122 



HISTORY OF MECHANICS. 



"The plan of this work," says the author, "is 

 entirely new. I have proposed to myself to reduce 

 the whole theory of this science, and the art of 

 resolving the problems which it includes, to general 

 formulae, of which the simple developement gives 

 all the equations necessary for the solution of the 

 problem." " The reader will find no figures in the 

 work. The methods which I deliver do not require 

 either constructions, or geometrical or mechanical 

 reasonings ; but only algebraical operations, subject 

 to a regular and uniform rule of proceeding." Thus 

 this writer makes Mechanics a branch of Analysis ; 

 instead of making, as had previously been done, 

 Analysis an implement of Mechanics 14 . The trans- 

 cendent generalizing genius of Lagrange, and his 

 matchless analytical skill and elegance, have made 

 this undertaking as successful as it is striking. 



The mathematical reader is aware that the lan- 

 guage of mathematical symbols is, in its nature, 

 more general than the language of words ; and that 

 in this way truths, translated into symbols, often 

 suggest their own generalizations. Something of 

 this kind has happened in Mechanics. The same 

 Formula expresses the general condition of Statics 

 and that of Dynamics. The tendency to generaliza- 

 tion which is thus introduced by analysis, makes 



14 Lagrange himself terms Mechanics, " An Analytical Geo- 

 metry of four dimensions." Besides the three co-ordinates which 

 determine the place of a body in space, the time enters as a, fourth 

 co-ordinate. [[Note by Littrow.] 





