D'ALEMBEKT. 395 



some important corrections of errors into which Pere 

 Reynau had fallen in his treatise 'Analyse Demon- 

 tree;' these errors D'Alembert had discovered when 

 studying the book in order to learn the calculus, and 

 they related to the integrals of binomials.* This me- 

 moir gave a most favourable impression of his capacity 

 to the eminent men who at that time formed the ma- 

 thematical portion of this illustrious body, Mairan, 

 Cassini, Camus, Fouchy, above all Clairaut, then in the 

 meridian of his great and just renown. The young 

 analyst became their acquaintance first, then their 

 friend. In 1741 he was admitted into the Society, at 

 the early age of twenty-four. Excepting Clairaut, 

 who for the maturity of his extraordinary faculties at 

 an early age is an exception to all rules, no one had 

 ever been an Academician so young. Clairaut had by 

 Royal Ordinance, dispensing with the rule that re- 

 quired the age of twenty complete, been admitted an 

 Adjoint at eighteen, and an Associate at twenty; but 

 at twelve he had presented a memoir upon an im- 

 portant analytical subject, and at the same early 

 age he had made some progress in his greatest work, 

 the ' Courbes a double Courbure,' which was nearly 

 completed at thirteen, and at sixteen was actually 

 published.! 



In 1743, two years after D'Alembert entered the 

 Academy, appeared his ' Traite de Dynamique,' which 

 at once placed him in the highest rank of geometri- 

 cians. The theory is deduced with perfect precision, 

 and with as great clearness and simplicity as the sub- 

 ject allows, from a principle which he first laid down 



* The 'Hist, de 1'Acad.' 1739, p. 30, records the reading with much 

 approbation of the Memoir of M. le Rond D'Alembert. 



f It would certainly have been published in 1725, before he was four- 

 teen years old, but for a violent head-ache which his labours brought on, 

 and which obliged him to give up writing. When his first paper was 

 read at the Academy, the good Father Eeynau burst into tears of joy at 

 so marvellous a performance. The ' Hist, de 1'Acad.' 1726, p. 45, records 

 his age to have been twelve years eight months. 



