Part 10

Demonstration.—For if AB is either heavy or light, it is either naturally moved to the middle, or from the middle: for, from the definitions, that is heavy which is moved to the middle, and that is light which is moved from the middle. But that which is moved either from or to the middle, is the same with some one of the things moved in a right line. AB, therefore, is the same with something moved in a right line, though naturally moved in a circle, which is impossible.

THEOREM 4.

Nothing is contrary to a circular motion.

Demonstration.—For if this be possible, let the motion from A to B be a circular motion, and let the motion contrary to this be either some one of the motions in a right line, or some one of those in a circle. If, then, the motion upwards is contrary to that in a circle, the motion downwards and that in a circle will be one. But if the motion downwards is contrary to that in a circle, the motion upwards and that in a circle will be the same with each other; for one motion is contrary to one into opposite places. But if the motion from A is contrary to the motion from B, there will be infinite spaces between two contraries; for between the points A, B infinite circumferences may be described. But let AB be a semicircle, and let the motion from A to B be contrary to the motion from B to A. If, therefore, that which moves in the semicircle from A to B stops at B, it is by no means a motion in a circle: for a circular motion is continually from the same to the same point. But, if it does not stop at B, but continually moves in the other semicircle, A is not contrary to B. And if this be the case, neither is the motion from A to B contrary to the motion from B to A: for contrary motions are from contraries to contraries. But let ABCD be a circle, and let the motion from A to C be contrary to the motion from C to A. If therefore that which is moved from A passes through all the places similarly, and there is one motion from A to D, C is not contrary to A. But if these are not contrary, neither are the motions from them contrary. And in a similar manner with respect to that which is moved from C, if it is moved with one motion to B, A is not contrary to C, so that neither will the motions from these be contrary.

THEOREM 5.

Things which are naturally moved in a circle, neither receive generation nor corruption.

Demonstration.—For let AB be that which is naturally moved in a circle, I say that AB is without generation and corruption: for if it is generable and corruptible, it is generated from a contrary, and is corrupted into a contrary. But that which is moved in a circle has not any contrary. It is therefore without generation and corruption. But that there is nothing contrary to things naturally moving in a circle, is evident from what has been previously demonstrated: for the motions of things contrary according to nature are contrary. But, as we have demonstrated, there is nothing contrary to the motion in a circle. Neither, therefore, has that which is moved in a circle any contrary.

THEOREM 6.

The powers of bodies terminated according to magnitude are not infinite.

Demonstration.—For, if possible, let B be the infinite power of the finite body A; and let the half of A be taken, which let be C, and let the power of this be D. But it is necessary that the power D should be less than the power B: for a part has a power less than that of the whole. Let the ratio, therefore, of C to A be taken, and D will measure B. The power B therefore is finite, and it is as C to A, so D to B; and alternately as C to D, so A to B. But the power D is the power of the magnitude C, and therefore B will be the power of the magnitude A. The magnitude A, therefore, has a finite power B; but it was infinite, which is impossible: for, that a power of the same species should be both finite and infinite in the same thing, is impossible.

THEOREM 7.

Simple bodies are terminated according to species.

Demonstration.—For let the magnitude A be a simple body. Since, therefore, a simple body is moved with a simple motion, A will be moved with a simple motion. And if it is moved in a circle, it will have one nature and one form. But if it is moved according to any one of the motions in a right line, if it is moved from the middle only, it will be fire, but if only to the middle, earth. But, if it is light with respect to one thing, and heavy with respect to another, it will be some one of the middle elements. The species therefore of simple bodies are terminated.

THEOREM 8.

Time is continued and perpetual.

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.

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.

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.