[I.] Almost innumerable are the arguments which are wont (or could) be made against the diurnal motion of the Earth—taken separately, or joined with the annual—if the motion of bodies (whether animate, or lacking a soul) toward the East is compared with the motion toward the poles or toward the West. But they are reduced to fewer, because most differ only by reason of the subject, while the form and the nature of the difficulty is the same: namely, that from the earth’s vertigo toward the East it seems to follow that the motion of terrestrial, aquatic, [and] flying bodies toward the East comes out swifter, toward the West slower (or even sometimes impossible), but toward the poles [holds] in a middle way—which [consequences], since they do not answer to the experiments, [show] that this motion must therefore be reckoned among the false hypotheses. Many of these George Buchanan elegantly touched, in the poems comprised in book 1 of [his] Sphere, in these verses:
[Margin: Buchanan’s poem against the Earth’s whirling.]
The very birds, too, swimming through the gentle air on the oarage of their wings, would bewail their forests snatched away by the earth’s swift whirl—and their nests, with the tender brood, and perhaps their dear mate; nor would the lone turtle-dove dare to trust itself to the Zephyr, lest, with the earth fleeing, its wedding-loves be borne far off, and the on-coming part [of the earth] impale itself, while the other part would never carry its wounds home; and the darts—the foes being snatched away by the earth’s whirling—would fall vain beside their master’s own footprints. What [shall we say], when the headlong earth twists itself ever toward the West, if the blue level plains of the deep lie sluggish, and unmoved in their lazy pools? Must not, meanwhile, either a great part of the earth float upon the waters—and, nature’s compact being broken, the light wave, bearing heavy rocks in its flood, not give way, and the moisture not pierce the high mountains (the moisture untaught, before now, even to carry the smallest pebbles)? Or, if the earth resist solid against the waves, and unbroken, would not the moist part of the deep daily overwhelm a part [of the land]; and her whom the Sun had just seen, now sunk in the strait, would not night ever behold squalid with formless sand?
But let us treat this matter seriously, with arguments selected from the motions of these things.
I. Argument, from things hanging or moving in the Air toward the West
[Margin: 1st Form of the Argument.]
[II.] If the Earth were moved by the diurnal vertigo, or even by the annual translation, the clouds hanging in the air, and the rising smoke, and the birds (however much they suspend themselves, or fly toward the East) would seem to be borne always toward the West. But this is against manifest experiments. Therefore the Earth is not moved by the diurnal vertigo, and much less by the annual translation.
The Minor is clear to observers; the Major is proved. For the part of the Earth on which we, standing, would observe the said things, would snatch us toward the East by a far swifter motion than any wind would impel the clouds, or any internal impetus the birds, toward the East: since (per what was said at ch. 19, no. 13) a point of the terrestrial Equator, in one Second of an hour—that is, in about one beat of the artery—would traverse 15″ of the terrestrial circumference, namely 376 Roman paces; but in one hour, 15 degrees, that is 1355 old Roman miles. This is nearly the argument of Ptolemy (bk. 1 of the Great Construction [Almagest], ch. 7), of Pierre d’Ailly (q. 3 on Sacrobosco’s sphere, conclusion 3), of Clavius (ch. 1 of the Sphere, p. 196 in my [copy]), and of Scheiner (in the Mathematical Disquisitions, from p. 30). But it pleases [me] to transcribe Ptolemy’s words here:
They think that nothing can resist them, if they suppose the heaven immobile, and the earth revolved daily from West to East on the same axis.
Against whom he adds:
For it escapes them that, as far indeed as concerns the appearances in the stars, perhaps nothing prevents one from thinking these things to be so; but from those things which happen around us and in the air, this will seem very ridiculous.
Why? Because they cannot deny that the revolution of the earth, if it were so turned, would be the swiftest of absolutely all the motions which are around it, inasmuch as it would complete so great a revolution in so brief a time; so that the things which are not in it would seem to be moved always by one motion contrary to the earth. Thus neither would the clouds ever, nor anything else of flying or thrown things, seem to be borne toward the East; but the earth itself would anticipate them all, and would so resist their motion toward the East that the rest, left behind, would seem to advance toward the West. For although they say that the air is carried around similarly, and with equal velocity, with the earth, nonetheless the things which condense in the air itself would always afterward be left behind by the motion of both, etc.
[Margin: Copernicus’s response to argument 1.]
Yet Copernicus responds very briefly, by implicitly denying the Major (bk. 1, ch. 8), in these words:
What then would we say of the clouds, and the other things hanging in any way in the air, or settling down, and tending up into the heights? Except that not only the earth, with the watery element joined to it, is so moved, but also no small part of the air, and whatever things have kinship with the earth in the same way. 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 it shares from the earth by contiguity, through perpetual revolution and without resistance.
And a little below:
We must confess that the motion of falling and rising [bodies] is, in relation to the world, twofold, and altogether composed of straight and circular. Since the things which are pressed down by their weight, being most especially earthy, [there is] no doubt that the parts keep the same nature as their whole—that is, the mo[tion]—
[…continues on p. 424 (PDF 459) with the catchword “mo-” (motum): completing Copernicus’s response, that the falling parts share the circular motion of their whole.]
(printed p. 424 — within Chapter XXI: the First Argument’s Copernican response concludes (Copernicus’s twofold common-and-proper motion, confirmed by Galileo’s ship-cabin), followed by the Second, Third, and Fourth Arguments — that westward motion would be harder, that fluid things would stream perpetually east, and that rapid rotation would dissipate things in the air — each answered by the air’s sharing the common motion. Then the Fifth Argument begins: Tycho and the Landgrave of Hesse’s celebrated cannon-ball argument, that balls fired east and west should have unequal ranges on a turning Earth.)
[Header: BOOK IX. SECTION IV. — 424]
…[that the falling parts] are moved by a twofold motion: one common to them and to all things which are kindred to water or earth, around the center of the earth (around which the earth and water are turned), which motion we cannot perceive, because we are carried along with the earth; the other proper [to them], and this alone we can notice. Wherefore, if the clouds, smoke, birds, etc., do not use a proper motion, yet because they are carried around toward the East by the common motion, they will seem to us—carried around together [with them]—to stand and hang in the air; but if they are moved by a proper motion toward the West or the East, this alone, separated from the motion common to us [and them], will appear.
Which response holds also concerning things hanging or moving in the most subtle air above the Peruvian and other mountains, where it is said that air fit for breathing is scarcely found; for those hanging bodies too, since they are of earthy or watery nature, partake of the common circular motion toward the East. Now the proper motion of these toward the West is nothing other than a certain subtraction and diminution of the common motion toward the East, as Galileo rightly explains (Dialogue 2, On the System of the World, Latin page 136), adding that if, in the larger cabin of a decked ship, flies, butterflies, and similar flying things be enclosed, and there be there a vessel full of water with fish; and whether the ship stand still or run, nevertheless the same proper motion of the flying and swimming things will appear in either case—so it happens to the proper motions of bodies, whether the Earth stand still or move.
II. Argument, from the motion that would be harder toward the West, and easier toward the East
[Margin: 2nd Form of the Argument.]
[III.] If the Earth were moved by the diurnal motion, it would be harder to walk, swim, [or] fly toward the West than toward the East. The consequent is false, and against common experiment. Therefore [so is] the antecedent.
Thus argue Pierre d’Ailly (on the sphere, q. 3, concl. 3) and Scheiner (in the disquisitions, p. 31). They prove the Major, because together with the earth the air too would have to move toward the East; therefore [things] which walked, swam, or flew toward the West would feel the air coming to meet them (and indeed most rapidly), and would be repelled by it toward the East; wherefore, to obtain any progress toward the West, they would need far greater force and effort. Concerning the Minor there is no controversy, for of itself, and for the most part, this difficulty is not felt.
[Margin: Response to argument 2.]
It is responded, however, by distinguishing the Major, and conceding it if bodies walking, swimming, or flying did not have, besides their proper motion, a motion common to them, the earth, and our air—circular, and toward the East—by which motion they would be borne toward the East prior in nature [to] their being impelled thither by the air. But if they have this [common motion], as it is supposed they have, the Major is denied.
III. Argument, from things (especially fluid) that would be turned toward the East
[Margin: 3rd Form of the Argument.]
[IV.] The diurnal whirling of the Earth being posited, the pinnacles of towers, and the hair of unkempt women, and the flames and smoke of fiery meteors (or their radiant tail, and that of comets), and threads tied to balls and thrown into the air, and the sails of ships, and the leaves of trees, and the ears of grain in open fields, and the smoke rising from chimneys and furnaces, would all be turned perpetually toward the East. The consequent is false. Therefore [so is] that whence it would follow—namely, the Earth’s whirling. And it is much more false that [the Earth] is moved by the annual motion beyond the diurnal, because the said effects would much more follow.
[Margin: Response to argument 3.]
It is responded, as above, the Major being conceded if the said bodies were not moved toward the East by a motion common with the earth, and circular, and with equal velocity; but otherwise the Major is denied.
IV. Argument, from the Dissipation of many things in the Air
[Margin: 4th Argument.]
[V.] If the Earth and the water, and with them all terrestrial and watery bodies, were moved by the diurnal whirling toward the same part of the world with equal velocity, [then] leaden bullets would liquefy in the air on account of the excessive heat conceived from so rapid an impetus; and water ascending from the pipes of fountains would be dissipated into insensible drops, and the clouds [dissipated] into mists by any [breeze], and flames would be extinguished in the open air, and the sound of bells would either be dissipated, or felt more easily and quickly in the Western part; and no fragrance of odors could be perceived by Easterners (since [they would be] most swiftly carried toward the East); finally, the atoms [motes] which we see flitting in a ray of the Sun would float about, dissipated elsewhere. But we see none of these [things] follow. Therefore neither the Earth, nor the water, nor these bodies move with the earth or water by the diurnal whirling.
[Margin: Response to the 4th Argument.]
It is responded by denying the Major, if the air moves with equal velocity, and toward the same part of the world, with the said bodies—as it is supposed to move by the assertors of the earth’s motion; for then the friction and resistance of the air ceases, on account of which those effects would otherwise follow.
V. Argument, from a cannon-ball exploded toward the West and toward the East
[VI.] This argument is most celebrated, and supported by the experiments of William, Landgrave of Hesse, and of Tycho; concerning which Tycho himself must especially be heard, in the Epistles, bk. 1, p. 189:
For that these things may be more clearly understood, he says, a ball of iron, shot obliquely from a very large cannon (which they call a “Cartow”), within two minutes of time, scarcely wearied in its motion, reaches the earth—in which [time] it would have to be revolved twenty thousand paces (a greater [distance]) by the diurnal motion in the parallel of Germany, if the Earth were subject to the diurnal motion.
For thus Rothmann himself indicated to me that his Prince [the Landgrave] had once made a trial in the explosion of a ball from a very large cannon (though not for this cause, but at least to test the space and time of the ball’s advance). Kepler adds (bk. 1 of the Epitome of Copernican Astronomy, p. 108):
The Landgrave and Brahe measured the time which meanwhile elapses when a great Cannon-ball, thrust out by the force of the fires, flies across through the air before it strikes the earth: they found it [to be] of two minutes; the space of the trajectory [being] a great German Mile.
And hence Herigone took [it], when he says (vol. 5, p. 625) that the said ball in that time had traversed four Italian Miles in the air before it struck the earth. But, returning to Tycho, he in that place suggests to us his argument against the earth’s motion, from these words:
And what, I ask, will happen, if from a larger cannon directed toward the East an iron (or leaden, or even stone) ball is exploded, and from the same [cannon], placed in the same spot, toward the West—and that on both sides at equal angles with the Horizon, [the cannon] being elevated with respect to the prior inclination? Is it to be thought possible that the ball, shot on both sides with the same quantity of powder and force, should traverse the same amount of space upon the earth, on account of the natural science of motion by which any ball formed from terrestrial [matter] would accompany the whole Earth? Where, then, will that most violent motion remain, excited beyond nature from the cannon-powder—which surely is, in a manner, a rival to that other natural [motion], by which the Earth would have to be turned in a circle, however swift [it may be]?
After these things he adds that in that ball there are three motions: one by which, by reason of gravity, it would tend to the center of the earth along a straight line, unless it were impeded; another by which, by consent with the earth, it would imitate exactly the circulation of the whole Earth, unless it were impeded by gravity; and a third, violent, [coming] from the saltpetre, sulphur, and inflamed charcoal, by which it is impelled thither whither it would not otherwise naturally proceed. These being posited, he argues thus. If that third motion, made from the cannon-powder, has so great a force that it impedes for a long time the natural descent of the ball intended by gravity—and impedes it so much that only after a long space traversed, and only after two Minutes of time, that ball is borne downward toward the Earth—by what privilege will the second motion (by which that ball is said to imitate the Earth’s circumvolution) not be impeded by that violent and third motion? Is it because the second motion is natural? But the first too, intended by gravity, is natural. Is it because the medium is different? By no means, for it is the same thin air, nor more resisting to the violent motion. If, therefore, it impeded that [second motion] too, some difference would appear in the motion and fall of the ball shot toward the East—
[…continues on p. 425 (PDF 460) with the catchword “Orien-” (Orientem): “…toward the East, from that [ball] which was [fired] toward the West—which difference, however, does not appear.”]
(printed p. 425 — within Chapter XXI: Tycho’s cannon-ball argument (the Fifth) concludes — equal charges give nearly equal ranges east and west, which a rotating Earth should not allow — and is cast into syllogistic form. The responses of Gilbert and Herigone are judged null, and a fourth response (that the eastward range should actually appear greater) is given. Then the Sixth Argument begins: Tycho’s second cannon argument, that shots near the poles and in diverse parallels give uniform results where rotation should produce differences.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 425]
…toward the East, from that [ball] which was [fired] toward the West—which [difference], however, does not appear.
For experience testifies, says Tycho there, that a ball of the same size and weight, shot in the way we said, conversely, by the force of cannon-powder of the same quantity and strength, leaves behind it nearly the same space of the earth’s surface, whether shot toward the East—at, as I said, the same inclination of the same cannon—as toward the West: especially when the air is quite tranquil, and promotes or retards this or that impulse nothing per accidens; whereas, on account of the Earth’s most rapid diurnal motion (if there were any), a ball shot toward the East could by no means measure out so much space of the Earth’s surface, the Earth anticipating [it] somewhat by its own motion; and that one which is fired conversely toward the West [would measure more], the Earth then subtracting something of [its] surface by [its] proper motion, and on that account increasing the intercepted space.
After which he relates the Landgrave’s experiment, which I reported at the beginning, and at last concludes:
By which single argument I think it sufficiently shown that there is no proper motion in the Earth from West to East—until he (namely Rothmann), with whom I was contending about this, or some other, shall have clearly shown, by unconquerable reasons, how it can come about that that exceedingly violent motion (of which I spoke) is impeded altogether nothing by those two natural [motions] which he assumes, or even disturbs these by no trace [at all].
Tycho’s argument, then, reduced to the laws of the syllogism, stands thus:
[Margin: 5th Form of the Argument.]
[VII.] If the Earth were subject to the diurnal whirling, the same ball, from the same cannon, exploded in the same way, would traverse less space [when shot] toward the East than [when] shot toward the West. But the same ball, from the same cannon, exploded in the same way, does not traverse less space toward the East than toward the West. Therefore the Earth is not subject to the diurnal whirling.
The Minor is certain from the experiments asserted by Tycho. The Major is proved by the discourse of Tycho adduced [above].
[Margin: Gilbert’s response to argument 5.]
William Gilbert responds (On the Magnet, bk. 6, ch. 5) by recurring to the magnetic effluvia of the Earth, which in the same way draw the cannon-ball in a circle, both toward the East and toward the West. For when he had said that some doubt how cannon-balls of a larger culverin—[fired] with a similar quantity and strength of powder, and also at an equal direction and altitude through the air—would be shot at an equal interval from one fixed place toward the East and toward the West, the earth being moved toward the East, he adds:
But they are deceived who bring forth arguments of this kind, not noticing the nature of the primary globes (of which kind is the globe of the earth), and [its] combination with its [own] globes, even if they are not joined by solid parts. But the Earth, by the diurnal revolution, [is] not [moved otherwise] than [is] the same [ball] exploded toward the East. On the contrary, a ball shot toward the East is, in the same interval of time, advanced by the snatching of the earth itself through 8 Miles, and itself adds a ninth, being indeed shot violently likewise toward the East. Thus, whether it be exploded toward the East or toward the West, it is always borne toward the East—only a little more in this [eastward] case than in that [westward] one. But this composite world-space has nothing to do with the space upon the earth which men can measure: this is nearly the same on both sides, because the force is the same, because the magnetic bonds are the same on both sides, from which the ball is, as it were, snatched and transported into [places] further on.
Yet he adds that, if some slight difference were to intervene, the opportunity of experimenting would be lacking: For who, he says, will make me certain of the same force of powder in each explosion, and of the other circumstances being the same on both sides?
[Margin: Herigone’s 3rd response.]
But the response of Pierre Herigone (vol. 5, p. 625) is not so perspicuous; and it supposes other measures—namely, that the said cannon-ball, exploded on the Equator toward the West, in two Minutes of an hour is moved toward the East through 26 Italian Miles, and strikes and overturns walls, on account of the swifter [motion] of the walls (by the force of the diurnal whirling) than the eastward motion of the cannon-ball; yet so, he says, that if the globe [Earth] stood altogether immobile, it would strike them more violently.
But responses of this kind are null, since they do not even touch the force of the Tychonic argument. For Tycho does not want the two motive powers of the ball to be so composed that nonetheless the ball’s elongation from the terminus of [its] motion really turns out such as would be understood to result if each force, singly (or even successively), produced its whole motion; but he contends that the said powers must be so joined that nonetheless the one is infringed and tempered [by the other]: namely, if the motive force toward the East would, by itself, have carried the cannon-ball through 8 Miles, [then] with the impetus of the kindled powder (moving 1 Mile toward the West) supervening upon it, it is weakened, nor is it understood in fact to carry the ball, for its part, except (for example) through 7½ Miles.
[Margin: 4th Response.]
Yet it is responded by denying the Major; because rather a greater space would appear traversed toward the East than toward the West, in that toward the East the natural motion of the diurnal whirling performed by the globe [Earth], and the motion from the kindled powder (then least violent), would conspire; but toward the West the violent motion from the kindled powder, although it would beat back the motion made by the diurnal whirling, would yet itself be beaten back by it—and indeed more so, as [being beaten back] by the stronger.
VI. Argument, from a ball of the same Cannon exploded near the poles, and in diverse Parallels
[VIII.] Another argument of Tycho, in the same Epistles (at the end of p. 189 and the beginning of 190), is contained in this discourse:
I add also this: that if, around the Earth’s poles—where the diurnal motion (if there were any) ends in rest—the same experiment by the gun were made (in the way said before) toward whatever part of the Horizon, it would happen in every way the same as if [it were done] in the middle between the two poles, near the Equator, where the motion of the earth’s circumference would have to be most rapid; as also, in any Horizon, if a ball is shot in like manner toward the East and the West, it completes the same [amount] of space as toward the South and the North, [when] shot with a similar impulse—whereas, if there were any diurnal motion in the Earth, it would regard the West and East, but not likewise the South and North. Since, therefore, these things happen uniformly everywhere, etc.
Now let the form of the argument [be]:
[Margin: 6th Form of the Argument.]
If the Earth were moved by the diurnal motion, a ball exploded in like manner from a cannon or gun would traverse a notably different space when shot near or toward the poles than when [shot] in parallels nearer the Equator, or when [shot] toward the South or North. But this is against experiments. Therefore the Earth is not moved by the diurnal motion.
The Minor seems to be established by the experiments themselves, if faith is given to Tycho. The Major is proved, because if a ball were exploded toward the poles along the plane of the same Meridian, a smaller diversity would be brought upon it by the diurnal motion than if [it were shot] now toward the East, now toward the West; but if [it were shot] in parallels nearer the pole, that ball would be borne more slowly with the earth, [and] if in [parallels] nearer the Equator, more swiftly with the earth—other things being supposed equal.
[…continues on p. 426 (PDF 461) with the catchword “Respon-” (Respondetur): the response to the Sixth Argument.]
(printed p. 426 — within Chapter XXI: the response to the Sixth Argument is rejected, then the Seventh — Galileo’s own cannon-target argument, that on a rotating Earth shots would strike above an eastern target and below a western one — with Galileo’s twofold reply (the aim shares the rotation, and the error would be far smaller than a gunner’s normal inaccuracy), Riccioli noting a slip in Galileo’s calculation. Then the Eighth Argument, Grimaldi’s, from the real percussion of a cannon-ball fired east versus north, begins with an engraved diagram.)
[Header: BOOK IX. SECTION IV. — 426]
It is wont to be responded by denying the Major, or by distinguishing it—and conceding it concerning the diversity of real space in world-space, [but] denying [it] concerning the diversity of apparent space (or [space] falling under our measurement). But in reality the argument holds, and this response is null, according to what was said for the preceding argument toward the end.
VII. Argument, taken likewise from a cannon-ball, and from the Target which it would strike toward the East and toward the West
[Margin: An argument against the diurnal motion of the earth, attributed by Galileo to Tycho.]
[IX.] I wonder that Galileo (Dialogue 2, On the System of the World) more than once mentioned the Tychonic Cannon, yet did not propose his [Tycho’s] argument, but one different from the Tychonic, which he sets forth thus (Latin page 131). If the shootings of cannon-balls were made toward an eastern target, and the earth moved, they would strike above the target; but if toward a western [target], they would strike below the target—because the Eastern parts of the earth, by the diurnal motion, are continually depressed below the tangent parallel to the Horizon, and on the contrary the western parts are exalted (from which the western stars seem to become lower); and accordingly the shootings, directed along the said tangent toward the eastern target (as being meanwhile depressed while the ball runs along the tangent), would have to become higher than right; and the western [shots] lower than right, the target being meanwhile exalted. But by experiments this variation of aiming is not confirmed. Therefore it is a sign that the earth does not move. Yet to this argument I draw out a twofold response from Galileo, which I shall bring forward after the argument [is] reduced to form.
[Margin: 7th Form of the Argument.]
If the Earth were moved by the diurnal motion, or even the annual, the ball of the same cannon—whether exploded toward the East or toward the West—would fail of striking the target to which it was directed. But it does not fail. Therefore the Earth is not moved by the diurnal motion.
The Minor is supposed certain from observation. The Major seems confirmed by the discourse of Galileo just adduced. Therefore, etc.
[Margin: 1st Response, from Galileo.]
Galileo responds, first, roughly, by denying the Major. For although the eastern target would be continually depressed below the Tangent by the force of the diurnal motion (if we speak of the first tangent in immobile world-space), nevertheless the cannon-ball, before it is inclined downward by the force of gravity, runs along one mobile tangent and another, which is continually inclined—just as the whole length of the cannon [is inclined] by the force of the diurnal motion—and does not cease to regard the same target. On the contrary, the cannon’s axis toward the West is exalted by the force of the diurnal motion, and along its length another and another raised tangent must be conceived, no less than the western target; wherefore the aiming, in neither case (otherwise rightly made), would fail of its effect.
[Margin: 2nd Response.]
The same Galileo responds, secondly—not indeed by denying the Minor, but by calling it into doubt—where he corrects certain Copernicans who, with excessive liberality, indulge the adversaries and grant them certain experiments as true and certain, even if they were never done; among which he suspects that this can be enumerated, namely whether the eastern shots come out too high and the western too low. Nay, he is persuaded that this was never tested by anyone, nor can this experiment easily be done; for no gunner will be found so skilled that he professes he can strike the target itself with every shot, or not stray from the target beyond one cubit, if he must shoot from an interval of about 500 cubits or more. Now if the Earth moved, the error on account of that motion could not be greater than one cubit, and therefore in this experiment—however much repeated—the falsity of the Earth’s motion could not be convinced, since so great an error can also happen with the earth at rest. To prove this by a rough calculation, he supposes the shot to be made with a larger culverin on the equinoctial line itself (where the greatest variation would arise, on account of the swiftest motion of the equinoctial parts of the earth), at a target distant 500 cubits toward the West; and he says it is certain that the culverin’s ball reaches the target most quickly, in no longer time than two paces are completed by a walker—which he affirms to be less than one Second of an hour. For if in one hour (or 3600 Seconds) a walker completes three Italian Miles (that is, 9000 cubits), therefore in one Second he completes two-and-a-half paces; wherefore for the cannon-ball’s motion up to the target, one Second of an hour is more than enough.
[Margin: The time in which the cannon-ball strikes the target.]
But in so tiny a time, by the force of the diurnal revolution, 15″ of the Equator ascend; and accordingly the target and the western Horizon, in that circle whose semidiameter is supposed [to be] 500 cubits, will be exalted by 15″. Now, from the tables of Sines, the chord of an arc of one Minute is less than 30 parts of which the Radius would be 100,000; therefore the chord of 15″ is less than 15 parts of which the semidiameter would be 200,000. Therefore it will be less than four hundredths of one of those parts, of which the semidiameter would be 500 cubits; wherefore the exaltation of the target, and the error of the ball on account of the diurnal motion of the earth, would not exceed four hundredths of one cubit, or nearly one finger in breadth; nor can it be convinced by such an experiment whether the Earth rests or moves. Here, further, it is neither free [from trouble] nor expedient to correct Galileo’s discourse and calculation; I only note that he confused the chord with the Sine of an arc of one minute—for the Sine of this is 29 parts of which the Radius is 100,000; wherefore the chord [of one minute] is, of such parts, not 30 but 58.
VIII. Argument, from a cannon-ball exploded now toward the North, now toward the East or West, devised by Fr. Francesco Maria Grimaldi against the Diurnal and Annual Motion of the Earth
[Margin: Theorem of Fr. Grimaldi against the motion of the Earth.]
[X.] As long as we look at the apparent spaces which are wont to be traversed by bodies, the arguments thence taken against the Earth’s motion do not have so manifest a force; but if we consider the real increment of percussion and impetus, somewhat stronger weapons are thence supplied to us against its motion, as from what was said at ch. 19. Hence, therefore, it seemed that another argument could be taken, resting on cannon-percussions. Let it be supposed first (for the sake of explanation, not of necessity) that a ball of the largest Cannon—that is, weighing 60 or 80 pounds—in the time of two beats of the human artery (or about two Seconds of an hour) reaches straight to a target distant 250 paces; which the skilled in this art would easily concede. And in the following diagram let the Cannon’s mouth be A, directed at the eastern target B, distant by the interval AB of 250 paces. Now if the Earth, with its kindred bodies, did not move by the common motion toward the East, the ball from A would reach the target B in the time of 2 Seconds; but because both are transferred by an equal motion on account of the diurnal whirling, and in two Seconds complete 30″ of the Equator (that is, 752 Geometric Roman paces, from the first table of ch. 19, no. 13, premised), let the chord of this arc be AC, for a nearly horizontal line, along which let the Cannon’s mouth A be understood [to be] translated to C, and the target from B to D, both having completed 752 paces; for the target D will be distant from the mouth C by the interval CD of 250 paces, as before, and the ball I, exploded from A, will strike it. Now let the Cannon PA be directed toward the northern target E, so that the cannon is in the position AQ, and the interval AE be 250 paces.
[Translator’s note — the engraved figure (fig. #38, lower right) shows Grimaldi’s apparatus: at left, a cannon lying horizontal, breech P, mouth A, aimed east at the round target B; below A a second cannon stands vertical at Q (the same gun re-aimed north). To the right, the whole system displaced eastward by the diurnal whirl: the mouth carried to C (with its cannon, and the vertical one at R below), the eastern target to D (the ball I·D at far right), the northern target to N, and the ball’s curved real path A·K·H·L·F·G·M traced across the top. The straight dotted lines are the apparent aim-lines; the solid arc is the ball’s true world-space path.]
[…continues on p. 427 (PDF 462) with the catchword “hoc” (hoc est): “…this being precisely equal to the interval AB,” continuing Grimaldi’s setup for the northward shot.]
(printed p. 427 — within Chapter XXI: Grimaldi’s Eighth Argument is completed — on a moving Earth a northward shot would strike a far weaker, glancing blow than an eastward one, testably so — and the Copernican response (the percussion remains direct, as on a moving ship) is rebutted as valid for the straightness but invalid for the vehemence of the blow. Then the Ninth Argument, Riccioli’s own, begins: a ball thrown east should strike harder than one thrown west, yet billiards shows equal blows.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 427]
…this being precisely equal to the interval AB; and let all the rest be equal—namely, the Cannon cooled, the same ball, the quantity and quality of gunpowder of the same measure and kind, the inclination or elevation of the Cannon, the temperature of the air, etc.—so that in the same time of 2 Seconds of an hour the ball from A could reach to E, along the straight line AE, if the Earth stood still. But because the Earth is supposed to be transferred by the diurnal motion at least, and with it every heavy body kindred to it: when the cannon, having completed the 752 paces of the interval AC, shall have been translated into the position CR, the target too, translated in its parallel, will be at N, and the cannon-ball at F, where it will strike it—having completed, as to appearance, only the interval CF of 250 paces; but in reality, in world-space, a journey much greater will have been completed by it, namely AKF, whose chord AHL will be of 825 paces, as will be established from the laws of Triangles: if, in the triangle ACF (right-angled at C), in which AC of 752 paces and CF of 250 paces are given, the base AHF be investigated; and on the same occasion the angle AFC will be found of 70° 35′, to which the angle NFM is equal.
[Margin: 1st cause of the weaker impetus toward the North.]
These being supposed, it seems that the cannon-ball will strike the Northern target N with a far weaker blow, and a feebler percussion, than the Eastern target D—so that the breaking of a wall, or the pushing-forward of another ball set as a target, would be notably less; which diversity would easily have been observed, or could be observed. For to weaken the impetus of the ball shot toward the North, two causes would concur. First, the impetus of the ball, in its exit from the Cannon’s mouth A, would be impressed all at once, and would be of such a kind in itself, and so great, that if the Earth were immobile it would strike the target B as [much as] E, along the straight line AB or AE, at an equal interval of 250 [paces]. But because both the earth and the ball are supposed to be transferred toward the East, and while the ball strives toward E it deviates—by the prevailing diurnal motion—and is twisted aside from the straight line AE, and is drawn along the curve AKF toward F (because at the beginning the motion is faster here, and the ball is borne beyond the straight line AHF which it would describe if the motion were uniform): therefore its impetus must necessarily be infringed and greatly weakened, while it is resisted by the diurnal motion, and while it is forced to go along the longer and oblique way AKF (it being otherwise about to go by the straight and shorter way AE to E). In the proportional manner [as] if someone, having dropped a leaden ball through a tube standing perpendicularly upon the hand, were to transfer the tube most swiftly—surely the ball’s impetus and descent would be greatly retarded and weakened, and it would strike the underlying hand with a much smaller blow by its fall than if it had been allowed to fall through the unmoved tube, from the same height.
[Margin: 2nd cause of the weaker impetus toward the North.]
Secondly, although the cannon-ball would seem, to the eye [observer] at C, to strike the target N at the point F (along the line FN), yet in reality it would strike it with a very oblique blow, along the line LM; and the line of direction, along which the impetus—twisted aside by the force of the diurnal motion from the straight AE and FN—would be diffused, would be AHL; nay, would be a portion of the curve AKF, declining from the straight CF even more than by the angle AFC (which we found above to be 70° 35′). Hence it would come about that the ball would strike the target not with its point G (which is forward in the motion, and carried, like a ram’s head, along the straight LG), but with its lateral point F, which declines from the real way of the impetus LGM (which it would traverse in world-space, and along which it would strike upon every obstacle in that channel): wherefore, not striking straight at F, but as it were with a fleeting and very oblique contact (which would deserve the name of rubbing or chafing rather than of a blow and a wound), it would scarcely strike the target N. And if at the side of N there were another target at G, placed to the right toward the North-East wind—even if the Cannon and ball were not directed at it—the ball would yet strike it with a much greater impetus, as being impacted on it according to the real direction of its impetus; and there it would break through the wall with greater ruin. And if target N and target G, equal in all other respects, were propellable, target G would be propelled much further (say, through the space GM) than the other (say, through a space equal to FN). For we see everywhere, in the game of trucks [billiards], or of a leather ball struck by rackets, how much weaker the blow and the thrust is, if either one ball is struck as if by a Tangent with a fleeting contact, or the ball is caught crosswise by a slanting racket and repelled, than if the diameter of one ball strikes straight upon the diameter of the other with full impetus, or the leather ball is caught and repelled by a perpendicular meeting. By these two causes, then—which would weaken the Northern blow in comparison with the Eastern or Western (yet not really weakening it)—it seems to be established that the Earth is not moved by the diurnal motion, and much less by the annual, which would weaken that blow more. Now let the Argument be in form.
[Margin: 8th Form of the Argument.]
If the Earth were moved by the diurnal motion, or even by the annual at the same time, the blow of a cannon-ball exploded toward the North or South would be much weaker than [one exploded] toward the West or East. The consequent is false. Therefore [so is] the antecedent, whence it follows.
But what is said of a cannon-ball holds for many other projectiles. The Major seems sufficiently proved by the preceding discourse; the Minor is supposed certain by an experiment doable by the most skilled gunners (who aim so surely that they can block the mouths of enemy cannons with their own balls); for they would have observed this diversity sometime, or could observe it.
[Margin: Response of the Copernicans.]
The Copernicans will perhaps respond by denying the Major, because the motion of the cannon-ball, insofar as it is from the kindled powder, has of itself its direction toward the target—which, from the very beginning (the species of motion being impressed), it intends to strike straight; and although it is transferred along an oblique way, yet because the target too is transferred together [with it] by an equal motion and velocity (even in that briefest, as it were, moment of time in which it is struck), it comes about that at last the percussion is made directly. Just as if an eye, looking through a narrow tube at a candle-flame placed toward the North, were transferred by the ship together with the candle toward the East, it will see the same [flame] by a direct gaze; and a ball on a gaming-table, carried along likewise by the ship toward the East, thrust against the northern ball, will strike it directly; and finally, a hammer—impelled by the arm of a sailor carried toward the East—striking the ship’s mast placed toward the North, will pierce the ship’s mast directly toward the North, however much the ball and the hammer are in reality snatched sideways by the ship’s motion, and traverse the oblique way intended by the two principles of motion mixed together.
[Margin: The invalidity of the Response.]
But the response is indeed good as to the straightness of the percussion; but invalid as to the vehemence of the percussion, which would be diminished and weakened the more, the more the motion snatching the ball (or hammer) sideways resists the impetus produced from the beginning. For we are certain, from very many experiments, that a motion once impressed and moving toward one part is weakened and diminished by an impetus moving not only into the contrary [part], but also into a foreign part, or sideways. It is indeed true that, in the example of the trucks and the hammer, on account of the brevity of the journey the diversity of the percussions—which are made once with the ship unmoved, and again with it moved—is not so notable; and much less in the hammer, whose impetus is restored by the arm (as by a conjoined principle), even if this restoration is not noticed.
IX. Our own Argument against the Diurnal and Annual motion of the Earth together, from the greater blow and percussion of a ball thrown toward the East than toward the West
[XI.] This argument proceeds in an entirely contrary way to the Tychonic [argument] adduced at number 7; for it is of this kind:
[Margin: 9th Form of the Argument.]
If the Earth were moved by the diurnal motion, or even by the annual, the same ball, thrust by the same force to the same distance toward an Eastern target once, and again toward a Western [target], would strike the eastern [target] with a stronger blow than the western. The consequent is false. Therefore [so is] the Antecedent.
The Minor is most certain by experiments—both of the trucks, by which we thrust ivory balls on a gaming-table against another ball [that is] unmoved and equally distant, now toward the East, now toward the West; and by many other similar projectiles. The Major is proved, because the impetus of a ball thrown toward the East would not be retarded by the diurnal or annual motion of the earth, but rather would be helped by it, and in turn would second it (inasmuch as both strive toward the same region); but on the contrary, the impetus of a ball shot toward the West would retard, or beat back, the impetus moving toward the East, and in turn [be beaten back by it]—
[…continues on p. 428 (PDF 463) with the catchword “cissim” (vicissim): “…and in turn [would be beaten back by it],” completing the proof of the Ninth Argument’s Major.]
(printed p. 428 — within Chapter XXI: the Ninth Argument (Riccioli’s own, from the unequal percussion of eastward and westward throws) is finished and marked insoluble. Then the Tenth Argument (from the contrariety of motions), the Eleventh (from the needless multiplication of motions of the same kind), and the Twelfth (that the motion should be assigned where the sense-foundation is greater and the bodies fewer — the heavens, not all sublunary bodies) are proposed with their Copernican answers.)
[Header: BOOK IX. SECTION IV. — 428]
…would in turn be beaten back by it, since they tend toward contrary parts (granted the impetus of the diurnal-and-annual motion together is much stronger); and therefore the one resists the other—not absolutely, but in a certain respect. Just as if a one-ounce clay ball, shot from a ballista downward from the top of a tower at a clay target 30 feet distant, strikes and perforates the clay with a far greater blow, and penetrates it further, than if the same ball—from the same ballista—is propelled upward against a clay target of the same softness, and 30 feet distant: because, namely, in the former case, besides the impetus impressed by the ballista, there is present an impetus produced by gravity (which of itself would strike the clay by a headlong fall), and each helps the other; but in the latter case the impetus produced by gravity resists the impetus impressed by the ballista, and beats it back more and more.
[Margin: No suitable response.]
To which argument, indeed, I find no solid response—nor one persuasible while the natures of things are kept safe. For the examples which could be brought forward, in the hypothesis of a standing Earth, concerning projectiles thrown over the deck or planks of ships (now toward the East, now toward the West, the ship being always carried toward the East), have either an uncertain or an unobservable diversity of percussion, on account of the brevity of the journey; or they fall short of a perfect similarity, and do not include two intrinsic impetuses which in one case help each other, in the other beat each other back by mutual resistance.
X. Argument, from the Contrariety of Motions
[Margin: 10th Form of the Argument.]
[XII.] If the Earth were moved by the diurnal motion, or even the annual, the same movable would be moved at the same time by two contrary motions. But it is Physically repugnant that the same movable be moved at the same time by two contrary motions. Therefore the Earth is moved neither by the diurnal nor by the annual motion.
The Major is proved, because it is manifest that many bodies are really moved toward the West; but if the Earth were moved toward the East (so that many other experiments be saved), it would be necessary that the same bodies be moved meanwhile toward the East by a certain motion common to all terrestrial and watery bodies—and this very thing Copernicus, with his followers, asserts; therefore at the same time they would be moved toward diverse regions and termini, and would approach by their proper motion that very western terminus from which meanwhile they would recede by the common motion; or, approaching the eastern terminus by the force of the common motion, would recede from the same by the force of their proper motion. The Minor is proved, because it is impossible for the same [thing], at the same time, to approach and recede with respect to the same terminus, since the recession has annexed the privation of approach to the terminus from which there is recession; but a privation and a form cannot Physically be exercised at the same time.
[Margin: 1st Response to Argument 10.]
It is responded, first, by denying the Major in that sense in which the Minor is true—that is, concerning two motions truly and really contrary, in order to termini fixed and immobile in World-space. For although, by comparing the terminus from which (on the surface of the earth or water) with the terminus to which bodies tending westward would apparently approach, they would seem to recede from the eastern terminus from which [they set out]; yet in reality they would always approach the eastern terminus fixed in world-space, because the common motion of the diurnal (and much more the annual) revolution of the Earth is swifter than the proper motion of any body tending westward—granted that, on account of this proper motion, the approach to the East would be diminished (being otherwise about to be greater, if there were no motion toward the West). By an example the response will be made clearer. Let a walker proceed, in the Equator, for one hour toward the West, departing from some column, and completing on the earth’s surface three thousand Roman paces: for meanwhile the diurnal conversion of the Earth will snatch him toward the East, as also the column; but the column it will snatch in such a way that in World-space it rolls it toward the East through 15 Degrees (that is, through 1,355,000 paces); but the walker it will snatch in such a way that it rolls him through only 1,352,000 paces (or 1352 Italian Miles)—3 Miles being subtracted, namely, which the walker meanwhile completed, not indeed by receding toward the West from the fixed place of the World in which the column was, but by receding less from that fixed place toward the East than he would have receded if he had permitted himself to be snatched by the common motion alone, without any proper [motion]. See the diagram and its exposition in Section 2 of this book, chapter 3, scholium 1.
[Margin: 2nd Response.]
Galileo responds, secondly (Dialogue 2, On the System of the World, Latin p. 200), by retorting the argument: for if these two motions are denied to the earth, two contrary motions must be attributed to the celestial bodies; by what reasoning, then, [they are reconciled] in the heaven, by the same [reasoning] they can be reconciled in the earth. He adds that if any fatigue were to be feared, it should rather be feared for the starry sphere than for the earth, inasmuch as it would have to carry much greater bodies than the Earth.
XI. Argument, from the by-no-means-necessary Multiplication of motions of the same kind
[Margin: 11th Form of the Argument.]
[XIII.] Motions must not be multiplied without necessity. But if the Earth were moved by the diurnal, or even the annual, motion, innumerable motions would be multiplied without necessity. Therefore the Earth is moved neither by the diurnal nor by the annual motion.
The Major is established by an Axiom received by all, and so urged by the Copernicans that even from this they try to take the diurnal motion from the Fixed stars and Planets and ascribe it to the Earth alone, and to perform the motions of the Epicycles of the five smaller Planets by the single motion of the Great Orb. The Minor is proved, because, to save the phenomena of the sublunary motions, it would be necessary that all and singular terrestrial and watery bodies (among which are innumerable mixed [bodies], partly animate, partly inanimate), besides their proper motions, have a common motion by which they would revolve with the Earth, daily and yearly, toward the East. But all these motions can be avoided, all the Phenomena being saved, if the Earth rests, as the Copernicans openly concede; wherefore they are multiplied without necessity.
[Margin: Response.]
It could be responded by the Copernicans, either by retorting the argument, or by distinguishing the Major and conceding it if—by not multiplying motions in sublunary bodies—the multiplication of motions of the same kind in the celestial [bodies] could be avoided, but otherwise denying it. But in whatever sense they concede the Major, they will deny the Minor: because if the diurnal motion is not conceded to the Earth and kindred bodies, it must be conceded to the innumerable Fixed [stars] and all the Planets; likewise, if the annual motion through the great orb is not attributed to the center of the Earth and the whole elemental system together with the Lunar heaven, it must be attributed to five distinct epicycles of the smaller Planets, or to other circles or ellipses equivalent to them. Since, therefore, in either set of bodies these two motions must be multiplied, and no necessity appears for multiplying them rather in the celestial than in the sub-celestial bodies, the reason for attributing them rather to the one than to the other must be sought elsewhere. There arises, therefore, the twelfth Argument.
XII. Argument, from the Multiplication of motions in those bodies in which the foundation for multiplying them is greater, and the multiplication is less
[Margin: 12th Form of the Argument.]
[XIV.] If the diurnal and annual motion must be attributed to either set of bodies, it must rather be attributed to those in which a greater foundation appears, and a lesser multiplication occurs, than to those in which a lesser foundation appears, and a greater multiplication occurs. But a greater foundation for attributing the diurnal and annual motion appears in the celestial bodies, and in them the multiplication would be less than in the Earth and the rest of the bodies. Therefore it must rather be attributed to the celestial [bodies].
The Major is clear. The Minor is easily proved, because we have a sufficient foundation for the diurnal and annual motion from the phenomena and observations manifest to sense, and there is no repugnance to the contrary, nor any argument for asserting that sense is deceived in these. Then, if the diurnal motion be attributed to the celestial bodies, it is attributed only to the eighth sphere (to whose single motion the Fixed [stars] can be moved), and to the Seven planets, with the 4 companions of Jupiter and the 2 of Saturn—that is, to 14 bodies in all. But if the annual [motion] be attributed to the Sun, and the motion proportional to it [be attributed] to the 5 Planets in [their] Epicycles, it is attributed only to six bodies; or, if here too you add the companions of Saturn and Jupiter, it is attributed only [to]—
[…continues on p. 429 (PDF 464) with the catchword “nisi” (nisi 13 corporibus): “…only to 13 bodies”; whereas the moving-Earth hypothesis would impose the motion on all the innumerable sublunary bodies.]
(printed p. 429 — Chapter XXI closes: the Twelfth Argument is finished and marked insoluble (the Copernicans, fleeing multiplicity of motions, fall into a greater one), then the Thirteenth (destroying apparent motions and substituting unapparent ones) and Fourteenth (endless non-uniformity of speed in the same movable by latitude, also insoluble) complete the chapter’s fourteen arguments, five of them Physically insoluble. Then Chapter XXII opens, proposing five weak arguments from the excessive velocity a moving Earth would require, and laying four foundations for its velocity-tables.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 429]
…only to 13 bodies. But if the diurnal and annual [motion] be attributed to the sublunary bodies, a motion is attributed to them resting on no sensible observation (that is, having no a-posteriori foundation had through the senses); and the diurnal must be attributed to the Earth, and to absolutely all sublunary bodies situated below the upper region of the air, which are both in number and in species much more than 14; and the annual not only to all sublunary [bodies], but also to the Moon itself and the Lunar heaven.
[Margin: No response to Argument 12.]
To this argument, indeed, I see no shadow of a solid response—unless the Copernicans, the foundation from sense being deserted and despised, recur to a-priori congruences. But since, among those, [the congruences] are chiefly placed in this—that the multiplicity of motions be avoided—they cut their own throat with their own sword, since they fall into a far more numerous multitude of motions, and meanwhile undermine the foundations of physics (that is, the sensations).
XIII. Argument, from the Destruction of motions which appear, and the Substitution of motions which do not appear
[Margin: 13th Form of the Argument.]
[XV.] If the diurnal motion, or even the annual, be attributed to the Earth, the motions which appear are destroyed without a necessary reason—so that they really are not [motions] at all—and in their place are substituted motions which never appear. But this is absurd. Therefore, etc.
The Minor is evident of itself. The Major is proved, because both the diurnal and the annual motion of the Earth (and of the other bodies imitating it in these motions) is greater than the proper motion of any [body]; from which it comes about that the proper motion which appears in these toward the West is not really a motion, since by it they do not approach the same fixed point toward the West, but there occurs only a diminution of the greater motion toward the East (as was said in the response to argument 10). But the diurnal and annual motion itself of the Earth and of kindred bodies, which is substituted as [if] real, in no way appears.
XIV. Argument, from the Manifold Inequality and non-uniformity of motion in the same movable, without necessity
[Margin: 14th Form of the Argument.]
[XVI.] If at least the diurnal motion be conceded to the Earth, a motion unequal and non-uniform with innumerable variety must be attributed to the same movable, without any necessity. But this is unfitting. Therefore, etc.
The Minor is certain of itself. The Major is clear, because the same terrestrial body—even when separated from the earth (say, a cannon-ball shot toward the East, or a cloud, or a bird)—must move faster in the Equator than in the nearest parallel, and in this faster than in the next, and so of the rest, [in parallels] describable to infinity right up to the poles. Wherefore, if a bird flies from the Equator toward the poles, straight or obliquely, it is necessary that—notwithstanding a flight uniform to appearance (or even faster and faster)—it nevertheless really move continually slower and slower, to attemper itself to the slower and slower motion of the parallels: which surely would happen more frequently, and in more [cases], than if the diurnal motion were attributed to the Fixed [stars]. And the Copernicans do not deny that this happens without necessity—[they] who cannot respond to this argument except [by saying] that this variety follows from their hypothesis, whose foundations they have, not in sensations, but in ideal reasonings and in certain congruences.
[Margin: No response.]
But among the greatest congruences is this, so often urged by them, that the simplicity and uniformity of motions be established—which, however, they injure far more numerously, by attributing it [the motion] to so many sublunary bodies. And so the response turns out null, and destroys itself. If you wish to know, to a certain measure, the inequality of the motion of terrestrial bodies—as they are either in the Equator or in other parallels, and as they move around midday or around midnight—run through the little tables to be delivered in the following chapter, at the end of number 1, especially [numbers] 5, 6, and 7.