[I.] It is assuredly necessary, for one wishing either to defend or to attack the Copernican hypothesis, first to have it thoroughly explored, and to look deep into all its parts; lest (as has hitherto happened to not a few) he expose himself to be laughed at and scorned by the Copernicans—and that one especially who thought the diurnal revolution of the earth comes about from East to West, whom Galileo deservedly brands (in the 2nd Dialogue). One must therefore know that three motions are attributed to the Earth by this sect: the First is called Diurnal, or [the motion] of the daily revolution, because in the space of 24 hours—in which one natural day is completed—the whole earth is revolved from the same to nearly the same point, about the center of its own body; the Second is called Annual, because its revolution is not completed save in one Solar year; the Third is called the motion of declination, or of parallelism—which we shall now explain distinctly.

The Diurnal revolution of the Earth is explained

[Margin: The region toward which the Earth’s diurnal motion tends.]

[II.] First, Copernicus (bk. 1 of the Revolutions, ch. 5 & 8) denies that the Fixed Stars and the Planets are moved by any motion of the Prime Mobile from East to West, as the Astronomers commonly suppose; but in place of this motion he substitutes a diurnal whirling of the Terrestrial globe (composed of earth, the water enclosed [in it], and the air poured around and akin [to it]), by which it is revolved, about the center and axis of its own body, in 24 Solar hours, from the West through the Meridian toward the East. For all [things] which are seen to move with respect to place are either seen to move so because they really change place, or because, they being unmoved, the sight or eye of the beholder is moved; or because both the object seen and the eye of the beholder are moved unequally: for if the sight and the object were moved with equal speed toward the same part of the world, no motion would be perceived between the thing seen and the eye of the beholder—as Copernicus excellently reasons in that ch. 5. Whether, therefore, the diurnal revolution toward the West be assigned to the stars, or that revolution be attributed to the Earth and to our sight (which beholds the stars from the earth), but toward the opposite part—namely toward the East—in just the same way all the phenomena of the diurnal motion will appear to us; and, as we go to meet [them], the stars will seem to rise, and gradually to ascend above the Horizon up to the Meridian; but, as we pass on beyond and leave the stars behind, they will seem to descend toward the Horizon, and at last to set. Nor will the stars themselves pass through the zenith or the Meridian by their own diurnal motion, but the vertical points of the Earth itself, and the Meridian circles themselves (to be conceived upon the Earth’s globe) will pass from the western region to the eastern; and thus the Sun, now covered, now uncovered, will represent the vicissitudes of night and day. Since, then, in either of the aforesaid ways the phenomena of the diurnal motion can come about, it seemed more probable to Copernicus to ascribe that motion not to the whole world, nor to the vast spheres of the Fixed [stars] and the Planets, but rather to the Earth—as being spherical and tiny in respect of the heaven, and as it were the contained and the placed [thing]. For he indicates these reasons in those words (ch. 5): “But if you shall have granted that the heaven itself has nothing of this motion, while the Earth turns from West to East: as regards the apparent rising and setting in the Sun, Moon, and Stars, if you seriously attend to it, you will find that the matter stands thus. And since the heaven is that which contains and conceals all things—the common place of all—it does not at once appear why motion should be attributed rather to the contained than to the container, to the placed than to the placer.” Of this opinion, indeed, were Heraclides and Ecphantus the Pythagoreans, and Nicetas of Syracuse (in Cicero), turning the earth in the middle of the world; for they thought that the stars set by the interposition of the earth, and rise by its withdrawal. Then (ch. 8), when he had established as certain that the Earth, enclosed by its poles, is bounded by a globose surface, he subjoined: “Why, then, do we still hesitate to grant it the mobility congruent by nature to its [own] form, rather than that the whole world should glide—whose end is unknown and cannot be known? and [why do we not] confess that of its daily revolution there is in the heaven an appearance, and in the earth a truth?” At length (bk. 1, ch. 11), asserting a threefold motion of the earth, he calls this Diurnal [motion] the First—which, he says, is called by the Greeks νυχθημερινόν [nychthēmerinon], the proper circuit of day and night, about the axis of the earth, inclining from West to East, just as [the heaven] is thought to be borne in the contrary [direction] of the world—by describing the equinoctial circle.

[Margin: By the simile of sailors there is set up against [it] the opinion of those who think the Earth does not move.]

[III.] But that the stars are commonly thought to be moved toward the West, rather than the Earth toward the East, this Copernicus ascribes to a popular error, very like that by which sailors sometimes think the ship stands still, and the shores and banks flee in the opposite direction. For he says (that ch. 5) that “this stands just as if the Virgilian Aeneas were to say: ‘We are carried forth from the harbor, and the lands and cities recede.’ For, the ship gliding under a calm, all the [things] that are outside are discerned by the sailors to move after the image of that [ship’s] motion; and in turn they think that they themselves rest, together with all that is with them. So indeed, in the motion of the earth, it can happen that the whole world is thought to go around.”

[Margin: The same simile, used by Cusanus and Buchanan.]

Which simile, used before Copernicus by Nicolaus Cusanus, I noted (ch. 2, num. 3). Nay, also not a few years before the publication of Copernicus’s Revolutions, George Buchanan the Scot (in bk. 1 of the Sphere, composed in most elegant verses) acknowledged the same simile, under the person of the ancient Pythagoreans, but rejected [it], when he sang:

“Since there is nowhere any violence of so great a mass / as could heave from its seat, and move by force, / the heap of the Earth. Nor again does it rotate into a circle, / as a great part of the ancient Sages had falsely believed— / the Samians, sworn to the words of [their] master: / [thinking] forsooth that the lights which gaze on the fires of the stars are deceived, / which suppose the heaven to be whirled around in a swift eddy / while the earth is unmoved; just as, from the shore, [the stern of] a ship / when it flees and skims the salt shallows with a following wind. / When the hills flee, and the woods and cities recede, / so does Night dull the bodily senses with darkness.”

[Margin: Kepler’s similes.]

Kepler too (bk. 1 of the Epitome of Copernican Astronomy, p. 130), besides this, heaps up other similes; for he adds: “He who sails down a river, if not forewarned, will think the nearby banks move in the opposite direction; and if the ship be carried past a stake, sunk [in the water] and washed by the waves, the passengers will cry out that an otter is rising up to meet them. He who is carried forward in a carriage between hedges will swear that the hedges on both sides rush in upon each other; he who [is carried] backward will swear the hedges flee: which impression the eyes conceive, and retain [it] deeply impressed, even when the man is at rest. And he who is swept backward in a carriage, away from some tower of notable height, along a road directed [straight] from the tower, will dread the ruin of the tower rushing down upon his head. So, having beheld a cloud, broadly spread out, moved gently from South to North, he will swear that the stars which fall into the rifts [of the cloud] and flash out from them are moved with a contrary motion, from North to South.”

[Margin: Gassendi’s other simile for this matter.]

But Pierre Gassendi (Epistle 2, On motion impressed by a translated mover) uses the example of two ships: for whether another ship be moved toward our [ship, which is] unmoved, or our [ship] be moved toward another unmoved one, he says that nevertheless the motion always appears [to be] not of our ship, but of the other: so that, if we be in the middle of the sea, and there be nothing but sky on every side and sea on every side, we shall seem to ourselves to stand plainly unmoved, however much we be both moved by a following wind and borne toward another ship fixed by anchors: which [other ship], accordingly, will seem only to approach us by just as much as we in reality approach it. Which would happen most of all to a man either born and bred in a ship, or carried into it while he sleeps and afterward waking, and having nothing else whereby to correct the illusion of the eyes: which [things] being premised, he subjoins: “Now indeed there is the globe of the Earth, into which we are, as it were, carried sleeping—or rather, in which, not think-

[…continues on p. 297 (PDF 332): “…not thinking, we are born” — the rest of Gassendi’s simile, then [IV.] Kepler on why the diurnal motion is commonly assigned to the stars, [V.] the precise character of the Earth’s diurnal vertigo (the terrestrial Equator and its parallels), [VI.] that the water and lower air share the motion (the trade-winds), and [VII.] Copernicus on gravity as an innate propensity of parts to their whole.]

(printed p. 297 — continuing Chapter IV on the diurnal motion: why common sense mis-assigns it to the stars (Kepler, Galileo); the precise character of the Earth’s equable circular vertigo; that the water and lower air share the motion, explaining the trade-wind; and the beginning of Copernicus’s account of gravity as an innate appetite of parts toward their own whole.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 297]

—ing, we are born. But from the moment we opened our eyes and contemplated, besides this globe, another—namely the Sun, [set] in the same expanse with the Earth, as it were, or in the same mundane space—the question was raised which of these globes rest befitted, and which motion? But we, without hesitation, pronounced that beyond doubt rest befits the Earth, and motion the Sun.” [So] Pythagoras, Plato, Aristarchus, and other more ancient [men] gave warning; and likewise the more recent—Copernicus, Galileo, Kepler—[and] several others, perhaps. But too absolutely does [Gassendi] involve Pythagoras and Plato in this opinion, as is clear from what was said (ch. 2).

[Margin: The cause why this motion is commonly attributed rather to the stars [than to the Earth].]

[IV.] But to one inquiring for what cause that motion—which could equally well be attributed to either [the stars or the Earth], with the phenomena saved—has been wont to be reckoned to the stars rather than to the Earth, Kepler answers (in the Epitome of Copernican Astronomy, p. 130): that the motion is not the proper object of sight, but is judged by the common sense, and that in this [judgment] one is deceived for two causes. For, first, a man thinks his eyes rest whenever he knows that the motion by which the eyes are carried does not arise from their own internal motive faculty—that is, when he does not discern that motion by any token of jolting: and therefore he reckons the object, rather than his own eyes, to be moved. Then, it is an easy slope, to those [things] which are far larger than the eye and are widely spread out, to attribute rest, as to [things] hardly mobile—especially if they keep the same position with respect to the eye—but to ascribe motion to smaller things; now the fields and seas of the earth appear far larger than the stars taken one by one, and so, from childhood onward, we have grown accustomed to attribute motion rather to the stars than to the Earth. And Galileo (Dialogue 2, On the Cosmic System) affirms that it is necessary that we not perceive this motion by [our] sense, and that it is imperceptible to us, because we inhabit the Earth and are alike partakers of its motion. But let these [things] be said parenthetically [παρενθετικῶς]; and we must return to unfolding the other conditions of this diurnal motion.

[Margin: The character of the Earth’s diurnal motion.]

[V.] The motion of the Earth, then—which thus far we have said, after Copernicus, to tend toward the East—is a certain whirling or eddying, by which the Equator of the terrestrial globe itself, together with all the terrestrial parallels, is turned about the axis of that same Equator in the space of 24 hours; which [terrestrial] Equator is in the plane of that imaginary [celestial] Equator which the writers on the Sphere commonly employ for explaining the motion of the Prime Mobile. But the axis of the Earth, if it were produced beyond it, and the Earth were moved by no other motion than this diurnal one, would meet both [the world’s poles]—[that is,] the poles of the World. Meanwhile it may be known that in the Earth’s globe there are two poles, or immobile points, resting (to sense) under two opposite points of the heaven. But the parts of the terrestrial surface nearer to those points describe small parallels, and accordingly move more slowly; the more remote, however, [describe] larger parallels, and [move] more swiftly; while the greatest circle, or terrestrial Equator, [moves] most swiftly. And in Copernicus’s opinion there is a single Equator, and that terrestrial; and its motion alone suffices to set forth all [the things] which others set forth by the celestial Equator and its parallels, as is clear from bk. 1, ch. 11, & bk. 3, ch. 1. Finally, this motion is to be judged equable and circular—by this token most of all: that (as Kepler notes, in the Epitome of Astronomy, p. 111) those who use Armillae—that is, perfect circles—after the example of Tycho, for the difference of right ascensions and for measuring the motion of the Prime Mobile, place them so that their axis is perpendicular to their planes, and elevated [by] just so much as is the elevation of the Pole of the World; and, sighting through the dioptras fixed to the rim of the Armillae upon the stars, they see the stars go round the rim of the Armillae equably. Besides which, the spherical figure of the Earth itself demands this circular whirling rather than [the figure] of any other diagram.

[Margin: The diurnal motion common to the Earth, Water, and the lowest Air.]

[VI.] Nor indeed is the element of the Earth alone, in Copernicus’s opinion, turned by the diurnal motion toward the Eastern region, but also the whole water enclosed in the cavities of the Earth, and that part of the air which is contained within and around all the loftiest mountains, or is raised a little above them—as being akin to the Earth and the Water, and consisting of the vapors and exhalations of both, granted that, on account of its thinness, it seems to us elementary air. Hence it comes about that, on account of this common whirling, neither those sailing toward the West, nor birds or clouds passing into the same region, experience any resistance of this water or air, as though [it were] striving against [them]. Nay, all bodies terrestrial and aquatic, and so all birds, and finally all mixed [bodies], so long as they have not gone beyond this lower region of the air, are partakers of this common motion—which therefore they do not feel, because it is common. But whether this motion of the water or of the lower air arises from a certain nature common to it and to the earth, or whether [it comes about] from a rapture effected by the earth, Copernicus did not determine: for (bk. 1, ch. 8) he says: “What, then, should we say of the clouds, and of the other [things] in any way hanging in the air, or subsiding, and again tending into the heights? Except that not only the earth, with the watery element joined to it, is moved thus, but also no small part of the air, and whatever has kinship in the same manner with the earth. Whether because the neighboring air, mixed with earthy or watery matter, follows the same nature as the earth, or because the motion of the air is acquired, which by contiguity it shares from the earth in perpetual revolution and without resistance.”

[Margin: By what force are the water and air set in this motion? — The upper region of the air [is] immune from the diurnal motion.]

But about the higher portion of the air—in which he thinks Comets are formed—he subjoins these words: “We, on account of [its] great distance from the earth, can say that that part of the air is destitute of that terrestrial motion. Accordingly the air which is nearest to the earth, and suspended in it, will appear calm—unless [it be] by a wind or some other impulse, [and] agitated to and fro, as it happens.” Thus you see all [things] interchanged in this hypothesis; for those who reckon the diurnal motion to the heavens think that the element of fire and the upper region of the air are snatched along with it toward the West, the lowest [region] being unmoved; but on the contrary, those who, with Copernicus, impose that whirling upon the Earth think that the lowest region of the air is snatched along with it toward the East, the highest being immobile. But a distinction must still be drawn between the lowest air—if any part of pure air, distinct from the vapors

[Margin: A perpetual breeze within the Torrid [zone] toward the West.]

and exhalations, be intermixed with it (for this is snatched by force from the very whirling of the land-and-water globe, and from the vapors and exhalations cast around [it]; but the vapors and exhalations themselves are moved by [their own] nature, and by the same faculty by which the earth and water itself are moved—of which faculty it will have to be spoken below). But if any part of the air around the earth is, on account of [its] distance from the poles, less subject to vapors and exhalations—of which kind is that [air] which is situated within the Tropics, and is widely diffused through the most open and vast spaces of the Ocean—that [part], as Galileo judged (Dialogue 4, On the Cosmic System, p. 327), and Pierre Gassendi (Epistle 2, On impressed motion), as we shall say (Scholium 5), less follows the terrestrial conversion; and therefore, in that tract, while the Earth is rolled toward the East, the air being more sluggishly carried thither, there is felt a certain perpetual breeze passing from the East, of so constant a tenor that ships too, by its benefit—besides [that] of the running waters—are happily carried to the West Indies, and, setting sail from the same Mexican shores, by the same favor are carried on [and] plow the Pacific sea toward the Molucca Islands and the Philippines; whereas, on the contrary, voyages toward the East are more difficult and of a slower course.

[Margin: What gravity and levity are in this hypothesis.]

[VII.] But since heavy bodies thrown upward, or let down through the air from a tower or the mast of a ship, are seen to fall perpendicularly into the same place of the Earth—and accordingly the Earth does not withdraw itself from under them—and [since] all heavy bodies tend, by their own nature, to the center not only of the Earth but of the world, while light [bodies] ascend from that center: lest this should hinder the terrestrial motion, Copernicus established (bk. 1, ch. 9) that gravity is not a principle of tending to the middle and center of the Universe, but an innate propensity of tending to one’s own whole, that [the parts] may be brought together with it, and may order themselves about the center of their own whole into a spherical figure. For he says: “Indeed I judge that gravity is nothing else than a certain natural appetite, implanted in the parts by the divine providence of the Maker of all, that they may betake themselves into their own unity and integrity, coming together into the form of a globe. Which affection it is credible is in the Sun, the Moon, and the other gleaming wandering [stars], that by its efficacy they may persist in that roundness in which they present themselves. Which [globes] nonetheless accomplish their circuits in many ways. And so, if any part of the Moon or Sun could be torn away from their globe, it—left afterward to itself—would fly together not to the center of the universe, but to the globe of the Sun, or of the Moon. For neither [is] the center of the Universe, [ut-

[…continues on p. 298 (PDF 333): ”…[ut]pote — being a point or nothing” — i.e. the world-center, as a mere point, has no power to attract; the gravity-passage then turns to Kepler. (Page-signature “P p”, catchword “pote”.)]

(printed p. 298 — continuing Chapter IV: the close of the account of Copernican gravity (heavy bodies tend to their own whole by a mixed straight-and-circular motion); then Kepler’s physics of the diurnal motion — the Earth’s inertia, its form or soul as mover, the magnet analogy — and his doctrine of magnetic fibers in the Earth, leading into the question of the Earth’s motive soul.)

[Header: BOOK IX. SECTION IV. — 298]

—being a point or nothing, and lacking all appetibility (as Kepler notes in the Epitome of Astronomy, p. 95), is rightly established as the terminus to which all heavy bodies tend; but rather the Earth itself, together with its center—not insofar as it is a center, but insofar as it is the middle of that whole [Earth], to which the kindred parts are borne. Yet Kepler there adds that this tendency of the parts to their own whole comes about not without a certain magnetic attraction—which, however, is excellently refuted by Cabeo (bk. 1 of the Magnetic Philosophy, ch. 19). But if you press that light things are borne upward, Copernicus will answer (bk. 1, ch. 8) that there is no fire other than this terrestrial [fire], or burning smoke, whose property is to extend whatever it has invaded, and that the extensive motion is from the center to the circumference; but that the terrestrial exhalation or smoke is snatched aloft and thrust out beyond its place, and therefore at once languishes—as though the cause of violence, which had been brought upon the terrestrial matter, were confessed: wherefore levity is not granted, or is not connatural to these bodies.

Therefore, from the motion of heavy bodies to the center (or of light [bodies] from the center of the earth), which would have to be made along the shortest line—and so a straight one—and from the motion of the whirling of those same [bodies], common with the earth, toward the East, it follows that [things] thrown or thrust upward, and [things] gliding down, ascend and descend by a certain mixed motion of straight and circular; granted that that common motion, by this very [fact] that it is common to the eye of the beholders and of [the things] carried with the earth, is not perceived, and accordingly that motion seems only rectilinear and made to the perpendicular: but that it is mixed of straight and circular, Copernicus taught (bk. 1, ch. 8), and that in it the circular prevails, because this is unfailing and uniform, and per se intended by the nature of these bodies, and common to the whole world; but the straight [motion] does not befit them except when badly placed and set outside their place; and it is unequal, nor is it distinguished from the circular in reality, but only in thought—just as a point from a line, and a line from a surface. But these very [things] we shall report in the words of Copernicus himself (ch. 5, num. 17). Here let those words suffice: “We must confess that the motion of falling and ascending [bodies] is twofold in comparison with the world, and altogether composed of straight and circular”; and below: “Since, therefore, the circular motion belongs to wholes, but the straight also to parts, we can say that the circular remains [together] with the straight, as an animal [remains] with being sick. And indeed this—that Aristotle distributed simple motion into three kinds: from the middle, to the middle, and about the middle—will be thought merely an act of reason. Just as we do distinguish a line, a point, a surface, although one cannot subsist without the other, and none of them without body.” Wherefore in this hypothesis the motion neither of heavy nor of light bodies, upward or downward, is made along a line really straight, but [along one] mixed of straight and circular, which however are distinguished only in reason—of what kind it is will be more conveniently disputed in the scholia of this chapter (lest we interrupt too much the thread of this narration), and more fully in chapter 17, from number 6.

[Margin: Kepler’s doctrine on the principle of the Earth’s diurnal motion.]

[VIII.] Thus far, with Copernicus, we have set forth the nature and conditions of the diurnal revolution of the whole globe (composed of earth and water and the atmosphere poured around it), and also of terrestrial and aquatic bodies, with a few [things] inserted from Kepler and Gassendi. Now certain other [things], which Kepler devised of his own or from Gilbert’s magnetic work, must be added. He, then, in the Epitome of Copernican Astronomy (bk. 1, from p. 116 to 128), investigating the effective and subjective cause, with the dispositions for this diurnal motion, established that the terrestrial globe—and the whole earth, insofar as it is whole—in respect of its matter has no natural motion, nay rather an inertia toward motion and a certain reluctance, especially in the denser parts and [those] nearer the center. But if its form be considered—which is a certain faculty and soul moving [it] in a circle—this whirling is natural to it, since nothing is more natural to matter than its form, and to a body than its soul. Thus the nature of the magnet, on account of gravity, tends downward, but from the kind of its form ascends to another magnet, and that ascent is not violent but natural: thus the courses of animals balancing themselves in the air, and the leaps and dartings of cats and serpents, are not violent to the whole animal, if you regard the soul demanding such motions; granted that, in respect of bodily gravity, they may in a certain way seem violent. But before this soul could move the earth,

[Margin: God the first author of this whirling.]

he says (p. 120) that God from the beginning impressed this diurnal whirling upon the earth, from which all subsequent rotations flowed by a continued vigor—just as boys, spinning a top, impress on it an impetus for very many gyrations—and that to this day more than twenty hundred-thousands [2,000,000] of diurnal whirlings have been accomplished; which vigor therefore still perseveres, because no external roughness or density of the ethereal air opposes it. And [he says] that no cause can be given why the earth is revolved rather into this region—namely toward the East—than into another, except this: that from the very beginning it was begun by the Creator to be rotated into this region. Since, however, the vigor of this motion could be weakened, on account of the inertia of the reluctant earth, or the flowing-away of an impetus gradually languishing, [Kepler] contributed to the perpetuity and uniformity of this whirling both the impression of motion made according to the disposition of the parts of the Earth, and a faculty and soul moving and conserving the original impetus, implanted by God.

[Margin: Magnetic fibers of a twofold kind in the Earth’s globe.]

[IX.] As to the disposition of the parts, Kepler (pp. 116 & 121) recognizes in the earth’s globe fibers or filaments of a twofold kind, just as in a great magnet. Of the first kind are the rectilinear fibers parallel to its axis, by force of which, if [the earth] be moved, it keeps itself in its primeval position—just as the axis of the earth, wherever it be transferred, directs itself into the same region of the world in which it was from the beginning, and remains always parallel to itself, and thus has the character as it were of [something] resting, or retaining the same position. Moreover, on account of such fibers parallel to the axis, there is in the terrestrial globe a faculty of directing magnets, and all magnetic [things], toward itself; and in magnets there is a mutual faculty of turning themselves to this region of the Earth, and of agreeing with its axis—or of directing themselves to the poles of the earth, as also [happens] with the little tongues or magnetic needles—unless they be forced to decline toward great continents, or neighboring lesser magnets, where the motion is mixed in proportion to the moving principles. Of the second kind are the circular fibers, like circular threads, with which the rectilinear fibers themselves, parallel to the axis, are interwoven, standing circularly about the axis: which could in some way be set forth by the example of certain spiders, interweaving their filaments with rectilinear rays and circular tracts. But Kepler (p. 122) preferred to use the example of fibers not merely twofold, as in the terrestrial globe, but threefold, found by the Anatomists in the substance of the [stomach-]ventricle, who likewise recognize, among those three orders of mutually interwoven fibers, three faculties of the ventricle—namely an attractive [faculty] according to the straight fibers upward, and a retentive according to the trans­verse, and an expulsive according to the oblique [fibers] downward. But we have a more fitting example in trees, in whose trunk, if it be cut by a plane orthogonal to the pith or its axis, the veins appear so arranged in a circle that nevertheless the ducts of the pores also tend upward (on account of which wood turns out cleavable), and crosswise, after the manner of rays, diverge from the pith toward the bark. Therefore it comes about, by force of these circular fibers, that the motion impressed according to them is [a motion] of a circular whirling about the axis, describing circles at right [angles] to the axis. And so Kepler says (p. 121) it is likely that that very continued species of the first rotation, impressed by God upon the earth, insinuated itself into the body of the earth according to the ductus of the rectilinear fibers (but [those] set circularly around the axis), and was transformed, as it were, into a special bodily form, the conserver of this diurnal motion—no longer a guest (as is the impetus in a top spun by boys), but a dweller [inquilina], and now the victress and tamer of the matter inert of itself: or at least that that impetus—the rectilinear fibers demanding rest in the same position, and the circular [fibers] demanding a circular motion, if any be impressed—is the proximate disposition required by the soul and the motive faculty. For he concludes (p. 122) that even if this bodily form of the fibers were the sole cause of motion, nevertheless that which is moved and [that which] moves would not be the same, and that the same globe, by reason of the rectilinear fibers, rests in the same position and underlies the motion, but by reason of the circular fibers continues the conceived impetus into circular motion.

[X.] Yet for many causes, besides the impetus once impressed on the earth by God, and besides its species conformed according to the position and disposition of the aforesaid fibers, Kepler judged that a certain soul and a non-intelle-

[…continues on p. 299 (PDF 334): “…non-intelle[ctive] faculty” — the Earth’s merely motive soul (subterranean heat and the formative faculty of crystals as its tokens; the Earth–Moon mutual approach), then [XI.] Gilbert’s magnet/Terrella argument, [XII.] Kepler’s fourth cause (the Sun), and (with a new sub-head) [XIII.] the Annual motion.]

(printed p. 299 — completing the account of Kepler’s Earth-soul as the internal source of rotation; then Gilbert’s magnet doctrine and Terrella experiment (refuted by Cabeo), and Kepler’s fourth cause, the Sun. Under a new sub-head the chapter turns to the Second (Annual) Motion — the Earth’s center carried about the Sun through the Great Orb in 365 days 6 hours.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 299]

—ctive, non-sensitive, non-vegetative, but merely motive faculty—and the conformer of certain figures—must be superadded to the Earth (Kepler, from p. 123): because, just as bones, nerves, and muscles are instruments and dispositions for motion rather than the motive cause, so [are] the magnetic fibers of the earth, and the impression made according to them; [and] then the vigor, speed, and uniformity of this motion will be more securely conserved

[Margin: Foundations for establishing a motive soul in the Earth’s globe.]

if it be from a soul as from an internal principle and source—which reproduces its own acts to itself as an Entelechy, and refreshes itself—than if it be from an external principle, or an impetus wandering in a foreign subject; and it will be more assimilated to the first mover, God, who is the supreme Intelligence, if it be a soul than [if it be] not a soul; and that very direction of the axis, drawn into act with so great a uniformity of circular motion and so perennial, is an argument of a soul—if not an intellective [one], at least by some instinct the moderatrix of this motion. To these are added other indications of this soul—namely the perpetual and sensible subterranean heat (for as cold is proper to matter, so heat is a vestige of soul); likewise the formative faculty of fossils, minerals, [and] hexagonal stones in certain crystals and salts—similar to that faculty which in the air forms hexagonal snow, flies, and locusts, and in water so many monsters. And in the Introduction to the Commentaries on Mars he says that, if the Moon and the Earth were not held back, each in its own circuit, by an animal force or another equivalent [one], the Earth would ascend toward the Moon [by] the fifty-fourth part of the interval, but the Moon would descend toward the Earth [by] the remaining fifty-three parts or so of the interval, and there they would have to be joined, on account of the mutual magnetic attraction—if, however, they were of the same density.

[Margin: The Earth a magnet, according to Gilbert.]

[XI.] But for these [things] which Kepler devised concerning the soul of the Earth and the ductus of the magnetic fibers, William Gilbert had gone before; for (bk. 5 On the Magnet, ch. 12) he had asserted that the magnetic force, on account of motions so various and wonderful, is either animate or an imitatrix of soul; and (especially bk. 6, ch. 4) he had tried to show, by experiments of the Terrella, that the globe of the Earth is a great magnet. Now a Terrella is nothing else than a magnet shaped into the form of a globe or sphere; in which it will be permitted to one experimenting to detect two poles and faces, bounding its axis; and magnetic needles superimposed always agree with its axis according to its length, but as to altitude are inclined more or less toward the poles of the Terrella, according as they are more or less distant from them. Since, therefore, similar [things] happen to magnetic needles in respect of the axis of the Earth, hence [Gilbert] thought he could gather, probably enough, that the Earth is a great magnet; and that, just as the globe of a Terrella—enclosed in a wooden box (that it may float) and set upon water, so that its northern pole inclines toward the South—turns itself by a circular motion about its center, until its northern pole regards the North; so the Earth is fit for the magnetic revolution, that it may conserve its position toward the poles of the World, which it once had. Which would be yet truer if (as Peter Peregrinus affirms) the globe of a Terrella, suspended over its poles in the meridian, were revolved in 24 hours. But that the Earth is not a great magnet, our Cabeo has excellently shown by arguments (bk. 1 of the Magnetic Philosophy, ch. 19); nor that the diurnal conversion of the Earth is rightly deduced from the conversion of a Terrella toward the poles—[as] we shall show below (ch. 7, num. 10 & 11). Moreover Gilbert himself (bk. 6, ch. 5) judged that gravity is the appetite of the terrestrial parts to tend to their own primary globe; which appetite he placed also in the parts of the celestial globes, in respect of their primary globes—namely the Sun, the Moon, etc.

[Margin: A fourth cause of the Earth’s diurnal motion, from Kepler — namely the Sun.]

[XII.] Besides the causes already aforesaid, by which the diurnal revolution of the earth comes about, Kepler recognizes yet a fourth (bk. 4 of the Epitome of Copernican Astronomy, from p. 550)—namely the Sun—that he may render a physical reason for the equation of natural days, which (bk. 1 & 3, or pp. 108 & 286) he had set forth, and about which we [treated] (bk. 3, ch. 32, num. 4): namely that [equation] which, as Tycho experienced in the Eclipses, supposes the summer revolution of the Earth a little slower than the winter, and that this arises from the greater interval between the Sun and the Earth in summer than in winter—on account of which the faculty of the Earth is then less strengthened by the Sun than in winter; which inequality of the diurnal revolution is recognized also by Longomontanus (bk. 1 of the Theorics, ch. On the Sun) and Bullialdus (bk. 2 of the Philolaic Astronomy, ch. 6). Kepler assumes, therefore, that the archetypal number of the earth’s revolutions within one year ought to have been round, and [of] 360 days, rather than composed of inarticulate, ignoble, and broken [numbers]—namely of 365¼ days; and that thus the earth, if it were not incited by the Sun, would be moved more slowly in [its] diurnal revolution, inasmuch as it would revolve 360 times within a year; therefore that it adds five supernumerary revolutions, with a quarter of a day, this is to be attributed to the speed of the Earth, incited by the Sun’s light so much the more strongly as it becomes nearer the Sun. But how that supernumerary portion is to be distributed into the parts of the Physical equation of natural days, we have already taught from Kepler himself (bk. 3, ch. 32, num. 4).

[Margin: The Earth’s diurnal revolution is the cause of the Moon’s proper motion, according to Kepler.]

Moreover, just as the Earth is incited in its diurnal revolution by the Sun, and just as all the primary Planets, by the whirling of themselves about their own center, emit a certain species by which they grasp, as it were by hand, their secondary Planets—namely the Sun [grasps] the six lesser Planets, and Jupiter its satellites, and whirl them around in a circle—so the Earth, by gyrating about its axis, emits from itself a certain species by which it grasps the Moon and twists it into a circle toward the same eastern region, as much as the inertia of the Moon permits itself to be carried around toward motion. And thus, just as he attributed the motion of the other Planets and of the Earth—but the annual [motion], toward the East—to the magnetic circumtraction of the Sun, through a species emanating from it while it turns about its center; so he attributes the proper motion of the Moon, toward the East, to the diurnal revolution of the magnetic Earth, drawing the Moon into a circle; and [says] that hence it comes about that the Moon is the swifter, the nearer it is to the earth—which he confirms from the kinship between the Moon and the Earth, since the Moon, through the Telescope, appears to be another earth, rough with mountains, seas, and valleys, and [since] the Moon, by its passage over the zeniths, effects the reciprocal tide of the sea. But let it now be enough, and more than enough, for [our] purpose, to have tasted these [things] from Kepler, for explaining, illustrating, and confirming Copernicus’s hypothesis about the diurnal revolution of the Earth.

The Second Motion of the Earth is explained, which is the Annual Translation of the terrestrial center through the Great Orb about the center of the Universe

[XIII.] The second motion, which Copernicus—with Philolaus and Aristarchus—attributed to the Earth, is called the annual translation, by which the center of the terrestrial globe, in the plane of the Ecliptic, is carried uniformly about the Sun (placed in the center, or near the center, of the World) according to the succession of the signs—that is, toward the East—and accomplishes its mean period in 365 days and 6 hours. And with the center of the terrestrial globe, not only the whole earth, but also the whole elementary sphere, and the very body of the Moon and [its] system, are carried around—since the Moon is the attendant of the earth, and as it were its secondary Planet. The Earth, then, turns out [to be] one of six Planets, and is not in the center of the universe. But the Sun, in this hypothesis, ceases to be a Planet, since it is moved neither by the motion of translation, nor even by the diurnal [motion] of whirling, but remains immovable near the center of the universe. And the Orb, or circle, which the center of the Earth describes by this motion in the plane of the celestial Ecliptic, is called by Copernicus everywhere the Annual Orb, but sometimes (as bk. 1, ch. 10) the Great Orb—comparatively to the terrestrial Equator, which the diurnal revolution of the earth describes on the terrestrial surface, [an Equator] which is indeed far smaller than this annual circle; since the annual circle, though different from the Solar one, is yet as great as is, in the Ptolemaic hypothesis, the orb of the Sun. Moreover it can be called great because it has a great equivalence and virtue, since it alone furnishes that which scarcely many other orbs in the Ptolemaic system can furnish—although in respect of the supreme sphere of the Fixed [stars] it is like a point. And to this Great Orb—which it may be permitted to call also the annual [orb] and the terrestrial Ecliptic—the terrestrial Equator is inclined at an angle of 23 degrees 30 minutes: namely, as great as is the obliquity of the celestial Ecliptic to the celestial Equator in the hypothesis of the standing earth, and as great likewise [as] the inclination of the axis of the Ecliptic to the axis of the Equator, or the distance of the Poles of the Zodiac and of the Equinoctial circle. These [things], which summarily about this

[…continues on p. 300 (PDF 335) — running signature “P p 2” — with the catchword “motu”: the rest of Riccioli’s summary exposition of the annual motion (and presumably the third, declination/parallelism motion).]

(printed p. 300 — continuing Chapter IV on the annual motion: Copernicus’s prelude to it from Rev. 1.5 and 1.9 (the planets’ varying diameters permit assigning the second anomaly to the Earth); then the Copernican order of the spheres with the system diagram (Sun at center, planets outward to the immobile fixed stars), and how the single annual motion replaces the Sun’s revolution.)

[Header: BOOK IX. SECTION IV. — 300]

—motion we have touched on; now they must be elucidated from the appendages [adduced] by Copernicus and the Copernicans.

[Margin: Copernicus’s prelude to the annual motion of the earth.]

[XIV.] First, then, Copernicus (bk. 1, ch. 5), when he had made mention of the diurnal motion of the earth, soon added: “If anyone should deny that the earth occupies the middle or center of the world, yet should not grant that the distance [to the fixed stars] is so great as to be comparable to the sphere of the non-wandering stars, but [should grant it] notable and conspicuous in respect of the orbs of the Sun and the other stars, and should think that the motion of those [stars] appears diverse on that account—as though they were regulated to another center than the center of the earth—he will perhaps be able to bring forward a not inapt reason for the apparent diverse motion. For that the wandering [stars] are seen now nearer the earth, now farther, necessarily proves that the center of the earth is not the center of their circles. By how much the less is it [even] settled whether the earth nods toward them, or they toward the earth. Nor would it be very wonderful, if someone, besides that daily revolution, should suppose some other motion of the earth: namely that the earth is moved, and wanders with several motions, and is one of the stars—as Philolaus the Pythagorean is reported to have held, a Mathematician no common one, since for the sake of seeing him Plato did not delay to seek out Italy, as those who have written Plato’s life relate.”

By which words, by a kind of prelude, he prepares his way to the motion of the Earth through the Great Orb; and first he requires the Earth’s distance from the center of the universe to be so great that it has an evident proportion to the distances of the Planets from that same center, but [one] inevident or imperceptible in respect of the distance of the Fixed [stars]. Then, from the fact that the diameters of the Planets appear now larger, now smaller, he gathers that the earth is not the center of their motions; and accordingly that that second diversity or inequality—the greater and more frequent one, which they call the anomaly of the orb, or the Argument, or [the one] which they attribute to the motion of the Planetary orbs (referred to the approach or recession of the Sun)—can not inaptly be attributed to the motion of the Earth, annually approaching them and receding [from them]; and he fortifies himself with the authority of Philolaus. After this, in the same bk. 1, ch. 9, when he had said that in the Sun and Moon and the other Planets there is an affection and inclination of the parts toward their own whole, that they may order themselves conglobately about their center and be conserved together with the whole, and that this propensity is such as heavy bodies have toward the center of the earth—and that nonetheless the center of those Planets is not the center of the universe, but [that they] accomplish their own circuits—he added: “If, therefore, the earth too should make other circuits—as, for instance, [one] according to the center—it will be necessary that they be [the same as] those which likewise appear externally in many [bodies], among which we find the annual circuit. For if it be transferred from the solar [motion] into the terrestrial, the Sun’s immobility being granted, the risings and settings of the signs and of the Fixed Stars (he speaks of the rising and setting in respect of the Solar rays, or the heliacal [one]), by which the morning and evening [phenomena] come about, will appear in the same way. The stations too, retrogradations, and progressions of the wandering [stars] will be seen to be motions not of them, but of the earth, which they borrow for their appearances. Finally the Sun itself will be thought to possess the middle of the world.” Behold how he teaches that the annual motion can be conceded to the Earth, and immobility to the Sun—yet in such a way that not only can all the appearances which were wont to be set forth, in the Sun and the other Planets, through the annual motion of the Sun come about, but also [come about] without imperfection of the real retrogradation and station of them.

[XV.] These [things] being tasted beforehand, Copernicus (in the following chapter—that is, the 10th) treats of the order of the Planets in the System of the World; and both from their light received from the Sun, and from the fact that the three superior [planets], about their evening rising—that is, when they are opposed to the Sun—become nearer the earth, but are removed most when, having become morning [stars], they are conjoined to the Sun; and [from the fact] that Venus and Mercury too, by the opinion of some of the ancients, go about the Sun: he concludes that not the Earth, but the Sun, is the center of their motion—about which Mercury, then Venus, afterward the Earth with [its] handmaid the Moon, hence Mars, Jupiter, and Saturn are revolved. And the annual motion of the earth, which (ch. 5 & 9) he had indicated, and had said [was] not inept for saving the Phenomena of the heaven, he now—shame at last being conquered—introduces absolutely into the System of the World, saying:

[Margin: Copernicus now absolutely introduces the annual motion of the Earth.]

“But indeed, all these [orbs] resting upon a single middle: it is necessary that the space which is left between the convex orb of Venus and the concave [orb] of Mars be discerned [as] an orb too, or a sphere, homocentric with those [two] according to either surface; which [space] may receive the earth, with its handmaid the Moon, and whatever is contained under the lunar globe. For in no way can we separate from the earth the Moon, which exists—beyond controversy—nearest to it; especially since in that space (that is, between the convex of Venus and the concave of Mars) we find a place suitable enough, and abundant, for it. Accordingly we are not ashamed to confess that this whole [region] which the Moon encircles, together with the center of the earth (that is, all the spheres of the Elements and of the Moon), passes through that great orb among the other wandering stars by an annual revolution about the Sun; and that about it (that is, near the Sun) is the center of the world: so that, the Sun also remaining immovable, whatever appears as a motion of the Sun is rather verified in the mobility of the earth.” There follows, therefore, the order of the spheres established and described by Copernicus, as you discern in the appended system.

[Translator’s note — engraved diagram, System VI = the Copernican (heliocentric) system: at the center, the radiant Sun (S); about it, in widening circles, ☿ Mercury (“Revolution of ~80 days”), ♀ Venus (“Revolution of ~9 months”), then the Annual Orb of the Earth and Moon (“Orbis Annuus Terræ et Lunæ — the annual orb revolves,” carrying the Earth ⊕ with the Moon, period 365¼ days), then ♂ Mars (“Revolution of [~2] years”), ♃ Jupiter (“Revolution of 12 years”), ♄ Saturn (“Revolution of 30 years”); the outermost band is the immobile sphere of the Fixed Stars (marked with ✶), to be separated from Saturn’s circuit by an almost immense interval.]

In which [system] the Sun is to be placed not indeed in the very center of the World (if you listen to Copernicus), but about, or near, the center of the world, [at] a distance from that center as great as is, among the Ptolemaics, the eccentricity of the Sun’s orb in respect of the center of the earth—because the Planets, according to the Ptolemaics, regard, in their second inequality or anomaly, the mean motions of the Sun (that is, the equal [motions]), which the annual motion of the Earth furnishes in this place about the world’s center; about which the nearest to the Sun, Mercury, is carried by a revolution of nearly 80 days; then, in a chaster (that is, wider and more remote) orb, Venus, by a revolution of about 9 months; about which [Sun] the globe of the Earth and water, with the whole elementary sphere, and with the Moon and the Lunar heaven, is turned in a period of 365 days with a quarter of a day; and above this orb Mars (in nearly a two-year [period]), Jupiter (in a twelve-year), and Saturn (in a three[ty]-year period) are all revolved toward the Eastern region; but the outermost sphere of the Fixed [stars], to be separated from Saturn’s circuit by an almost immense interval, rests immovable.

[Margin: The effect of the Earth’s annual motion in respect of the Sun alone.]

[XVI.] This annual motion of the Earth being substituted for the annual revolution of the Sun, two kinds of τῶν φαινομένων [tōn phainomenōn], or appearances, are simply explained: the first in the Sun and Moon, the second in the five lesser Planets. Of the Phenomena pertaining to the Sun let us hear Copernicus (bk. 1, ch. 11) thus discoursing: “The second is the annual motion of the center of the earth, which describes the circle of the Signs about the Sun, running likewise from West into East—that is, advancing in consequentia [eastward]—between Venus and Mars, as we said, together with the [things] resting upon it: namely, with the elements and the Lunar heaven, [which] lean upon the center of the Earth. Whence it comes about that the Sun itself seems, by a similar motion, to pass through the Zodiac; just as—for example—the center of the earth passing through Capricorn, the Sun seems to pass through Cancer; out of Aquarius [the Sun seems to pass into] Leo, and so on, as we said.”

For let there be, for clarity’s sake, in the next following diagram, near the center of the Universe the Sun at S; from which center describe the celestial Ecliptic with the four cardinal points, which the appropriate letters indicate—namely A, the beginning of Aries, C of Cancer, L of Libra, and K of Capricorn; but in the plane of this Ecliptic, and from its same center, describe the interior circle EFBD, which the center

[…continues on p. 301 (PDF 336): ”…[which the center] of the Earth delineates yearly by its motion, from E through F and B to D, until it returns again to E” — with two engraved figures (the annual parallelism of the axis, and the combined annual-plus-diurnal motion with the lunar system), and Riccioli’s account of the seasons, the Sun’s apogee/perigee vs. the Earth’s aphelion/perihelion, and lunar phases & eclipses.]

(printed p. 301 — continuing Chapter IV: Riccioli’s worked example of the annual motion using a first diagram — the Earth at four seasonal stations about the Sun, its axis kept parallel — showing how it yields the seasons, apsides, and eclipses exactly as in the geocentric hypothesis. A second diagram then combines the annual and diurnal motions with the lunar system and phases.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 301]

[which the center] of the Earth delineates yearly by its motion, from E through F and B to D, until it returns again to E. For it will be manifest that, if the center of the earth be at E, under the beginning of Aries, [then] to an eye G, on the

[Translator’s note — engraved Diagram 1 (annual parallelism): the radiant Sun (S) at the center of the celestial Ecliptic, whose four cardinal points are A (Aries), C (Cancer), L (Libra), K (Capricorn). On the inner circle (the Earth’s annual orb) the Earth-globe is drawn at four positions — E (toward Aries), F (toward Cancer, top), B (toward Libra), D (toward Capricorn, bottom) — each globe carrying its pole P, its ecliptic-line G…I, and H, with the axis kept always parallel to itself; the Moon (N) is shown beside the Earth at B. The figure shows that, as the Earth runs E→F→B→D, the Sun appears successively under the opposite signs.]

surface of the earth looking toward the Sun S along the line EGSBL, the Sun itself will appear under L, the beginning of Libra; but the center of the Earth having advanced from E to F, under the beginning of Cancer, the inhabitant of the Earth will see the Sun S along the line FSK, under the beginning of Capricorn; hence, the Earth proceeding into B, or to the beginning of Libra, the Sun will be seen to be under the beginning of Aries A; and the Earth carried forward to D, under the beginning of Capricorn, the Sun will appear to it under C, which is the beginning of Cancer; and so concerning the other Signs all [things] are to be understood, according to opposition. Wherefore, when the Vernal Equinox happens for us, the Earth is in the autumnal section—that is, under the beginning of Libra in respect of the Fixed [stars], or rather in respect of the Rational Zodiac; and when the Autumnal Equinox happens, the Earth is under the vernal section; and when the [summer] Solstice happens, it is under the beginning of Capricorn; but when the Winter-solstice [Bruma], under the beginning of Cancer. Wherefore, just as the revolution of the diurnal whirling of the Earth effects for us the vicissitudes of days and nights, so the annual revolution [effects] the four seasons of the year, and brings back every variety within them which the Sun [brings] in the Ptolemaic hypothesis—the axis of the terrestrial Equator being supposed, however, inclined to the plane of the Ecliptic by 23½ degrees, and at right [angles] to the Equator, and always parallel to itself, as we shall say below.

[Margin: How the Sun’s apogee and perigee correspond to the Earth’s aphelion and perihelion.]

Moreover, since the center of the annual or great orb is distant from the center of the Solar body by as great a portion on the line of the Apsides as, in other hypotheses, is supposed to be the Eccentricity of the Solar orb (that is, [its] distance from the center of the universe); and [since], in this age, the greatest distance of the Sun from the Earth—or its Apogee—is about the beginning of Cancer, or about the 7th degree of it, but the Perigee about the 7th degree of Capricorn: it follows that the Sun is then apogee (that is, most distant from the Earth) when the Earth itself, by its own motion, has come under the 7th degree of Capricorn—for then it will behold the Sun under the 7th degree of Cancer, and itself in turn will be aphelion (that is, most distant from the Sun); but on the contrary the Sun will be perigee, and the Earth perihelion, when the Earth has come to the 7th degree of Cancer, where it will behold the Sun under the 7th degree of Capricorn.

[Margin: The effect of the annual orb in respect of the Sun compared with the Moon.]

And since the Earth carries with itself the Lunar heaven, and the Moon goes about the Earth—now interposed between the earth and the Sun, at the new moons, now having the Earth between itself and the Sun, as at the full moons—not only eclipses, but also the other aspects of the Moon to the Sun, are represented to the Earth itself just as if the Earth rested in the center of the world, and the Sun were carried around through its annual orb.

[XVII.] It pleases [me], however, to set before the eyes by a peculiar diagram those [things] which we have said about the annual revolution mixed with the diurnal, and about the Moon. Therefore, from A, the center—in which the center of the Sun nearly is—describe the Earth’s annual orb BECD; and, a center being made on its periphery at C, describe from it the terrestrial globe, whose Ecliptic FGOH is in the plane of the great orb BECD, but whose Equator FIOL is inclined to it

[…right column, p. 301 (PDF 336) — running head “TERRAE MOTAE. 301” — continues:]

at an angle GFI, or HFL, of 23½ degrees. Let the portion of the earth illuminated by the Sun—that is, the diurnal hemisphere—be HFI, and the nocturnal HOI, casting into the part turned away from the Sun the terrestrial shadow HXZI, which—although the figure shows it truncated—do you conceive extended right up to the apex of its cone. Then draw through C, to the surface of the terrestrial globe, several straight lines designating the greatest circles of the earth, at right [angles] to its Equator if you choose the position of a right sphere, or oblique if [the position] of an oblique [sphere], which may serve now for the Meridian, now for the Horizon: of which kind, for example, let FCO be, which represents the meridian of the inhabitant F, who has midday, and of the inhabitant O, who has midnight; whose right Horizon to the Equator is HCI.

[Margin: The succession of hours from the Earth’s diurnal revolution.]

And since the Earth, [resting] upon C, is turned about the center of its body toward the East, from O to H, and in the space of 24 hours is wholly revolved, it comes about that to the eye [at] H the Sun rises, and to the eye [at] I it sets; while to the eye [at] F it is midday, and to the eye [at] O midnight. But after three equinoctial hours, the Meridian FO rolls down to the position PQ, and the Horizon HI to the position MN; neither actually discharges the office of Meridian or of Horizon, but retains only the common character of a circle of Declination and an Hour-circle. Wherefore, the eye [at] O being transferred to Q, it will be the 3rd hour after midnight; and the eye [at] Q being borne to H, the Sun will rise; but the eye which was at H, carried down to M, it will be the 3rd hour after sunrise; and the eye [at] M—for which before it was the 3rd Babylonian hour, or 3 before midday—being now borne to F, it will be midday; but the eye [at] F, which first enjoyed midday, being rolled down to P, it will be the 3rd hour after midday; and the eye [at] P, borne to I, the Sun will now set; and the eye which three hours before was at I, carried off to N, it will be the 3rd hour after sunset, or 3 before midnight; at last the eye which had been at N, revolved to O, it will be midnight. And so concerning the other hours of the day, and the vicissitudes of days, according as the Horizons designated to the Equator on the terrestrial globe are more or less right or oblique.

[Translator’s note — engraved Diagram 2 (combined annual + diurnal motion, with the lunar system): a large outer circle (the Earth’s annual orb D…E…B) about the central radiant Sun (A); near the top, the Earth-globe is drawn greatly enlarged at position C, tilted, with its day-hemisphere toward the Sun and its dark shadow-cone (X…Z) stretching away above; around it are marked the ecliptic and equator points (F, G, O, H, I, L), the rotating meridian/horizon positions (M, N, P, Q, R), and the encircling lunar orbit STRV with the Moon shown at successive phases (new at S, dichotomy at T, full at R, etc.); below, the small inner system about the Sun A shows the Moon’s phase-globes (n, r, m, u) and points p, q.]

[Margin: Lunar Phases and Eclipses, [given] the Earth placed outside the center of the world.]

Now, for the Lunar system, from the center of the earth C describe the circle or orbit of the Lunar heaven STRV, in which the new Moon—interposed between the earth C and the Sun A, illuminated toward the Sun but dark toward the earth—will be able, if its latitude from the great Ecliptic of itself, or on account of the parallax of latitude, does not stand in the way, to cover the Sun from the Earth by a total or partial Eclipse; but the same [Moon], in the first quarter, will be seen διχότομος [dichotomos], or bisected, at T, and such will it appear to the eye [at] I, the Sun setting; or nearly such to eyes not far removed on this side or beyond I. Now, a semicircle being completed, the Moon will be at R, and will appear, to the hemisphere HOI, full of light—unless a slight latitude from the plane of the Ecliptic has carried it within the sha-

[…continues on p. 302 (PDF 337) with the catchword “bram”: “…within the sha[dow]” — the rest of the lunar-eclipse account (the full Moon darkened in the Earth’s shadow), and presumably the third (declination/parallelism) motion of the Earth.]

(printed p. 302 — continuing Chapter IV: the lunar-phase account closes, followed by the phases of Venus and Mercury and the apparent stations and retrogradations produced by the two motions. Then begins the “compendium” by which the Earth’s single annual motion explains the phenomena of the five lesser planets, set out in numbered heads — the motion of commutation, the shared mean motions, and the merely apparent stations and retrogradations.)

[Header: BOOK IX. SECTION IV. — 302]

—shadow of the earth; for then it will undergo an Eclipse. At last, at V, at the time of the second quarter, it will appear bisected—and indeed, to the eye [at] H, the Sun rising; from which phases the others are most easily given to be understood. You see, therefore, that it is not necessary, for these [phases] or for the Eclipses of the Luminaries, that the earth be in the center of the universe A; but that the Sun can be in it, and the Earth be removed by a due interval from that center, provided that it carries with itself, through the annual orb, the system of the Lunar heaven and the elementary sphere, resting upon that same center C.

[Margin: Certain things about the phases of ♀ Venus and ☿ Mercury are tasted beforehand.]

But if it please [you] to describe, from A, the interior orbs of Venus (u p n) and of Mercury (m q r), which the great orb contains within itself, it will at once appear how, to the eye [at] I (for which we set the Sun to set), Venus appears at u [as] an evening [star], in its greatest digression from the Sun, and nearly horned, not yet plainly bisected; as also Mercury [is] an evening [star] at m. But to the eye [at] H, for which the Sun rises, Venus will appear at n [as] a morning [star], and Mercury at r [as] a morning [star], each with a sickle-shaped light; but in the other places of its orb [each appears] now in one phase, now in another; while at p and q they will be hidden utterly behind the back of the Sun.

[Margin: A certain station, direction, and retrogradation of terrestrial bodies, by force of the diurnal and annual motion.]

Lastly, from these two motions—the Diurnal, by which the Earth [is turned] about its own center, and the Annual, by which the center of the Earth, with the whole atmosphere and the Lunar heaven, is transferred toward the East—it follows that the motion which these bodies daily undergo by force of the annual motion turns out unequal by force of the diurnal: because the Diurnal [motion] of the points of the terrestrial surface, in the whole arc IOH (which is nearly the nocturnal arc), is direct and swift, and toward the same eastern region in which is the motion of the center C; and therefore it adds to the Annual motion, and most of all at the point O, of midnight, where the highest velocity occurs. But in the arc HFI (which is nearly the diurnal arc), the diurnal motion is, as it were, retrograde toward the western region, and subtracts from the annual motion of the center—especially at F, the point of midday, where the highest slowness is; but near the points H (for which the Sun rises) and I (for which it sets), the motion is nearly stationary, and the diurnal [motion] adds nothing to, nor takes anything from, the annual motion of the center C: for which diversity consult the Tables to be set down (ch. 22, num. 1). Wherefore all the points of the Earth set outside the center, and all bodies earthy and watery, or of thicker air, following the motion of the Earth, daily turn out once direct, once retrograde, and twice stationary; and such would they appear to an eye established at A, the center of the annual orb.

[Margin: The Moon stationary and retrograde by force of these [motions].]

But the Moon too, in its circle STRV, is each month compelled to be once Direct in the arc TRV—namely from the first quarter T to the second V, and swiftest at the full moon R, as to its monthly motion conjoined with the annual—but from the second quarter to the first of the other Lunation it becomes Retrograde, and slowest at the new moon S, but at the quarters Stationary. But about these stations, directions, and retrogradations of the Earth and Moon, see, if it please [you], what we shall more conveniently say below (ch. 14, from num. 4, and ch. 19, from number 12).

[Margin: The effect of the Earth’s annual motion in respect of the lesser Planets.]

[XVIII.] Now further, the effects of the Annual motion of the Earth in respect of the five lesser Planets, and the phenomena represented through it by a truly wonderful compendium, are very many, and are summarily indicated by Copernicus (bk. 1, toward the end of ch. 9), where he says of the annual circuit: “Since, if it be transferred from the solar [motion] into the terrestrial, the Sun’s immobility being granted, the risings and settings of the Signs and of the Stars (namely the heliacal [ones]), by which the morning and evening [phenomena] come about, will appear in the same way: the stations too, retrogradations, and progressions of the wandering [stars] will be seen to be motions not of them, but of the Earth, which they borrow for their appearances.” But in the same book (ch. 10, and bk. 5, ch. 2 & 3, and ch. 21 and 26) he explains many other of their phenomena through the annual orb, for representing their second inequality or anomaly of the orb; and the same [things] have been diligently reviewed by Georg Joachim Rheticus (in his First Narration), Kepler (in the Cosmographic Mystery, ch. 1, and in the Epitome of Copernican Astronomy, bk. 4, from p. 542, and in the Introduction to the Commentaries on Mars), Galileo (Dialogue 3, On the System of the World), Pierre Gassendi (Epist. 2, On motion impressed by a translated mover, and in the Astronomical Institution, bk. 3), and the Philolaus revived, published at Paris. Of which it is permitted to enumerate the chief, briefly.

[Margin: The second anomaly of the inequality of the Planets explained by the single Great Orb.]

First. Since it has been observed that the five lesser Planets, besides the first equality or anomaly which they have in their periodic motions independently of the Sun, have also another (and that the greater and more frequent one), depending on the Mean motion of the Sun according to the ancients, or the True [motion] according to the more recent Astronomers (per what was said in bk. 7, sect. 1, ch. 7); and since that diversity arises, in the ancient hypothesis, from the revolution of the Sun toward the Planets—which is swifter than their own proper motion in Saturn, Jupiter, and Mars, but slower in Venus and Mercury—all that anomaly is excused through the annual approach of the Earth itself (from which we behold the Planets) toward the Planets, or its recession from them; and the Sun turns out [to be] the center of the Planetary system, as it is the fount of motion and of light. Which equivalence Copernicus indicates (bk. 1, ch. 5, from those words “Which being assumed, etc.”), and (bk. 5, ch. 1), where he calls the motion of the Earth toward the Planets the motion of commutation. For he says:

[Margin: What is the “motion of commutation” in Copernicus?]

“There is, then, privately to each Planet, its own revolution of commutation—I mean the motion of the Earth toward the Planet, which they unfold between themselves. For we say that the motion of commutation is nothing else than that in which the equal motion of the Earth exceeds the motion of those [planets]—as in Saturn, Jupiter, Mars—or is exceeded [by it], as in Venus and Mercury.” Wherefore that Anomaly, which in Ptolemy is called the motion of inequality or of diversity, and among the Alfonsines the Anomaly of the argument, and by Longomontanus the Motion of Anomaly, and by many the Anomaly of the orb; [and which] in Copernicus and in the Prutenic Tables is called the Anomaly of Commutation; and which is explained by the ancients through five orbs, together with the Sun’s Eccentric—this is represented by Copernicus through the single Great Orb of the Earth’s annual motion; and thus are removed the three epicycles of the superior [planets] and the two Eccentrics of the inferior, which Ptolemy employed for explaining that second diversity.

[Margin: The Earth’s annual motion causes the identity of the [mean] motion of ☉ Sun, ♀ Venus, ☿ Mercury.]

Second. There seems to be rendered the reason why the Sun, Venus, and Mercury are equal in [their] mean motion of longitude—that is, have equal revolutions of longitude—according to that [saying] of Plutarch (On the Opinions of the Philosophers, bk. 2, ch. 16): “Plato and the Mathematicians think the Sun, Venus, and Mercury are moved with equal motions.” Whence it comes about that the table of the mean motion of the Sun serves also for computing the mean motions of Venus and Mercury. For the reason, according to Copernicus, is that they do not have three distinct orbs, as in Ptolemy, but the single annual motion of the Earth accomplishes their motion in longitude—as being enclosed within the great orb. And from the fact that the Earth is revolved about these three Planets, the Earth-dwellers reckon that those [planets] are carried about themselves [as] immovable, and out of one motion they make three. Hence, pressing the ancient system, Copernicus (bk. 1, ch. 10) says: “But what cause will they allege, who place Venus under the Sun, then Mercury, or separate [them] in another order, that they should not likewise make separated circuits, and diverse from the Sun, as the rest of the wandering [stars]?”

[Margin: The appearance of stations and retrogradations from the single annual motion of the Earth.]

Third. There seems to be rendered the reason why the five lesser Planets appear Stationary and Retrograde, and do not always go forward Direct—which seems the greatest imperfection in the celestial bodies, and which kept the ancients much troubled, as may be seen in Vitruvius (bk. 9, ch. 4) and Pliny (bk. 2, ch. 16), and before them Apollonius, as we narrated more fully (bk. 7, sect. 5, ch. 3). For in the Ptolemaic system, in reality, on account of the motion of the superiors [being] hindered in their Epicycles, or tempered by the motion of the other orb of the inferior Planets in their Eccentric orbs, sometimes they move not at all as to true motion beneath the Fixed [stars], but seem to stand; but sometimes they go back toward the West. But in the Copernican hypothesis a Phenomenon of this kind is a mere appearance, arisen not from the object itself or the real motion of the Planets, but from the translation of our eye with the Earth. For because the Earth, overtaking by its annual motion the superior and exterior Planets, is swifter than they, and leaves behind it those [planets] which it saw before it, afterward, at its back, toward the opposite regions of the world; but on the contrary is slower than Venus and Mercury, the interior Planets (or [those] enclosed in the great orb), and allows itself to be surpassed by them in antecedentia—[hence] they seem sometimes to go back, and in the transit from a direct course to a retrograde, or from a retrograde to a direct, to stand still; whereas in reality it is the Earth that makes these commutations of aspects and of motions by its single motion. How this happens we have already set forth by diagrams suited to it (bk. 7, sect. 5, ch. 4).

[Margin: The Earth’s annual motion frees the Sun and Moon from stations and retrogradations.]

Fourth. Hence there seems to be rendered the reason why the Luminaries do not appear stationary or retrograde: for the cause is that the Sun indeed rests, while the Earth is always moved with an equal motion in consequentia; wherefore the Sun too [seems] toward the opposite par-

[…continues on p. 303 (PDF 338): “…the opposite par[ts]” — the Sun always seems to advance, the Moon neither to stand nor recede (its motion being common to Earth and lunar heaven); then Fifth through Eleventh more Copernican advantages, and [XIX.] the fixed-star parallax objection with its Aristarchus/Copernicus solution.]

(printed p. 303 — continuing the numbered compendium of what the annual motion explains: why the Moon is never stationary or retrograde, the sizes of the retrograde arcs, the planets’ elongations, epicycle proportions, the superiors’ behavior at conjunction and opposition, latitudes, and altitude variations. The page then raises the great objection — that the annual orbit should cause a parallax of the fixed stars — answered by their immense distance.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 303]

—parts always seems to advance to itself; but the Moon seems neither to stand nor to go back, because the annual motion of the Earth is common to the Earth and the Lunar heaven; and two mobiles which have the same motion toward the same regions seem to be mutually at rest: whence the motion of the earth is not discerned in the Moon, as in the other planets. But in the Ptolemaic hypothesis the reason for this difference is rendered more laboriously.

[Margin: The variety of the arcs of station and retrogradation, from the earth’s annual motion.]

Fifth. From the same place is sought the reason why a greater progress, and a smaller regress, appears in the Planets nearer the Earth than in the more remote—that is, why the arc of direction is larger in Mars than in Jupiter, and in Jupiter than in Saturn; larger likewise in Venus than in Mercury; but the arc of Retrogradation [is] smaller in the same, as is clear from the table set down (bk. 7, sect. 5, ch. 2, num. 4). But, on the contrary, why the alternations of station and retrogression appear more frequently in ♄ [Saturn] than in ♃ [Jupiter], and in ♃ than in ♂ [Mars], and likewise more frequently in Mercury than in Venus. Namely because the Earth, by its motion, more swiftly overtakes Saturn than Jupiter, and Jupiter than Mars; but contrariwise [it is overtaken] more slowly by Venus than by Mercury. Which vicissitudes Copernicus touched in those words (bk. 1, ch. 10): “For hence it is permitted to observe—to one contemplating not sluggishly—why a greater progress appears in Jupiter than in Saturn, and a smaller than in Mars; and in Venus [a greater] than in Mercury. And [why] such a reciprocation appears more frequent in Saturn than in Jupiter, but rarer still in Mars, and in Venus than in Mercury.”

[Margin: The reason for the elongations from the Sun, from the annual orb.]

Sixth. Hence likewise appears why Saturn, Jupiter, and Mars can elongate from the Sun by a whole semicircle, but Venus and Mercury not by a whole semicircle, but far less. Namely because the orbs of the three superior Planets are outside the great orb of the Earth, and larger than it; but [the orbs] of the inferior [planets] are interior and smaller, as will be clear to one contemplating the system set down at number 15. But if you stand by the Ptolemaic hypothesis of nature, [then,] observations being set aside, no cause appears why an orb as great as is Mars’s, and Jupiter’s, or Saturn’s Epicycle, could not be assigned to Venus and Mercury, and [why] they could not, embracing the earth by their circuit, elongate from the Sun by a whole semicircle.

[Margin: The size of the Epicycles and Equants, from the annual orb.]

Seventh. From the same situation and motion of the Earth there seems to stand the reason why in the larger orbs the Epicycles are smaller, and in the smaller [orbs] larger. For in Ptolemy, if one wishes to maintain the prosthaphaereses of the orb, Saturn’s Epicycle is smaller than Jupiter’s, and Jupiter’s than Mars’s, while nevertheless the Eccentric carrying Saturn’s Epicycle is larger than Jupiter’s, and Jupiter’s than Mars’s: which is to ask why the prosthaphaeresis of Mars’s orb is larger than Jupiter’s, and Jupiter’s larger than Saturn’s, and Venus’s larger than Mercury’s. But the reason is, that as each of the superior Planets is nearer to the Earth’s orb, the annual orb of the earth has a larger proportion to it, and appears larger. But the true orbs of Mercury and Venus about the Sun are those which the ancients thought [to be] Epicycles; and Mercury’s, as being the swiftest, is also the smallest orb. Thus is removed the vastness of the Epicycle of Venus, and of Mars—[a vastness] certainly excessive, in Ptolemy, in respect of the Deferent.

[Margin: The direction of the Superiors at conjunction, and retrogradation at opposition with the Sun, from the Earth’s annual motion.]

Eighth. The annual motion of the Earth seems to bring with it the cause why the Superior Planets are always direct at conjunction with the Sun, and retrograde at opposition—which Ptolemy cannot give a priori, if it be asked why they do not always move with the Epicycle in antecedentia. But by the single annual motion of the Earth into the same parts into which the Planets move in their orb, it follows that the Earth, being placed between them and the Sun (that is, in oppositions with the Sun), leaves them behind, at its back, by its velocity; but in conjunctions has them before itself, [though they be] slower. And thus far as to the motion of longitude.

[Margin: The Earth’s annual motion renders the Planets’ inclinations to the Ecliptic constant.]

Ninth. The variation of latitudes from inclination, arisen from the approach of the Planets toward the Earth, or [their] recession, in the Ptolemaic Epicycle, requires five diverse librations and variations of the inclinations; but if the Earth itself be supposed to approach them and recede [from them] by [its] annual motion, all the orbs will be inclined most constantly to the Ecliptic, and those superfluous librations will be removed; and thus much more simply, and through a prior cause, the Phenomena of latitudes are saved—especially in Venus and Mercury. See, however, what we said (bk. 7, sect. 4, ch. 5, Scholium 3).

[Margin: The Earth’s annual motion is the cause why ♄ ♃ ♂ appear larger and nearer at opposition with the Sun.]

Tenth. As to the motion in altitude: through the single annual orb of the Earth approaching the lesser Planets and receding from them, the reason at once appears why the three superiors at opposition with the Sun appear largest and are perigee (since the Earth then approaches them); and at conjunction appear smallest and are apogee, namely because the Earth is then most elongated from them. Hence too it becomes manifest why Venus and Mercury, about the evening conjunction, are both perigee and larger, but especially Venus. But hear what Copernicus says of Mars (bk. 1, ch. 10): “For hence it is permitted to observe, etc. Moreover, that Saturn, Jupiter, and Mars are nearer the earth at their acronychal [rising] than about their occultation and apparition. Especially Mars, made all-night-visible [pernox], seems to equal Jupiter in magnitude, distinguished only by [its] ruddy color; but there—that is, about [its] conjunction with the Sun—it is scarcely found among the second-magnitude stars, [and is] known [only] to those pursuing [it] with diligent observation. All which proceed from the same cause as is in the earth’s motion.” For these and similar causes, and to remove the imperfection of the Ptolemaic Equant (which begs the equality of motions from a foreign circle), Copernicus betook himself to the annual motion of the earth—which he himself confesses (bk. 5, ch. 2), saying: “These and similar [things] furnished us an occasion of thinking about the mobility of the earth, and other modes [of thinking], by which the equality and the principles of the art might remain, and the reason of the apparent inequality be rendered more constant.”

[Margin: Given the Earth’s annual motion, the Planets’ motion is simple, nor through another’s heaven.]

Eleventh. All the motions of the Planets being considered—in length, breadth, and depth—and the solid orbs being removed, as they ought to be, it is necessary, in the hypothesis of the resting Earth, that the Planets be carried about through far most perplexed spirals, and such as we sketched, in Mars, from Kepler (bk. 7, at the end of sect. 1); and that Mars, Venus, and Mercury enter the heaven of the Sun. But, the annual motion of the Earth being posited (besides the diurnal), the Planets describe the simplest orbs about the Sun, nor does any of them intrude itself into the region of another. Wherefore [it is] no wonder if, by so many allurements of a most beautiful and most compendious equivalence, the Copernicans so greatly loved this hypothesis; and Copernicus called the annual orb of the Earth the Great Orb, as we said. Which would be of greater excellence if (as some think) through it alone the reason were rendered of the motion of the Solar spots, of the Lunar libration, of the passage of Comets, [and] of the flux and reflux of the sea—about which below.

[Margin: The effects of the [Earth’s] motion and of the annual Orb in respect of the Fixed stars.]

[XIX.] But although the Phenomena of the Sun and of the other Planets, through the annual orb of the Earth (carrying the Moon with it), are saved, yet the Phenomena of the Fixed [stars] do not seem able to be saved. For it would be necessary that, the Earth receding from the Fixed [stars] through the whole diameter of the great orb (which is as great as the doubled distance of the Sun from the earth), and again approaching just as much, the Fixed Stars should appear there smaller, here larger; nay, the meridian altitudes of the same Fixed [stars], observed from the Earth existing under Cancer, would appear much different than when the Earth is under Capricorn. Which diversity, however, has appeared in no phenomena up to now. But for this inconvenience most sagaciously did Aristarchus provide (as Archimedes reports at the beginning of the Sand-Reckoner), and Copernicus—when they posited so great a distance of the Fixed [stars] from the world’s center that the semidiameter of the great orb, compared to it, has no sensible ratio, and on that account exhibits no perceptible parallax in the Fixed [stars]; or (what falls back to the same) by positing the whole great orb [as] so tiny, and the sphere of the Fixed [stars] so vast, that in respect of it the annual orb is like a point—by nearly the same reasoning by which the earth itself, in respect of the supreme heaven, is said to be a point. And this indeed is the cause why Copernicus, meeting these objections (bk. 1, ch. 5), said that he does rightly: “if anyone deny that the earth obtains the middle or center of the world, yet does not confess that the distance is so great as to be comparable to the sphere of the non-wandering stars.” And again (ch. 10): “Accordingly we are not ashamed to confess, etc., that the magnitude of the world is so great that, although the earth’s distance from the Sun, compared to any other orbs of the wandering stars, has a magnitude evident enough in proportion to their amplitudes, [yet] compared to the sphere of the non-wandering stars it does not appear: which I think is more easily to be conceded than that the intellect be distracted into an almost infinite multitude of orbs—which they were compelled to do who held the earth in the middle of the world.” And at last, at the end of the same chapter, [he says] that distance

[…continues on p. 304 (PDF 339) with the catchword “illam”: “…that distance” — the rest of the Copernicus quotation on the immensity of the fixed-star sphere, and (presumably) the third Copernican motion (the declination / parallelism of the Earth’s axis).]

(printed p. 304 — completing the parallax objection with Copernicus’s exclamation on the immensity of the world; then what Kepler and Bullialdus added to the annual orb (the elliptical orbit with apsidal line through the Sun). Under a new sub-head the Third Motion — the declination or parallelism of the Earth’s axis — opens, with its nature, authors, and the spinning-top analogy.)

[Header: BOOK IX. SECTION IV. — 304]

—that [distance] of the Fixed [stars]—confirming [it] from the constant appearance of [their] magnitude, and from [their] scintillation—he concludes: “But that nothing of these [things] appears in the fixed [stars]—that is, no variation in [their] apparent diameter—argues their immense loftiness, which makes even the orb of the annual motion (or its image) vanish from the eyes, if indeed the annual orb were beheld from the Fixed [stars]: since every visible [thing] has some length of distance, beyond which it is no longer beheld, as is demonstrated in optics. For that there is still a very great [interval] between the highest of the wandering [stars], Saturn, and the sphere of the Fixed [stars], their scintillating lights demonstrate: by which token they are chiefly distinguished from the Planets; and [because] between the moved and the non-moved there had to be the greatest difference. So great, forsooth, is this divine fabric of the Best and Greatest [God].”

[Margin: Copernicus’s exclamation [epiphonema] for the immensity of the World.]

But in ch. 8 he had said that the end or boundary of the world cannot be known, and accordingly that it cannot even be determined whether it be finite or infinite. And (ch. 11) he says: “Provided you remember that the distance of the Sun and Earth has already exceeded our sight in the sphere of the fixed stars”; and (bk. 3, ch. 15): “If there be between the Sun and the Earth a distance which cannot be estimated [compared] to the immensity of the sphere of the fixed [stars].”

[Margin: What Kepler and Bullialdus added to the Copernican annual orb and motion.]

[XX.] Thus far the tenets of Copernicus about the motion of the Earth—the annual [motion]—to which Kepler and Bullialdus [added] two other characters, and Kepler moreover a third also. For Kepler (in the Epitome of Copernican Astronomy, pp. 538, 718, & 763, and in the Commentaries on Mars, ch. 5, 6, 33, & 52), and Bullialdus (bk. 11 of the Philolaic Astronomy, theorems 2, 6, 11, 12), taught that the line of the Planetary apsides passes through the center of the body of the Planet and of the Sun—and so that the Earth’s apsis too is drawn through the same center of the Sun; and that the center of the Sun is the center of the universe, but that the center of the great orb is distant from it not indeed by the whole, but by half the Eccentricity of the Solar orb asserted by Ptolemy or Copernicus. Then each [of them] tried to show that the path of the Planets—and so the Earth’s orbit—is not perfectly circular, but Elliptical. Lastly Kepler contended that the Earth, no otherwise than the other five Planets, is carried about by the Sun by a magnetic virtue, while [the Sun], rolled about its own center with an almost monthly whirling, emits from itself a certain species or quality, which whirls about the Planets [as if] grasped by hand, according to the measure of [their] distance and interval—which, however, Bullialdus denies. Which [things] are explained elsewhere, nor are they to be importunely repeated here. But we must come to the third and fourth motion of the Earth.

The Third Motion of the Earth is explained, [the motion] which includes the Declination of the Axis of the Equator, turning itself into the antecedent [signs]

[XXI.] We have not yet exhausted the whole depth of the Copernican hypothesis; and the deeper one descends into it, the more of genius and precious subtlety it is permitted to dig out. A third motion, then (which includes within itself a fourth and almost a fifth), Copernicus saw must be admitted—that he might represent the unequal vicissitudes of the artificial days and of the diurnal arcs, and at the same time the anomaly of the precession of the Equinoxes (which others call the unequal motion of the Fixed [stars], with a trepidation or libration toward East and West), and finally the anomaly of the obliquity of the Ecliptic (which others call a second trepidation, or libration toward the sides of the world)—transferring [all this] from the celestial spheres into the single globe of the Earth, [so as] to represent it through one libratory and nodding [nutabundus] conversion of the terrestrial axis: which motion he called the [motion] of declination, or of the convertible Inclination of the terrestrial axis, or of the reflexion of the axis into the antecedent [signs], with an adjoined libration. Which motion is indeed most difficult to our apprehension, especially since it is involved with the diurnal revolution of the Earth and with the annual circuit of the center—as Galileo himself confesses (Dialogue 3, On the System of the World, Latin p. 289—for we have said it is now translated from the Italian into the Latin idiom); granted that he confesses the system of Copernicus, which is arduous to our imagination, [to be] most easy in effect to nature herself. I shall try, however, to exhibit this motion likewise as little obscure as may be, out of those [things] which Copernicus handed down to us about it (bk. 1, ch. 11), from those words: “To this circle, which is through the middle of the Signs, and [to] its surface, the Equinoctial circle and the axis of the earth must be understood to have a convertible inclination: as far as

[Right column, p. 304 (PDF 339) — running head “LIBRI IX. SECTIO IV.” — continues:]

to the end of the chapter,” and (bk. 3, ch. 3 & 4); [and] Georg Joachim Rheticus (in his First Narration, from those words: “Thirdly, [that] the equinoctial and the axis of the earth have a convertible inclination to the plane of the Ecliptic,” as far as those [words]: “But concerning the Sun’s apogee”—or, if you read its old edition, from column 31 to 40); Kepler (in the Epitome of Copernican Astronomy, from p. 113 to 118); Galileo (Dialogue 3, On the System of the World, from Italian page 372 to 394, but from the Latin

[Margin: Authors who explained the Third motion of the Earth more lucidly.]

[page] 280 to 297); the Philolaus revived; and Pierre Gassendi (Epistle 2, On motion impressed by a translated mover, from p. 128 to 132, and again from p. 137 to 141)—who, taken together by me, seem to have embraced all [the things] necessary for understanding this motion. But lest the medley of these motions—more entangled and disparate than contrary—should seem to anyone impossible, the imagination must be prepared and disposed by some similitude of better-known motions. Let there be, then, in the first place, a Top [Turbo] AB, whose axis [is] CD; which top, bound about with a whip-cord (as boys are wont [to do]), and then thrown onto the pavement by the force of the impetus impressed from the boy’s arm, describes—by a slower gyre—the arc of a larger circle CEF; but, by the force of the motion impressed from the cord, it has conceived a very swift whirling, and, before it is rolled from C, through E, to F, it marks out very many little circles spirally, or screw-wise [cochleatim], on the pavement—say at C, O, E, P, F—and indeed by turning itself into the same part,

[Translator’s note — engraved diagram (the spinning-top analogy): a child’s top AB (axis CD), shown skipping along an arc and marking little loops at C, O, E, P, F (proceeding from G through H toward K), with the top drawn large at the right as a wobbling cone — its nodding cusp C, handle/crown D, and the axis seen “split” into the directions DC, ML, NI. A side-note warns: “In this figure the little circles around C, O, E, P, F ought not to be concentric, as the engraver badly formed [them], but [should be] a spiral, or screw [helix].”]

namely from G, through H, toward K. Observe then the titubation [staggering] of the axis DC, by which it so wavers this way and that that it seems ever to threaten itself with a fall; and, on account of that vibration of the nodding cusp C and of the crown or handle D, [observe it] to flicker with three-forked tongues, so that not one but a manifold axis can seem [to be present], or [the axis seems] split into three—namely DC, ML, NI—or into more. At last, when, gravity prevailing and [the top] inclined to one side from the line of the center of gravity, it has fallen down, you will see it, as to appearance, revolved by the contact of the pavement into the contrary region. By this example, therefore—dissimilar indeed in some conditions, but similar in many—you will easily understand how it can come about that the globe of the Earth slowly describes, with its center, the circle of the annual or great orb, and yet at the same time is revolved into the same eastern part, top-wise into itself, by a diurnal whirling repeated 365¼ [times], and nonetheless its axis, by a certain third motion of libration, wavers about, and is able to describe either little circles or twisted garlands [corollas].

In another way you will conceive the same readily. Let there be a round wooden table, or a wooden disc, whose half meanwhile the preceding figure CEF represents; and to its margin let there be fixed a little vessel full of water—say at C—on which water floats a little wooden globule, having beneath an iron point, [and] above a wooden [point] over against the iron, as though produced on both sides from the axis of the globule, so that the iron [point] stands out under the water, the wooden above the water; then, a finger being put into the water along the margins of the vessel, drive it [the water] around, and with it [drive] the water from G, through H, into K, so that the water conceives a very swift whirling; and at once, the finger being withdrawn, turn around about its own axis R the wooden disc—slowly, however, from C to O: for you will see, meanwhile, the water, by several eddies, enwrap with itself the wooden globe into the same region, and at the same time the wooden cusp of it nod somewhat, and waver tremblingly, by describing a certain little orb or garland. By which example, and others like these, it is given to understand how easily nature, or some Intelligence, can revolve the terrestrial globe about by three similar motions.

[XXII.] This preparation being supposed (although to more robust minds by no means necessary), let us now betake ourselves to Copernicus, who (bk. 1, ch. 11), when he had said that, the plane of the great orb being placed in the plane of the Ecliptic, the terrestrial Equa-

[…continues on p. 305 (PDF 340): “…the terrestrial Equa[tor] and its axis must have a convertible inclination” — Copernicus’s reasoning that, without this third motion, there would be no variation of seasons; the figure (no. XVI) redrawn for the four seasons; and a second figure for the solstitial days.]

(printed p. 305 — continuing on the third motion: Copernicus’s reasoning that without it there would be no variation of seasons, so the axis is turned back into the antecedent signs to remain always parallel to itself, the small residual being the precession. Riccioli redraws Copernicus’s figures in two diagrams walking through the four seasons, and notes the axis’s “reflexion” is more like rest than motion.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 305]

[the terrestrial] Equa[tor] and its axis must have a convertible inclination, at once subjoins the reason: “Since, if they remained fixed—namely the terrestrial Equator and axis—and simply followed the motion of the center [alone], no inequality of days and nights would appear, but always either the [summer] solstice, or the winter-solstice, or the equinox, or summer, or winter, or whatever same quality of season, would remain like itself. There follows, therefore, a third motion, of declination, by an annual revolution likewise, but [reflecting] into the antecedent [signs]—that is, reflecting contrary to the motion of the center. And so, the two [motions] being mutually almost equal and opposite, it comes about that the axis of the earth, and in it the greatest of the parallels, the equinoctial, look toward almost the same part of the world, just as if they remained immovable. The Sun meanwhile is discerned to be moved through the obliquity of the Zodiac by that motion by which the center of the earth [is moved]: no otherwise than if it [the Sun] were the center of the world—provided you remember that the distance of the Sun and earth has exceeded our sight in the sphere of the fixed stars (that is, [that it] is imperceptible and of no sensible quantity, if it were beheld from the fixed [stars]).” Lest, therefore, the axis and the terrestrial Equator be moved according to the ductus of the great orb (or Ecliptic), but remain always parallel to itself, or keep itself equidistant in that position in which it once was at the time of the first Equinox or Solstice, Copernicus thinks there is need that, while the center of the earth is turned in the periphery of the annual orb, the axis of the terrestrial Equator reflect itself little by little into the antecedent [signs], and thus have a convertible inclination to the Ecliptic or great orb, so that—if it were produced—it would run, throughout the whole circuit of the year, into nearly the same parts of the world. Now, that he might in some way set before the eyes the difference of the solstitial days among themselves in an oblique sphere—and [the difference] from the equinoctial [days]—arisen from this threefold motion, Copernicus (in the same ch. 11) delineated that figure which we, with the Sun S added in the midst, and above EFBD the annual orb, [and] ACLK the celestial ecliptic, described at number XVI. Which is here to be set down again.

[Translator’s note — engraved Diagram A (the third motion / parallelism of the axis; = fig. no. XVI redrawn): the radiant Sun S at the center of the celestial Ecliptic (cardinal points C = Cancer above, L = Libra left, K = Capricorn below, A = Aries right). On the Earth’s annual orb the Earth-globe is drawn at four positions — F (under Cancer), B (under Libra), D (under Capricorn), E (under Aries) — each carrying its pole P, the equinoctial diameter G…I, and H, with the axis kept always parallel to itself; the Moon (N) is shown beside the Earth at B. Thus the Sun appears under the sign opposite the Earth’s position.]

Let now the center of the earth be first at F, under the beginning of Cancer, from which let the terrestrial Equinoctial PGHI be described—not in the plane of the Ecliptic or great orb EFBD, yet in such a way that the diameter GFI is the common section both of the terrestrial Equinoctial and of the great orb or Ecliptic. Then draw the diameter HFP at right angles to that GFI; and let the southern limit of the greatest declination of the two planes (or of the obliquity of the Ecliptic to the Equator, or rather of the Equator to the Ecliptic) be P, but the northern H—which obliquity the angle HFS on the one side, [and] CFP on the other, measures, [of] 23 degrees 30 minutes.

[Margin: Representation of the winter-solstice [brumal] day.]

These things being set forth, the terrestrial inhabitants, while the earth is at F, under C [Cancer], will see the Sun S under Capricorn, effecting the winter [brumal] conversion—which the greatest northern declination H, turned toward the Sun, will exhibit: “Since,” says Copernicus, “the declivity of the Equinoctial toward the line FS, through the diurnal revolution, turns out for itself the winter tropic parallel to the terrestrial Equator, according to the distance which the angle of inclination SFH comprehends.” Or, perhaps more clearly: a line conceived immovably from the center of the Sun to the center of the earth is then understood, in the time of one diurnal revolution, to designate on the terrestrial surface a circle parallel to the terrestrial Equator, with as great a declination as is the angle SFH.

[Margin: Representation of the Vernal Equinox.]

Let now the center of the earth set out in consequentia; and, a quadrant being completed, let it be at B; and meanwhile let P, the limit of greatest declination, recede just about as much in antecedentia, a quadrant as it were of its own little circle being completed; and let the angle SFI meanwhile remain (on account of the equality of the revolutions) equal to the angle FSB—for the diameters will remain mutually parallel, namely PFH to PBH, and GFI to GBI; and likewise the terrestrial Equinoctial will be conserved parallel to itself; and these [things] will appear likewise designated in the supreme heaven, on account of its immense distance. Now to the Earth at B, under the beginning of Libra, the Sun S will appear under the beginning of Aries; and the common section of the great orb and of the Equator will coincide into one and the same line GBIS, to which the diurnal revolution admits no obliquity of the aforesaid circles, or declination—for every declination will be at the sides. Wherefore the Sun will appear at the vernal Equinox. Yet still the diameter GI will be in the common section of the aforesaid circles, nor on that account will the plane of the terrestrial Equator coincide with the plane of the great orb.

[Margin: Representation of the summer-solstice day.]

Let the center of the Earth now depart hence, the aforesaid conditions being kept; and, the other quadrant being completed, let it be at D, under the beginning of Capricorn—for the Sun S will be seen by it to enter Cancer C; and because P, the southern limit of declination by which the Equator is inclined to the Ecliptic, has been turned toward the Sun, it will make the Sun be seen in the opposite region (that is, northern), and running through the summer tropic, according to the measure of the angle SDP, which measures the inclination.

[Margin: Representation of the Autumnal Equinox.]

At last let the center of the earth go hence; and, a third quadrant being likewise completed, let it come to E, under the beginning of Aries; for on account of the aforesaid parallelism of the axis with itself, and of the Equator with itself, the common section GEI of the terrestrial Equator and of the annual orb (or Ecliptic) will fall into the line SE, without any declination; and accordingly the Sun S will be seen, having entered Libra L, to celebrate the Autumnal equinox.

[Margin: Another representation of the solstitial days.]

In another way, and by [another] diagram, Copernicus (bk. 1, toward the end of ch. 11) exhibits, on the terrestrial globe, the winter and summer tropic parallel, on the surface of the terrestrial globe, to its Equator, thus. In the subjacent plane let there be AC, the diameter of the Great orb, and the common section of a circle erected to this same plane; in which [circle], from the center of the Earth A (placed under Cancer) and C (under Capricorn), let there be designated, through the poles, the circle DGFI; and let the terrestrial equinoctial axis be DF, and let the Boreal [northern] pole be D, but the Austral [southern] F; and let GI be the diameter of the aforesaid Equinoctial.

[Translator’s note — engraved Diagram B (the solstitial days): two Earth-globes joined by their common axis-line, one at A (under Cancer), one at C (under Capricorn); each globe shows the polar circle DGFI, the axis DF (north pole D = “Boreas,” south pole F = “Auster”), the equinoctial diameter GI, and the winter/summer tropics KL / MN.]

These being posited: when the pole F turns itself toward the Sun, and the inclination of the Equinoctial circle to the great orb (or to the Ecliptic), [being] Boreal, is under the angle IAL, then the diurnal revolution about the axis will describe the tropic KL of Capricorn, or [a circle] parallel to the southern Equator according to the distance IL, and will make the Sun appear at the beginning of Capricorn. Or, speaking more correctly, the diurnal motion about that axis will, to the sight, complete a conical surface, whose apex will be at A, the center of the earth, but [whose] base [is] KL, on a circle parallel to the Equinoctial. In like manner, but with the conditions reversed, all [things] will happen, the center of the earth being placed at C, under the beginning of Capricorn: for the diurnal revolution will describe the parallel, or northern tropic, MN, and will make the Sun appear at the beginning of Cancer. From which it follows, if nothing else befall this reflexion of the axis, that it [the axis] describes on the terrestrial surface, here and there, a little circle, about the axis of the terrestrial Ecliptic, [the latter] always equidistant from the great orb. Or rather—because the terrestrial axis conserves the same position toward the supreme regions of the heaven—the manner in which this retention comes about is more like rest than motion: [it is], as it were, a certain continence and cohibi-

[…continues on p. 306 (PDF 341) — running signature “Q q” — with the catchword “nem”: “…cohibi[tion]” — i.e. the axis’s “third motion” is rather a holding-fast that keeps it parallel to itself; then, presumably, the fourth motion (the precession-libration) and Riccioli’s appraisal.]

(printed p. 306 — continuing Chapter IV: Galileo’s figure for the threefold motion of the Earth, walked through the four seasons; then begins the observation that the parallel axis, prolonged, would describe a giant cylinder whose bases mark a circle on the firmament seen only as a point — so the axis seems to regard the same point of heaven forever, Galileo’s “admirable accident.”)

[Header: BOOK IX. SECTION IV. — 306]

—tion, as Galileo and Gassendi acutely note.

[Margin: Galileo’s diagram for the threefold motion of the Earth.]

[XXIII.] Opportunely, however, the mention of Galileo suggests to us another way, and another figure, by which he (Dialogue 3, On the System of the World) gave to view this admixture of the three motions of the earth—which figure we shall expound more briefly. Therefore, from O, near the center of the Sun, let the Great Orb ♋, ♎, ♑, ♈ be understood [as] described; and at these four cardinal points let the Earth be understood [as] established by turns, by the annual revolution of the terrestrial center, whose axis—produced by imagination outside it—is AB, parallel to itself in every place of the annual orb; and let the diameter of the great orb from Capricorn to Cancer be ♑ O ♋, over which (or, [reckoning] to the plane of the great orb) the axis AB is inclined [by] 23½ degrees—or so that the angle O♋B, or O♑A, is 66½ degrees. For you must conceive the axis AB, with the line ♑O♋, [to be] in one and the same plane, which is right (or orthogonal) to the Ecliptic plane of the great orb ♋ ♎ ♑ ♈—which Galileo with difficulty represents through this figure. And let the Boreal [northern] pole of the terrestrial axis be A, above, and the Austral [southern], below, B—about which axis the Earth, by a revolution of 24 hours, describes innumerable parallels; but, for clarity’s sake, let there be designated on its surface now the Equinoctial CD, and parallel to it the winter Tropic GN and the summer Tropic EF; then the Arctic circle IK, and the Antarctic LM.

[Translator’s note — engraved Galileo’s figure for the threefold motion: the radiant Sun O at the center of the annual orb, whose four cardinal points are marked with the signs ♋ Cancer, ♎ Libra, ♑ Capricorn, ♈ Aries (with the intervening signs along the rim). The Earth-globe is drawn at the four cardinal positions, each shown with its tilted axis A (north) –B (south), the Equator CD, the tropics EF (summer) / GN (winter), the polar circles IK (arctic) / LM (antarctic), and the day/night (bright/dark) hemispheres turned toward or away from the Sun — the axis kept always parallel to itself.]

[Margin: Representation of the [summer-solstice] day and of the summer tropic.]

Let us now consider the Earth placed at the beginning of Capricorn. Since the axis AB declines from the perpendicular—[set up] over the diameter of Capricorn and Cancer—[by] 23½ degrees toward the Sun O, and the arc IK is [of] 47 degrees (but its half [of] 23½ degrees): the illumination of the Sun will light up the terrestrial hemisphere exposed to the Sun, and divided from the shadowy part by the boundary [finitor] IM—which boundary divides in two the greatest circle CD, but [divides] the other parallels into unequal parts, since IM does not pass through their poles AB; but the parallel IK, with [those] enclosed within it, will remain wholly in the illuminated part; just as the parallel LM, and [those] enclosed within it, will remain wholly in the shadowy part. Moreover, since the arc IK is equal to the distance of the Tropics FDN, and the half of that half [is] FD, and the arc from F to the pole A is common to both, the arcs IKF and AFD will be equal, and each will constitute a quadrant. And because the whole arc IDM is a semicircle, the arc FM will be a quadrant, and equal to the arc FKI; and accordingly the Sun O, in this place of the Earth, will be vertical to [one] existing at the point F. But on account of the diurnal revolution about the stable axis AB, all the points of the parallel EF pass through the same point F; therefore on this day the Sun, at the point of midday, will be vertical successively to all dwelling on the said parallel EF; and it will be seen by them to describe, by an apparent motion (which in reality is the earth’s), that Tropic which we call [the Tropic] of Cancer. But to all inhabitants beyond the parallel EF, toward the Boreal pole A, the Sun will decline from their zenith toward the South; but on the contrary, to those dwelling on this side of EF, toward the Equinoctial CD and the Austral pole B, the midday Sun

[Right column, p. 306 (PDF 341) — running head “LIBRI IX. SECTIO IV.” — continues:]

will decline from their zenith toward the Boreal pole A. In this place likewise it appears that the semi-diurnal arc ♑D is equal to the semi-nocturnal ♑C, on the Equator CD, because the boundary of light IM alone cuts it in two; but the semi-diurnal arcs on the parallels above CD, toward the Boreal pole A, are larger than the semi-nocturnal; but on the contrary, below CD, toward B, [they are] smaller than the semi-nocturnal; and those who are in the illuminated part, or [within] the arctic circle IK and within it toward A, enjoy perpetual day; whereas those who are in the Antarctic LM and within [it] are wrapped in perpetual night.

[Margin: Representation of the [winter-solstice] day and of the winter tropic.]

Let the Earth now be in the situation diametrically opposite—that is, under the beginning of Cancer ♋. For it will be manifest, since the Axis AB has remained parallel to itself, nor has sensibly changed [its] inclination, that the aspect and situation of the Earth toward the Sun retains all the rest as in the former situation—similarly indeed, but with an opposite similitude. For the hemisphere which before was shadowy is illuminated by the Sun, to which it is turned; and the Sun becomes, at midday, vertical to those dwelling on the parallel GN; but it has declined toward the South for the inhabitants of the parallel EF, descending from their zenith through the whole arc ECG of 47 degrees; and so the Sun has passed from one Tropic to the other, descending in the Meridians through the said space of 47 degrees. Moreover, those who dwell under the Arctic parallel IK, and within it, are overwhelmed by perpetual night; but those who [dwell] under the Antarctic LM, or within it, enjoy perpetual day; and the semi-diurnal arcs on this side of the Equator CD, toward the Austral pole B, are larger than the semi-nocturnal; but beyond the Equator, smaller than the semi-nocturnal; and to those dwelling on the parallel EF, the Sun O will be seen to describe that Tropic which we call [the Tropic] of Capricorn.

[Margin: Representation of the equinoctial days.]

Let us now behold the Earth, in the upper figure, at the beginning of Libra ♎—from which it discerns the Sun O under the beginning of Aries ♈. Now the axis of the earth (which in the former figures was understood [to be] inclined over the diameter of Capricorn and Cancer, and accordingly to be in the same plane which, cutting the plane of the great orb along the line of Capricorn and Cancer, was erected perpendicularly to it)—if it be transferred to the present figure, and, keeping its parallelism to itself, will be in a plane likewise erected to the surface of the great orb, and parallel to that plane which orthogonally cuts the same surface along the diameter of Capricorn and Cancer. Hence it comes about that the line O♎, which is drawn from the center of the Sun to the center of the Earth, turns out perpendicular to the axis AB. But the same line, drawn from the center of the Sun to the center of the Earth, is always perpendicular to the circle that bounds the light [terminator]; therefore the circle bounding the light will pass through the poles A, B, and in its plane will be the axis AB. But from the Spherics of Theodosius, the greatest circle passing through the poles of the parallels divides them all in two, or into equal portions; therefore the boundary-of-light circle ACBD will divide the parallels so that IK, EF, CD, GN, and LM are each semicircles; and the illuminated hemisphere will be that which [is turned] toward us in this diagram; and the Vernal Equinox will come about for all the inhabitants of the earth. From which is given to be understood the cause of the other, the Autumnal Equinox, when the Earth shall be at the beginning of Aries ♈.

[Margin: Two notable [things] in the parallelism of the terrestrial Axis.]

[XXIV.] But Galileo adds—and likewise Kepler and Gassendi—that, from the fact that the axis of the terrestrial Equator remains parallel to itself throughout the whole circuit of the year, if it were produced on both sides outside the earth as far as the firmament, it would come about that it would describe a huge cylinder (or column), whose either base would designate on the firmament a circle as great indeed as is the annual orb, but which—beheld from the earth, on account of the immense distance of the fixed [stars]—would be like a point; and on that account the axis of the earth is said to regard perpetually the same part of the heaven, and to be turned toward the same point. Granted [that], in strictness, this hypothesis, just as it does not acknowledge an Equator in the supreme heaven, so neither [acknowledges] a pole of the Equator; but the aforesaid bases could be substituted for the poles, which the terrestrial axis would be said to regard. But Galileo, using a subtler scrutiny, noticed in this very place a certain admirable accident. For just as the axis of the earth, keeping the same direction toward the supreme sphere of the Fixed [stars], makes the Sun seem to us, within the circle of one year, to be elevated in the meridian through an arc of 47 degrees, and meanwhile exhibits no [perceptible] ascension of any one and the same Fixed [star] in the meridian, or sensible change of declination; so, on the contrary, if the axis of the earth persi-

[…continues on p. 307 (PDF 342): ”…[if the axis] persisted continually in the same inclination toward the Sun” — there would be no change of seasons, but a 47° annual change of fixed-star declination; then [XXV.] Riccioli’s own clarification of the parallelism (the cone-figure), and [XXVI.] the oblique-cylinder construction.]

(printed p. 307 — completing the “admirable accident” (a Sun-fixed axis would give no seasons but 47° of stellar declination change); then Riccioli’s clarification: if the axis kept a fixed inclination to the great-orb’s axis it would describe a cone and the pole-star would shift 47° in six months, proved with a cone-diagram. Hence the axis must instead be kept parallel on an oblique cylinder.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 307]

—[if the axis] persisted continually in the same inclination toward the Sun—or (what is just the same) toward the axis of the Zodiac—no change would appear in the meridian declination of the Sun: wherefore the inhabitants of the same place would always have the same diversities of days and nights, and the same constitution of the four seasons of the year; and accordingly some would be compelled to endure perpetual winter, some perpetual summer, but others would enjoy perpetual Spring or Autumn. But, on the contrary, the greatest change would appear in the Fixed Stars as to declination, so that, in the Meridian within one year, they would vary [their] declination by 47 degrees—as great as is the distance of the Tropics.

[Margin: Our explanation for the aforesaid parallelism.]

[XXV.] But indeed, since Copernicus explains the conservation of the axis of the terrestrial Equator, and of the Equator itself, each in its own parallelism, by a certain motion of the axis in antecedentia—which motion, however, does not seem to some necessary, or necessarily to be distinguished from the other motions; and [since] it could still seem obscure to someone what it is to lead the center of the terrestrial globe according to the ductus of the Great Orb, or what it is for the terrestrial axis and Equator to follow simply the motion of the earth’s center—that each scruple may be removed by us as far as can be done: First we say [that], if the axis of the Equator, always inclined to the plane of the great orb (or Ecliptic) [by] 23½ degrees, were so carried around with the center of the terrestrial globe about the periphery of the great orb that it always kept the same inclination to the axis of the great orb, it would keep neither its own [parallelism] with itself, nor the parallelism of its Equator with its [own] Equator, nor would it regard the same regions of the supreme heaven, but other and other: for it would describe, by its annual motion, either the frustum of a right cone—or, if it be understood [to be] produced, a right cone, whose axis would be at right [angles] to the circle cutting the cone, and the lines of the terrestrial axis, produced for the diverse situations, would cut one another beyond at the apex of the cone, making with the axis of the cone an angle of 23½ degrees. Wherefore, if the pole of the terrestrial axis, inclined toward the axis of the great orb, were the Boreal pole (which now dwells under the Boreal pole, and sees above its zenith the Cynosure, or pole star—or at least one not distant from its zenith by a whole 3 degrees), after six months it would see that [star] distant from its zenith by about 47 degrees. For the evidence of which matter: let ABCD be the great orb, whose diameter is AEC, and at right angles to it [let there be] the axis of the great orb OER. Let there now be assumed, at A, the angle EAK, of 66½ degrees, and

[Translator’s note — engraved cone-diagram (the alternative that Riccioli rejects): the great orb ABCD (diameter AEC, Sun/center E, the orb’s axis OER). The Earth-globe is drawn at eight positions — A (Cancer), I (mid-Leo), B (Libra), L (mid-Scorpio), C (Capricorn), N (mid-Aquarius), D (Aries), G (mid-Taurus) — each globe OMSQ with Equator MQ and axis OS drawn tilted. If the axis kept a fixed inclination to the orb’s axis, all the axis-lines would converge at an apex K (to the right), forming the cone YKZ, and on the left the cone FKX; the far points Z (Cynosure) and Y mark where the prolonged axis would meet the firmament.]

likewise at C an angle equal to it, ECK; for, AK and CK being produced equally on both sides, on this side beyond the point of concourse K as far as Z and Y, but on the other side beyond the diameter of the great orb—KA indeed to F, but KC to X, and

[Running head, p. 307 (PDF 342): “DE SYSTEMATE TERRAE MOTAE. 307” — right column continues:]

[these being] connected by the straight line FOX, with the termini F and X, and by the straight [line] YRZ, with the termini Y and Z: there will be designated the sides and the diameters of the bases of two right cones—namely the cone FKX and YKZ—of which the former is cut orthogonally by the plane of the great orb. Let there then be chosen eight situations of the center of the terrestrial globe on the periphery of the annual orb; namely, the beginning of Cancer at A, the middle of Leo at I, the beginning of Libra at B, the middle of Scorpio at L, the beginning of Capricorn at C, the middle of Aquarius at N, the beginning of Aries at D, the middle of Taurus at G; and from these points let there be described a circle OMSQ, indicating in some way the globe of the Earth, in which let the Equator be MQ, and its axis, at right angles to its Equator, be OS—yet in such a way that, in whatever place of the Earth, the axis of the terrestrial Equator so keeps an inclination of 23½ degrees to the plane of the Ecliptic that, produced by imagination, it concurs on one side at that same point K, the axis of the great orb (at which we said AK and CK concur), and thence is drawn as far as the line YZ; [and] on the other side, produced, it is understood [to reach] as far as the line FX. For these [things] being kept, the directive line of the axis, while the earth is at I, will be PIK; while at B, will be OBK; while at L, will be TLK; while at N, will be VNK; while at D, will be ODK; and while the Earth shall be at G, the directive line of the axis will be HGK; and so of the other places of the earth. And thus, on account of the same inclination kept to the axis of the great orb (or on account of the concourse of the lines of the produced axis at the same point K), there will be described the surface of a right cone at the end of the annual circuit; but neither will the terrestrial axis be parallel to itself, nor the terrestrial Equator to itself, since the axes of the Equators converge and concur at the point K. Let us now imagine that, while the earth is at A, the eye is at the northern pole S of the terrestrial axis, and sees in its zenith the Cynosure Z (or [a star] on the vertical line ASKZ, but situated at an immense distance): for when, after six months, the Earth shall have come to C, the eye at S, remaining at the Boreal pole, will have for its vertical line the line CSKY, and through it will see its vertical point or Zenith distant from the Cynosure by as great an angle as is YKZ—namely 47 degrees. For since, by construction and hypothesis, the angle CAK is 66½ degrees, and as many [for] ACK—that is, together 133 degrees—the angle AKC will be (by [Elements] 1.32 & 15) the complement to two right [angles], namely [the angle] which is vertical to it, YKZ, [of] 47 degrees; and its half AKE, 23½ degrees. Wherefore KA, or KC, will indeed be longer than CA (granted it is expressed otherwise in the figure), yet not so [much] that, in respect of the far greatest KY or KZ, it cannot be neglected; so that if from A a straight line be drawn to the most remote Y, this will be, to sense, parallel to that KY: and so, just as the whole AEC, on account of the huge distance of the firmament, vanishes and is as a point, so also AK; and accordingly it is the same [thing] for the eye to be at S, the earth being placed at A or at C, as if it were at K; but it would first regard the zenith through KZ, and afterward through KY; therefore it would see the star Z, after 6 months, distant from its zenith by the whole angle YKZ, which we have shown to be 47 degrees.

[XXVI.] Since, therefore, the same inclination of the terrestrial axis being kept not only to the plane of the Ecliptic (or great orb), but also to the axis of that same great orb, it is impossible that the parallelism of the terrestrial axis with itself, and of the terrestrial Equator with itself, be kept: in order that we may obtain this parallelism, we shall so carry the center of the terrestrial globe around the circumference of the great orb that, the axis being produced both ways by the intellect, we conceive its length [to lie] in the surface of a cylinder oblique to the great orb, and through that surface we shall carry the axis around in the great orb; as may be beheld in the following figure, in which let the great orb, as above, be ABCD, and its diameter from Cancer A to Capricorn C be AC, which great orb cuts obliquely the cylinder FAYZCV. The earth, therefore, being placed at the aforesaid eight places A, I, B, L, C, N, D, G, set its axis OAS upon the side of the cylinder FAY; for if you carry it around, keeping it upon the surface of this cylinder, you will see, in every place of the earth, the axes OS parallel to themselves, and accordingly the Equators too MQ parallel to themselves, as being orthogonally permeable by their own axis. And conversely, if you have kept that axis parallel to itself throughout the whole annual circuit, you will describe by the axis itself a certain cylinder, which—if it be further produced as far as the Fixed [stars]—will designate, on either side in the firmament, a circle equal to the annual orb (namely, on this side FPV, on that YKZ), but which, on account of the immense distance, would be seen as a point; and accordingly, whether the earth be at A, or at B, or at C, etc., it will al-

[…continues on p. 308 (PDF 343) — running signature “Q q 2” — with the catchword “per”: ”…[it will] al[ways]” — with the second (oblique-cylinder) figure, completing Riccioli’s demonstration that the “third motion” is really just the axis’s parallelism (a holding-fast), not a separate libration.]

(printed p. 308 — completing the oblique-cylinder figure, which shows the axis kept parallel by the single annual motion without a really-distinct third motion; then, under a new sub-head, the Fourth Motion — the precession of the equinoxes and change of obliquity, represented by a single axis-libration — with corollaries that the 3-vs-4-motion count is merely formal and that if the fixed stars move eastward no third motion is needed at all.)

[Header: BOOK IX. SECTION IV. — 308]

—ways the axis OS will regard, to sense, the same little part of the heaven.

[Translator’s note — engraved oblique-cylinder figure: a cylinder FAYZCV (its two slant sides drawn as hatched columns at left H–P–T and right Y–K–B–V), cut obliquely by the great orb; along the oblique mid-line the Earth-globe is drawn at the eight positions A, I, B, L, C, N, D, G, each globe OMSQ with Equator MQ and axis OS — all the axes drawn parallel to one another (lying on the cylinder’s surface). It shows that carrying the axis around on the cylinder keeps it self-parallel by the annual motion alone.]

[Margin: Whether the 3rd motion of the axis is superfluous in the hypothesis of Copernicus.]

By this demonstration it appears that, if anyone, having grasped the terrestrial axis through its poles, carry it around—keeping both poles retained on the surface of the aforesaid cylinder, so that the center of the terrestrial globe is always on the periphery of the annual orb—by one and the same annual motion, without a third motion really distinct [from it], he will keep the parallelism necessary for representing the inequalities and vicissitudes of days and of the seasons. Nor, as to this, is the reflexion of the terrestrial axis into the antecedent [signs] necessary—granted that, for representing other phenomena, some other motion of the terrestrial axis could seem necessary, as we shall say presently; on account of which [other phenomena], and not precisely on account of this parallelism, Copernicus perhaps numbered that [reflexion] as a third or distinct motion (bk. 1, ch. 11).

The Fourth Motion of the Earth, adjoined by the Copernicans, is explained — which however to Copernicus is the Third

[XXVII.] We were just now saying that, for the parallelism of the terrestrial axis with itself—and so for representing those vicissitudes of days and nights which dwellers in an oblique sphere experience—a third motion really distinct from the diurnal revolution of the terrestrial globe and from the annual revolution is not necessary, provided that one so carries the axis of the earth around (while moving its center) as to keep it on the surface of a Cylinder oblique to the great orb, on whose surface, along its length and with both its poles, it shall once have been. But because the Fixed Stars seem to be moved in longitude by a certain slow progress—and Copernicus judged that this very motion (let alone the diurnal [motion] of the prime mobile) must be denied to the sphere of the Fixed [stars]—he transcribed the cause of this appearance to a motion of the earth’s axis, so reflecting itself into the antecedent [signs] that the annual revolution of this reflexion is a little slower than the revolution of the center of the terrestrial globe: for hence it comes about that the equinoctial sections—or the points of the annual orb at which the equinoxes occur—turn out, each year (but scarcely sensibly), more and more western, or seem to go back into the antecedent [signs] against the series of the signs; but only after many years at length does this regression become known. Since, therefore, the apparent progress of the Fixed [stars] toward the East was apprehended by observations, by Hipparchus, Ptolemy, and the rest of the later Astronomers, no otherwise than by counting toward the East their distance from the Equinoctial points on some parallel of the Ecliptic: in just the same way they will seem to be elongated from those points—whether the Fixed [stars] themselves really move, or, they remaining immovable in their sphere, the equinoctial points themselves move, but toward the West. And therefore Copernicus substituted this precession of the Equinoxes (or of the Equinoctial points) for the motion of the Fixed [stars], referring its cause to the difference which is between the annual revolution of the center of the terrestrial globe (going in consequentia) and the annual revolution of the declining axis—so that it imperceptibly departs from its parallelism: which is to feign that the aforesaid cylinder, or its axis, is so moved little by little, by its extremities P, K, into the antecedent [signs], that with these same [extremities] it describes in the sphere of the Fixed [stars] as it were polar circles about the poles of the Ecliptic. Hence you will understand those words of Copernicus (bk. 1, ch. 11): “There follows, therefore, a third motion, of declination, by an annual revolution likewise (understand, of the axis), but reflecting into the antecedent [signs]—that is, contrary to the motion of the center. And so, the two being mutually almost equal (understand, motions) and opposite, it comes about that the axis of the earth, and in it the greatest of the parallels, the equinoctial, look toward almost the same part of the world, just as if they remained immovable.” But why he applied the limitation, using the particle “almost,” he sets forth toward the end of the same chapter in these words: “We were saying that the annual revolutions of the center and of the declination are very nearly equal; for if it were exactly so, the equinoctial and solstitial points, and the whole obliquity of the Zodiac, ought by no means to be changed under the sphere of the fixed stars: but since there is a slight difference, growing great only with time, it has been laid open—from Ptolemy down to us—[to be] of nearly 21 parts, by which they now anticipate. For which cause some have believed that the sphere of the fixed stars too is moved; to whom on that account a ninth sphere, the superior, has been pleasing; which, when it did not suffice, the more recent now superadd a tenth—yet not even so attaining the end which we hope to attain from the motion of the earth.”

[Margin: What the “Royal Road” [Via Regia] is in Kepler.]

Wherefore, to defend both the apparent motion of the Fixed [stars] in longitude (together with its anomaly, asserted especially by the Alfonsines) and the changes of the obliquity of the Ecliptic, Copernicus substituted a single motion of the terrestrial axis (but nodding with a twofold libration) for the motion which others ascribed to the eighth, ninth, and tenth sphere. But how this libration of the terrestrial axis comes about, and by what reasoning both anomalies (namely of the precession of the Equinoxes and of the Obliquity of the Ecliptic) happen through it, Copernicus then sets forth (bk. 3, from ch. 3 to 6), and Rheticus (in the First Narration), and Kepler (bk. 7 of the Copernican Astronomy), and we ourselves have already sufficiently set [it] forth (bk. 2, ch. 29). Kepler adds, however, that to this motion too there concur both the magnetic fibers and that animal faculty of which [we spoke] above; and that, in order that the variation of the obliquity of the Ecliptic and the apparent [variation] of latitude in some fixed [stars] may be discerned and recalled to a just measure, one must conceive in the heaven a certain mean Ecliptic, fixed in the plane of the great orb, which he himself calls the Royal Road [Via Regia]. From these [things] gather now:

[Margin: First Corollary.]

First, that it is not repugnant to Copernicus or Kepler—who, in the aforesaid places, ascribe only three motions to the Earth, and call “the third” this one which we set forth (under nos. 21 and 27) as the third and fourth—it is not repugnant, I say, to Rheticus, Galileo, and Gassendi, who attribute four motions to it; for that modification which the terrestrial axis receives from the twofold libration (one in longitude, the other in latitude), for saving the anomaly of the precession of the equinoxes and of the obliquity of the Ecliptic, they take for a certain distinct motion—if not really (as it is said in the schools), at least formally.

[Margin: Second Corollary.]

Second, if a motion in longitude toward the East be conceded also to the Fixed [stars] themselves—as among the Copernicans Lansberge and Bullialdus do concede—and this motion be posited equal, so that there is no anomaly of the precession of the equinoxes (which I have taught to be more probable, bk. 3, ch. 28 & 30, and bk. 6, ch. 17), and finally [if] there be no variation of the obliquity of the Ecliptic—let alone any anomaly of this very variation (as I have likewise shown to be more likely, bk. 3, ch. 27)—then no third motion will be necessary to the Earth, and the Copernican hypothesis will be far easier both in understanding and in effect: for we have already said that, for representing all the other phenomena, the diurnal and annual revolution of the Earth suffices, provided that the annual orb have, with respect to the distance of the Fixed [stars], no

[…continues on p. 309 (PDF 344): “…no sensible ratio” — the rest of the Second Corollary; then a Third (Riccioli’s encomium of Copernicus); then the SCHOLIA on the motion of falling/rising bodies (Copernicus, Kepler, Gassendi — with a tower/parabola figure).]

(printed p. 309 — completing the corollaries, including Riccioli’s encomium of Copernicus (“would that he had restrained himself within the limits of this hypothesis”); then a Scholia on the motion of falling and rising bodies in the Copernican system: the composite straight-and-circular fall, Kepler’s nearly parabolic figure, and Gassendi’s tower-and-cannonball argument tracing a parabola in world-space.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 309]

—no sensible ratio, and the axis of the terrestrial Equator be conserved always in its parallelism; which we taught a little before can come about without a distinct motion.

[Margin: Third Corollary — Encomium of Copernicus.]

Third. Never have posterity sufficiently admired—nor will they [sufficiently] admire—the loftiness of the Copernican mind, and the depth of that breast, and the keenness of [his] genius, who by the motion of a single globe (how tiny is the earth in respect of the whole heaven)—and that a threefold [motion]—achieved what scarcely the greatest part of the Astronomers before him could celebrate, not without insane machines of spheres. For by the diurnal motion of the earth he represented the prime mobile, and freed all the other Planets—nay, the Fixed [stars] too—from that motion, which otherwise would have had to be accomplished by the vastest orbs or circles or spirals, not without an apparent repugnance to their own proper motion; and for the three Eccentrics of the Sun, Venus, and Mercury, and the three Epicycles of Saturn, Jupiter, and Mars, and their second anomaly in motion, he substituted a single orb and motion, the annual [motion] of the Earth; by which also he eliminated the apparent imperfection, in the same [planets], of Stations and Retrogradations, and the libration of inconstant latitude and of inclination to the Ecliptic. Finally, by the librational revolution of the single terrestrial axis, he absolved [accounted for] the proper motion of the fixed [stars], and the change of the obliquity of the Ecliptic, with the anomaly of each—that is, he cast three huge spheres down out of the heaven and did away with [them]. And what so many Atlases before [him] could not [do], this one Hercules dared to sustain. But would that he had restrained himself within the limits of this hypothesis!

SCHOLIA

[I.] Above, at number 7, we taught, from Copernicus, that the motion of heavy and light [bodies] naturally descending through the atmosphere (or the part of the air full of aqueous and earthy vapors and exhalations) does not in reality come about, in the space of the world, along a straight line perpendicular to the terrestrial surface, but along another line. And [we taught] that this motion is composed of straight and circular, and that the circular predominates in these bodies—because the straight does not befit them save when they are in a disordered state and translated outside their place, whereas the circular befits them per se in the first place, as being perpetually suitable to them, and consenting with the motion of the whole earth, of which they are parts: this, I say, Copernicus taught (bk. 1, ch. 8), and Galileo (Dialogues 1 and 2, On the System of the World); but of what figure and kind that line is, along which they thus ascend or descend, Copernicus did not determine; Galileo, however, taught that it is circular—as I shall more conveniently set forth (ch. 17), where also I shall explain Bullialdus’s opinion, who judges this motion to be mixed of two circulars, and I shall show their error in the same place, at numbers 16, 17, 18.

[Margin: The error of the unnamed author about the serpentine line of descending heavy bodies.]

[II.] But what Kepler judged, he himself disclosed in a few [words] (bk. 1 of the Epitome of Copernican Astronomy, p. 132), where he first reproves I-know-not-whom, [as] affirming too inconsiderately that the fall of a stone toward the earth fluctuates with serpentine flexures on this side or beyond the perpendicular, so that the number of the flexures answers to the gyrations of the earth: against which assertion he noted that the stone, deserted by the parts of the Earth over which it hung perpendicularly from the beginning, comes into the raptus [snatching] of the succeeding neighboring parts, [being] always deflected toward that region into which the Earth is rolled—weakly indeed at the beginning, but at the end more and more, because the raptus from the nearer ravisher is stronger. For he thinks that heavy bodies tend toward the earth by a mutual magnetic force, that they may be united to it, and are snatched or drawn by the earth, that it may unite them to itself for the conservation of its whole globe.

[Margin: The figure of the descent of heavy bodies according to Kepler.]

[III.] This error being eliminated, Kepler at once subjoins there that, if some heavy body should fall from the most remote celestial place A toward the earth, [the earth being] rotated in one certain place, the figure of the motion would be nearly that which he depicts (with rude Minerva) in the prior part of the appended diagram; in which the circle of the earth is divided into 24 parts, and into as many [parts] the line of fall AEF—but unequal, and above shorter, below longer; and the parts of the circle, each in its order having now discharged its office of drawing, now restored to their places; but, for example, the three preceding [parts] alone, at the end of the fall, did not draw [the heavy body] perpendicularly from the fall of the heavy [body]. And so the figure of the said fall, when it approaches the earth, seems nearly to imitate a parabolic line. But Kepler’s error will be made manifest from what will be said (ch. 17, num. 16 to 18).

[Margin: Gassendi’s opinion on the figure of the said motion.]

[IV.] But Pierre Gassendi (in Epistle 2, On motion impressed by a translated mover) teaches that motions of this kind—which seem to us perpendicular, whether in descent or in ascent—are in reality, in the mundane space, parabolic; yet he uses a heavy [body] thrown up to the perpendicular, and the following figure of the said motion (which we, however, have delineated more similar to a parabola). Let there be, then, a Tower AB, from whose foot A an iron ball is exploded upward by a firelock [sclopus] to the perpendicular; and let us imagine it, according to the experience of our sense, to arrive as far as the summit B: now, if the Earth moved not at all, the ascent being completed it would at once fall back from B into A, to the perpendicular. Let the Earth now be moved

[Translator’s note — engraved tower / parabolic-trajectory figure: at the right stands the Tower A(foot)–B(top); at the left the rotating Earth-circle (center B, marked C above and D below). Along the horizontal baseline are the equal stages the tower occupies as the Earth carries it east — K, I, H, G, F, E, D, C, A — with the tower redrawn upright at each (CL, DN, EP, FR, GS, HV, IY, Kβ). The cannonball’s path through world-space is the curve A–M–O–Q–R(apex)–T–X–Z–K, a parabola: it rises while the tower advances from A to FR, and descends while the tower completes FK.]

from A, the western point, toward the eastern K, and together with it the Tower; and let there be marked, by equal intervals, the spaces of the Tower occupied in the motion, which let be CL, DN, EP, FR, GS, HV, IY, Kβ; and when the ball reaches the summit of the Tower, by then the Tower itself will have completed the half AF of the interval AK, and will be at FR; but the remaining half FK it traverses meanwhile, while the ball descends from the summit of the Tower to its lowest foot. These [things] being posited, Gassendi affirms that, although the earth moves, the Tower nevertheless—translated from AB into CL—would desert the ball, if the earth at A did not adhere to him who throws [it]: in the same way as, if someone standing outside a running ship, on the nearby shore, while the mast of the ship passes by over against him, should throw a ball upward to the perpendicular by a firelock; for a ball of this kind will not follow the mast, but will be deserted by it. But on the contrary, just as, if he who throws that ball along the height of the mast adheres to the running ship, the ball follows the mast, nor is deserted by it—because he impresses on the ball a mixed impetus, namely mixed of that which the fire impresses upward, and of that which the transverse motion of the ship and of the sailor (as of one mover) impresses on the ball: so likewise, because he who throws the ball upward from A adheres to the running earth (going from A toward K), and is with it one mover, he impresses on the ball a motion mixed of the straight-upward and of the circular (or quasi-circular) transverse toward C; it follows that the ball is nowhere deserted by the Tower. Now, just as a ball thrown from a ship along the mast describes, to the eyes of the sailors, both in ascent and in descent, a straight perpendicular line—nor can the sailors in the same ship notice any other figure of the curvilinear motion, because that transverse motion is common to them and to the ball (but when two mobiles are moved with equal or similar velocity toward the same region, neither seems to the other to change place, but to stand in the same place over against the other)—and yet in reality that ball is moved along a transverse and curvilinear path very like a parabola, as those notice who, standing on the shore, are not moved with the motion of the ship: so indeed, because the motion of the ball thrown up from the foot of the Tower A by a mover resting upon the Earth itself (which meanwhile runs from A toward K, through C, D, etc.) is mixed of the perpendicular and the horizontal; and by the proper force of the throwing man the ball is exploded upward as far as the summit of the tower; but by the force of the earth’s motion (carrying the tower from A to F) it arrives from A as far as R; and then, by the force of the same motion (from F to K, whither the Tower arrives, the other half of the interval being completed), and so that ball designates a parabolic line in the mundane space—namely the line AMOQRTXZK. For when the Tower is at CL, the ball ascends to M; and the Tower being carried to DH, the ball ascends to O; and the Tower being advanced into EP, the ball is carried up to

[…continues on p. 310 (PDF 345) with the catchword “ad”: ”…[carried up] to [Q]” — the rest of Gassendi’s stage-by-stage trajectory, and presumably Riccioli’s appraisal of these falling-body accounts.]

(printed p. 310 — completing the Scholia that close Chapter IV: Gassendi’s cannonball trajectory, the answer to the “griffin-basket” objection, the trade-wind, the dropped-from-the-mast experiment (Galileo against Tycho and Chiaramonti), and further examples of mixed parabolic motion such as the ball thrown in a chariot. The page ends Chapter IV.)

[Header: BOOK IX. SECTION IV. — 310]

—to Q; and the tower being carried to FR, the ball reaches the summit R; presently about to descend, and by an even descent it glides down from R, through T, X, Z, into K. Granted that neither that man who threw the ball upward, nor the bystanders adhering to the earth, notice that transverse motion—as being common to themselves and to the ball, and likewise swift and made toward the same region of the world; and therefore it seems to them to ascend and descend by a rectilinear and perpendicular motion only.

[Margin: A pre-emption of the objection, and its solution.]

[V.] “You will say,” says Gassendi in the same place, “what if someone be held in the air, within a basket snatched up by a griffin? Will he notice the parabolic motion of the ball?” He answers, by no means: because he himself too, together with the griffin, the basket, and this lowest air, is (according to the Copernicans) carried toward the East by the common motion—no otherwise than, a quince being rolled about, its down is rolled around with it at the same time, and whatever little animal (say an ant) is contained within that down. Granted that he confesses that the air, on account of its fluidity, does not cohere so firmly with the watery vapors and exhalations, and therefore resists its raptus toward the East ever so little, and therefore seems to move gently toward the West; and that hence are those fannings of a continuous breeze which, in the open plains and on the Ocean within the Torrid Zone (where the motion of the earth toward the East is more vehement, but the resistance of the purer air toward the West appears greater), are felt much more evidently than in the valleys, or in the parts of the earth near the poles, [which are] slower—which very [thing] we said was noticed before by Galileo (preceding chapter, num. 6); about which wind I remember to have read in the Ramusian Navigations, and in our [own José de] Acosta.

[Margin: The perpetual wind within the Tropics toward the West.]

He himself adds—and Galileo (Dialogue 2)—that, just as, if within a running ship there be a vat full of water and live fishes swimming in that water at will, or the cabin of the ship be full of birds, flies, etc., the motion of the ship does not at all impede the proper passages of the fishes, bending themselves whithersoever; nor, if you leap on the deck of the ship toward one part, do you gain more or less space in the ship than if the same were done with the ship standing still: so neither does the common motion of the atmosphere impede the proper flights of birds, flies, etc., nor the peculiar blasts of winds, which drive clouds, chaff, and shavings. Since, however, the ball (of which [we spoke] in Scholium 4), when it begins to descend from the summit R, does not have an impetus impressed from the earth, nor perhaps from the air—or not so much as it had before from the earth—but is moved transversely by the common motion alone [shared by] all terrestrial things; it is therefore probable that, in this hypothesis, it will descend a little sooner from R into K, or rather [land] between K and I; but by a difference imperceptible to us.

[Margin: A heavy body from the mast of a running ship descends perpendicularly to the foot of the mast.]

[VI.] But because Gassendi seems to suppose for certain that a stone thrown up by a sailor to the perpendicular, along the length of the mast, or [dropped] by a man who is at the summit of the mast, descends to the perpendicular into the same place of the ship—lest you think this gratuitously supposed by him, consult his prior epistle, written On motion impressed by a translated mover to Pierre Dupuy [Puteanus]: for there, from p. 15, he narrates, as from a sure experiment, [that] if someone go out upon the Seine in a wherry, downstream, the boat being driven also by oars, that it may be borne with as great a speed as can be; and throw pebbles straight up from the prow, they fall back to the prow; if from the stern, to the stern; if from mid-ship, they glide back likewise to the middle; and although to those who are carried in the same boat the ascent and descent of the pebble seem made to the perpendicular (because they are borne by the common horizontal motion to the same [place]), yet to those who stand on the shore it seems to describe a parabolic line, begun upward from the place of projection, and terminated at the place of fall. And the very same [thing] about a heavy body let down from the mast of a ship—whether moving or unmoved—and in either case falling willingly to the foot of the mast, Galileo asserts (Dialogue 2, On the System of the World, Latin pp. 104 and 111), against the obstinate imagination of certain [men] who think (without any experiment) that, if the ship stand, it falls to the perpendicular at the foot of the mast; but if the ship move swiftly toward the East, that heavy body falls far beyond the foot of the mast toward the West—among whom were Tycho (in the Epistles, p. 190) and Chiaramonti (in the Defense of the Anti-Tycho). Nay, [Galileo] adds that if, the ship resting, a stone plucked from the top of the mast, or dropped by a man clinging to the summit of the mast, falls in the time of two artery-pulses; and then the ship be moved so swiftly that within the same [amount] of time it advances 20 cubits—the stone will nevertheless fall to the foot of the mast, and in no greater time than [that] of two artery-pulses, although it ran through a much longer way in the second case, because the length of the space to be traversed was compensated by the greater velocity (on account of the motion impressed from the mover, which is one [thing] with the moving ship).

[Margin: Notable [things] about motion impressed by a translated mover, from Galileo and Gassendi.]

[VII.] I now pass over many other—though otherwise worth-knowing—experiments and admirable effects of the mixed motion (as being impressed from a mover while it too is translated, whether by itself or by another), which Galileo pursues at length (the said Dialogue 2, from Latin p. 113), and Cabeo (bk. 1 of the Meteors, text 17, from q. 2 to 10), and Gassendi (in the prior of the aforesaid Epistles); and for our purpose I add only two more worthy of note.

[Margin: The motion of a ball thrown upward by a runner.]

The first is about a ball thrown by a man carried elsewhere in a chariot. For bid the charioteer urge on the horses and loosen the reins, and presently do you, who sit or stand in the chariot, throw a ball straight up with whatever impetus you will or can: for it will fall back into your hand, if you wish to recover it; for that ball follows the runner—because, namely, besides the impetus upward (from the force of your arm, considered alone) cast into it, you have moreover impressed an impetus of horizontal motion crosswise, by the force of the motion of the whole body, by which you were being carried along together with the chariot. And to you indeed, who are snatched crosswise by an equal motion, the ball will seem, in ascending and falling back, to describe a rectilinear and perpendicular motion; but to another, [standing] on a road at rest and not carried elsewhere by the same motion of the chariot, it will manifestly appear to describe a forward, curved, and parabolic path—of which kind is nearly the line ARK, designated above in the last diagram. The very same will happen, but downward, if from the running chariot you let the ball drop: for it will seem to you to fall into a point on which your eye perpendicularly rests; but he who is outside the chariot will see it borne forward, and fall down to the earth by a curved path.

[Margin: The skill of those who strike birds while they fly.]

The second is the experiment, or skill, of those who infest flying birds with a firelock so by-guess [stochasticè] that they mostly strike and bring them down: for, observing the bird’s course and path, and its velocity (whether it flies up by an opposing or a following path, or flies away), in firing the ball or the leaden grains, they bend the barrel or iron tube; and by that bending there is impressed on the ball an impetus mixed of the straight-upward (by the force of the fire) and the transverse (by the force of the bending of the arm and of the firelock)—which accordingly either overtakes the bird as it flees, or anticipates it as it flies up to meet [them]. And hence at last it comes about that [a thing] leaping down from a driven chariot falls [forward], and the wine or water bursting from the spout of a cask, and a cannon-ball, fall to the earth along a parabolic line—namely on account of the motion impressed from a twofold mover or moving force: the perpendicular indeed downward, from native gravity; but the transverse, from the fire, or from the upper parts of the wine or water thrusting the lower [parts] out through the transverse spout. What I have said about the cannon-ball and its parabolic fall, our Cabeo too observed (in the Meteors, bk. 1, text 17, q. 4).

[Margin: The velocity of the parabolic path, and its proportion in velocity.]

[VIII.] That, then, the line of heavy bodies thrown upward by a direct effort, and gliding back down, is parabolic—if the earth be moved by the diurnal motion—seems sufficiently proved to Gassendi from the similar experiment of a globe or ball thrown up from a chariot or from a ship, but with a spectator outside the chariot and ship observing the way of the ascent and descent. But why, in the ascent, it traverses a longer way in an equal time toward the beginning (of which kind is AM) than toward the end (of which kind is QR); but contrariwise, in the descent, RT is shorter than TX, etc.—the cause is that in the beginning of the ascent the impetus of the thrower-upward is stronger, and predominates over the transverse impetus; but when the ball has reached the summit R, the impetus by the force of gravity begins to move [it] downward, and sluggishly, but at the end more intensely. But more must be said about this figure below (ch. 17, num. 16, 17, & 18), where, from other and firmer arguments, we shall inquire into the figure of this line: for more [things] will have to be supposed from our own experiments (let alone Galileo’s) about the descent of heavy bodies and the increase of velocity, which here would be too importunely inserted.

[End of Chapter IV. The page closes with an ornament rule and the catchword “CA-” → Chapter V begins on the next printed page (p. 311, PDF 346): the ten arguments for the Earth’s diurnal rotation are now to be proposed and refuted.]

(printed p. 311 — opening Chapter V, which proposes and dissolves the ten arguments for the Earth’s diurnal rotation drawn from comparing the Earth with the eighth sphere. After a methodological admonition to weigh every argument fairly, the First Argument, from the Figure is stated — that diurnal motion better suits the certainly-spherical Earth than the heaven, whose shape is uncertain — with a survey of the Fathers on the heaven’s shape, and the argument cast in syllogistic form.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 311]