34 SCIENCE ABSOLUTE OF SPACE. 

 Hence the whole surface of the sphere 



and the surfaces of spheres are to each other 

 as the second powers of their great circles. 



VII. In like manner, in S, the volume of 

 the sphere of radius x is found 



the surface generated by the rev- 

 olution of the line CD about AB 



A T~ B and the body described by CABDC 

 FIG. 29. = i/_v2^/r) Q~M 2 



But in what manner all things treated 

 from (IV] even to here, also may be reached 

 apart from integration, for the sake of brev- 

 ity is suppressed. 



It can be demonstrated that the limit of 

 every expression containing the letter i (and 

 so resting upon the hypothesis that i is given), [19] 

 when i increases to infinity, expresses the 

 quantity simply for I (and so for the hypoth- 

 esis of no i), if indeed the equations do not be- 

 come identical. 



But beware lest you understand to be sup- 

 posed, that the system itself may be varied 

 (for it is entirely determined in itself and by 

 itself) ; but only the hypothesis, which may be 



