Lecture 26 — Proof of the earth's rest in the middle

379 Let us first decide the question whether the earth moves or is at rest.

380 For, as we said, there are some who make it one of the stars, and others who, setting it at the center, suppose it to be 'rolled' and in motion about the pole as axis.

381 That both views are untenable will be clear if we take as our starting-point the fact that the earth's motion, whether the earth be at the center or away from it, must needs be a constrained motion. It cannot be the movement of the earth itself. If it were, any portion of it would have this movement; but in fact every part moves in a straight line to the center. Being, then, constrained and unnatural, the movement could not be eternal. But the order of the universe is eternal.

382 Again, everything that moves with the circular movement, except the first sphere, is observed to be passed, and to move with more than one motion. The earth, then, also, whether it move about the center or as stationary at it, must necessarily move with two motions. But if this were so, there would have to be passings and turnings of the fixed stars. Yet no such thing is observed. The same stars always rise and set in the same parts of the earth.

383 Further, the natural movement of the earth, part and whole alike, is the center of the whole—whence the fact that it is now actually situated at the center—

384 but it might be questioned since both centers are the same, which center it is that portions of earth and other heavy things move to. Is this their goal because it is the center of the earth or because it is the center of the whole?

385 The goal, surely, must be the center of the whole. For fire and other light things move to the extremity of the area which contains the center. It happens, however, that the center of the earth and of the whole is the same. Thus they do move to the center of the earth, but accidentally, in virtue of the fact that the earth's center lies at the center of the whole.

386 That the center of the earth is the goal of their movement is indicated by the fact that heavy bodies moving towards the earth do not parallel but so as to make equal angles, and thus to a single center, that of the earth.

387 It is clear, then, that the earth must be at the center and immovable, not only for the reasons already given,

388 but also because heavy bodies forcibly thrown quite straight upward return to the point from which they started, even if they are thrown to an infinite distance.

389 From these considerations then it is clear that the earth does not move and does not lie elsewhere than at the center.

390 From what we have said the explanation of the earth's immobility is also apparent. If it is the nature of earth, as observation shows, to move from any point to the center, as of fire contrariwise to move from the center to the extremity, it is impossible that any portion of earth should move away from the center except by constraint. For a single thing has a single movement, and a simple thing a simple: contrary movements cannot belong to the same thing, and movement away from the center is the contrary of movement to it. If then no portion of earth can move away from the center, obviously still less can the earth as a whole so move. For it is the nature of the whole to move to the point to which the part naturally moves. Since, then, it would require a force greater than itself to move it, it must needs stay at the center.

391 This view is further supported by the contributions of mathematicians to astronomy, since the observations made as the shapes change by which the order of the stars is determined, are fully accounted for on the hypothesis that the earth lies at the center.

392 Of the position of the earth and of the manner of its rest or movement, our discussion may here end.

521. After pursuing the opinions of others concerning the earth, the Philosopher here determines about it according to the truth.

First he determines the question of the earth's place and rest;

secondly, that of its shape, at its shape must necessarily be spherical (L. 27; 297a8).

As to the first he does two things:

first he determines the truth by arguments of nature;

secondly, by signs taken from astronomy, at this view is further supported (297a2; [530]).

Regarding the first he does two things:

first he shows that it is impossible for the earth to be in motion;

secondly, from the foregoing he assigns the true reason of the earth's rest, at from what we have said (296b26; [529]).

Regarding the first he does three things.

First he states his intention (296a24), namely, that we must first say whether the earth is in motion or at rest. For it is from motion that we must approach the other points to be considered about the earth. Therefore he presents this first in order to take it as a principle of what is to follow.

Secondly, at for, as we said (296a25) he states why it is necessary to make this enquiry For, as has been said above, some, namely, the Pythagoreans, assumed that it is in motion about the middle of the world, as though it were one of the stars; but others, as is written in the Timaeus, assuming that the earth is in the middle, assert that it is revolved about the middle of the pole, i.e., about the axis which divides the heaven through the middle.

522. Thirdly, at that both views are untenable (296a27) he shows that it is impossible for the earth to be thus in motion with four arguments. In the first of these he takes as a principle the fact that, if the earth is moved circularly, whether in the middle of the world or outside the middle, such a motion, as far as the earth is concerned, would have to be a compulsory one. For it is manifest that a circular motion is not the proper and natural motion for the earth, because, if it were, then every particle of earth would have to have this motion, since the natural motion of the whole and of the part is the same, as was said above. Now observation shows that this is false, for all the parts of earth are moved with a straight motion toward the middle of the world. But if a circular motion of earth is a compulsory one and beside its nature, it cannot be eternal, because, as was held in a previous lecture, nothing compulsory is eternal. But if the earth is in circular motion, that motion has to be eternal, supposing, according to his opinion, that the world is eternal—because, according to this, the world's order must be eternal, and the motion, or rest, of the chief parts of the world pertain to its order. Thus it follows, therefore, that the earth is not being moved circularly.

523. The second argument at again, everything (296a34) is this: all bodies in circular motion seem to be hesitant, i.e., they do not always retain a uniform position, since each of them is moved by several motions and not just one, except the first sphere, which is moved with one motion, and this, according to him, is the sphere of the fixed stars. If, therefore, the earth has a circular motion, whether being in the middle or outside the middle, it would have to be moved with several motions, namely, with the motion of the first sphere about the poles of the equinoctial circle and with another proper motion about the poles of the Zodiac. But this cannot be, because, if it were, there would be changes and turnings of the fixed stars in relation to the earth, which, because of its own motion, would fail [i.e., be slowed up] and would not return to the same point simultaneously with a fixed star, either in the case of the whole earth or of some indicated part, as happens with the planets. Consequently, it would follow that the fixed stars would not always be seen to rise and set according to the same part of the earth. But this does not happen—rather they always rise and set according to the same designated places. Therefore, the earth is not circularly moved.

524. At further, the natural movement (296b6) he gives a third argument which takes its start from the motion of the parts of the earth and of the whole. Hence with respect to this he does three things:

first he proposes the condition of the natural motion of the earth and of its parts;

secondly, he raises a problem on this point, at but it might be questioned (296b9; [525]);

thirdly, he concludes to what he intended (296b21; [527]).

He says therefore first (296b6) that the motion of parts of the earth is, according to their nature, to the middle of the whole world. In like manner, if the whole earth were outside the middle of the world, it would be moved to the middle of the world according to its nature, because the natural motion of the whole and of the part is the same.

525. Then at but it might be questioned (296b9) he raises a certain problem on this point.

First he proposes it, and says that if it be assumed that the earth is in the middle or center of the world, in such a way that the center of the whole world and of the earth is the same, there can be a problem as to which of these middles do heavy bodies, and especially parts of the earth move according to nature, namely, whether to the middle as it is the middle of the world, or as it is the middle of the earth.

Secondly, at the goal, surely (296b12), he solves the problem, saying that it is necessary that heavy bodies be moved to the middle as it is the middle of the whole world. For the motion of heavy bodies is contrary to the motion of the light. But light bodies, and in particular, fire, are moved toward the outer boundary of the heavenly body; therefore, heavy bodies, and in particular, earth, are moved to the middle of the world. But because it happens that the middle of the earth and the middle of the world are the same, the consequence is that the parts of earth are moved to the middle of the earth, not per se, but per accidens, namely, insofar as the middle of the earth and the middle of the world are the same as to subject—thus, if I know Coriscus, I know per accidens the one who is approaching, because Coriscus is the one approaching.

526. Thirdly, at that the center of the earth (296b18) he proves what he had assumed, namely, that heavy bodies and the parts of earth are moved to the middle. And he says that a sign of this is that heavy bodies are naturally borne toward the earth, not side by side, i.e., not along equidistant lines that never meet, but according to similar angles, i.e., right angles with respect to the surface, or a line tangent to the earth's surface. And this happens no matter from which direction a heavy body is moved toward the earth. And a sign of this is that if a pillar anywhere on earth is not erected according to right angles, but leans, it will fall in the direction with which it makes an acute angle. Now it is proved in book III of Euclid that, if a line is tangent to a circle, and another line is drawn down perpendicular to the tangent line at the point of contact with the circle, necessarily it will, if extended, pass through the center of the circle. Thus it is plain that all heavy bodies are moved toward the center of the earth, in such a way that, if there were no obstacle, things moved from different directions would meet in the center of the earth. The reason for this is that each of them would be moving along a straight line falling perpendicularly on a tangent at its point of contact [with the earth]. Consequently all heavy bodies must be borne toward the one middle of the world and of the earth.

527. Then, at it is clear, then (296b21), he concludes his proposition. And he draws two conclusions.

The first of these is that the earth is in the middle of the world. This conclusion is derived thus from the foregoing. All heavy bodies are moved per se to the middle of the world. But all are likewise moved to the middle of the earth, as has been proved. Therefore, the middle of the earth is the middle of the world. And so the earth is in the middle of the world.

The second conclusion is that the earth is immovable. This is concluded from the foregoing as follows: Nothing is moved in the place toward which it is naturally moved. But the earth is naturally moved to the middle of the world. Therefore, it is not in motion there. But it is nowhere but in the middle of the world, as has been proved, Therefore the earth is not in motion in any way

528. He gives a fourth argument at but also because (296b23) For we observe that if a stone at rest on a tablet is thrown straight up into the air and then falls along the same straight line that it described in its upward flight, and the tablet is not moved, the stone will fall into the same place where it previously was. But if the tablet is moved, the stone will fall in another place [than the tablet], so much the more distant as the stone was thrown higher—since, according to this, there will be more time between the beginning of the throwing and the end of the fall. However, when heavy objects are thrown upward according to rule, i.e., according to a straight line, they again return to the same place on earth whence they were thrown. And lest anyone should say that this happens due to the slowness of the earth's motion, which makes the difference between the two places to be imperceptible, he adds that the same thing will happen if someone throws the stone up an infinite number of times, one after the other, i.e., long enough to make perceptible the distance intervening between the places. Thus it is plain that the earth is not in motion.

Then in summing up he concludes (296b25) that it is plain from the foregoing that the earth is neither in motion nor has any position outside the middle of the earth.

529. Then, at from what we have said (296b26), he assigns the cause of the earth's rest. And he says that from the foregoing it is plain what the cause of its rest is. For, as has been said, earth is naturally inclined to be borne to the middle from every direction, as our sense observations indicate—and similarly it is apparent to sense that fire is naturally moved from the middle of the world to the extreme. Hence it follows that no particle of earth, small or large, can be moved from the middle except by violence; for, as was had in book I, one body has one natural motion, and to a simple body belongs a simple motion, so that two contrary motions cannot belong to a simple body. But a motion from the middle is contrary to one toward the middle. And so, if it is true that no portion of earth can be borne from the middle except through violence, it is plainly much more impossible that the entire earth be moved from the middle. However, someone could object that the whole earth is not in motion to the middle. But he excludes this by saying that the whole earth is apt to be borne whither a part is apt to be borne. And so, if a part of the earth is naturally moved to the middle, then the whole earth will be naturally moved thither. And so it is impossible that it be moved from the middle; hence it is necessary that it rest in the middle.

530. Then, at this view is further supported (297a2), he uses the findings of astronomers to confirm his teachings about the earth's position and state of rest. And he says that what has been said, namely, that the earth is in the middle and rests there, is attested to by the statements of the mathematicians concerning astronomy. For what sensibly appears concerning the shifting of configurations, determined by the position and order of the stars, can be saved if the earth is at rest in the middle and not otherwise.

For as Ptolemy says, if the earth were not in the middle, then it would have to be subject to one of three dispositions. One of these is that the axis of the world would be outside the earth, and yet the earth would be equidistant from each of the poles. The second is that the earth would be on the axis and would approach closer to one pole than to the other. The third is that the earth is neither on the axis nor equidistant from each of the poles.

Now if the earth were situated in the first way, namely, so that the earth would be outside the axis but equidistant from each pole, then, whether it were above or below the axis, the horizon of people living in the right sphere would have to divide the equinoctial circle and all equidistant circles into unequal parts; consequently, there would never be an equinox in the right sphere. In the oblique sphere either there never would be an equinox, or else it would not occur between two solstices—because the horizon could never divide the greatest of the equidistant circles into two halves, although perhaps one of the others. But if the earth leaned away from the axis in either an easterly or westerly direction, it would follow, first of all, that the stars would not appear equal in their rising and setting on account of the inequality of distance. Secondly, it would follow that the interval of time from sunrise to highest elevation, when it is most above our heads, would not be equal to the space of time until sunset.

But if the earth were disposed in the second way, namely, with the earth on the axis but nearer to one of the poles than to the other, two unacceptable things would follow. First of all, because it would be in the right sphere alone that the horizon would divide the heaven into two halves, whereas in the oblique sphere the smaller part of the heaven would always be related to the visible pole, and the larger part to the hidden pole. And thus it would follow that the horizon of the oblique sphere would not divide the Zodiac into two halves; the contrary of which is apparent from the fact that we see six signs over the earth. Secondly, because if the earth were not directly situated under the equinoctial circle [i.e., the equator], it would follow that the eastern shadows of erect bodies at the equinoxes would not be in a straight line with those of the west—but the contrary of this is observed.

And from this it is plain that neither is the third way possible, namely, that the earth be neither on the axis nor equidistant from each of the poles, because, on this position, all the aforesaid impossibilities would follow. Moreover, no matter which way the earth should fail to be in the middle of the world, the entire order in the increasing and decreasing of days and nights would be confused. Similarly disturbed would be the rules of eclipses; for eclipses of the moon would not always occur when sun and moon are in direct opposition, if the earth were not in the middle.

531. That the earth is not in a motion that passes from place to place is due to its always being in the middle. And again it would follow, no matter with what sort of motion it were moved, that the swiftness of its motion would conceal from us all other motions whether of clouds or of animals. For a slower moving object does not seem to be in motion when side by aide with a faster moving object.

Thus, therefore, in summary, the Philosopher concludes (297a6) that so much has been said above about the manner of the earth's place and its motion and rest.