CHANGING IDENTITIES 



Then the ball C being projected against the ball 

 B must either be repelled in the same straight line 

 or projection or carry the ball B along with itself 

 in a continuation of the same straight line C D E. 



But the balls do not run together or separate 

 in that line C D E any more than in the line 

 BDF. 



For the ball B will move off, after being struck, 

 in the line D L, which bisects the angle B D E, 

 and the ball C will move off in the line D M, which 

 bisects the angle E D F. Therefore, the ball acts 

 as if the whole acquired force were situated neither 

 in the point of contact, nor in the whole mass of 

 the ball, but in a point midway between; that is, 

 the centre. 



PROPOSITION XII. 



In the transmission of force from one body to 

 another body, every body, spherical or not spher- 

 ical, acts as if the whole force proceeded from or 

 ivas directed to the centre of gravity. 



Let Figure A represent a lever resting upon a 

 fulcrum; and let the long arm be nine times as 

 long as the short arm. 



90 O 



Fig. A 

 49 



