»jtcT. ..] DISSERTATION SECOND. 21 



is certain, that, without the necessary preparation, he 

 boldly challenged Bernoulli to produce a solution. 



Bernoulli resolved the question in a very short time, 

 not only for a resistance proportional to the square, but 

 to any power whatsoever of the velocity, and by the con- 

 ditions which he affixed to the publication of his solution, 

 took care to expose the weakness of his antagonist. He 

 repeatedly offered to send his solution to a confidential 

 person in London, providing Keill would do the same* 

 Keill never made ai;y reply to a proposal so fair, that 

 there could only be one reason for declining it. Bernoulli, 

 of course, exulted over him cruelly, breaking out in a 

 torrent of vulgar abuse, and losing sight of every maxim 

 of candour and good taste. 



Such, then, were the circumstances under which the 

 infinitesimal analysis, — the greatest discovery ever made in 

 the mathematical sciences, — was ushered into the world. 

 Every where, as it became known, it enlarged the views, 

 roused the activity, and increased the power of the ge- 

 ometer, while it directed the warmest sentiments of his 

 gratitude and admiration toward the great inventors. In 

 one respect, only, its effects were different from those 

 which one would have wished to see produced. It ex- 

 cited jealousy between two great men who ought to have 

 been the friends of one another, and disturbed in both 

 that philosophic tranquillity of mind, for the loss of which 

 even glory itself is scarcely an adequate recompense. 



In order to form a correct estimate of the magnitude 

 and value of this discovery, it may be useful to look back 

 at the steps by which the mathematical sciences had been 

 prepared for it. When we attempt to trace those steps 

 to their origin, we find the principle of the infinitesimal 

 analysis making its first appearance in the method of Ex- 

 haustions, as exemplified in the writings of Euclid and Ar- 



