Demonstration.—Let the circular motion be that of the circle A B, I say that it is perpetual: for, since time is perpetual, it is also necessary that motion should be perpetual. And since time is continued, (for there is the same now in the past and present time,) it is necessary that there should be some one continued motion: for time is the number of motion. However, all other motions are not perpetual: for they are generated from contraries into contraries. A circular motion, therefore, is alone perpetual: for to this, as we have demonstrated, nothing is contrary. But that all the motions which subsist between contraries, are bounded, and are not perpetual, we thus demonstrate. Let A B be a motion between the two contraries A and B. The motion, therefore, of A B is bounded by A and B, and is not infinite. But the motion from A is not continued with that from B. But, when that which is moved returns, it will stand still in B: for, if the motion from A is one continued motion, and also that from B, that which is moved from B will be moved into the same. It will therefore be moved in vain, being now in A. But nature does nothing in vain: and hence, there is not one motion. The motions, therefore, between contraries are not perpetual. Nor is it possible for a thing to be moved to infinity in a right line: for contraries are the boundaries. Nor when it returns will it make one motion.
THEOREM 10.
That which moves a perpetual motion is perpetual.
Demonstration.—For let A be that which moves a perpetual motion. I say that A also is perpetual: for, if it is not, it will not then move when it is not. But this not moving, neither does the motion subsist, which it moved before. It is however supposed to be perpetual. But, nothing else moving, that will be immoveable which is perpetually moved. And if anything else moves when A is no more, the motion is not continual; which is impossible. Hence, that which moves a perpetual motion is itself perpetual.
THEOREM 11.
That which is immoveable is the leader of things moving and moved.
Demonstration.—For let A be moved by B, and B by C, I say that this will some time or other stop, and that not everything which moves will be itself moved: for, if possible, let this take place. Motions, therefore, are either in a circle, or ad infinitum. But, if things moving and moved are infinite, there will be infinite multitude and magnitude: for everything which is moved is divisible, and moves from contact. Hence, that which consists from things moving and moved infinite in multitude, will be infinite in magnitude. But it is impossible that any body, whether composite or simple, can be infinite. But if motions are in a circle, some one of things moved at a certain time, will be the cause of perpetual motion, if all things move and are moved by each other in a circle. This, however, is impossible: for that which moves a perpetual motion is perpetual. Neither, therefore, is the motion of things moved, in a circle, nor ad infinitum. There is, therefore, that which moves immoveably, and which is perpetual.
But from hence it is evident, that all things are not moved; for there is also something which is immoveable. Nor are all things at rest; for there are also things which are moved. Nor are some things always at rest, but others always moved; for there are also things which are sometimes at rest, and sometimes moved, such as are things which are moved from contraries into contraries. Nor are all things sometimes at rest, and sometimes moved; for there is that which is perpetually moved, and also that which is perpetually immoveable.
THEOREM 12.
Everything which is moved, is moved by something.