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.