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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 some- 

 thing moved in a right line, though naturally 

 moved in a circle, which is impossible. 



THEOREM 4s 



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 con- 

 trary 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 mo- 

 tion 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 infi- 

 nite spaces between two contraries ; for between 

 the points A, B infinite circumferences may be de- 

 scribed. 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 



