LECTURE 19 (264 b 9-265 a 27)

HE SHOWS WITH PROPER PROOFS THAT CIRCULAR MOTION CAN BE CONTINUOUS AND THAT CIRCULAR MOTION IS THE FIRST MOTION

1129. After the Philosopher has shown that no local motion other than circular motion can be continuous, he shows here that circular motion can be continuous and that it is the first motion.

             He proves this first with proper arguments, and secondly, with common and logical arguments, where he says, 'Moreover the result . . .' (265 a 28).

             Concerning the first part he makes two points. First he shows that circular motion is continuous. Secondly, where he says, 'It can now be shown . . .' (265 a 13), he shows that circular motion is the first motion.

             Concerning the first part he makes two points. First he gives two arguments to show that circular motion can be continuous. Secondly, where he says, 'This differentiation . . .' (264 b 29), he concludes from these same arguments that no other motion can be continuous.

             1130. His first proof that circular motion is continuous and one is as follows.

             That is said to be possible which involves no impossible consequence. And there is no impossible consequence if we say that circular motion is eternally continuous.

             This is clear from the fact that in circular motion that which is moved from some point, for example, A, is simultaneously being moved toward that same point with respect to the same position, that is, with respect to the same course of the mobile object, and the same order of parts is preserved. This does not happen in reflex motion. For when something is reflected, it is disposed to motion with a contrary order of parts, for either the part of the mobile object which was prior in the first motion becomes posterior in the reflex motion, or else that part of the mobile object which faced one direction of place in the first motion, for example, right or up, faces the contrary direction in the reflex motion. But when a thing moves toward that from which it withdrew with circular motion, the same position is preserved. So it can be said that from the beginning of its motion, while it was withdrawing from A, it was being moved toward where it will arrive, namely, A.

             And the impossibility of being simultaneously moved by contrary or opposed motions does not follow here as it did with straight motion. For not every motion to a terminus is contrary or opposed to motion from that same terminus. Rather such contrariety is found in a straight line, with respect to which contrariety of place is present. For there is no contrariety between two termini of a circular line, each part of which belongs to the circumference. Rather there is contrariety only with respect to the diameter. For contraries are at the greatest distance from each other. But the greatest distance between two termini is not measured by a circular line, but by a straight line. For infinite curved lines may be described between two points, but only one straight line. Moreover, that which is one is the measure in any genus.

             Therefore, it is clear that if a circle is divided in half, and its diameter is AB, motion through the diameter from A to B is contrary to motion through the same diameter from B to A. But semi-circular motion from A to B is not contrary to the other semi-circular motion from B to A. Contrariety, however, was that hindrance which made it impossible for reflex motion to be continuous, as is clear from the earlier arguments. Therefore, there is no hindrance, contrariety is removed, and circular motion is continuous and never ceases.

             The reason for this is that a circular motion has its own complement since it is from the same thing to the same thing. Therefore there is no hindrance to its continuity. But straight motion has its complement insofar as it is from the same thing to another. Hence if it is returned from that other to the same thing from which it began to be moved, it will not be one continuous motion, but two.

             1131. Next where he says, 'Moreover the progress . . .' (264 b 21), he gives the second argument. He says that circular motion is not in the same things, but straight motion is repeatedly in the same things. This is to be understood as follows.

             If something is moved through a diameter from A to B, and again from B to A through the same diameter, it must return through the same mid-points which it passed through earlier; and so it is repeatedly moved through the same things. But if something is moved from A to B through a semicircle, and again from B to A through the other semicircle, that is, if it is moved circularly, it is clear that it does not return to the same place through the same mid-points.

             But opposites by their nature [ratio] are concerned with the same thing. Hence it is clear that to be moved from the same thing to the same thing involves no opposition with respect to circular motion, but to be moved from the same thing to the same thing with reflex motion does involve opposition.

             Therefore, it is clear that circular motion, which does not return to the same point through the same mid-points, but always passes through different points, can be one and continuous because it has no opposition. But that motion, namely, reflex motion, which while returning to the same point, does so by passing through the same mid-points many times, cannot be eternally continuous. For it would be necessary for the thing to be moved by simultaneous contrary motions, as was shown above.

             From this same argument it can be concluded that neither motion in a semicircle, nor motion in any other portion of a circle can be eternally continuous. For in these motions the same mid-points must be traversed many times, and the objects must be moved by contrary motions if a return to the beginning is to occur. This is so because neither in a straight line, nor in a semicircle, nor in any portion of a circle, is the end joined to the beginning. Rather they are at a distance from each other. Only in circular motion is the end joined to the beginning.

             Therefore, only circular motion is perfect, for a thing is perfect if it comes in contact with its beginning.

             1132. Next where he says, 'This differentiation . . .' (264 b 29), he uses the same argument to show that no motion in any other genus can be continuous.

             First he proves his position. Secondly, where he says, 'Moreover it is plain . . .' (265 a 3), he infers a corollary from what has been said.

             He says, therefore, first that from the distinction established between circular motion and other local motions it is clear that no motion in the other genera of motion is infinitely continuous. For in all the other genera of motion, if a thing is to be moved from the same thing to the same thing, it follows that it passes through the same things many times. For example, in alteration it is necessary to pass through intermediate qualities. The object passes from hot to cold through warmness, and if it is to be returned from cold to hot, it must pass through warmness. The same thing is apparent in quantitative motion. If what is moved from large to small is again returned to large, it must twice have been the half-quantity. The same is true of generation and corruption. If air comes to be from fire, and again fire comes to be from air, it must twice pass through the middle dispositions (for a middle can be posited in generation and corruption insofar as one considers the transmutation of dispositions .

             And since in the various kinds of mutation the object passes through intermediaries, he adds that it makes no difference whether there are few or many intermediaries through which a thing is moved from one extremity to the other. Nor does it make any difference if the intermediary is positive, as pale between white and black, or if it is remote, as that which is neither good nor evil between the good and the evil. For no matter how the intermediaries are related, it always happens that the same things are passed through repeatedly.

             1133. Next where he says, 'Moreover it is plain . . .' (265 a 3), he concludes from the foregoing that the ancient natural philosophers did not speak correctly when they said that all sensible things are always moved. For these objects would necessarily have to be moved by one of the motions mentioned above, concerning which we have shown that eternal continuity is impossible. This is especially so because they said that alteration is an eternally continuous motion.

             For they said that everything is constantly decaying and being corrupted. And they add to this that generation and corruption is nothing other than alteration. Hence when they say that all things are constantly being corrupted, they say that all things are constantly being altered.

             In the argument introduced above, however, it was established that no motion is eternal except circular motion. Hence it follows that neither in respect to alteration nor in respect to increase can all things be always moved, as they said.

             Finally he summarizes and concludes to his main point; namely, no mutation other than circular motion can be infinite and continuous.

             1134. Next where he says, 'It can now be shown . . .' (265 a 13), he proves with two arguments that circular motion is the first of motions. The first argument is as follows.

             As we said before, every local motion is either circular, straight, or a mixture of the two. Circular and straight motions are prior to mixed motion, since the latter is composed of them. Of these two, circular motion is prior to straight motion, for circular motion is more simple and perfect than straight motion.

             He proves this as follows. Straight motion cannot proceed to infinity, for this would have to occur in one of two ways. First there might be an infinite magnitude through which straight motion passes. But this is impossible. And even if there were some infinite magnitude, nothing would be moved to infinity. That which cannot be never occurs or is generated. It is impossible, however, to pass through infinity. Therefore, nothing is moved in such a way that it passes through infinity. Therefore, there cannot be infinite straight motion over an infinite magnitude.

             Secondly, infinite straight motion could be understood to occur over a finite magnitude by reflection. But reflex motion is not one, as was proven above, but is composed of two motions.

             If, however, reflection does not occur over a finite straight line, the motion will be imperfect and corrupt: imperfect, because it is possible to add to it; corrupt, because when it has reached the terminus of the magnitude, the motion will cease.

             Therefore, it is clear that circular motion, which is not composed of two motions, and which is not corrupted when it reaches the terminus (since its beginning and end are the same), is more simple and more perfect than straight motion. The perfect, moreover, is prior to the imperfect, and similarly, the incorruptible to the corruptible, in nature, and in reason [ratio], and in time, as was proven above when it was shown that local motion is prior to the other motions. Circular motion, therefore, must be prior to straight motion.

             1135. Next where he says, 'Again, a motion . . .' (265 a 24), he gives the second argument, which is as follows.

             Motion which can be eternal is prior to motion which cannot be eternal, for the eternal is prior to the non-eternal both in time and in nature. Circular motion, however, can be eternal. But no other motions can be eternal because rest must succeed them. And when rest intervenes the motion is corrupted. It follows, therefore, that circular motion is prior to all other motions. The things which he supposes in this argument are clear from the earlier arguments.