Library / Almagestum Novum, Book IX: On the System of the World

Section IV — On the System of the Earth in Motion

Chapter XXII, Five Arguments are proposed, but weak, from the excessive Impetus and Velocity of the Earth and of its Kindred Bodies, if they were moved by a motion whether Diurnal only, or also Annual; and the Measure of each motion is, on this occasion, delivered by a different method than was done at chapter 19, number 13—that perhaps by this [method] satisfaction may be given to some.

[I.] Before we discuss the effects which the velocity of the moved Earth would generate, that velocity itself must be explained in determinate and known parts of the space which the Earth would traverse in one hour, or in one horary Minute, or Second. For which thing we need four elements, or foundations, for constructing the following Table.

[Margin: 1st Foundation of the following Tables.]

The First is, how many Miles are contained in the Diameter and greatest Circumference of the Earth (of which kind is the Equator): about which we reported very many opinions in bk. 2, ch. 7, at the end of scholium 9. But since the Authors who dispute about the Earth’s motion—most, with the Germans and certain Navigators—attribute to one Degree of the terrestrial Equator 60 Italian Miles (or 15 German), and to the Earth’s diameter 1720 German [miles]: as do Tycho, Longomontanus, William Gilbert, Maestlin, Mercator, Herigone, Scheiner, and usually Kepler—but we, by exact measurement, found in one degree of this Equator 72¼ Bolognese Italian Miles, and in the Earth’s diameter 8278; to which Gassendi (who [says] 73), most Navigators (who 70), most of the Arabs, and also Fernel and Snell (who attribute about 68 Italian Miles to it) come nearest, as we said in the same place: therefore, according to only these two opinions—namely of 60 Italian (or 15 German), and of 72¼ Italian—we shall construct the table.

[Margin: 2nd Foundation of the Table.]

The Second which we need is, how many Minutes in the Equator answer to one degree of a parallel equally distant on either side from the Equator and from the Poles of the Equator (that is, declining 45 degrees); and likewise how many [answer] to one degree of an almost-smallest parallel (that is, distant from the pole by a single degree, and declining from the Equator by 89 degrees)—so that from the middle and the extremes a judgment can be made about the rest. Now, by the Problem delivered by Giuseppe Moletti and Giovanni Antonio Magini on chapter 23 of book 1 of Ptolemy’s Geography, and by the table constructed by the same Moletti: to one degree of a parallel declining 45 degrees, there answer in the Equator 42′ 24″ 35‴; but to one degree of [a parallel] declining 89 degrees, there answer in the Equator 1′ 2″ 51⁗.

[Margin: 3rd Foundation of the Table.]

The Third which we need is the semidiameter of the Great Orb, which, doubled, gives the diameter.

[Margin: 4th Foundation of the Table.]

[The Fourth:] wherefore, if it be made—as 100 to 314, so the given diameter to another—the circumference of the Great Orb is had (by the rules delivered in bk. 1, ch. 4); and the circumference, divided by 360, gives the quantity of one degree; and a Degree, divided by 60, [that] of one Minute; and a Minute, subdivided by 60, gives the quantity of one Second. Now, among the opinions about the semidiameter of the Great Orb (that is, about the mean distance between the Sun and the Earth), there are several, reported by us in bk. 3, ch. 7, at the end; but it will suffice to follow two as the extremes and one as the mean: the first is Copernicus’s, who puts that distance [at] 1142 terrestrial semidiameters (and many use this in the present controversy); the other is ours, by which we attributed to this distance 7300 terrestrial semidiameters; the third, as it were a mean between these, was Kepler’s, who finally attributed to it 3381 terrestrial semidiameters. Now, if (following the Germans and many others) we attribute to the Earth’s diameter 1720 German Miles (or 6880 Italian), [then] in the diameter of the Great Orb—which on Copernicus’s [view] is 2284 semidia[meters]—

[…continues on p. 430 (PDF 465) with the catchword “me-” (semidiametros): completing the reduction of the Great Orb’s diameter to miles, toward the velocity-table.]


(printed p. 430 — within Chapter XXII: the four foundations are applied and five velocity-tables are built — the Earth’s dimensions and the linear value of arc at various latitudes; the diurnal speed of a terrestrial point at the Equator and at 45° and 89°; the Great Orb’s dimensions on the Copernican, Keplerian, and Ricciolian distances; the Earth’s center’s annual speed; and the combined diurnal-plus-annual motion at sunrise and sunset — all to expose the excessive speeds a moving Earth would require.)


[Header: BOOK IX. SECTION IV. — 430]

…[2284] terrestrial semidiameters, there will be 3,928,480 German Miles (or 15,713,920 Italian). But on Kepler’s [view], for whom that diameter is 6762 terrestrial semidiameters, there will be 11,630,640 German Miles (or 46,522,560 Italian). But on ours, for whom that diameter is 14,606 terrestrial semidiameters, [there will be still more]. With these four foundations laid, we may explain how much space the Earth would traverse in one hour, or in one Minute, or one Second, by the diurnal revolution; and how many Minutes of the Great Orb’s circumference its center would traverse in one Hour, Minute, or Second — that we may apply to them the congruent number of Miles. For [the case is] as follows.

[Translator’s note — the seven velocity-tables of this chapter (Tables I–V here, VI–VII on p. 431) are printed in very dense sexagesimal fractions; the whole-number values and principal fractions below are read at full resolution, but the smallest sub-fractions (sixtieths, thousandths) are reconstructed as legibly as the print allows. “Ger.” = German miles (15 to a degree), “It.” = Italian miles (the standard 60 to a degree, or Riccioli’s measured 72¼), “pc.” = paces. “Nobis” = Riccioli’s own measure.]

TABLE IDimensions of the Earth, and the value of one degree / minute / second of its arc:

Ger. miIt. mipaces(Nobis) It. mi(Nobis) pc.
Diameter of the Earth172068808278
Circumference of the Earth540021,60026,010
Equator — 1 degree156072¼
Equator — 1 minute¼11 204⁄1000
Equator — 1 second0016⅗020 1⁄15
Parallel declining 45° — 1 degree10⅝42 5⁄1851⅛
Parallel 45° — 1 minute00706 11⁄120852¾
Parallel 45° — 1 second0011 47⁄60014¼
Parallel declining 89° — 1 degree1 1⁄20
Parallel 89° — 1 minute0017½020⅚
Parallel 89° — 1 second000≈2⁄7

TABLE IIA terrestrial point traverses [by the diurnal motion]:

Ger. miIt. mipaces(Nobis) It. mi(Nobis) pc.
In 1 Hour (15°) — at the Equator2259001087½
— in the parallel declining 45°157½636¾767½
— in the parallel declining 89°≈415¾18¾
In 1 Minute (15′) — at the Equator1518 6⁄100
— parallel 45°2 65⁄10010 804⁄100012 791⁄1000
— parallel 89°00262½0312½
In 1 Second (15″) — at the Equator002500301
— parallel 45°00175¼0213¼

TABLE IIIDimensions of the Great Orb (Copernicus / Kepler / Riccioli):

Cop. Ger.Cop. It.Kep. Ger.Kep. It.Nobis It.
Diameter3,928,48015,713,92011,630,64046,522,560120,858,800
Circumference12,335,427⅓48,941,708¾36,520,209⅗146,080,838⅖379,496,632
1 degree33,987 11⁄36135,949⅔101,445 1⁄16405,780⅓1,054,157¼
1 minute566 37⁄602265 13⁄601690¾676117,569¼

TABLE IVThe Earth’s center traverses in the Great Orb [by the annual motion]:

Cop. Ger.Cop. It.Kep. Ger.Kep. It.Nobis It.
In 1 Hour (2′ 28″)1397½55893607¼14,428¾43,338
In 1 Minute (2″ 28‴)23 1⁄1893 1⁄1560 7⁄16240 7⁄15722 1⁄10
In 1 Second (2‴ 28⁗)0 23⁄601 23⁄601412 1⁄10

TABLE VIf the Sun rises or sets for some point of the Earth, that point traverses [diurnal + annual combined, the two being then perpendicular]: the values come out the same as in Table IV (the annual motion alone), because at the rising or setting point the diurnal velocity is perpendicular to the annual, and so adds to it insensibly.

[…continues on p. 431 (PDF 466) with the catchword “Sed” (Sed si sit Media nox): “But if it be Midnight for some point of the Earth, that point traverses a space composed of the diurnal and the annual”—Tables VI (midnight, the two added) and VII (midday, the diurnal subtracted).]


(printed p. 431 — within Chapter XXII: the last two velocity-tables give the maximum (midnight, diurnal plus annual) and minimum (midday) combined speeds. Then the First weak argument — the Earth, cause of all heaviness and grossest of bodies, is naturally incapable of so swift a circular motion — with the denials of Galileo and Kepler; and the Second, that a turning Earth would outrun any arrow, bird, or cannon-shot so that nothing could reach its eastern mark, is stated with Buchanan’s verse, the Copernican response beginning.)


[Header: ON THE SYSTEM OF THE MOVED EARTH — 431]

But if it be Midnight for some point of the Earth, that point traverses a space composed of the diurnal and the annual space—that is:

TABLE VI (diurnal and annual added):

Cop. Ger.Cop. It.Kep. Ger.Kep. It.Nobis It.
In 1 Hour — at the Equator16226488383215,32844,425½
— parallel declining 45°15556220376515,06044,105½
— parallel declining 89°14015604361114,44443,356¾
In 1 Minute — at the Equator2710875¼300¾740
— parallel 45°2610470⅔282⅖735
— parallel 89°23¾93¾49⅔197⅖723
In 1 Second — at the Equator0 33⁄601 13⁄201 1⁄1612 301⁄1000

On the contrary, if it be Midday for some point of the Earth, the diurnal space must be subtracted from the annual, and so that point traverses the miles written below:

TABLE VII (diurnal subtracted from annual):

Cop. Ger.Cop. It.Kep. Ger.Kep. It.Nobis It.
In 1 Hour — at the Equator11724688338213,52842,250½
— parallel declining 45°12404960345013,80042,570½
— parallel declining 89°13935572360314,41243,319¼
In 1 Minute — at the Equator19¼7745 7⁄10180⅔704
— parallel 45°20 65⁄10082¾49¾197⅗709¼
— parallel 89°23⅓92⅔59⅔239721¼
In 1 Second — at the Equator0 33⁄601 15⁄200 1⁄1611 699⁄1000

I. Argument, from the Velocity of the Earth toward all motion—especially circular, and so swift

[II.] The Earth is the cause of all heaviness, and the grossest body among creatures… [therefore it is naturally incapable of all motion, especially circular and so swift]… Therefore, if the Earth is the heaviest of all bodies, it must occupy with its center the center of the Universe, and rest there; but if it were removed from it, it would naturally return to it by no other motion than a rectilinear one. This is the sum of the argument, and of its proof—which the Peripatetics implicitly have, in other words, with Aristotle (On the Heavens II, ch. 13) and Tycho (in the epistles, p. 147). But the Copernicans, and especially Galileo, will easily deny the consequence of this argument, as is clear from their foundations premised at ch. 20, nos. 2 and 3. For they will say that gravity is not a force of tending to the Universe’s center, but an inclination which the parts have to be united with their wholes and primary globes; and that straight motion befits those parts only apparently, but really only the circular [befits them] per se; but if they are outside their place, a curved motion befits them, mixed of the circular and another striving toward the straight (but not straight); whereas to the primary globes of the world themselves (of which kind is the Earth), the circular [motion] befits per se, around the center of the world—so that, if it were placed at the center of the world, it would recede thence by a certain curve to the periphery of the great orb, and thereafter continue its circuit through it. But Kepler (bk. 1 of the Epitome of Copernican Astronomy, p. 108) denies that the whole Earth can be called heavy, insofar as it is whole, since there is nothing outside it which attracts it—granted he attributes to the Sun a force of attracting or revolving the Earth and the other Planets; adding that the motion which must be attributed to the Fixed [stars], if it be denied to the Earth, is much swifter.

II. Argument, from the excessive Velocity of the Earth, which no movable could attain toward the East

[Margin: Buchanan’s argument against the motion of the Earth.]

[III.] This popular argument George Buchanan painted in poetic colors, enclosed in the verses of book 1 of [his] Sphere, in these lines:

Imagine in your mind that the Pole stands still—with sluggish stars and unmoved body—and that the Earth revolves itself in a circle, and through so many hours (eight by eight) of darkness and of light closes its perpetual gyre along its own tracks. This force [of speed] neither could the swift arrows equal in their course, nor the wings of birds, nor the blasts of the wind, nor [that force] with which the sulphurous violence of flame drives the rocks—as often as the heat, enclosed in the hollow bronze, rages.

The argument, then, can be formed thus:

[Margin: 2nd Form of the Argument.]

If the Earth were turned toward the East by the diurnal motion, or even the annual, no elementary body could attain, toward the East, the places of the earth to which it tends—at least near the Equator. But this is against manifest experiments. Therefore the Earth is moved neither by the diurnal nor by the annual motion.

[Margin: Proof of the Minor.]

The Minor is clear, for birds flying to [their] nest, and ships [sailing] to an eastern port, and arrows, and the balls of guns and Cannons directed at an eastern target, reach there.

[Margin: Proof of the Major.]

The Major is proved by comparing the velocity of the Earth (exhibited in the tables premised at no. 1) with the natural velocity of any bodies whatever, especially near the Equator. For by the diurnal motion alone, a point of the earth at the Equator traverses, in one Second of an hour (that is, in about one beat of the human artery), 301 paces—whereas not only does no ship or bird, but not even the ball of the largest culverin, traverse beyond about 125 paces in one Second. But if the portion of the annual motion be joined with the diurnal, it is not necessary to restrict the argument to a body that is at the Equator; for even when the motion is least (that is, around midday), a point of the earth traverses, in one Second, nearly 12 Italian Miles—whether it be at the Equator or near the Pole, as is clear from the last cells of the 7th Table, placed opposite [the row of] one Second of an hour.

It is responded, however, by denying the Major, because birds, ships—

[…continues on p. 432 (PDF 467) with the catchword “na-” (naues): “…because birds, ships [and the rest share the common eastward motion of the Earth and the air],” continuing the response to the Second Argument.]


(printed p. 432 — within Chapter XXII: the Second Argument’s response finishes (projectiles share the Earth’s common motion). Then the Third Argument — a rotating Earth would raise a perpetual wind and immense roar — is answered by the trade-winds and by the lower air’s moving with the earth; and the Fourth — the shaking and ruin of buildings and the hurling-off of loosely adhering bodies (Buchanan, Clavius) — begins, Galileo and Kepler having raised and dissolved it themselves.)


[Header: BOOK IX. SECTION IV. — 432]

[Margin: Response to Argument 2.]

…birds, arrows, cannon-balls, and all bodies of this kind are moved not only by the proper motion which appears to us, but also by the common motion by which the earth is moved (though it does not appear to us); and this motion is as great as the Earth’s; and therefore they can reach the place and the eastern target—carried by an equal motion—by their proper motion, which they add over and above the common. Thus indeed the Copernicans.

III. Argument, from the immense Sound, the Lashing of the Air, and a perpetual Wind

[Margin: Buchanan’s argument against the motion of the Earth.]

[IV.] This argument likewise George Buchanan did not pass over (bk. 1 of [his] Sphere), when he sang:

Do you not see, when boys shake little rattles in their right hand, or when an arrow, shot from the twanging string, flies; or when the wind, released from the mouth of a bellows, fosters the panting fire in the furnaces? Do you not see with how great a murmur the air hisses, and groans as it is poured forth? If, then, in a small moment the air, [thus] struck, roars and bellows back with sound—what sound, what murmurs, should we imagine the Earth [would make], while, set in headlong motion, it twists itself into a circle, and so many forests at once, and the steep summits of mountains, cut and tear and bore through the indignant air?

The same thing Simplicius objects to Salviati (that is, to Galileo) in Galileo’s Dialogue 2, On the System of the World (Latin page 186), in the person of a certain author: The author goes on to show that, in Copernicus’s doctrine, one must deny the most valid senses and sensations—as would be the case if we, who feel the breath of the lightest breeze whatever, could not feel the impetus of a perpetual Wind striking us with so great a velocity that in an hour it flies more than 2529 Miles; for the center of the earth, by the annual motion, transmits so much space in one hour, through the circumference of the great orb, as he accurately computes. But, says the same author, on Copernicus’s view, the surrounding air would be moved with the earth, and yet the motion of the air—swifter than any wind—is not felt; rather, unless something else supervene, [there is] the utmost tranquillity: what, then, is it truly to deceive the sense, if this is not the deception? Finally Kepler objects similar things to himself (bk. 1 of the Epitome of Copernican Astronomy, p. 137), in that little question: If the Earth were turned by this most swift motion, would a perpetual wind be felt from the opposite [quarter] of the motion? But the responses to these will soon be adduced, when the argument has been forced into form, in this way:

[Margin: 3rd Form of the Argument.]

If the Earth were turned by the diurnal or even the annual motion, a perpetual wind blowing toward the West would be felt by us, and the air, dashed against the mountains, the towers, and the leaves of the trees, would utter an immense sound and hissing. But neither is felt by us, or by any mortal. Therefore the Earth is turned neither by the diurnal nor by the annual motion.

The Minor seems certain from daily experiments, when the air is tranquil and no winds blow from elsewhere.

[Margin: Proof of the Major.]

The Major is proved, because either the air surrounding us is not moved with the earth at an equal velocity—and so, with us and the mountains and forests carried eastward, going to meet the unmoved air, it would turn out just as if the air met us, the mountains, and the forests (unmoved) at an equal velocity; or the air too is moved with the earth at an equal velocity—and so, in one hour, by the force of the annual motion, it flies through 5589 Italian Miles on the Copernican [distance], 14,428⅔ on Kepler’s, 43,338 on ours, as is clear from no. 1, table 4. How then can it be that so rapid a motion of the air—by day toward the East, by night toward the West, by the force of the annual motion—should not be felt by us?

[Margin: 1st Response to Argument 3.]

It is responded, first, by the Copernicans, by denying the second part of the Minor—namely, that a perpetual wind or breeze blowing toward the West is not felt by any mortal. For Galileo (Dialogue 4, p. 327), and with him Gassendi (Epistle 2, On impressed motion), holds that within the Tropics a perpetual breeze and wind is felt, and that therefore navigation toward the West is more expeditious than toward the East (as we said elsewhere, ch. 4 at the end of no. 6, and in its scholium 5, and ch. 7 no. 4); yet that it is not felt as vehement as the velocity of the terrestrial motion would otherwise require, because the air is moved together with the earth toward the East, but somewhat more slowly, since by its fluidity it does not entirely obey the earth’s motion. But it is supposed, in this response, that the air’s being snatched toward the East is from the earth’s contact; otherwise, if it were from an intrinsic principle, its fluidity would not hinder it from being moved at an equal velocity with the earth. A similar response, from other effects, Kepler premises (p. 138 of the Epitome of Copernican Astronomy), answering that question about the sensation of a perpetual wind thus: This could be conceded concerning the highest summits of mountains; and from this refrigeration the cause could be sought of the perennial snows even under the Torrid Zone, likewise of the coldness of the eastern winds, of the pleasantness of the morning, and the like—provided that both the lower mountains, and the valleys hidden within their summits (which animals inhabit), were safe, and the air in them—through this exterior friction—undisturbed and quiet, and [provided there were] freedom in it for the boiling vapors to rush in every direction. But it is not necessary that we concede what is objected. Therefore he brings another response, which we shall subjoin at once.

[Margin: 2nd Response to Argument 3.]

It is responded, secondly, with the Copernicans, by denying the Major: because the whole air which is in the lowest and middle region of the air (as being full of terrestrial and watery vapors and exhalations) is moved, by the intrinsic force of the motion common to them and to the land-and-water globe, at an equal velocity with the earth toward the East; and we likewise, and the mountains, and the forests with their leaves, are moved thither—wherefore, just as we do not feel the blow of a spear pursuing us, if we flee from it at an equal velocity of flight (says Galileo, p. 187, dialogue 2), so neither [do we feel] the blow of the air, when we are carried at an equal velocity with it toward the same quarter. But Kepler (bk. 1 of the Epitome of Astronomy, p. 38) says that the aetherial breeze, which is not moved with our air, is so many times thinner than our air which animals breathe, that the friction against the aetherial breeze over a thousand miles in one hour is calmer—and so less perceptible—than the friction of a man’s face against the air, walking through it half a mile in one hour. Thus (p. 108) he had said: The aetherial breeze, through which the highest mountain-ridges are carried, is thinner than the air through which a leaden ball is carried—not only eightfold, but by almost infinite times. Therefore the flying-through of the ridges through the aether is many times calmer than [that] of the iron ball through the air. Wherefore Kepler holds that the air enclosed within the usual mountains is moved with the earth (as being watery), and that the aetherial breeze begins from the highest mountain-ridges; and that this [breeze], although it is not moved to the earth’s motion, yet cannot—because of its thinness—produce blasts, or very sensible winds, much less a great sound and crash.

IV. Argument, from the Shaking and ruin of buildings, and the Hurling-off of bodies weakly adhering to the Earth

[Margin: Buchanan’s argument against the motion of the Earth. — And Clavius’s.]

[V.] This argument, such as it is, [belongs] to very many [authors], against both motions of the earth, but especially the diurnal—among whom Buchanan (bk. 1 of the Sphere) sings thus:

Therefore, if the Earth—set in so swift a motion—went toward the West, and came back again to the East, it would shake all things at once with it, and with a vast crash would overwhelm temples, houses, and cities (with their wretched citizens too) in a sudden, unexpected ruin.

Clavius too, pointedly (bk. 1 on the Sphere, p. 196 in my [copy]), says: If the Earth were turned about the world’s axis with such speed that it completed its circuit in the space of 24 hours, as some fable, all buildings would collapse, and could by no means long subsist—which no one fails to see is entirely false. For the response of certain people is invalid, who say that buildings would not collapse, on account of the excessive speed of the motion—just as neither does water contained in some vessel flow out, if the vessel is whirled around very swiftly. It is invalid, I say, because the whole impetus of the water is impressed toward the lower parts of the vessel, but not toward its mouth; whereas the impetus is impressed on buildings toward the outermost parts of the earth, etc. Yet the true cause why the water, in that case, does not fall is that the impetus impressed on the water and the vessel together (and moving [them] in a circle) is greater than that which the water’s gravity produces downward; and, continued in a circle very swiftly, it transfers the upper parts of the water to another place, in which they are no longer higher than the air. This same argument Galileo objects to himself and dissolves (Dialogue 2, On the System of the World, from Latin p. 139 to 148, but from the Italian p. 184 to 213); Kepler [too], in the Epitome of Astro—

[…continues on p. 433 (PDF 468) with the catchword “Astro-” (Astronomiae): “…of [Copernican] Astronomy, pp. 136 & 137,” continuing the authorities for the Fourth Argument (Philolaus, Baranzano, Copernicus, Ptolemy).]


(printed p. 433 — Chapter XXII closes: the Fourth Argument (a rotating Earth would topple buildings and fling off bodies, as spinning wheels sling water and mud) is put in form and answered — earth-bound bodies share the common motion uniformly, so nothing is shaken off. Then the Fifth Argument, from the sensation of impetus we should feel if moved with the Earth, is answered from Kepler: we feel impetus only where there is a struggle of impetuses, not in a uniform common motion.)


[Header: ON THE SYSTEM OF THE MOVED EARTH — 433]

…[the Epitome of Copernican] Astronomy, pp. 136 and 137; Philolaus, part 1, ch. 6; and Redento Baranzano (part 1 of the Uranoscopia, p. 111). But before all these, Copernicus (bk. 1, ch. 7), where he also attributes this argument to Ptolemy. Copernicus’s words are:

[Margin: Copernicus’s casting [of the argument] against himself.]

For the motion [of the earth] would have to be most rapid, and its swiftness insuperable, which in 24 hours would transmit the whole circuit of the earth. But things which are set in motion by a sudden whirling seem utterly unfit for cohering, and [things] more united to be dispersed, unless they are held together by some firmness of cohesion: and long ago—he says (namely Ptolemy, whom he had just named)—the earth being dissipated, [the earth] would have fallen out of the heaven itself (which is quite ridiculous); and all the more would animals, and all other loose loads, by no means remain unshaken.

To which objection he responds at chapter 8.

[Margin: Ptolemy’s argument against the motion of the earth.]

But Ptolemy’s words (bk. 1 of the Almagest, ch. 7) had been: If a motion common to the other heavy bodies, and a singular one, were also in the Earth itself, it is clear that—on account of so great an excess [of speed], in relation to its magnitude—it would, in [its] revolution, anticipate [outrun them]; and, the animals and other weights being left behind in the air, it would itself most swiftly fall out even beyond the heaven itself. To which Chiaramonti subscribes (in the Anti-Philolaus, parts 1 and 6). Let the argument now be collected into form, as below:

[Margin: 4th Form of the Argument.]

[VI.] If the Earth went round by the diurnal, or also the annual, motion, all buildings, [being] shaken, would fall; and the rest [of the things] standing upon the earth’s surface but cohering little firmly, shaken off by its whirling, would be hurled away. But neither happens. Therefore the Earth goes round neither by the diurnal nor by the annual motion.

The Minor is clear: for we do not experience perpetual collapses or earthquakes, but [only] rarely, and [those] from another cause than the whirling of the whole earth. The Major is proved from the very rapid whirling of wheels: for [things] which have been placed on their circumference, and do not cohere very firmly with them, are thrust out and hurled far. Thus the half-projecting wheels of mills wet the neighboring places by the sprinkling of thrown drops; thus the wheels of carts, when driven fast, push out the adhering mud; and boys, the reed being whirled in a circle, hurl a stone inserted in the slit of the reed (as in tongs) to a long distance. Much more, then, would the Earth at last shake loose the buildings, [once] shaken, and not only shake apples and leaves from the trees, but thrust out the animals creeping upon it, and ships, and the stones which are in the channels of waterless torrents, and sands and the like—by as much as its whirling is swifter than the whirling of all wheels.

[Margin: Response to argument 4.]

The Copernicans already named respond, however, by denying the Major; and, as to its proof drawn from a similar [case], they deny the parity. For bodies placed upon wheels are not moved of themselves, nor at an equal velocity with the wheel; and the impetus which is impressed on them by the wheel is along a straight line tangent to the wheel at the point where those bodies are (and from which the impetus issues)—granted that, by reason of their own gravity, they then decline downward from the straightness of that tangent; and the same is to be said of the stone thrust out from the slit of the reed. But all heavy bodies—whether firmly fixed to the earth (like buildings) or infirmly (like sands, ships, the stones of torrents, the leaves and fruits of trees)—are moved by the common motion, and at an equal speed with the earth, in an entirely uniform manner, and neither collide nor are shaken by a reciprocal back-and-forth agitation. Just as cups full of wine are not even overturned, if a vessel is carried very swiftly, but at an even velocity, down a river; nor do the Antipodes fall off, because they strive toward the earth’s center by an equal conspiration [common tendency]. If anyone desires more about the cause for which bodies thrown upon wheels are thrust out, let him consult Galileo (in the places adduced a little before), and Niccolò Cabeo (bk. 1 of the Meteors, text 17, q. 8), where he denies that [things] so thrust out are moved along the Tangent of the circle at the point from which the thrown [bodies] are torn away—because gravity inclines those thrown [bodies] downward, and twists [them] aside from the straightness of the Tangent.

V. Argument, from the Sensation of impetus that would be in us, if we were moved with the Earth

[VII.] Before I had read the seeds of this argument in Kepler (bk. 1 of the Epitome of Copernican Astronomy, p. 136), it had long seemed to me that it could not but be that any animals—and we above all—would feel, in our very selves and in all the viscera and vessels of our body, an impetus impressed either by the earth or by our own common motive faculty, if we were carried round together with the earth at so great a velocity as we expressed in the tables shown at no. 1. Yet the likeness of those who are carried in a ship seemed to remove this suspicion. Nor had Fr. Francesco Maria Grimaldi read Kepler in that place; and yet he too, in disputing about this matter, asserted to me—just as one falling from a window, even if he falls straight to the perpendicular and has [his] eyes closed, feels himself gliding downward—so it would be that we too would feel our motion and impetus, if we were turned with the earth by so headlong, or precipitous, a whirling. Not long after, re-reading the said place of Kepler on another occasion akin to this, I found this very objection conceived in this question:

[Margin: Kepler’s argument against the motion of the earth, and the Response.]

But surely we would feel this motion, at least in our bodies, even with [our] eyes closed? To which he responds at once: By no means; for not even in ships is the motion always felt, when they run evenly—although there the natural bodies are snatched by their gravity, not toward the ships as toward the ships, but beyond the ships outward, and downward to the lands beneath (which are at rest with respect to the river), while the ship snatches them across [transverse to] this line. By how much less shall we feel the Earth’s motion—we who, by the gravity of our bodies, are attracted nowhere else than toward the going earth on which we stand, and accordingly are not snatched outside the line of natural attraction, since that line accompanies us, snatched along together [with it]? These [things] he [says], and nearly sufficiently; yet I ought, for the sake of the natural philosophers and the dialecticians, to dissolve this very argument, reduced to the canons of the syllogism:

[Margin: 5th Form of the Argument.]

If the Earth, and we with the Earth, were snatched at an equal velocity toward the East, it could not but be that we would sometime feel this motion in our very selves. But we never feel such a motion. Therefore neither the Earth, nor we with the Earth, are snatched at an equal velocity toward the East.

About the Minor I think there is no doubt to anyone. The Major is proved, because we—in a fall downward, or in a leap upward and a falling-back downward—even if we close our eyes meanwhile, nevertheless feel our impetus impressed on our bodies (either upward by the soul, or downward by gravity); therefore likewise, whether the Earth and the terrestrial or watery air carry us toward the East, or [whether] in our bodies there be a common faculty and force of going in a circle and following the Earth, we ought nevertheless to feel this very impetus (as subjectively received in us, and perhaps effectively emanating from us) by some sense at last, at least the common [sense].

[Margin: Response to the 5th Argument.]

It is responded, however, by denying the Major, on account of the reason and the likeness just adduced from Kepler. But the [things] which are adduced to confirm the Major are weak, and have a disparity. For in the cases adduced we feel the motion and impetus because neither the air nor the earth are moved with us by the same motion upward or downward—whence it comes about that, if not by [our] eyes, at least by touch we feel ourselves leaving one place and acquiring another; and in a leap upward there intervenes a struggle of the impetus [going] upward from the soul with the impetus [going] downward from gravity. But in the common motion toward the East, nothing of the sort happens, nor do we have any indication of this common motion, or of a new place acquired through it—whether we compare the place we occupy to the Fixed stars, or to other [things]—understand, as long as we are not moved by a proper motion; for this [proper motion] is apparent to us. Nor should it seem strange that there is in us some faculty which exercises its act without our feeling it; for the vital faculty does this perpetually, in concocting and digesting foods.

[…Chapter XXII ends here. Continues on p. 434 (PDF 469) with the catchword “CA-” (CAPVT XXIII): the next chapter.]


(printed p. 434 — Chapter XXIII opens, turning to four celestial arguments against the Earth’s motion, judged weak but not to be despised. The First, from the apparent setting of the stars (a rotating Earth should make the western mountains seem to rise), is answered from Kepler. The Second, from a Fixed star seen from a narrow well — which should vanish in a pulse-beat on a rotating Earth — is answered by Riccioli: the visibility-duration is an optical quantity measured by the visual angle, not the well’s physical width; the geometric demonstration begins.)


[Header: BOOK IX. SECTION IV.]