SEQUEL TO THE GENERALIZATION. 367 



higher or brighter. The great discoveries of Copernicus, Galileo, 

 Newton, had fixed all eyes on those portions of human knowledge on 

 which their successors employed their labors. The certainty belong- 

 ing to this line of speculation seemed to elevate mathematicians above 

 the students of other subjects ; and the beauty of mathematical rela- 

 tions, and the subtlety of intellect which may be shown in dealing 

 with them, were fitted to win unbounded applause. The successors of 

 Newton and the Bernoullis, as Euler, Clairaut, D'Alembert, Lagrange, 

 Laplace, not to introduce living names, have been some of the most 

 remarkable men of talent which the world has seen. That their talent 

 is, for the most part, of a different kind from that by which the laws 

 of nature were discovered, I shall have occasion to explain elsewhere ; 

 for the present, I must endeavor to arrange the principal achievements 

 of those whom I have mentioned. 



The series of persons is connected by social relations. Euler was the 

 pupil of the first generation of Bernoullis, and the intimate friend of 

 the second generation ; and all these extraordinary men, as well as 

 Hermann, were of the city of Basil, in that age a spot fertile of great 

 mathematicians to an unparalleled degree. In 1740, Clairaut and Mau- 

 pertuis visited John Bernoulli, at that time the Nestor of mathemati- 

 cians, who died, full of age and honors, in 1748. Euler, several of the 

 Bernoullis, Maupertuis, Lagrange, among other mathematicians of 

 smaller note, were called into the north by Catharine of Russia and 

 Frederic of Prussia, to inspire and instruct academies which the bril- 

 liant fame then attached to science, had induced those monarchs to 

 establish. The prizes proposed by these societies, and by the French 

 Academy of Sciences, gave occasion to many of the most valuable ma- 

 thematical works of the century. 



7. The Problem of Three Bodies. — In 1747, Clairaut and D'Alem- 

 bert sent, on the same day, to this body, their solutions of the celebrated 

 " Problem of Three Bodies," which, from that time, became the great 

 object of attention of mathematicians ; — the bow in which each tried 

 his strength, and endeavored to shoot further than his predecessors. 



This problem was, in fact, the astronomical question of the effect 

 produced by the attraction of the sun, in disturbing the motions of the 

 moon about the earth ; or by the attraction of one planet, disturbing 

 the motion of another planet about the sun ; but being expressed gen- 

 erally, as referring to one body which disturbs any two others, it 

 became a mechanical problem, and the history of it belongs to the 

 present subject. 



