30 HISTORY OF MECHANICS. 



flection and curvature in the path of a body thrown 

 obliquely, constantly increases the velocity of a 

 body when it falls vertically downwards. The uni- 

 versality of this increase was obvious, both from 

 reasoning and in fact ; the law of it could only be 

 discovered by closer consideration; and the full 

 analysis of the problem required a distinct measure 

 of the quantity of Accelerating Force. Galileo, 

 who first solved this problem, began by viewing it 

 as a question of fact, but conjectured the solution 

 by taking for granted that the rule must be the 

 simplest possible. " Bodies," he says 7 , " will fall 

 in the most simple way, because Natural Motions 

 are always the most simple. When a stone falls, 

 if we consider the matter attentively, we shall find 

 that there is no addition, no increase, of the velocity 

 more simple than that which is always added in 

 the same manner," that is, when equal additions 

 take place in equal times ; " which we shall easily 

 understand if we attend to the close connexion of 

 motion and time." From this Law, thus assumed, 

 he deduced that the spaces described from the be- 

 ginning of the motion must be as the squares of 

 the times; and, again, assuming that the laws of 

 descent for balls rolling down inclined planes, must 

 be the same as for bodies falling freely, he verified 

 this conclusion by experiment. 



It will, perhaps, occur to the reader that this 

 argument, from the simplicity of the assumed law, 



7 Dial Sc. iv. p. 91. 



