[I.] Most ancient and most celebrated is the subdivision of simple Local motion into that which is toward the center of the universe, and that which is from the center, and that which is around the center, or in[to a circular path]—
[…continues on p. 418 (PDF 453) with the catchword “circu-” (circularem): “…or into a circular [motion],” opening Chapter XX’s six arguments from rectilinear/perpendicular fall and rise.]
(printed p. 418 — within Chapter XX, the doxographic setup and the First Argument’s statement. Aristotle’s threefold division of simple motion and his perpendicular-fall argument for the Earth’s rest are set out, then Copernicus’s and Galileo’s attacks upon them (compound motion, the ship-mast stone, the charge that Aristotle presupposes the Earth at rest). Riccioli answers with the chapter’s First Argument in syllogistic form — bodies fall and rise along one perpendicular line, which a moving Earth would not allow — and begins proving the Minor.)
[Header: BOOK IX. SECTION IV. — 418]
…[or into] a circular [motion], which befits the celestial bodies; and a straight-down [motion], which [befits] heavy bodies; and a straight-up [motion], which suits light ones—whether they be elementary or mixed, but inanimate, or [bodies] not allotted another motion by a soul. Which division Aristotle delivers in the first [book], On the Heavens, ch. 2 (or text 5 and 6), in these words:
Every motion that occurs according to place—which we call lation—is either straight, or circular, or mixed of these: for these two alone are simple. And the cause is that of magnitudes too only these are simple, the straight and the circular. The circular, then, is that which occurs around the center. The straight, that which is upward and downward. And I call “upward” that which is from the center, “downward” that which is to the center. Wherefore every simple lation must be either this from the center, or this to the center, or this circular.
Then (ch. 3, or text 17):
Let the heavy, then, be that whose nature is to be borne to the center; the light, that [whose nature is to be borne] from the center. The heaviest is that which underlies all things borne downward; the lightest, that which is above all things borne upward.
—which he repeats at bk. 4, text 26. On which foundation supposed, among other arguments by which he establishes the immobility of the earth (bk. 2, On the Heavens, ch. 13, text 101), he has this:
It is manifest, therefore, that the earth must be in the middle of the universe, and immobile—both on account of the said causes, and because weights which are violently thrown upward are borne back again perpendicularly to the same [point], even if the force should throw them to infinity.
[Margin: The three kinds of simple Local motion, from Aristotle.]
[II.] But Copernicus (bk. 1 of the Revolutions, ch. 8) endeavored to overturn this Peripatetic doctrine as contrary to his hypotheses: [holding] that the motion of heavy and light bodies is composed of straight and circular, and so is not a simple motion; and that in it the circular predominates per se, as perpetual and befitting a body now sound (that is, set in its own place), but the straight [befits it] per accidens, as [it befits] one sick and disordered, as being placed outside its own place; and that there is no straight motion in reality, but [one] distinguished from the circular only by thought. Let us select his own words. First he says:
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.
Then, having said that not only terrestrial but igneous things (as kindled from terrestrial matter) follow the nature of their whole—that is, are carried around with the earth—he adds:
Therefore, what they say—that the motion of a simple body is simple—is verified primarily of the circular, so long as the simple body remains in its natural place and in its unity: for in [its] place there is no other than circular motion, which remains wholly within itself, like [a thing] at rest. But the straight supervenes upon those things which wander or are thrust out from their whole natural place, etc. And nothing is so repugnant to the order of the whole and to the form of the world as to be outside one’s own place. Straight motion, therefore, does not befall except things not rightly disposed, nor perfect according to their nature, while they are separated from their whole and depart from its unity.
Then, a few things being interposed about the unequal motion of heavy and light bodies (slow at the start but swifter in progress), and about the equality of circular motion, he concludes:
Since, therefore, circular motion belongs to wholes, but straight [motion] also to parts, we can say that the circular remains together with the straight, as an animal [remains together] with [being] sick. And indeed this too—that Aristotle distributed simple motion into three kinds, from the center, to the center, and around the center—will be thought an act of reason only: just as we [conceptually] distinguish a line, a point, and a surface, although the one cannot subsist without the other, and none of them without a body.
And thus far, indeed, Copernicus.
[Margin: Copernicus’s doctrine on the distinction of Straight and Circular motion.]
[III.] But Galileo, by far with more mines, tried—from the very beginning of Dialogue 1, On the twofold System of the World—to perforate and undermine the said foundations of the Aristotelian [doctrine of] motion. For first he says that a helical line made around a cylinder seems to be counted among the simple lines; and he reproaches Aristotle, that he takes the simplicity of motion only from the simplicity of the line, and so delivers a defective doctrine, while among the simple motions he counts only that straight one which occurs upward and downward—since [motions] can be straight, and hence simple, even if they do not occur upward or downward, but forward, backward, rightward, leftward (provided [they come] from a moving principle), and provided he recognize that motion which occurs in a straight line from a heavy or light body, in a certain respect, as composite.
[Margin: Galileo’s doctrine on straight and circular motion, against Aristotle.]
Then he says that straight motion cannot exist in a well-ordered World—both because it does not befit anything except disordered things placed outside their place, and because straight motion is by its nature infinite (in that a straight line is of itself infinite and indeterminate); but nature, with Aristotle agreeing, does not undertake of itself those things which cannot be completed, such as infinite motion. Besides, he approves Plato’s speculation about straight motion, at the beginning of the world—that through it the bodies which were in Chaos acquired a determinate degree of velocity, but afterward [this was] converted into the circular and per se intended [motion]; and that in circular motion each point of the circumference is a beginning and an end. Further, he denies that it is sufficiently proved by Aristotle that heavy bodies move to the center of the Universe, from the fact that they move to the center of the Earth or downward—for those two centers are not one and the same, and the center of the universe is an imaginary point destitute of all power. Again he carps at the Peripatetics, that they attribute to the whole earth, as natural, a straight downward motion to the universe’s center—which motion, however, it never had, but is supposed about to have, if it were placed outside it; whereas the circular motion of fire in a circle, which they in fact concede to it, they call preternatural.
And in Dialogue 2 (Italian page 119 and 132, but [pages] 90 and 99 of the Latin version) he proposes Aristotle’s argument for the earth’s rest, taken from the perpendicular descent of heavy bodies, or the falling-back of projectiles into the same place from which they were thrown up perpendicularly along a straight line: which argument he denies holds, unless the Earth be supposed to rest. For unless this be supposed, as long as we are uncertain whether the Earth moves or not, we are uncertain too whether the descent of heavy bodies occurs along a really straight and perpendicular line, or along a curved and oblique one—since it is certain that, if the earth moves, it must occur along a curved [line], or one mixed of straight and circular; which motion Aristotle ought not to have denied to heavy bodies falling downward, since he conceded it to fire tending straight up of itself but carried around circularly on account of the heaven’s motion. And he adduces the so-often-repeated example of the stone which falls from the top of a ship’s mast to the foot, whether the ship move or rest; but [says] that if it rests, the descent is rectilinear, while if the ship moves, it turns out in reality curvilinear and transverse—of which we said more in the scholia of chapter 4.
Notwithstanding these things, however, we shall teach that the Argument of Aristotle, Ptolemy, and others for the earth’s rest holds. Which can be formed thus:
[Margin: 1st Form of the Argument.]
[IV.] Heavy bodies dropped of themselves through air or through water descend of themselves to the earth along a straight line falling perpendicularly upon the earth; and heavy bodies thrown up along a straight line perpendicular to the earth fall back of themselves into the same place whence they were thrown, along the same straight line, likewise falling perpendicularly upon the earth. But if the Earth were moved by the Diurnal vertigo of 24 hours alone, or even by the Annual motion, they would not descend, nor fall back into the same place, along a straight line perpendicular to the earth. Therefore the Earth is moved neither by the Diurnal vertigo of 24 hours, nor by the Annual motion.
Thus it pleased [us] to form the argument, which Aristotle indicated to us above in a few words (bk. 2, On the Heavens, ch. 13, text 10); and which not only his interpreters there receive, but also Peter Alhazen (9.2, conclusion 3 on the sphere); Clavius (ch. 1 of the Sphere, page 96 in my [copy]); Tycho (in the Epistles, p. 167); Scheiner (in the Mathematical Disquisitions, from p. 30); Chiaramonti (in the defense of the Anti-Tycho, Italian, part 2, ch. 3); and most Physicists and Cosmographers. Now I added in the Major the particle “of itself” (per se), in order to exclude an impediment which could occur per accidens from a wind or other mover disturbing the descending body transversely; but in the Minor I expressed that vertigo of the earth which the Copernicans posit—namely, that which is wholly completed in 24 hours—otherwise, if the revolution were much slower, it could be feigned so slow that it would not physically vary the straightness of the descent of heavy bodies descending in the briefest time. These things being set out, the Major and Minor must be proved; but we shall show the Minor first, because we shall get free of it more briefly, and almost the whole difficulty is in the Major.
[Margin: Proof of the Minor.]
[V.] The Minor, then, is proved, because in that time in which heavy bodies are wont to descend or fall back into the same place, the Earth, by the diurnal vertigo toward the East—and much more [by the annual motion]—
[…continues on p. 419 (PDF 454) with the catchword “gis” (magis): “…and much more by the annual motion, [the Earth] would withdraw that place of the terrestrial surface above which the heavy body had been dropped.”]
(printed p. 419 — within Chapter XX, First Argument. The Minor’s proof completes: on a moving Earth the fall would be really curvilinear though apparently straight, as the Copernicans themselves confess. The Major’s proof then opens with a long epistemological digression: rightly applied senses present things as they are or are corrected by more-manifest sensations, and the degrees of evidence — Metaphysical/Mathematical, Physical, and Moral — bind assent until a higher light proves the opposite; mere Copernican “possibility” cannot overturn the physically evident perpendicular fall.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 419]
…[much] more by the annual motion, [the Earth] would withdraw that place of the terrestrial surface—above which the heavy body had been dropped, or from which it had been thrown up perpendicularly—from that place of world-space in which it had been when first the dropping or throwing of the heavy body was made; and indeed [withdraw it] far and notably. Wherefore, for that heavy body to appear always in the same straight perpendicular line, and to fall back apparently into the same place, it would be necessary that it recede from its original straight line, and so descend that, by following the earth’s original place, it would move transversely, and indeed along a curved line, really falling obliquely upon the earth—as is clear from the figures set out at chapter 17, nos. 16, 17, and 18; and from the confession both of Copernicus and Galileo (in the places adduced at nos. 2 and 3), and of Kepler, Gassendi, and Bullialdus, who teach that this motion is really curvilinear (per what was said at ch. 4, scholia 2 and 4, and ch. 17, no. 3). Wherefore that descent or rebound would apparently seem rectilinear and perpendicular to the earth, but in world-space would really be curvilinear, and falling obliquely upon the earth.
[Margin: Proof of the Major.]
[VI.] The Major is proved. For that is to be asserted [as true] which is Physically evident, and is not established to be false from a higher light (that is, from more evident, or at least more certain, principles); for, to deny it or to assert the opposite, it does not suffice that the opposite is possible, or has certain congruences, or perfections desirable under some respect. But that heavy bodies dropped, or thrown up perpendicularly, descend or fall back along one and the same straight line perpendicular to the earth—this is of itself so physically evident that it is not established to be false from a higher light (that is, neither from more evident, nor at least from more certain, principles). Therefore it must be asserted that such motion is straight; and accordingly it is straight. Now we have included two propositions in this proof, which themselves seem to need further proof.
[Margin: Proof of the first proposition.]
The first is, that one must affirm that to be such [= true] which is so Physically evident that it is not established to be false from principles of a higher light producing greater evidence or certitude; and that it does not suffice, for denying it, that the opposite be possible, or have certain congruences. Which proposition, indeed, is manifest from the whole science of Physics—which would otherwise perish, unless this were true—since the whole [of it] rests on first principles [drawn] from sensations duly had. But [sensations] are not duly had, nor fit to generate Physical evidence, if from other sensations equally or more manifest they are detected to be fallacious and in need of correction: as when, a stick being drawn out of water, we see, and confirm by touch, that it is straight which before appeared curved; or when we see a stone dropped perpendicularly from a masthead—the ship meanwhile running—describe in the air (as seen from the bank or shore) a curved line falling obliquely on the ship’s bottom, which to us (or to others carried along in that ship) appeared to descend along a straight and perpendicular line; or when we prove that the Sun (which seems to us a foot wide) is not a foot wide, from the Sun’s distance [found] by Eclipses or by Lunar dichotomies, and so by other more certain sensations. Wherefore, since the senses of themselves—that is, for the most part, nay always, if they are applied in the due manner—represent to us such objects as they are on the side of the thing, or manifest some other [things] by which we may be able to correct the fallacy of other sensations: possession stands for the sensations, and presumption must be made in their favor, as long as the opposite is not convinced from principles of a higher light—whether of the Catholic Faith (which has certitude without evidence), or of Metaphysics, Mathematics, or a science subalternate to Mathematics and Physics, but in which the principles of Mathematics predominate.
[Margin: Natural evidence, four degrees.]
At which place I judge it should be recalled to memory—or even brought to the notice of those who perhaps never learned it—that there are four degrees of evidence in the natural sciences, according to the four total natural sciences (taking “natural” as it is opposed to “supernatural”): namely Metaphysics, Mathematics, Physics, and Moral [science]; which, however, are reduced to three, because Metaphysical and Mathematical evidence have the same force.
Now Metaphysical and Mathematical evidence is that which renders some proposition so evident that it is altogether impossible for the thing to be otherwise, the first principles of Metaphysics and Mathematics being saved—[principles] which are most absolutely true, and rest on this axiom most manifest of all, It is impossible for the same thing to be and not to be; or on axioms arising thence proximately or very nearly, of which kind are very many divisions of beings—as when we say, Every being is either corporeal or incorporeal; either substance or accident; either finite or infinite, etc.; or when we say, Every whole is greater than its part, or, If from equals you take equals, the remainders are equal. For these are so true that not even by the divine power can they fail to be true.
The second evidence is Physical, which renders some proposition so evident that it is impossible for it not to be such, the first principles of Physics being saved (that is, the mode of being and operating of natural things and causes)—granted it be not repugnant for it to be otherwise, the principles of Metaphysics or Mathematics being saved, or by God’s absolute power. In which way it is evident that “Every heavy body dropped of itself tends downward”; “Every fire is combustive”; “Daily in the Torrid and Temperate Zone the Sun rises above the horizon, and always moves in a circle”; “Every animal is mortal—nay, about to die”; “A Solar Eclipse occurs only at New Moons”; “Under every accident there lies some proper substance”; and so of the like—granted that, if God should will (as He has sometimes willed), these could be otherwise. Since the axe floated upon the water at Elisha’s command, and St. Peter’s body upon the sea at Christ’s bidding; and the fire of the Babylonian furnace did not burn the three boys; and the Sun stood still at Joshua’s command; and at the Savior’s death the Sun suffered an Eclipse from a Moon that was at the Full; and daily, in the Most Holy Sacrament of the Eucharist, Physical accidents are found without the proper substance of bread and wine. Wherefore evidence of this kind is not altogether absolute, but has implicitly annexed a certain hypothesis and tacit limitation—namely, if Nature exists and operates according to its accustomed and due mode; or if the mode of being and operating of natural causes, as such, be regarded.
Lastly, Moral Evidence is when, the principles of prudence being saved, the thing cannot be otherwise—granted it be repugnant neither to Metaphysical nor to Physical principles for it to be otherwise. In which way it is evident, to one who has never seen these, that Rome or the Ocean exists, but has heard from the constant report of upright men that both are found. Further, Physical and Moral evidence persists, and has the force of determining the intellect to assent, as long as it is not established (from divine revelation, or from the principles of Metaphysics or Mathematics) that the opposite is true. In which way the probability of an opinion, too, remains, as long as the opposite has not been evidently known.
These things being posited, I said that that is to be asserted which is so Physically evident that it is not established to be false from principles of a higher light—otherwise that evidence ceases, because that tacit condition on which it rested ceases. Yet I said that it does not suffice, for denying [something] to be, that [its opposite] has been made manifest by such evidence—if its opposite be possible, or have some congruences for its real existence. Otherwise, of all things which are possible (and which, if they existed, would surely have some goodness and perfection), we could assert real existence—which is erroneous, even if we had no sign of either’s existence between the two contradictories. By how much more, therefore, is it erroneous to deny something such to be, of which we have sufficient signs—and to deny it [merely] because its opposite has some congruences and desirabilities, and is not otherwise impossible? Is not the equality of the Lunar month, and the uniformity of the motion of the Moon and of all the Planets, and the configurations of the fixed stars according to regular figures, possible—nay, do they not have great and desirable congruences? Quite truly. Would anyone on that account dare to deny that some Lunations are shorter, others longer? Or, if you refer this to apparent inequality, what of the figures of the stars? Are these too to be called really regular, and only optically irregular? If anyone should dare to say this, let him by all means go on and rub his forehead further [past all shame], and affirm that in reality there is no summer, no winter, no pains, no diseases, no death—but that these only appear [to be]; on the ground that the temperateness and evenness of weather and of the humors, and immortal life, are possible and more desirable beings. For it is no more evident that summer and winter exist, etc., than that the natural descent of heavy bodies is rectilinear and perpendicular to the earth.
[…continues on p. 420 (PDF 455) with the catchword “terrę” (terrae): “…perpendicular to the earth,” completing the sentence and continuing the Major’s proof.]
(printed p. 420 — within Chapter XX, the First Argument (from the perpendicular fall of heavy bodies) concludes: the perpendicular fall is Physically evident, no divine authority or Metaphysical reason contradicting, so the Aristotelian argument stands. Then the Copernican response (Rothmann, Galileo, and especially Gassendi’s dissertation on the fallibility of sense) is set out and rejected: Physical evidence requires only that sense not be deceived after due examination, and the burden of proof falls on whoever claims it is.)
[Header: BOOK IX. SECTION IV. — 420]
…[perpendicular] to the earth. But if you say that, in the examples enumerated, the appearance of them cannot be conjoined with the privation of [their] real existence, or at least cannot [be] without a miracle—I too will say that neither can the appearance of the straight motion of heavy bodies be conjoined with the real privation of straightness without a miracle; and in the controversy on the notion and definition of a miracle, I shall have as supporters all the best Theologians, who recognize so great a miracle in the motion of the whole earth, and in the rest of the Sun, that they deny this motion could come about naturally by the whole Angelic power. And to these we ought rather to adhere than to the Galileists and the rest of the Copernicans, for whom, without any miracle, the Sun stands and the Earth is revolved. Lastly, it must be noted that this proposition—“Heavy bodies descend either along a straight line, or along a non-straight one” (which alone the adversaries concede to be evident)—is evident Metaphysically (understand, on the supposition that they descend); but we here only require and defend the Physical evidence.
[Margin: Proof of the 2nd proposition.]
[VII.] Secondly, in the proof of the Major we said that it is Physically evident that heavy bodies dropped, or thrown up to the perpendicular, descend and fall back along one and the same straight line falling perpendicularly upon the earth; and [it is] so evident that the falsity of this straightness cannot be convinced from any higher light, or more certain principles. For it is established by the experiments of all ages and places that this motion appears straight—not [straight] to some, or sometimes, but not [straight] to others, or at other times, but [straight] to all and always. Nor does any authority of God gainsay this appearance, since it rather most especially supports it by this very fact, that [God] most often affirms the Earth to be immobile to us. Lastly, no reason taken from Metaphysics or from Mathematics certainly and evidently resists the straightness of this motion; as is clear both from the solution of the arguments adduced for the earth’s motion (from chapter 5 to chapter 19), and from the confession of the Copernicans, who openly concede that, on either hypothesis (namely, of the Earth immobile and moved), all the Phenomena can be saved. And indeed Galileo (Dialogue 2, On the System of the World, Latin page 81) says most pointedly:
And this motion of 24 hours, as to this first appearance, in no way prevents it from being able to be in the Earth alone, as much as in the whole rest of the world except the Earth. For the same appearance would be beheld in the one position as in the other.
From no effect, therefore, can it be convinced that the Earth moves, and so that the descent of heavy bodies is not—as it appears—rectilinear and perpendicular with respect to the earth. And let these things suffice for the Aristotelian argument. Yet let us hear the responses of the Copernicans.
Response of the Copernicans to the 1st Argument, and its Invalidity
[VIII.] Rothmann, however (in the Tychonic epistles, p. 185), Galileo (Dialogue 2, On the System of the World), and Gassendi (Epistle 2, On motion impressed by a translated mover, pp. 80 and 106) respond by distinguishing the Major, and conceding it if it is certain from elsewhere that the Earth does not move and that our senses are not deceived in judging the rectilinear motion of Heavy bodies, or if the earth’s motion is not common both to us observing the motion of the heavy bodies and to the heavy bodies themselves; but otherwise denying the Major. And they press the example of one who, ignorant of the motion of the ship in which he is carried, would accordingly judge the fall of a stone dropped from the masthead (or the descent of a globe dropped through the water of a vessel enclosed in that ship) to be rectilinear—which in reality, on account of the ship’s motion, would be curvilinear in world-space (granted it would not be recognized, because the eye observing that motion would be carried along together with the ship). And Gassendi indeed, granted he withholds assent, yet adds certain things there which (to use Chiaramonti’s words) would altogether destroy the Criterion of sense—that is, the judicative power resting on the sensations—however rightly the sensitive power were disposed, and the object duly presented, and the medium not disturbing the sensation. For Gassendi says:
[Margin: Gassendi’s dissertation against the fallacy of the Senses.]
But now the globe is the Earth, into which we were transferred as if sleeping, or rather in which we were born without thinking. But from when we opened our eyes, and beheld, besides this globe, another—namely the Sun—in the same sea (as it were), or world-space, with the Earth, it was asked to which of these globes rest belonged, [and] to which motion? But we without hesitation pronounced that without doubt rest belongs to the Earth, and motion to the Sun. Pythagoras, Plato, Aristarchus, other ancients, and likewise Copernicus, Galileo, Kepler, and many more recent ones, warned [us] that perhaps we are deceived, and that the Sun rests and the Earth moves; yet we persisted against [them], and were made the more obstinate, the more, attending, we observed that the parts of the Earth are not mutually torn apart from one another—but that yonder mountain is always to the North, this city to the South, yonder river to the East, this island to the West; and that we meanwhile run about upon the Earth just as we run about through the house or city in which we were born; so that, just as neither the house runs about through the city, nor the city through the province or the Earth, so neither may the Earth itself seem to run about through the spaces of the world. And thus indeed our imagination is disposed from [our] birth; nor do we notice that the Earth is perhaps like a ship, and that it can come about that, existing on the Earth, we are deceived just as that Mediterranean[-sailor] while he is in the ship. For what will be the difference? Or what reason of difference? And what way of discerning either truth or error [from within]? And I do not indeed say that the Earth therefore moves, [and] the Sun rests; but I say that better reasons must be sought than those drawn from sense itself. And if indeed we had never experienced the fallacy of our sight, we would seem excusable, and could object that nothing is more manifest or more certain than sight, and that, faith being withdrawn from the eyes, nothing would be worthy of persuasion. But because experience has taught us that sight is so greatly deceived, and that faith is not always to be placed in the eyes—and that especially when motion is in question—what else can be answered than that both sight and the other senses are to be corrected by reason?
These [things] he [says], with a declamatory elegance of style, indeed, but striking nothing, and not even pricking Aristotle.
[Margin: The adduced response is rejected.]
[IX.] For the aforesaid response and distinction is worth nothing, because for Physical evidence it is not required that we be certain from elsewhere that the Earth rests, and that our sense is in no way deceived; but [only] that it is not deceived when every application of the [sensitive] power, and every examination of the medium and object naturally possible to us, has been made. Otherwise we would have to proceed to infinity from one sensation to another and another, with a perpetual fear of error; or, if this certitude had to be sought from other principles supposing no sensation, then it would not be Physical certitude, but either Metaphysical, or Mathematical, or Theological—which would be importunately and unskillfully required in this place. But the example of one observing the fall of a heavy body in a ship has no parity; since not all, nor always, are ignorant that the ship moves, and there are natural means of detecting that ignorance, and accordingly of correcting the fallacy of sense. On the contrary, however, there is no natural means by which we could certainly and evidently detect that the Earth moves, and we with the Earth, and accordingly that sense is deceived in judging the rectilinear motion of heavy bodies. Nay rather, from the more vehement percussion, if they fall from a higher place, we have an argument—from the sensations themselves—that the increment of velocity is real, and so that the Earth does not move, as is clear from the preceding chapter. And the a-priori reasons for the Earth’s motion, [drawn] from certain congruences, are now abundantly solved, from ch. 5 to 19; and there are not lacking, in the Earth’s motion, many other absurdities—just as there are not lacking, in its rest, very many utilities, and congruences with the end intended by God and desirable by us. Wherefore, even if the weights of the a-priori reasons were equal on both sides, in this there will always be a disparity: that for the Earth’s rest and the rectilinear motion of heavy bodies stands the universal sensation of all men, at any time and place; but for the curvilinear motion of heavy bodies, and the motion of the Earth, there is no sensation, nor can there be. And upon him who asserts that sense is deceived falls the burden of proof—and indeed a most valid one; otherwise all tribunals will adjudge the lawsuit against so many eyewitnesses.
[…continues on p. 421 (PDF 456) with the catchword “II. Ar-” (Argumentum): the Second Argument of Chapter XX, “from the Brevity and Shortcut of the journey of Heavy and Light bodies naturally hastening to their own place.”]
(printed p. 421 — within Chapter XX: the Second Argument, from the brevity and shortcut of the journey of heavy and light bodies — nature demands the shortest path, but a moving Earth would force falling bodies onto enormously longer curved transverse paths; two Copernican responses are rebutted. Then the Third Argument, from the simplicity of motion, begins: a moving Earth needlessly multiplies motion-species, inequalities, and velocity-degrees in the same falling body, varying by latitude.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 421]
II. Argument, from the Brevity and Shortcut of the journey of Heavy and Light bodies naturally hastening to their own place
[Margin: 2nd Form of the Argument.]
[X.] The nature of Heavy and Light Bodies demands that, if they are outside the place due to them, [the impediments] being removed, they reach it by tending along the shortest possible way. But if the Earth were moved either by the diurnal motion only, or even by the annual, neither Heavy nor Light bodies placed outside the place due to them would—however much the impediments were removed—reach it by tending along the shortest way. Therefore the Earth is moved neither by the diurnal nor by the annual motion.
[Margin: Proof of the Minor.]
The Minor is proved in the first place, because there is no controversy about its truth, nor can it be denied by the adversaries if the way it would have to traverse in the hypothesis of the moved earth be compared with the way [it would traverse] in the hypothesis of the resting earth. For if the Earth in no way moves, Heavy and Light bodies dropped tend and reach their place along a straight line perpendicular to that place toward which they tend—than which no way can be shorter. But if the Earth moves by the diurnal motion only (and much more if also by the annual motion), it is necessary that heavy bodies divert downward from the straight way, following the Earth and its motion—both the diurnal, that they may fall to that point above which they were dropped perpendicularly or thrown up (which point has now, on account of the earth’s vertigo, been withdrawn from the original perpendicular); and the annual, lest they fall outside the whole earth. Wherefore they must describe, by their motion, a transverse and curvilinear way, such as we sketched at ch. 17 from no. 16. And the same is to be said of Light bodies tending upward, for these too must appear to the eye (carried along with the earth) in the same straight line, and drawn up perpendicularly from the earth’s surface. And so, for example, the clay globe—which (per ch. 16, no. 12) we observed to descend from an apparent height of 240 feet in the time of 4 Seconds of an hour—if it followed only the diurnal motion of the Earth, then, in order to fall into the same place above which it was dropped, it would have had to traverse, if it were on the Equator, at least 7527 Roman feet (as many, namely, as are contained in one Minute of the Equator, per ch. 19, no. 13, in the first part of the table; for in four Seconds of an hour one Minute of the Equator is revolved). And if it further followed the annual motion of the Earth—since the Earth’s center traverses, in each Second of an hour, 2‴ 28⁗ of the annual orb (that is, in four Seconds, 9‴ 52⁗)—it would have had to traverse, by the force of this motion alone, at least 23,860 feet (or 4772 Roman paces, that is 4 4/5 miles), if we follow the Copernican Diameter of the Great Orb; but if [we follow] ours, it must have traversed at least 142,760 Roman feet (or 28,552 paces, that is 28 2/5 old Roman miles)—as may be gathered from the table of chapter 19, number 13. Which [distances], by a very long interval, exceed the shortest and perpendicular way of 240 feet.
[Margin: Proof of the Major.]
The Major is proved, because in inanimate bodies—whose motion is not determined by a soul—Nature uses a shortcut, nor does it do through more what it can [do] through fewer: which axiom indeed the Copernicans use, or rather abuse, to attribute the simplicity and unity of the diurnal motion to the Earth alone, and deny it to the Fixed [stars] and the Planets. Besides, that very increment of impetus, by which Heavy and Light bodies are moved faster and faster toward the end [of their journey], is an argument of nature striving for the shortest and most expeditious journey, that they may reach their place. Yet the response must be heard which the Copernicans could devise.
[Margin: 1st Response to the 2nd Argument, equally weak.]
For it can be responded, first, by distinguishing the Major, and conceding it comparatively with respect to the place of its whole (to which they wish [the body] to be conjoined), [the place] meanwhile translated, and on the supposition of imitating the motion by which their place moves—for, these being kept, they cannot be borne by a shorter way; but denying it absolutely, or [denying it] when comparison is made with the place over which they perpendicularly hung or rested when first they were dropped. But who does not see that this is fabricated from the necessity of the hypothesis about the Earth’s motion—which, since it is controverted, ought not to be presumed as certain; but the controversy must be settled from other more-known [things]? Now it is more known that the Nature of these bodies requires [the shortest way] a priori; nay, if we acquiesce in the observation and testimony of the senses, it is also more known a posteriori that [Nature] pursues that conjunction of the parts with their whole, and their restitution to their place by the shortest way; surely it would be better to be united to it at once by a straight [line], and afterward, if it [the whole] moves circularly, to be moved circularly with it.
[Margin: 2nd Response.]
It is responded, secondly, by conceding the Major, if the brevity of the journey of the elementary bodies does not suppose multiple motions and the journeys of the celestial bodies—[but] denying [it], if it does suppose [them]. Now, if the brevity of the journey of Heavy and Light bodies along a line perpendicular to the Earth is retained, the diurnal and annual motion of the Earth must be transferred from the Earth to the stars; but it seems that the simplicity of the celestial bodies (as being simple) should rather be favored than that of the elementary bodies. Yet always, in the hypothesis of an immobile earth, the foundation drawn from the sensations prevails—on account of which both the earth’s rest and the diurnal motion of the stars is reasonably asserted—which foundation the hypothesis of a moved earth lacks. Then, already at ch. 6 (from no. 11 to 15) and ch. 9 (from no. 1 to 5), we showed that more motions are multiplied if the Earth moves (the necessary motions of the stars also being computed) than if it rests.
III. Argument, from the Simplicity of the motion of Heavy and Light bodies
[Margin: 3rd Form of the Argument.]
[XI.] The species of motions, or the diverse inequalities and diverse degrees of velocity in the same Movable, must not be multiplied without necessity. But if the Earth were moved by the diurnal or even the annual motion, there would be multiplied, in heavy and light bodies, the species of motions, and the diverse inequalities and degrees of velocity in the same movable, without necessity. Therefore the Earth is moved by neither motion.
[Margin: Proof of the Major.]
The Major is used by the Copernicans, in order to substitute the single diurnal motion of the earth, and the single annual [motion], for so many other motions of the Fixed [stars] and the Planets, which would have to be admitted if the Earth were immobile (as is clear from ch. 6, no. 14, and ch. 9, no. 2); and it rests on those axioms, God and nature do nothing in vain, and likewise, Beings must not be multiplied without necessity. The Minor is easily shown from the diverse figures of motions which Heavy bodies would describe in descending, if the Earth were turned by both, or at least by one, motion—which figures we delineated, after a fashion, at ch. 17, nos. 16, 17, and 18.
[Margin: How various, unequal, and not everywhere constant the motion of Heavy bodies would be, if the Earth moved.]
How various [they would be]! For if a heavy body were dropped above the poles of the terrestrial Equator, and the earth moved by the diurnal motion only, the descent would be made along a straight line perpendicular to the earth; but if [it moved] also by the annual motion, [the body] would describe a curved and oblique line upon a cylindrical surface; if [dropped] in the Parallels of the Equator, it would describe a curved line about a conical surface—and indeed of a varied cone (or one translated by the annual motion to diverse places); but if [dropped] in the Equator, that [line] would be described in nearly the same plane, as we showed in the same place. To this is added that, following the earth’s diurnal motion, [bodies] would have to traverse, in the same time, more journey in the Equator than in the parallels, since in these the motion of the parts of the terrestrial surface is slower. And so the same heavy body, dropped above diverse places of the earth, would descend by diverse ways and with very diverse degrees of velocity. Besides which, it would obtain yet another inequality from the diverse times of the same day, at which the diurnal motion would sometimes add to the annual, sometimes subtract [from it], but sometimes add or subtract nothing (per what was said at ch. 19, no. 12). And the same things are to be understood proportionally of the ascent of Light bodies. Further, no necessity appears for multiplying so many varieties of motions, since, the Earth resting, all the celestial Phenomena are saved, and all the experiments of the elementary motions.
[Margin: A response not very valid.]
The Copernicans will respond by denying the Minor; for there is a necessity—not indeed a posteriori, from sensations or Phenomena, but a priori—lest in the celestial [bodies] motions be multiplied without necessity; and in an equal conflict between celestial and elementary bodies, the multiplicity of motions is to be permitted rather to the elementary than to the celestial; for through it (as supposing the earth’s motion) very many other motions are excused, which otherwise in the heaven would have to be recognized—
[…continues on p. 422 (PDF 457) with the catchword “agno-” (agnoscantur): “…would have to be recognized,” continuing the Copernican response to the Third Argument and its rebuttal.]
(printed p. 422 — within Chapter XX: the Third Argument closes, then the Fourth Argument, from the terminus of the motion of heavy and light bodies — on a moving Earth no reason antecedent to the disputed hypothesis explains why bodies tend to this terminus rather than another, whereas Earth-rest explains it by the restoration of elemental order; Kepler’s objection about the mathematical center is answered. Then the Fifth Argument begins: an Angel dropping a chained metal sphere would find it hang perpendicular only over a resting Earth.)
[Header: BOOK IX. SECTION IV. — 422]
…[would otherwise in the heaven have to be] recognized, if they are excluded from the earth. But in reality there are more motions in the world if the Earth moves than if it rests; for in the heaven motions are not really multiplied, but there is a single diurnal [motion] in each [star]—granted slower in some, faster in others. Then the disparity always prevails, on account of the physical evidence of the motion of the celestial bodies and of the rest of the earth.
IV. Argument, from the Terminus of the motion of Heavy and Light bodies, to which they tend
[Margin: 4th Argument, an Enthymeme.]
[XII.] If the Earth is moved by the diurnal motion, no reason can be given antecedent to the hypothesis of the earth’s motion or rest, on account of which Heavy and Light bodies tend to that terminus to which they tend, rather than to another of the same—or even of a better—condition for terminating that motion. But it can [be given], if the Earth does not move. Therefore the hypothesis of an immobile Earth is to be preferred to the hypothesis of a mobile Earth.
Concerning the consequence, at least if other things are equal, there seems to be no room for doubt. But the prior part of the Antecedent is proved by assuming one example, that judgment may be made of the others.
[Margin: The 1st part of the Antecedent is proved.]
Let there be, upon some Rock placed on the Equator, a glass sphere, which is thrown up from there to the perpendicular, or certainly dropped above that rock from a tower: it is certain from observations that this sphere will fall onto that rock, unless per accidens it is violently impelled elsewhere, or drawn back, or impeded. Let there be, besides, on the terrestrial Equator, a lake or pond, distant from the said rock toward the West by so many paces that, if the glass sphere descended really by a straight way and did not follow the vertigo of the terrestrial conversion, it would fall into the lake or pond. For, the Earth’s diurnal vertigo being posited, I ask: why does that glass fall onto the rock? If you say this happens because that glass is a partaker of that motion which the whole earth has (since it is a terrestrial body), and therefore must move toward that part toward which the Earth [moves], and around the same center around which the Earth is moved—now this reason is not antecedent to this controverted hypothesis about the Earth’s motion, but supposes it; and supposes it in such a way that, even if its contradictory were supposed (namely, the privation of motion in the Earth), the glass would nonetheless fall onto that rock; wherefore no more can the motion than the rest of the earth be adduced as the cause of the descent onto the rock. If you say this happens that [the glass] may be united to its whole, or be better preserved there, or on account of the kinship which the glass sphere has with the rock, or because it is magnetically drawn by the Earth toward it—you do not satisfy; for it has no greater kinship with the rock than with the water of the lake or pond; nor is it more conserved there than here (since rather it is broken by the rock); nor is there in the rock a glassy mass having the nature of [its] whole. But if the nature of [its] whole is in the whole land-and-water globe, it will no less be united to its whole, or be drawn by it, if it falls into the water than if [it falls] onto the rock. To these [points], as Scheiner rightly argues (in the Mathematical Disquisitions, p. 30): if around the Earth’s center there were a watery globe, and around this globe the earth, yet a clod of earth placed at that center would not ascend to its whole, but would remain there; therefore heavy bodies do not descend to be united to their whole, but to lie beneath things lighter than themselves. (Yet the instance has greater force if the clod is distant from the center, lest they say it does not move because neither does the center move.) If you say it falls onto the rock so that its motion may be represented to us always in the same straight line, you feign the cause arbitrarily, for our sight is not the end of that fall. What then will you say of a raindrop falling upon sand, or upon the embers of a fire? And so, wherever you turn, you can devise no solid cause of the said fall, antecedent to the hypothesis of the earth’s motion.
[Margin: The 2nd part of the Antecedent is proved.]
[XIII.] The posterior part of the Antecedent is proved. For the cause for which a heavy body falls back into that place over which it perpendicularly hangs is not an appetite of uniting itself to its whole (otherwise a rock, for example, dropped through a well would have to unite itself to the side of the well, sunk in the earth), but [it is] that the parts of the universe, in the elemental system, may return as soon as possible to their place, and their order as to position be restored—namely, that the heavier may lie beneath the lighter, and the lighter rest upon the heavier; and this cannot be done as soon as possible, nor by a shorter way, than along a line perpendicular to the earth, or straight tending to the center of all heavy bodies. For although this center is a point, and is not of itself the mover or the terminus of the motion of all heavy bodies, it is nevertheless directive—as that toward which, if they tend, it is certain they will return as quickly as possible to the place due to them in the order of the universe. Just as a standard [flag] is not a sign under which all soldiers can be gathered (as a place or covering capable of [holding] them all), but is directive of their motion; nor is the cynosure [pole-star] the port of sailors, but directive of [their] navigation. For even if the whole earth had burst into various parts, they would not flow together again to the center to be in the center, but to lie beneath the lighter; for which it was necessary that they have a certain common point which would objectively determine their shortest and surest way. Similarly the Lighter must recede from the center of the heavier, on the supposition that around this center—especially in a straight line—the heavier exist unimpeded from descending beneath the lighter; and therefore they are said to move “from the center.” Wherefore it is no obstacle that Kepler (in the Introduction to the Commentaries on Mars) urges that the center of the Earth is a mathematical point and nothing, and so can move heavy bodies to itself neither effectively nor objectively. This author’s words are these:
Whether the mathematical point, or the center of the world, exist or not, it can move heavy bodies neither effectively nor objectively, so that they approach it. Let the Physicists prove that this power belongs to a point—which is neither a body, nor is understood otherwise than from mere relation. It is impossible that the form of a stone, in moving its body, should seek a mathematical point or the world’s middle, without regard to the body in which that point is. Let the Physicists prove that natural things have a sympathy toward that which is nothing.
But we do not say [they] tend to the center without regard to the body whose center it is; nay, we suppose that around it heavier bodies are placed on all sides, and that heavy bodies tend toward these to lie beneath the lighter, and so be coordinated with them in the universe. Now Nature, and God the Geometer, used this center as a terminus toward which the Heavier, and from which the Lighter, must be borne—but not as a terminus at which, and in which, they must be placed: just as he who describes a circumference uses the center, in [the circumference of] which some things must be placed. It is false, therefore, that the center does not move [bodies] objectively, and by way of a sign, or even of a terminus of respect and order. And what Kepler adds in the same place—Heavy bodies (even if we most especially place the Earth in the center of the world) are not borne to the center of the world as to the center of the world, but as to the center of the round kindred body, namely the Earth—this we admit as far as it goes; but from this it follows that this center is the terminus from which their distance in the round body must be measured, and that their direction must be taken in such a line as is the radius or semidiameter of the round body (for this alone is that which, by its revolution about the center, constitutes the round body); and so [it follows] that the motion of heavy and light bodies naturally descending or ascending must occur in a line perpendicular to the round surface of the terrestrial globe—which cannot happen, the phenomena and the falling-back into the same place being saved, unless the Earth rests.
Yet it could be responded by the Copernicans that the consequence of the Enthymeme is true if other things are equal, or if a suitable reason can be given for the many phenomena which appear in the heaven, the Earth’s immobility being supposed; but otherwise [it is] not true: and so they seem somehow able to escape the force of this argument—[holding it] only within the bounds of probability. Yet always the foundation from the sensations prevails, which the hypothesis of a moved earth lacks.
V. Argument, from a sphere hung by a little chain and dropped downward by an Angel
[XIV.] If an Angel, hanging over a terrestrial point, dropped a metallic sphere downward—but tied by a chain, the other end of the chain being retained [by him]—that sphere would tend straight toward the earth, and would stretch the chain in the perpendicular, above the original point of the earth. But this could not be, if the Earth moved.
The Copernicans will respond by denying the Major: for the sphere would tend by an oblique motion toward the East, and would thereby draw the chain with it. Or, if the Angel’s force in retaining the chain were greater, the chain would indeed at last come to rest—but made oblique toward the East.
[…continues on p. 423 (PDF 458) with the catchword “VI. Ar-” (Argumentum): the Sixth Argument of Chapter XX, “from the confusion of Lines and Figures, and of Measures.”]
(printed p. 423 — Chapter XX closes with the Sixth Argument, from the confusion of lines, figures, and measures: on a moving Earth the straight lines and right angles of architects and surveyors would be such only optically, not in world-space. Then Chapter XXI opens, proposing fourteen arguments from the motion of elementary bodies toward the cardinal points against the diurnal motion, five of them Physically insoluble; its First Argument (Ptolemy’s — clouds, smoke, and birds should drift west on a rotating Earth) is stated, with Copernicus’s kinship-of-the-air response begun.)
[Header: ON THE SYSTEM OF THE MOVED EARTH — 423]
VI. Argument, from the confusion of Lines and Figures, and of Measures
[XV.] I bring back this argument under the title of this chapter, because it has great affinity with what was said about the straight line described by the motion of heavy and light bodies. For just as it is Physically evident that these bodies designate a straight line by their descent or ascent, so it is evident to architects that they designate a straight line by a plumb-line extended and let down; and to Practical Geometers, that by the help of a Ruler or a stretched thread they draw a straight line, by the help of a compass a circular periphery, and by the help of a square (or by problems of practical Geometry) a right angle, and thence construct for themselves various rectangular figures. But if the Earth moved, these would not be such in reality in world-space, but only optically (or apparently) on a board, paper, wall, etc.; nor would the line of sight be continued along one and the same straight line. Nor could one who ran toward the East, or drew furrows with a plow, truly say that he had run three miles in one hour, or completed the plowing of one acre in one day; for he would have measured out much more space in the world—especially if the Earth moved also by the annual motion: for besides the apparent motion, he would have completed that [motion] which the Earth had meanwhile completed by its own motion. But all these things, however alien to common sense, and paradoxical to the vulgar, the Copernicans will deny to be absurd to an intellect that knows the reasons for which the Earth’s motion is asserted by them.