j Et r. i.] DISSERTATION SECOND. 11 



series, yet they afforded no indication of the nature of that 

 method, or the principles on which it proceeded. 



In what manner Newton's communications in the two let- 

 ters already referred to, may have acted, in stimulating the 

 curiosity and extending or even directing the views of such 

 a man as Leibnitz, I shall not presume to decide (nor even, 

 if such effect be admitted, will it take from the originality of 

 his discoveries); but that in the authenticated communications 

 which took place between these philosophers, there was 

 nothing which could make known the nature of the fluxiona- 

 ry calculus, I consider as a fact most fully established. 



Of the new or infinitesimal analysis, we are, therefore, to 

 consider Newton as the first inventor, Leibnitz as the se- 

 cond ; his discovery, though posterior in time, having been 

 made independently of the other, and having no less claim 

 to originality. It had the advantage also of being first made 

 known to the world ; an account of it, and of its peculiar al- 

 gorithm, having been inserted in the first volume of the 

 Acta Eruditorum, in 1684. Thus, while Newton's dis- 

 covery remained a secret, communicated only to a few 

 friends, the geometry of Leibnitz was spreading with great 

 rapidity over the Continent. Two most able coadjutors, the 

 brothers James and John Bernoulli, joined their talents to 

 those of the original inventor, and illustrated the new me* 

 thods by the solution of a great variety of difficult and inte- 

 resting problems. The reserve of Newton still kept his 

 countrymen ignorant of his geometrical discoveries, and the 

 first book that appeared in England on the new geome- 

 try, was that of Craig, who professedly derived his knowledge 

 from the writings of Leibnitz and his friends. Nothing, 

 however, like rivalship or hostility between these inventors 

 had yet appeared ; each seemed willing to admit the origin- 

 ality of the other's discoveries ; and Newton, in the passage 



