NEWTON S PRINCIPIA. 



83 



V D F L will be/y d x. Describe the circle V X Y with 

 C V as radius. Let V X = z, and Y X will be d z, and N K 



x d z 



= ~~^~ Tlien I C K being as the time, and d t being 

 constant, that triangle, or IC * KN , i s constant, and 

 K N is as a constant quantity divided by I C, or as Q* 





If we take - to VA VLB (proportioned to the force at 

 any one point Y and therefore given), as K N to I K 

 therefore this will in all points be the proportion ; and the 



squares will be proportional, or fy d x :Q?::I K 2 , or 



C 



K N 2 + I N 2 , to K N 2 ; and therefore / y d x - 



: :: I N 2 , or rf 



2 



Therefore 



G 2 



