D'ALEMBERT. 405 



at that time formed the mathematical portion of this 

 illustrious body, Mairau, 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. Except- 

 ing 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 

 required 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 important 

 analytical subject, and at the same early age he had made 

 some progress in his greatest work, the ' Courbes & 

 double Courbure/ which was nearly completed at thir- 

 teen, and at sixteen was actually published. * 



In 1743, two years after D'Aleinbert entered the 

 Academy, appeared his e Traite de Dynamique/ which at 

 once placed him in the highest rank of geometricians. 

 The theory is deduced with perfect precision, and with as 

 great clearness and simplicity as the subject allows, from 

 a principle which he first laid down and explained, though, 

 it be deducible from the equality of action and re-action, a 

 physical rather than a mathematical truth, and derived 

 from universal induction, not from abstract reasoning & 

 priori. 



The Principle is this. (' Dyn.' pt. 2. ch. i.) If there 



* It would certainly have been published in 1725, before he was 

 fourteen 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 Reynau burst 

 into tears of joy at so marvellous a performance. 



