34 DISSERTATION SECOND. [part is. 



fectly unfolded, if the two excellent geometers just named 

 had not come to his assistance. Their tracts were also, like 

 his, scattered in the different periodic works of that time, 

 and several years elapsed before any elementary treatise 

 explained the general methods, and illustrated them by ex- 

 amples. The first book in which this was done, so far at 

 least as concerned the differential or direct calculus, was the 

 Analyse des Injiniment Petits of the Marquis de PH6pital y 

 published in 1696, a work of great merit, which did 

 much to diffuse the knowledge of the new analysis. It 

 was well received at that time, and has maintained its 

 character to the present day. The author, a man of genius, 

 indefatigable and ardent in the pursuits of science, had 

 enjoyed the viva voce instructions of John Bernoulli, on 

 the subject of the new geometry, and therefore came for- 

 ward with every possible advantage. 



It was long after this before the works of the Bernoul- 

 lis were collected together, those of James in two quarto 

 volumes, and of John in four. 1 In the third of these last 

 volumes is a tract of considerable length, with the title of 

 Lectiones de Methodo Integralium, written in 1691 and 

 1692, for the use of M. de THopital, to whose book on 

 the differential calculus it seems to have been intended as 

 a sequel. It is a work of great merit ; and affords a dis- 

 tinct view of many of the most general methods of inte- 

 gration, with their application to the most interesting pro- 

 blems ; so that, though the earliest treatise on that sub- 

 ject, it remains at this day one of the best compends of 

 the new analysis of which the mathematical world is in 

 possession. Indeed, the whole of the volumes just refer- 

 red to are highly interesting, as containing the original 



1 Those of James were published at Geneva in 1744 ; of John 

 at Lausanne and Geneva in 1742. 



