330 A SHORT HISTORY OF SCIENCE 



property of all who would lay claim to the rank of scientific mathe- 

 maticians. Hankel. 



When we have grasped the spirit of the infinitesimal method, 

 and have verified the exactness of its results either by the geometrical 

 method of prime and ultimate ratios, or by the analytical method of 

 derived functions, we may employ infinitely small quantities as a sure 

 and valuable means of shortening and simplifying our proofs. 



Lagrange. 



Lagrange also applied his great powers of analysis to problems 

 in astronomy and in cartography. 



CELESTIAL MECHANICS. Pierre Simon Laplace (1749-1827) 

 was of humble Norman antecedents which he in later life somewhat 

 disdained, and played a great part in the scientific activity under 

 Napoleon. In the five volumes of his Mecanique celeste, he pro- 

 duced a permanent monument to his own genius. It was his lofty 

 ambition 



to offer a complete solution of the great mechanical problem pre- 

 sented by the solar system, and bring theory to coincide so closely 

 with observation that empirical equations should no longer find a 

 place in astronomical tables. 



He regarded analysis merely as a means of attacking physical prob- 

 lems, though the ability with which he invented the necessary anal- 

 ysis is almost phenomenal. As long as his results were true he took 

 very little trouble to explain the steps by which he arrived at them ; 

 he never studied elegance or symmetry in his processes, and it was 

 sufficient for him if he could by any means solve the particular ques- 

 tion he was discussing. Ball. 



Bowditch, the American translator of his great work, remarks 

 significantly : 



I never come across one of Laplace's ' Thus it plainly appears ' without 

 feeling sure that I have hours of hard work before me to fill up the 

 chasm and find out and show how it plainly appears. 



In the words of the historian Todhunter, 



a complete evolution of the history will restore the reputation of La- 

 place to its just eminence. The advance of mathematical science is 



