148 



NEWTON S PRINCIPIA. 



A P = b } the force of any particle of the ring is as , 



X 



and the attraction of the ring, described by M m, is as 

 x D d x P D, or as b y d x 9 and the whole attrac 



tion of the circle whose radius is A M, being the sum of 

 all the rings, will be as bfy d x, or the area of the curve 

 L N I, which is found by substituting for y its value in x, 

 that is x n . This fluent or area is therefore = ~bfx n d x 



= h C ; and C = ^~ Also, making P b 



= P E in order to have the whole area of L N I, which 

 measures the attraction of the whole circle whose radius is 



b c n+l b 



F A, we have (x being = P b = c) 



n+l 



n + 2 



for 



