Lecture 27 — Proof of the earth's spherical shape from motion

393 Its shape must necessarily be spherical. For every portion of earth has weight until it reaches the center, and the jostling of parts greater and smaller would bring about not a waved surface, but rather compression and convergence of part and part until the center is reached.

394 The process should be conceived by supposing the earth to come into being in the way that some of the natural philosophers describe. Only they attribute the downward movement to constraint, and it is better to keep to the truth and say that the reason of this motion is that a thing which possesses weight is naturally endowed with a centripetal movement. When the mixture, then, was merely potential, the things that were separated off moved similarly from every side towards the center.

395 Whether the parts which came together at the center were distributed at the extremities evenly, or in some other way, makes no difference. If, on the one hand, there were a similar movement from each quarter of the extremity to the single center, it is obvious that the resulting mass would be similar on every side. For if an equal amount is added on every side the extremity of the mass will be everywhere equidistant from its center, i.e. the figure will be spherical. But neither will it in any way affect the argument if there is not a similar accession of concurrent fragments from every side. For the greater quantity, finding a lesser in front of it, must necessarily drive it on, both having an impulse whose goal is the center, and the greater weight driving the lesser forward till this goal is reached.

396 In this we have also the solution of a possible difficulty. The earth, it might be argued, is at the center and spherical in shape: if, then, a weight many times that of the earth were added to one hemisphere, the center of the earth and of the whole will no longer be coincident. So that either the earth will not stay still at the center, or if it does, it will be at rest without having its center at the place to which it is still its nature to move. Such is the difficulty.

397 A short consideration will give us an easy answer, if we first give precision to our postulate that any body endowed with weight, of whatever size, moves towards the center. Clearly it will not stop when its edge touches the center. The greater quantity must prevail until the body's center occupies the center. For that is the goal of its impulse. Now it makes no difference whether we apply this to a clod or common fragment of earth or to the earth as a whole. The fact indicated does not depend upon degrees of size but applies universally to everything that has the centripetal impulse. Therefore earth in motion, whether in a mass or in fragments, necessarily continues to move until it occupies the center equally every way, the less being forced to equalize itself by the greater owing to the forward drive of the impulse.

398 If the earth was generated, then, it must have been formed in this way, and so clearly its generation was spherical; and if it is ungenerated and has remained so always, its character must be that which the initial generation, if it had occurred, would have given it.

532. Having determined the truth about the earth's place and about its motion or rest, the Philosopher here determines the truth about its shape.

First he proves that the earth is spherical with natural reasons taken on the part of motion;

secondly, with mathematical and astronomical reasons based on sense observations, at the evidence of the senses (L. 28; 297b23).

About the first he does two things:

first he shows his proposition with an argument taken from the species of the natural motion of earth;

secondly, from the figure of its motion, at but the spherical shape (L. 28; 297b17).

Regarding the first he does three things:

first he presents his reason;

secondly, he compares it with the reason assigned by the ancients, at the process should be conceived (297a12; [534]);

thirdly, he excludes certain objections to the aforesaid reason, at whether the parts which came together (297a19; [535]).

533. He says therefore first (297a8) that it is necessary that the earth have a spherical shape for this reason, namely, that each of its parts has heaviness toward the middle, i.e., is naturally moved to the middle by its heaviness, as is plain from what has been said above. But we must here consider, with respect to the motion of parts of the earth, that a larger part crowds out a smaller until the larger part reaches the middle. The reason for this is that a larger portion of earth has greater heaviness, and consequently greater power to be moved to the middle, a lesser power being always overcome by a greater. And therefore it is not possible that, as portions of earth are moved to the middle, any part should billow or rise and fall, so that one part of earth should have a position above another, as occurs in the waves of the sea, as though the earth were here not compressed and there compressed. Rather, since all parts of earth tend toward the middle, the upper parts of earth must press down on the lower, and one part, as it were, consent to another by yielding to it, until the middle is reached. And so, as a result, the parts of earth being, as it were, from all sides compressed toward the middle, the earth must have a spherical shape.

534. Then, at the process should be conceived (297a12), he clarifies the foregoing reason by comparing it with the reason others assigned for the shape of the earth. And he says that the foregoing reason must be understood as though one were positing that the earth was newly generated by the parts of earth coming together from all directions to the middle, as the ancient natural philosophers posited. Nevertheless, there is this difference, namely, that whereas they posit that this motion of parts of earth toward the middle is caused by the violence of the heaven's gyration, as was said above, it is better and truer to suppose that this motion of the parts of earth occurs naturally, on account of the parts of earth possessing heaviness that inclines them toward the middle. If, therefore, we posit that the earth was at first in potency, as the ancients posited, the consequence will be that its parts, at first dispersed and unconnected, will have been borne, when become heavy in act, from every direction to the middle. And from this will result an earth spherical in shape.

535. Then, at whether the parts which came together (297a19), he excludes three objections against the foregoing reason.

The first of these is that someone can say that the foregoing reason does not force the earth's shape to be spherical, unless one supposes that, during the coming-to-be of the earth, parts of earth from all sides similarly and equally moved together to the middle. But it could have happened that when the parts were still disassociated, more parts of earth were found in one region of the place above than in another; consequently, more parts of earth have been assembled at one part of it than at another—which is against the nature of a spherical shape.

536. But he says that the same results as to the shape of the earth whether the previously disassociated parts of earth come together similarly from the extremities of the earth to the middle or something other is the case. For it is manifest that, if the parts of the earth are carried in a similar fashion and in equal amounts from all directions to the middle, then of course the resulting mass of earth will be everywhere equal—since, because an equal quantity of parts is added to the middle on all sides, necessarily the periphery of the earth will be everywhere equidistant from the middle. And that makes for a sphere, because a sphere is nothing else than a body from the center of which all lines to its surface are equal. This argument is not affected if someone should insist that the parts do not gather in the middle in a similar way and in equal amounts, since the larger portions, being heavier, always jostle the smaller portions so far, i.e., until the middle is reached. Now this can be interpreted in two ways. In one way, as meaning that a less heavy part would be pushed until it reached the middle, by a heavier part. But this does not fit Aristotle's intention, because, on the basis of such an interpretation, there will still remain a greater amount in one region of the earth, where more parts come together. In another way so far can mean until the heavier body reaches the middle. And this interpretation is more fitting, because every heavy body naturally tends to this, namely, that it be in its own place, and not that something else be in its own place. Wherefore, a heavier body, in striving to get closer to the middle, violently shoves a less heavy body from the middle—as in the case of a stone thrown into water, which shoves aside the water from contact with the earth. It is along these lines that Aristotle's reason proceeds. For if a larger quantity of earth finds itself in one section of the earth, then, in order to get closer to the middle, it violently jostles a smaller part from the middle until there is found an equal weight everywhere on the earth.

537. A second objection is excluded at in this we have also (297a30).

First, he states it because, as he says, it has the same solution as that which has gone before. The problem is this: let us suppose that the earth does exist in the middle, that it is spherical in shape, and that much more quantity is accumulated on one hemisphere of earth than on the other (this is cited in order to exclude an objection that could be raised on account of the mountains, which are seen to rise above other parts of the earth; for the size of mountains is as nothing in comparison with the total quantity of the earth, but is rather like a hair laid on the side of a copper sphere). Now, if we suppose that enough of a heavy body were added to one place so that it would have a notable quantity with respect to the whole earth, the result would be that there would not be the same middle of the world and of the earth. Hence it would follow either that the earth would not be at rest in the middle or if it did rest, without being in the middle, then now, when it is in the middle, it is capable of being in motion. This therefore is the problem.

538. Secondly, he gives the solution at a short consideration (297b2). And he says that the solution is not difficult to see if someone is willing to consider only slightly and distinguish how we hold that any magnitude having heaviness is borne to the middle of the world. For it is manifest that it will be borne to the middle of the world, not just until its lower surface touches the center of the world, but, unless prevented, it must be borne, with a greater part prevailing over a lesser, to the point where the center of the moved body coincides with the center of the world, in accordance with the inclination that all heavy bodies have. Thus, if the only heavy body in the world were one stone dropped from on high, it would have to keep falling until the center of the stone touched the center of the world. This would be because a greater part of it would repel a lesser from the middle until an equal heaviness should be everywhere found, as was said above. He concludes therefore that it makes no difference whether we apply this to a clod of earth or to the whole earth. For what has been said about the movement of the heavy to the middle is not due to largeness or smallness; rather, it is verified of everything that has an inclination to the middle by reason of its heaviness. Hence, whether the whole earth is being borne from some part of the heaven to the middle, or parts of it, the motion must continue until earth approaches the center in a similar way from all sides, and this is brought about by the smaller parts being made equal to the larger ones through the displacing of the smaller by the larger, as has been said.

539. The third objection he excludes at if the earth was generated (297b14). For someone could say that the foregoing argument proceeds on the assumption that the earth is generated. But this he rejects when he says that, whether the earth was generated, it has to have so come to exist in the middle as has been described, namely, in such a way that its middle touches the middle of the world, and so its figure will be spherical; or whether it was not generated, it must be in the same state as if it had been generated—for the terminus of generation is the nature of the thing; hence anything that is not generated must be such as it would have been had it been generated. And it is according to this that he concludes the shape of the earth to be spherical.