90 



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 natu- 

 rally 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, there- 

 fore, 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 



