sict. i.] DISSERTATION SECOND. 41 



of the men engaged in scientific pursuits ; and must oblige 

 many, after descending from the stations they formerly occu- 

 pied, to take a lower position in the scale of intellectual ad- 

 vancement. The enmity of such men, if they be not ani- 

 mated by a spirit of real candour and the love of truth, is 

 likely to be directed against methods, by which their vanity 

 is mortified, and their importance lessened. Though such 

 changes as this must have everywhere accompanied the as- 

 cendency acquired by the calculus, for the credit of mathe- 

 maticians it must be observed, that no one of any considera- 

 ble eminence has had the misfortune to enrol his name 

 among the adversaries of the new science ; and that Huy- 

 gens, the most distinguished and most profound of the older 

 mathematicians then living, was one of the most forward to 

 acknowledge the excellence of that science, and to make 

 himself master of its rules, and of their application. 



Nevertheless, certain adversaries arose successively in 

 Germany, France, and England, the countries in which the 

 new methods first became known. 



Nieuentit, an author commendable as a naturalist, and as a 

 writer on morals, but a very superficial geometer, aimed the 

 first blow at the Differential Calculus. He objected to the 

 explanation of Leibnitz, and to the notion of quantities infi- 

 nitely small. 1 It seemed as if he were unwilling to believe 

 in the reality of objects smaller than those discovered by his 

 own microscope, and were jealous of any one who should 

 come nearer to the limit of extension than he himself had 

 done. Leibnitz thought his objections not undeserving of a 

 reply ; but the reply was not altogether satisfactory. A se- 

 cond was given with better success ; and afterwards Herman 



1 He published Analysis Infinitorum at Amsterdam, in 1695 ; 

 and another tract, Consider ationcs circa Calculi Diffcrcnlialis 

 Principia, in the year following. This last was answered by 

 Herman. 



