42 DISSERTATION SECOND. [i>ahth. 



and Bernoulli each severally defeated an adversary, who was 

 but very ill able to contend with either of them. 



Soon after this, the calculus had to sustain an attack from 

 two French academicians, which drew more attention than 

 that of the Dutch naturalist. One of these, Rolle, was a 

 mathematician of no inconsiderable acquirement, but whose 

 chief gratification consisted in finding out faults in the works 

 of others. He founded his objections to the differential calcu- 

 lus, not on the score of principles or of general methods, but 

 on certain cases which he had sought out with great-industry, 

 in which those methods seemed to him to lead to false and 

 contradictory conclusions. On examination, however, it 

 turned out, that in every one of those instances the error was 

 entirely his own ; that he had misapplied the rules, and that 

 his eagerness to discover faults had led him to commit them. 

 His errors were detected and pointed out with demonstra- 

 tive evidence by Varignon, Saurin, and some others, who 

 were among the first to perceive the excellence and to de- 

 fend the solidity of the new geometry. These disputes were 

 of consequence enough to occupy the attention of the Acade- 

 my of Sciences during a great part of the year 1701. 



The Abbe Gallois joined with Rolle in his hostility to the 

 calculus, and though he added very little to the force of the 

 attack, he kept the field after the other had retired from the 

 combat. Fontenelle, in his Eloge on the Abbe, has given an 

 elegant turn to the apology he makes for him. — " His taste 

 for antiquity made him suspicious of the geometry of infi- 

 nites. He was, in general, no friend to any thing that was 

 new, and was always prepared with a kind of Ostracism to 

 put down whatever appeared too conspicuous for a free state 

 like that of letters. The geometry of infinites had both 

 these faults, and particularly the latter." 



After all these disputt were quieted in France, and the 

 new analysis appeared completely victorious, it had an at- 



