SEQUEL TO THE GENERALIZATION. 101 



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 mathematicians, who died, full of age and 

 honours, in 1748. Euler, several of the Bernoullis, 

 Maupertuis, Lagrange, among other mathemati- 

 cians of smaller note, were called into the north by 

 Catharine of Russia and Frederic of Prussia, to 

 inspire and instruct academies which the brilliant 

 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 valu- 

 able mathematical works of the century. 



7. The Problem of three Bodies. In 1747, 

 Clairaut and D'Alembert sent, on the same day, 

 to this body, their solutions of the celebrated " Pro- 

 blem of Three Bodies," which, from that time, 

 became the great object of attention of mathemati- 

 cians ; the bow in which each tried his strength, and 

 endeavoured 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 generally, as referring to 

 one body which disturbs any two others, it became 

 a mechanical problem, and the history of it be- 

 longs to the present subject. 



