Lecture 11 — Proof that the stars move, not of themselves, but as carried by the motion of the spheres, from a comparison with their, circles

296 Since changes evidently occur not only in the position of the stars but also in that of the whole heaven, there are three possibilities. Either both are at rest, or both are in motion, or the one is at rest and the other in motion.

297 That both should be at rest is impossible; for, if the earth is at rest, the hypothesis does not account for the observations; and we take it as granted that the earth is at rest. It remains either that both are moved, or that the one is moved and the other at rest.

298 On the view, first, that both are in motion, we have the absurdity that the stars and the circles move with the same speed, i.e. that the ace of every star is that of the circle in it moves. For star and circle are seen to come back to the same place at the same moment; from which it follows that the star has traversed the circle and the circle has completed its own movement, i.e. traversed its own circumference, at one and the same moment.

299 But it is difficult to conceive that the pace of each star should be exactly proportioned to the size of its circle. That the pace of each circle should be proportionate to its size is not absurd but inevitable: but that the same should be true of the movement of the stars contained in the circles is quite incredible. For if, on the one and, we suppose that the star which moves on the greater circle is necessarily swifter, clearly we also admit that if stars shifted their position so as to exchange circles, the slower would become swifter and the swifter slower. But this would show that their movement was not their own, but due to the circles. If, on the other hand, the arrangement was a chance combination, the coincidence in every case of a greater circle with a swifter movement of the star contained in it is too much to believe. In one or two cases it might not inconceivably fall out so, but to imagine it in every case alike is a mere fiction. Besides, chance has no place in that which is natural, and what happens everywhere and in every case is no matter of chance.

300 The same absurdity is equally plain if it is supposed that the circles stand still and that it is the stars themselves which move. For it will follow that the outer stars are the swifter, and that the pace of the stars corresponds to the size of their circles.

301 Since, then, we cannot reasonably suppose either that both are in motion or that the star alone moves, the remaining alternative is that the circles should move, while the stars are at rest and move with the circles to which they are attached. Only on this supposition are we involved in no absurd consequence. For, in the first place, the quicker movement of the larger circle is natural when all the circles are attached to the same center. Whenever bodies are moving with their proper motion, the larger moves quicker. It is the same here with the revolving bodies: for the are intercepted by two radii will be larger in the larger circle, and hence it is not surprising that the revolution of the larger circle should take the same time as that of the smaller. And secondly, the fact that the heavens do not break in pieces follows not only from this but also from the proof already given of the continuity of the whole.

395. After showing what the nature of the stars is, the Philosopher here determines their motion.

First he shows how the stars are moved;

secondly, he shows whether a sound is produced as a result of their motion, at from all this it is clear (L. 14; 290b12).

With respect to the first he shows, by three arguments, that the stars do not move of themselves but are carried along by the motion of their orbs.

The first of these arguments rests on comparing the stars to the orbs [or spheres]. In this argument he presupposes a fact which is sensibly evident: we see the stars and the whole heaven moving. Now there are three ways in which this must happen: In one way, so that both the star and its orb are at rest; in another, so that both are in motion; in a third, so that one of them is at rest and the other in motion. Then having presented this division, he considers each one.

396. First, he considers the first one that both should be (289b4), and says that it is impossible that both, i.e., the star and its orb, be at rest if we assume that the earth is also at rest. For the apparent motion of the stars cannot be saved if both the stars which appear to be in motion are at rest, and the men who see them. For, that motion should appear, this must be caused either by the motion of the thing seen or of the one seeing. For this reason, some, positing the stars and the whole heaven to be at rest, posited the earth on which we live to be moved from west to east around the equinoxial poles [i.e., its axis] once a day. According to this, it is due to our own motion that the stars seem to move in a contrary direction. This is said to have been the opinion of Heraclitus of Pontus and Aristarchus. However, Aristotle is supposing for the present that the earth is at rest—which fact he will later prove. Hence it remains, the first member, in which the .heaven and the stars were assumed to be at rest, having been set aside, to verify one of the two others—namely, that stating that both, i.e., the star and the orb, are in motion, or that stating one to be in motion and the other at rest.

397. Then, at on the view, first, that both are in motion (289b7) he destroys one member, namely, that holding both the star and the orb as being in motion. And he says that if both are being moved, something unreasonable is seen to follow, namely, that there is the same velocity for the star and the circle carrying it. For if both are being moved, then we must say that the velocity of each star is equal to that of the circle in which it is being carried—for the stars appear along with their circles, returning to the same spot whence they had begun to be moved. This is indeed very plain if we speak of the fixed stars which exist in the eighth sphere. For all such stars are seen to move together with the whole sphere with one motion, in such a way that a star in the equinoxial circle [i.e., the equator],'which is the largest circle dividing the sphere through its center, completes its whole great circle in the same time that another star, in a smaller circle located toward one of the poles, completes its small circle. Consequently, since a thing is swifter if it covers a greater distance in equal time, as is plain from Physics VI, it follows that the larger the circle in which a star exists, the swifter its motion. Similarly, the larger the circle itself is, the swifter its motion. This explanation can also be understood, as Alexander says, in adaptation to the circles of the planets. For to the extent that the planets are moved by the diurnal motion, they are revolved along with the supreme sphere, except insofar as the planets through their own motions retrogress somewhat in their own circles. And since the circle of the superior planet is larger, that planet will be swifter as to its diurnal motion—for in the same time it is being revolved through a larger circle.

Thus, therefore, it happens to some extent, both to the fixed stars and the planets, that the star is at once completing a complete circle while that circle itself is moved by a motion of its own as it traverses its own periphery, i.e., circumference. This is to be understood in the sense that some designated point in the circle returns to its original place.

398. Therefore, having shown what happens from the assumption of equal velocities for the stars and for their circles, he shows that this is unreasonable, as he had supposed, at but it is difficult (289b13).

First of all he proposes that it is not reasonable that there should be a same proportion between the velocity of the stars and the size of their circles, so that by so much is a star swifter as it is moved in a larger circle.

Secondly, he shows that it is not unreasonable to say this of the circles themselves. Indeed, it seems to be necessary that their velocities be analogous, i.e., proportionate, to their sizes—since that is what we see in all natural bodies; namely, that so much the greater something is, so much the swifter does it move by its proper motion. Consequently, if it is not reasonable for the velocity of the stars to be proportionate to the size of their circles, it is nevertheless reasonable for the velocity of the circles to be proportionate to their own size. From this it follows that it is unreasonable for the velocity of the stars and of the circles to be equal.

That it is not reasonable for the motion of each star to be proportionate in velocity to the size of its circle he shows in the following way: Such a thing would happen either from necessity of nature or from chance. But if it should occur from natural necessity that a star be swifter on account of being moved in a larger circle, it follows that if stars were transposed into other circles, so that a star previously in a larger circle should be placed in a smaller circle, then the star that previously was slower would be faster, and vice versa. So, it will appear that the stars do not possess a motion of their own but are moved by the circles—from the fact that a star does not preserve some proper velocity in its own motion but its velocity depends on the sole size of the circle. But if it be maintained that chance is the explanation why a star in a larger circle is moved more swiftly, he disproves this in two ways.

First of all, because, if this were due to chance, it would not be reasonable to find this in the case of all circles and stars, namely, that a greater size of the circle goes hand in hand with a greater velocity of a star's motion. For that this should happen in one or two cases would not seem impossible, but that it happen in all cases, and be a result of chance is seen to be a fiction—for things that are due to chance do not occur in the same way in all cases, or in the majority of cases, but only in a lesser number.

Secondly, he shows that this cannot be due to chance, on the ground that chance has no place in things that are due to nature; rather, things that happen fortuitously are outside the order of nature. That is why things produced by chance or fortune do not occur in the same way in all cases, as do things due to nature. Therefore, since there is nothing outside nature in the motions of the heavenly bodies, as was had above, it cannot be that the case under discussion is due to chance. Thus it is plainly not true that the circle and the star are moved together, and with equal velocity.

It is possible to offer yet another reason to disprove this assertion: for, as Alexander says, it would follow that one or other of the motions would be superfluous, which does not occur in things from nature.

399. Then, at the same absurdity (289b27), he investigates the third possibility.

First he shows that it is not possible for the star to be moved and the circle to be at rest, and says that, if one should hold the circles to remain in the same position and the stars to move, the same unreasonable things as before will follow. For it will turn out that the star which is outside is moved more swiftly. And if this refers to the fixed stars, a star will be said to be outside if it is outside the poles and nearer the equinoxial circle [the equator]; if it refers to planets, a star will be said to be outside if it is in a containing circle (for the contained is within the container). In either case, the circle which is outside is greater. Consequently, it will follow that the velocities of the stars will be proportioned to the size of the circles—which has already been disproved.

400. Secondly, at since, then (289b30), he verifies the last member of the division and says that, since it is not reasonable for both, i.e., the star and the circle, to be moved or for the star alone to be moved, what remains is that the circles, i.e., the spheres, are moved, and the stars are at rest with respect to themselves, in the sense of not being moved per se, but with the motion of the spheres in which they are fixed. They will be moved together not as two things with different natures (as happens in the case of a nail embedded in a wooden wheel) but as two things of the same nature. It is as though the stars were the more noble part of the sphere, in which light and active power are concentrated.

Now this is a reasonable supposition, since, one it is assumed, nothing unreasonable follows. For in the first place it is not unreasonable for the greater circle to have a greater velocity, so long as the circles in question are related to the same center. If "center" be here taken in its proper sense, this must be referred to the various circles of the planets, which, according to Aristotle, are all about the same center, namely, the earth—for the astronomers of his time did not posit eccentrics, nor epicycles. But this could not be applied to the various circles described by the fixed stars in their motion, for not all those circles have the same center. However, if we desire to apply it to the fixed stars, then we must take the word "center" as meaning the "pole" [i.e., axis] since, just as the center is to a circle on a plane surface, so is the pole [axis] in a way to a circle on a spherical surface. Now since various circles can be designated on the same sphere with respect to the same poles, a circle is smaller and its motion slower according to its nearness to the pole, just as, among circles set one under the other, that circle is less and slower which is nearer the center. Hence the center and the pole are indivisible and completely immovable.

The reason why he says this is reasonable is that, in other bodies also, which are moved with rectilinear motion, the greater the body, the more rapidly is it moved by its own natural motion—as a larger portion of earth is moved downward with greater speed (while the contrary happens in compulsory motion, in which the motion is slower according as the body is larger). Hence, too, in bodies that are moved with a circular motion, since their motion is natural, it is reasonable that the larger the circle, the more rapidly it be moved.

That the motion of a larger circle is swifter is plain from the fact that, if two lines be drawn from the center through all the circles to the last, the portion cut off [i.e., the arc] by those two lines will be greater in a larger circle and less in a smaller. And the same holds if two circular [longitudinal] lines be drawn from the pole through all the circles to the largest of them [at the equator]. When, therefore, one of the said circular lines shall as a whole reach the place previously occupied by the other, it is plain that in the greater circle it will traverse a greater distance in the same time, which is to be moved more rapidly, as is said in Physics VI, namely, to traverse a greater distance in equal time. It will thus be reasonable, therefore, that a greater circle will traverse a greater distance in an equal amount of time, and that thus its motion will be swifter.

401. Secondly, there does not occur the unacceptable consequence that the heaven would be torn apart, i.e., rent, which we would have to say if the stars are moved and their orbs are at rest—especially since it has been shown that the entire heaven is continuous, in such a way that the lower sphere is wholly in contact with the higher. If, then, the orbs should be at rest and the stars in motion, and assuming that the stars are embedded in the bodies of the spheres, it would follow that the stars by their motion would split or shatter the very substance of the spheres. But if they were moved on the surface of the higher sphere, either the lower sphere would have to be split by the motion of the star, or else there would have to be an intermediate space between the two spheres, depending on the size of the star. Now this space would have to be either empty, or full of some passible body that would be rent, after the manner of air or water, by the passage of the moving body. But both these alternatives are impossible. All these unacceptable situations are avoided, however, if we suppose the stars not to be moved per se but only by the motion of the orbs.

This explanation which has been given fits both the fixed stars and the planets. It can, however, be applied in another way referring to the fixed stars only. Since he had proved that the motion of the larger circle is more rapid on the basis of the portions cut off by the two lines drawn from the center or from the pole, he proves this [i.e., that the stars are carried in their spheres] once more with another argument: Unless the greater circle in the sphere of fixed stars were not in more rapid motion, it would follow that the sphere of the stars would not be a continuous whole, but would be separated into parts—since a star in a smaller circle, if it had a motion equally as swift, would necessarily complete its circuit in less time, for the notion of the equally rapid is that in a lesser time it traverses a lesser distance.