D'ALEMBERT. 433 



complete, having, in the article ' Series ' of the ' Encyclo- 

 pedic/ first given the remaining terms left out by Taylor, 

 and also a demonstration of the whole, better than the 

 original inventor's. Condorcet, who only knew the 

 Theorem from this exposition of it, treats him as certainly 

 being its author ; and D'Alembert himself, citing no other 

 discoverer, plainly gives it as altogether his own*"". 



I have thought it better to pursue the same method in 

 treating of D'Alembert's works that I adopted respecting 

 Voltaire's, giving all his scientific researches, his import- 

 ant physical and analytical discoveries, in a connected 

 order, and thus avoiding the interruption of the series 

 which an exclusive regard to the chronological succession 

 of his different works on all subjects would have occa- 

 sioned. We must now return to the history of his life, 

 and the other pursuits with which his severer studies 

 were interrupted, and his enjoyments, as it were, varie- 

 gated. 



In those scientific pursuits, the history of which we 

 have been surveying, he passed the first eighteen years 

 after he left the College, and he passed them in un- 

 interrupted tranquillity and happiness, in tasting the 

 pleasure of contemplating the relations of necessary 

 truths, in adding to the number which had been before 

 ascertained, and in enlarging the sphere of his own use- 



* If very small things might be compared to great, I should note 

 the circumstance the accident, I may well term it of my having 

 hit upon the Binomial Theorem, and given it as an exercise to 

 Professor Play fair, when attending his class in 1794. He kept my 

 paper, and used to mention this circumstance. He said- he concluded 

 I had found it only by induction, which was true. The demonstra- 

 tion is, indeed, very difficult. 



2P 



