First Argument, from the diameter, motion, and apparent distance of the Fixed [stars] being varied

[I.] I remember that I read in someone (or at least received from letters sent to me from Germany) that a certain [person] dared to assert that the same Fixed stars seemed to him larger in the Boreal [northern] region when the Earth saw the Sun at the beginning of Capricorn, than when it saw it at the beginning of Cancer: whence he gathered that this happened by the Earth’s approach toward the Boreal region, by force of which Arcturus would then seem larger than itself [usual], than when the Earth had receded to the Austral [southern] Region. But also Jean Pena and Johannes Stadius (as I reported, ch. 3, schol. 2) thought that, by the Earth’s approach, the motion of the Fixed [stars] seemed swifter, and by [its] recession slower; whom we there refuted.

[Margin: The variety in the magnitude of the Fixed [stars] not demonstrated.]

Rothmann, finally, in Tycho (tome 1, p. 684), said that the distances of the Fixed [stars] among themselves are increased by two minutes by the Earth’s approach, and diminished by [its] recession, and that he had observed this. But this is either a plainly arbitrary Fiction—since to us, observing the stars for many years past, nothing of the kind has appeared—or that phenomenon arose from the diverse thickness of vapors in summer and winter nights. Otherwise it is sufficiently plain, from Copernicus himself (bk. 1 of the Revolutions, chh. 5, 6, and 10), that the whole annual orb (through which the Earth is supposed to be moved) has no sensible proportion to the eighth Orb, or the sphere of the Fixed [stars], but is as a point [to it]; and so, whether Arcturus, or any other Fixed [star], be viewed from the Earth [situated] under Cancer, or from the same [Earth situated] under Capricorn, no diversity can of itself appear in either its apparent magnitude or its meridian altitude. Which [diversity], however, if it did appear, the greatest ought to appear in the stars placed in the Ecliptic, but in those distant from the Ecliptic less, and in those which are near the poles of the Ecliptic none—as Galileo demonstrates (Dialogue 3 On the System of the World, from p. 281 of the Latin).

Second Argument, from the Satellites of Jupiter

[Margin: By what method the revolutions of the Jovian Satellites [are] regular.]

[II.] Go to Kepler (in the Epitome of Copernican Astronomy, bk. 4, part 2, p. 537), and you will read in him such an argument: “Marius,” says he, “in his Jovian World, found that the restitutions [returns] of the Jovian satellites about Jupiter are by no means regular, which we project [reckon] from the center of the earth toward Jupiter; but that they are regular, if they be compared to lines drawn out from the center of the Sun through Jupiter. Doubtless this is in place of a very great argument, that Jupiter’s orbit around the Sun is ordered, and that the distance of the Sun from the center of the Jovian orbit is certain and fixed in a manner: but that the Earth varies its distances from this center through the year.” But it can be answered that neither was this demonstrated by Simon Marius, but deduced only from conjectures [that are] not very strong; and, this being granted, [that] it does not follow hence necessarily, or very probably, that the Earth is moved by an annual motion rather than the Sun, but at most that the Sun is the center of the Jovian system; or [that], just as the Sun is the first exemplar of revolving around itself its satellites Mercury, Venus, and Mars, so it belongs to Jupiter to lead around its [own] satellites.

[…continues on p. 346 (PDF 381) with the catchword “III. Ar”: “III. Argumentum…”—the Third Argument of Chapter X.]

(printed p. 346 — within Chapter X. The Third Argument, from the lunar Variation and libration (Tycho, Kepler, Bullialdus, Galileo), is answered: an epicycle or bodily libration explains the phenomena equally. The Fourth Argument, from the new star of 1572 (Digges), is refuted by its actual fading and fixed place. The Fifth Argument opens: Kepler’s claim that the comets of 1618 show a rectilinear path made tortuous only by the Earth’s motion.)

[Header: BOOK IX. SECTION IV. — 346]

Third Argument, from the Lunar Variation and Libration

[Margin: The cause of the Lunar Variation.]

[III.] Tycho observed that, besides the first and second inequality (or anomaly) which the Moon suffers, it has yet a third inequality, more manifest in the Octants [octiles], but ceasing in the Syzygies and quadratures, as we expounded (bk. 4, ch. 18, num. 8, and ch. 26, num. 9). And Tycho and Longomontanus refer the cause of it to a libration of the Lunar Epicycle, as we taught in the same place; but Kepler [refers it] to the illumination of the Sun, and the species [image] of it reflected from the earth onto the Moon, as we expounded in the same [bk. 4, ch. 27, from num. 5, and scholio 6]. But Ismaël Bullialdus (bk. 3 of the Philolaic Astronomy, ch. 11) thinks the truer cause of this Variation to be the Reflection of the line of the Lunar apogee, arising from the annual motion of the Earth, by which the whole Lunar system is carried: for the apogee being advanced, through the reflection, from the Syzygies to the dichotomies [quarters], the Moon hence acquires a new acceleration; but, it being drawn back from the quadratures to the Syzygies, it undergoes a certain slowness in the Zodiac; and this he thinks to be the genuine, proximate, and simple cause of this Variation, the measure of which he investigates afterward (ch. 12). See more on these [things], if you please (our bk. 4, ch. 27, nums. 13 and 14).

[Margin: The cause of the Lunar Libration.]

[IV.] Besides this Variation, there has been observed in the Moon a certain Libration, by force of which the Lunar spots [maculae] appear now nearer, now more remote, to the Eastern and Western limb—so that when the Caspian Spot is most remotely distant from the Western margin of the Moon, then the Spot called by Langren and by us the “Lake of Posidonius” (but Galileo [calls it] the “Corican,” Hevelius the “Mareotic”) is nearest to the Eastern limb of the Moon, etc.—concerning which libration [I shall say] more below, in the Appendix to book 4, on the Moon. But this libration Galileo, in the Dialogues, said was instituted [established] so that the Moon may keep a certain direction toward the axis of the moving earth: but Bullialdus (bk. 3 of the Philolaic Astronomy, ch. 13) disapproves this, and concludes that the axis of the Moon, upon which that libration is carried out, is either perpendicular to the plane of the Ecliptic, or insensibly inclined to it—perhaps by as great an angle as the planes of the Ecliptic and of the Lunar orbit are inclined to each other, namely about 5⅓ degrees: see the diagram of this matter in us (bk. 4, ch. 9, num. 4). These [things] being premised, let there be the Argument.

[Margin: The argument in form. And the double Response.]

[V.] The Variation of the Lunar motion, and the Libration of the Lunar body, is better explained by supposing the annual motion of the Earth than by supposing [its] rest. Therefore the annual motion of the Earth is to be supposed rather than its rest. It is answered, first, by denying the antecedent, for it is equally well explained by a libration of the Lunar Epicycle, or of the Lunar body itself, according to what is to be said in the Appendix to bk. 4. I answer, secondly, the antecedent being granted, by denying the Consequence—because other things are not equal; nay rather, there are also other greater absurdities in the annual motion of the Earth, the exclusion of which prevails over this very slight convenience by which, through the annual motion of the Earth, a partial cause of the Lunar Variation and Libration could be brought forward; and that Lunar Libration is wholly completed within a month, nor has it any analogy with the annual motion of the earth. Besides which, the [things] which Bullialdus and Hevelius have hitherto divulged about that libration agree neither with themselves nor with our observations; so that, accordingly, one must deliberate on this matter more maturely, and a more uncertain cause is not to be sought from uncertain phenomena.

Fourth Argument, from the New Stars

[VI.] Thomas Digges, an Englishman of Kent, on the occasion of the new star which was seen in the year 1572 in Cassiopeia, thought—that I may use his words, as reported in Tycho (tome 1, p. 658)—that “A handle [opportunity] was offered of trying whether the motion of the Earth, supposed in the theories of Copernicus, will be the sole cause why this star [should be] diminished in apparent magnitude. For if it were so, [the star], always decreasing at the vernal Equinox, would be beheld in its least magnitude. But afterward, if it lasted, gradually increasing, in the following July it would be of nearly the same brilliance as in its first apparition. But at the autumnal Equinox it would seem of unwonted magnitude, and also of splendor.” But of such a diversity of the apparent quantities [sizes] no other cause could be assigned than its [the star’s] elongations from the Earth. Thus Digges—but with an entirely vain hope: for that star, in the year 1572, around the beginning of November, was seen to exceed Lyra [Vega], Sirius, and Jupiter itself [when] acronychal; but in January of the year 1573, [it was] a little less than Jupiter, but a little greater than Lyra; but in February and March it was seen equal to Lyra; in April and May it matched stars of the second magnitude, and in June, July, August stars of the third rank; but in September, October, and November, more attenuated, it scarcely equaled stars of the fourth class; in December of the year 1573 and January of the year 1574 it was equal to stars of the fifth brilliance, and in February to [those] of the sixth, and at last in March it turned out invisible, as Tycho narrates (tome 1, p. 301). Wherefore it did not change [its] magnitude by that reckoning which the Earth’s approach and recession would require: for it ought to have been seen again, in November of the year 1573, equal to Jupiter.

[Margin: Thomas Digges’s vain conjecture on the Earth’s motion from the new star’s magnitude.]

Besides—as Tycho notes against Thomas (p. 660)—it ought to have appeared largest, the Sun being engaged around the beginning of Scorpio and the Earth around the beginning of Taurus; and smallest, the Sun [being] around the beginning of Taurus, but the Earth placed around the beginning of Scorpio, if that diversity had come about from the annual motion of the Earth; for the longitude of the star was around the 7th degree of Taurus. “But let us grant,” says Tycho in the same place (from p. 658), “that the star grew and diminished according to the reckoning of its approach to the lands [Earth]; and that it was, as Digges will have it, around the region of Mars, with a parallax of 2 minutes—it would assuredly have suffered the parallax of the annual orb, nor would it have been seen at the autumnal Equinox under the same place of the Fixed [stars], and equally distant from the Fixed [stars] of Cassiopeia, under which it was seen at the vernal Equinox”; and yet Digges confesses, in his treatise on this star, that it, through the whole time of its apparition, stood immovable, and was seen under the same place of the Fixed [stars]. But if he had placed it in the eighth sphere, so great is its distance from the Earth (according to Copernicus) that the diameter of the annual orb is insensible with respect to it, nor could any variation in the apparent magnitude of the star have been detected from the mere approach and recession of the Earth. Since, therefore, that star continually decreased, let Digges acknowledge that it either withdrew itself into the depth of the ether, or gradually perished.

Fifth Argument, from the Trajectory of Comets

[Margin: Kepler’s argument for the Annual motion of the Earth from the motion of Comets.]

[VII.] But here Kepler triumphs, in the history of the three Comets which appeared in the year 1618: for there, in the 8th Epicheirema [attempted argument] (which is had on p. 91), he discourses thus: “A rectilinear trajectory of the Comet being posited, and that [trajectory] languishing [slowing] from an even [motion], by decrements gradually ordered [regular]: the Comet of the year 1618 affords a twofold testimony to the motion of the Earth—one by the motion of longitude, the other by the motion of latitude.” Concerning the longitude, he contends to prove it thus: that the orbit of the Comet, divided into diurnal motions, appeared divided disorderedly [irregularly]: “But no straight line,” says he, “divided into parts by ordered decrements, can appear divided disorderedly, the Earth resting; but it can, if the Earth go around the Sun, and make progressions sensible with respect to the Comet’s speed.” See his Theorem 30 of the same little work. But concerning the latitude he busies himself to insinuate the same, [namely] that, the latitudes of the Comet being observed, the Comet at two places deflected from the direct path of the great circle toward the Ecliptic—first in Libra and Virgo, and again in Cancer, the Earth deflecting toward the Sun, and [that the comet] declined little from the straight line parallel to the straight line of the trajectory through which he supposes the Comet to have advanced: for by this supposition he concludes (p. 92): “Wherefore the apparent path of the Comet, if indeed the true trajectory keeps its own order of decrements, necessarily becomes tortuous; and conversely, because it was tortuous, [such] was the Comet’s path; a rectilinear and ordered trajectory being posited, it follows that the Earth is moved,” etc. But on p. 93 he says that he was led to assert the rectilinear motion of the Comets, not from a lust of innovating, but because he found evident causes of many appearances in rectilinear motion, which in a circular motion of the Comet it is not even easy to dream of: and on p. 97, inquiring why the Comets of the years 1607, 1618, and many others, [when] made slow, began to curve their paths, he answers that it was a mere deception of sight, like the stations and regressions of the Planets; and that this arises from the recession of the Earth—for the Comet, much elongated from the Earth, [moving] through a straight line, also much

[…continues on p. 347 (PDF 382) with the catchword “quoq.”: ”…[much] also diminishes the appearance of latitude”—the close of the comet-argument, the end of Chapter X, and the opening of Chapter XI (the Meridian-line change).]

(printed p. 347 — closes Chapter X, answering Kepler’s comet argument (it rests on a feigned, undemonstrated rectilinear comet-path, and Tycho held the comets refuted the Earth’s motion). Chapter XI then opens, on two arguments from the change of the meridian line and of the pole’s altitude. The First Argument (meridian change) begins: Scaliger’s fiction of mobile equinoctial poles is refuted, and Marsili’s claimed shift of the meridian is examined via the St. Petronius meridian line at Bologna.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 347]

[the Comet, much elongated from the Earth, moving through a straight line,] also much diminishes the appearance of latitude, and the progressions in longitude. Lastly (p. 98) he terminates the first booklet with this clause: “Finally, as many as are the Comets in the heaven, so many are the arguments (besides those which are deduced from the motions of the Planets) that the Earth is moved by an annual motion around the Sun. Farewell, Ptolemy; I return to Aristarchus, with Copernicus as [my] leader.”

[Margin: The solution of the Fifth Argument.]

But what the appearances of the Comets are, which seem to be better explained by the rectilinear motion of the Comets mixed with the annual motion of the Earth, I have now sufficiently taught from Kepler (bk. 8, sect. 1, ch. 26), where [I treated] of this argument somewhat more fully; and there, from num. 5, [I showed] that this argument—not lacking some probability of itself—is nevertheless dissolved by four instances [counter-examples] adduced against Kepler, to which let the Reader have recourse, lest we be compelled to repeat the same here; and besides, let him remember that the absurdities which are in the annual motion of the Earth (now recounted in ch. 9 of this section, after num. 5) prevail over this little spark of probability [drawn] from the Comets for the annual motion, as [a spark] violently struck out of a flint: especially since Kepler’s argument does not proceed absolutely, but from a feigned hypothesis—both of the rectilinear motion of the Comets, and of [their motion] decreasing regularly—but he has demonstrated neither hypothesis. Besides, Tycho would answer with those words which are had in the Epistle written to Magini in the year 1590, on the Calends of December, and is on p. 81 of Magini’s Directions of the Prime Mobile, where [he says] thus: “Nay, even the Comets themselves, of which I have spoken—in so far as some of them advanced around the part opposite the Sun—gainsaid the annual motion of the earth asserted by Copernicus: for it [that motion] took nothing away from their appointed course, much less compelled them to be driven backward, or retarded with a slower step, while we looked on.”