_Demonstration._—For, if it is neither continued nor eternal, it will have a certain beginning. Let, therefore, A B be time, and let its beginning be A. But if A is time, it is divisible, and we shall not yet have the beginning of time, but there will be another beginning of the beginning. But, if A is a moment or _the now_, it will be indivisible, and the boundary of another time: for _the now_ is not only a beginning, but an end. There will therefore be time before A. Again: if B is the boundary of time, if B is time, it may be divided to infinity, and into the many boundaries which it contains. But if B is _the now_, the same will also be a beginning: for _the now_ is not only a boundary, but a beginning[60]. THEOREM 9. A motion which is naturally circular is perpetual. _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.