344 HISTORY OF MECHANICS. 



Percussion (1684), had asserted this proposition for the case of direct 

 impact. But by the reasoners of Newton's time, the dynamical prop- 

 osition, that the motion of the centre of gravity is not altered by the 

 actual free motion and impact of bodies, was associated with the 

 statical proposition, that when bodies are in equilibrium, the centre ot 

 gravity cannot be made to ascend or descend by the virtual motions 

 of the bodies. This latter is a proposition which was assumed as self-- 

 evident by Torricelli ; but which may more philosophically be proved 

 from elementary statical principles. 



This disposition to identify the elementary laws of equilibrium and 

 of motion, led men to think too slightingly of the ancient solid and 

 sufficient foundation of Statics, the doctrine of the lever. When the 

 progress of thought had opened men's minds to a more general view 

 of the subject, it was considered as a blemish in the science to found 

 it on the properties of one particular machine. Descartes says in his 

 Letters, that "it is ridiculous to prove the pulley by means of the 

 lever." And Varignon was led by similar reflections to the project of 

 his Nouvelle Mecanigue, in which the whole of statics should be 

 founded on the composition of forces. This project was published in 

 1687; but the work did not appear till 1725, after the death of the 

 author. Though the attempt to reduce the equilibrium of all machines 

 to the composition of forces, is philosophical and meritorious, the 

 attempt to reduce the composition of Pressures to the composition of 

 Motions, with which Varignon's work is occupied, was a retrograde 

 step in the subject, so far as the progress of distinct mechanical ideas 

 was concerned. 



Thus, at the period at which we have now arrived, the Principles of 

 Elementary Mechanics were generally known and accepted ; and there 

 was in the minds of mathematicians a prevalent tendency to reduce 

 them to the most simple and comprehensive form of which they 

 admitted. The execution of this simplification and extension, which 

 we term the generalization of the laws, is so important an event, that 

 though it forms part of the natural sequel of Galileo, we shall treat of 

 it in a separate chapter. But we must first bring up the history oi 

 the mechanics of fluids to the corresponding point. 



