, so that over the parallels nearer to the Equator it moves more swiftly; and this, although it [the clod] is not conjoined to the Earth in the way the Fixed stars are conjoined to the eighth sphere—and so [one must feign it] to change innumerably the property of [its] velo-
[…continues on p. 325 (PDF 360) with the catchword “velo-”: ”…[the property of its] velo[city]“—the completion of the Second Response and a Third Response to Argument 4, then the Fifth and Sixth Arguments.]
(printed p. 325 — within Chapter VI. Finishes the reply to the fourth (simplicity) argument with a completed second Response and a retortion. The Fifth Argument, from the unequal participation of the diurnal motion (Galileo’s “fourth difficulty”), is refuted as no absurdity — outer parts of any rotating sphere necessarily move faster. The Sixth Argument, from the inconstant declination and velocity of the fixed stars (Galileo’s “fifth inconvenience”), is then proposed, cast in form, and met with a First Response; a second begins.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 325]
—the property of [its] velocity, and that line of motion to turn out manifoldly composite. But if this is not a real composition, but [only] a diverse affection and modification of a single motion, then it is far truer that in each Planet there is no real composition of motions, but only diverse affections of a single motion.
[Margin: Third Response.]
I answer, therefore, thirdly, by retorting the argument thus: “Of two motions, that one is to be chosen which is simpler and single, rather than that which is multiple and composite. But the diurnal motion attributed to the Fixed stars and Planets, together with the rectilinear motion of heavy and light bodies, is simple and single in each of the simple bodies; whereas it is not such if the proper motions be attributed to the Fixed stars and Planets, and the diurnal [motion] to the Earth. Therefore.” In the Major we both agree; the Minor has now been set forth in the second response, and proved—since, in place of eight motions in the heaven, and two in the Elements (one upward, the other downward), a ninth [motion], of the Earth, is posited, and to the rectilinear [motion] of the elements is added a mixture of the curvilinear, and the ascent and descent of those [elements] is made by a longer way than if they were borne by a rectilinear and perpendicular path by their own nature. It behooved the Copernicans, therefore, to look round at these [things] more attentively, or not to dissemble the multiplicity of motions and of the accidents in the motions, which lies hidden in their hypothesis.
Fifth Argument, from the Unequal Participation of the Diurnal Motion, or from the Unequal Velocity of those [stars] by which they are moved by the diurnal motion
[Margin: Galileo’s discourse, but plainly fallacious.]
[XVI.] Truly, flattering is that Self-love by which each one has long been affected toward his own opinion, and to which he has so accustomed himself, that in his own hypothesis he does not recognize those very spots or blemishes by which he thinks the hypothesis of others deformed. Lo, behold Galileo (Dialogue 2 On the System of the World, p. 85 of the Latin version), thus inveighing against the common hypothesis, which concedes the diurnal revolution to the Fixed stars: “The fourth difficulty is the immense disparity between the motions of those same stars, of which some will be moved most swiftly, in vastest circles, others most slowly, in least circles—according as these or those shall have been nearer to the poles, or less near: which indeed is very inconvenient; both because we see those [stars], of whose motion there is no doubt, all moved in the greatest circles; and also because it seems absurd to set up bodies movable circularly at immense distances from the center, and to attribute to their motions the least circles.” These are the very words of Galileo, seriously brought forth, as appears; for which [words], however, some raw recruit, lightly imbued with the elements of the doctrine of the sphere, would (I know well enough) be soundly thrashed by [Galileo] himself.
[Margin: Refutation of the Galilean Argument.]
And so there is no need to form an argument, that we may spit out [reject] its fallacy: for there is no inconvenience that, of the same sphere driven round by a single whirling about its [own] poles, the parts which are in the circumference of the great circles should be moved more swiftly than those in the circumference of the lesser circles and nearer the poles; but it is necessary by Geometric necessity, since in the same time the former traverse greater, the latter lesser arcs—whether then that sphere be great or small. Otherwise, if it were an inconvenience, it would be no less so in the diurnal revolution of the Earth, whose parts placed at the Equator it would assuredly be necessary [should] be moved much more swiftly than the parts situated in the polar circles, or near the poles. It is moreover false that the stars, of whose motion we least doubt, are all moved in the greatest circles; for the Planets, neither do they by their proper motion always dwell in the Ecliptic, but, having gained from it a latitude of several degrees, describe lesser circles—especially if they are then perigee or perihelion; nor is their common motion (which is no less evident to sense in them and in the Fixed stars, inasmuch as it is daily and daily observable) made through the greatest circles, but through ever-different [circles] parallel to the Equator. Lastly, the circles which in the heaven are called least, because nearest to the Poles, are not called least comparatively to the circles of the Earth, but to the greatest circles of the same heaven or sphere; but by the very reason by which they are, and are called, least, they are not the swiftest but the slowest—namely, in comparison of the motion which in the same time is made through the greatest circles. There is, therefore, no absurdity, if at whatever interval they be distant from the earth they nevertheless describe circles which are least comparatively to the greatest [circles] of the same sphere, and which are not least comparatively to the circles of the Earth. Nay, if there were any absurdity [in] this, it would be multiplied the more by moving the Earth; for then there would be an appearance of unequal velocity in the heaven, AND a real inequality in the parts of the Earth, more or less remote from the poles.
Sixth Argument, from the Inconstant Declination and Velocity of the Fixed stars
[Margin: Galileo’s other argumentation, but ineffective.]
[XVII.] Galileo sets out, but does not get on; and in the same Dialogue 2 On the System of the World, and on the same page 85, he passes to another (as he himself calls it) inconvenience, which follows from the diurnal motion attributed to the Fixed stars [as heavenly bodies]: “For”—to use his own words—“the stars themselves will vary their circles and their velocity (which is the fifth inconvenience): for those [stars] which, two thousand years ago, were on the Equinoctial [celestial equator], and consequently by their motion described the greatest circles—since in our time they decline many degrees from the Equinoctial, must necessarily have become slower in motion too, and reduced to this, that they describe lesser circles. And it is but little wanting that it could happen that a time should come in which some one of them, always before moved, when it shall have been united with the Pole, should stand devoid of all motion, and after a rest of some time should begin to be moved again: whereas, nevertheless, other stars, which without doubt are moved, all describe (as was said) the greatest circle of their orb, and are turned in it without variation.” Are these the inconveniences, O Galileo? And are these [things] said by you in earnest, or feignedly? But let the argument be formed—although there is scarcely need.
[Margin: The Form of the Sixth Argument.]
[XVIII.] “If the Fixed stars be moved by the diurnal motion, it is necessary that the same Fixed stars at some time describe the greatest circles, and be the swiftest; but at some [other] time [describe] lesser and least [circles], or even none, and so turn out less or least swift, or even not move at all. But this is an inconvenience. Therefore the Fixed stars are not moved by the diurnal motion: it remains, therefore, that such a motion be the Earth’s.”
[Margin: First Response.]
I answer, first, the Major being conceded—if to the diurnal motion of the Fixed stars [there] be conceded a proper [motion] in longitude—but by denying the Minor: for that is no more an inconvenience than [that] the Planets at different times vary either their declinations or their latitudes, and are now swifter, now slower. Or—to draw an example from Copernicus’s own store—this is no more an inconvenience than, in Copernicus’s hypothesis, [that] men, fishes, [and] birds, who daily, by walking, swimming, [and] flying straight or obliquely from South toward North, or in turn from North toward South, vary [their] declination and the parallels of the Equator, [and] are moved now more slowly, now more swiftly, with the Earth on which they rest, or whose diurnal motion they follow; nay, that those who dwell under the poles of the terrestrial Equator are moved nothing, or almost nothing, by this motion. And yet a variation of this kind is far more frequent, and involved in very many perplexities of animal motions, and—what is the chief [point]—feigned against all the evidence of the senses; whereas, on the contrary, that variation in the Fixed stars as to declination and velocity is confirmed by the evident experiment of observations through many centuries, and from it follow many [things] most worthy to be known, and theorems and problems leading us by the hand to the Glory of God the Creator—some of which, new and hitherto unheard, we brought forth (bk. 6, ch. 11). But especially (ch. 19), where (Problem 5) we taught the conditions required that some star may be able to arrive at the poles of the world; and that [the star] which we now call the Pole star never was, nor will be, exactly at the very Pole of the World. And (Problems 10 and 11) that there are some Fixed stars, of which—the Longitude increasing—nevertheless the Right Ascension in some centuries or times increases, in some decreases, by a certain retrograde motion of declination; and that 94 such stars are found in the heaven out of those which have hitherto been numbered by the naked eye: teaching, besides, the way of discerning geometrically the position of these stars, and of determining the times in which their Right Ascension ought to increase, and in which to decrease. And if Galileo had known this, what a specious inconvenience would he have brought forth against the hypothesis of the diurnal motion of the Fixed stars!
[…continues on p. 326 (PDF 361) with the catchword “Respon-”: “Respon[deo]“—Riccioli’s Second Response to the Sixth Argument, and the remaining arguments of Chapter VI.]
(printed p. 326 — completes Chapter VI’s sixth argument with a retortion, then proposes and dissolves the seventh and last, Kepler’s argument from the inequality of the natural days. Chapter VI ends and Chapter VII opens — the three remaining arguments for the diurnal motion — beginning with the First Argument, from comets (Seneca, Copernicus, Gassendi), cast in form and answered: the same Intelligence that moves a comet on its wandering path can move it diurnally too.)
[Header: BOOK IX. SECTION IV. — 326]
[Margin: Second Response.]
I answer, secondly, by retorting the argument—and not absolutely, but ad hominem, as is wont to be said—rejecting the aforesaid inconvenience back upon the Copernican hypothesis in this way: “If the Earth were moved by the diurnal motion, it would be necessary that very many living things, following the common motion of the Earth, should most frequently vary their declination and velocity in this motion. But this, by your own [account], is an inconvenience. Therefore.” The Major has now been shown, on account of the change of the parallels through which the living things pass. Moreover, it would be necessary that the axis of the Earth nod and librate hither and thither with so great an inequality and anomaly, that the appearance of the declination of the Fixed stars might be saved through it; but this inconstancy is no less an inconvenience than the variation of declination in the Fixed stars: therefore neither on this account is the diurnal motion to be attributed to the Earth.
Seventh Argument, from the Inequality of the Natural Days, arising from the Inequality of the Diurnal Motions
[Margin: Kepler’s acute but weak argument.]
[XIX.] Kepler sharpened a more subtle argument (in the Epitome of Copernican Astronomy, p. 108), which I once indicated (bk. 3, ch. 32, nn. 2 and 3); in which it is supposed—as in reality it appears—that the individual diurnal motions are indeed equal among themselves and in their parts, to sense, but, compared with other diurnal [motions], are unequal, and slower indeed when the Sun is in [its] Apogee, but swifter when in [its] Perigee. These [things] being supposed, Kepler discourses thus: “If, the Sole Earth being excepted, all the rest of the machine of the World sustained its own motion, no cause could be feigned why the laws of this inequality—adjusted to the motion of the single Solar sphere alone—should redound upon the whole machine. But if, the machine of the world resting, the earth is rotated, the cause of this inequality is easily rendered, from the change of the interval between the Sun and the Earth in the same proportion, since the Sun is the minister and helper of all motion.” And he indicates the same cause (p. 550 of the same Epitome). But we deny that no cause of the aforesaid effect can be rendered: for the cause is, that the Solar days are the measure commonly used in numbering the motions of the other Planets, and therefore their inequality redounds upon the motions of the others. But if the cause of the aforesaid inequality is the change of the interval or distance between the Sun and the Earth, it makes no difference as to this, whether the Earth itself be moved by approaching and receding toward the Sun (even if it be said to be incited by the Sun—magnetically, or by a force diffused through light—when it is nearer, and not so incited when it is farther); or whether the Sun approach and recede toward the Earth, and in approaching be objectively allured by the Earth, in whose gravity it is moved, so that it is then somewhat swifter, but in receding is not so allured.