THE HISTORY OF MATHEMATICS 401 



and for his work on the theory of the moon's motion. With respect to 

 the last it may be said that every modern method of treatment can be 

 found to have started with Euler. He continued his work to the end of 

 his life in 1783 in spite of losing his sight some fourteen years earlier 

 and his papers by a fire in 1777. 



J. L. Lagrange was born at Turin in 1736 and was, like Newton, 

 practically self-educated as far as his mathematical studies were con- 

 cerned. It gives some insight into the comparatively small body of 

 mathematical literature at the time he was seventeen years old and his 

 own great ability, that an accident directed his taste for mathematics 

 and that after two years work he was able to solve a problem in the 

 calculus of variations which had been under discussion for half a 

 century. At the age of twenty-five his published work showed that in 

 ability he had no rival. Before his death, at the age of seventy-seven, 

 he had left his influence on almost every department of pure and ap- 

 plied mathematics. His generalizations of the equations of mechanics 

 have proved to be fundamental in all modern investigations and his 

 applications to dynamical theory of the principle of virtual work and 

 of the calculus of variations are now even more important than at any 

 time in the past. The latter is applied not only to particles and rigid 

 bodies, but also to fluids. To celestial mechanics he contributed several 

 new methods in both the theoretical and practical sides of the subject 

 in which such topics as the general problem of three bodies, stability 

 of a planetary system, mechanical quadratures and interpolation are 

 developed. In pure mathematics his lectures on the theory of analytic 

 functions, afterwards expanded in treatises, form the basis on which 

 later writers built. He also founded the science of differential equa- 

 tions by considering them as a whole rather than a treatment of such 

 special equations as might arise in particular problems. And he con- 

 tributed some important memoirs on the theory of numbers. His in- 

 fluence was undoubtedly much increased by a remarkable gift of ex- 

 position both in lecturing and writing: those who have read his 

 Mecanique Analytique in which his most important dynamical con- 

 tributions were placed will appreciate this fact. And this may be said 

 independently of the simpler problem before him than has the modern 

 mathematician with the enormous mass of past work which he has to 

 consider and the selection which must necessarily be made. 



P. S. Laplace, whose mathematical ability is unquestioned, was 

 essentially an applied mathematician in that he devoted himself almost 

 entirely to the solution of the problems of nature by mathematical 

 methods. In general, he was not particular about mathematical proofs 

 or logic, provided he could obtain results: in many respects he may be 

 said to be the founder of the more modern schools of mathematical 

 physicists. His most enduring work has proved to be in the theory of 



VOL. XII.— 26. 



