CHAPTER XI 



CRITICISMS OF FLUXIONS BY BRITISH WRITERS 

 UNDER THE INFLUENCE OF D'ALEMBERT, 

 LAGRANGE, AND LACROIX 



Review of Lagrange's '■^ Fonctions analytiques^'' 1799 



220. Important is a review ^ of Lagraiige's Théorie 

 des fonctions analytiques^ which, as is well known, is 

 an attempt to deduce the principles of the calculus, 

 diverted of ali reference to infinitely small or evan- 

 escent quantities, limits or fluxions, and reduced to 

 the algebra of finite quantities. The reviewer gives 

 a general criticism of the methods of fluxions and the 

 difìferential calculus. He discusses the principle of 

 motion : '' It will not be denied that this principle is 

 introduced purely for the purpose of illustration, . . . 

 on th^ ground of convenience. . . . The mathe- 

 matica! principle, on which the doctrine of fluxions 

 depends, is a definition . . . and fluxions were 

 defined to be velocities. . . . Novv velocity is 

 nothing real, but is only the relation between the 

 space described and the time of describing it ; — of 

 which relation we have a clear idea when the motion 

 is uniform." The reviewer continues : *' In variable 



^ Monthly Review, London, voi. xxviii, 1799, Appendix. 

 255 



