44 HISTORY OF MECHANICS. 



Stevinus's proof of the Inclined Plane ; which, as 

 we have seen, was rigorously inferred from the 

 sound axiom, that a body cannot put itself in 

 motion. If we were to assent to the really self- 

 evident axioms of Stevinus, only in virtue of the 

 unproved verbal generalization of Galileo, we should 

 be in great danger of allowing ourselves to be re- 

 ferred successively from one truth to another, with- 

 out any reasonable hope of ever arriving at any- 

 thing ultimate and fundamental. 



But though this Principle of Virtual Velocity 

 cannot be looked upon as a great discovery of Ga- 

 lileo, it is a highly useful rule; and the varied 

 forms under which he and his successors urged it, 

 tended much to dissipate the vague wonder with 

 which the effects of machines had been looked 

 upon ; and thus to diffuse sounder and clearer no- 

 tions on such subjects. 



The Principle of Virtual Velocities also affected 

 the progress of mechanical science in another way ; 

 it suggested some of the analogies by the aid of 

 which the Third Law of Motion was made out ; 

 leading to the adoption of the notion of Momentum 

 as the arithmetical product of weight and velocity. 

 Since on a machine on which a weight of two 

 pounds at one part balances three pounds at an- 

 other part, the former weight would move through 

 three inches while the latter would move through 

 two inches ; we see (since three multiplied into two 

 is equal to two multiplied into three,) that the 



