20 DISSERTATION SECOND. [mm n. 



cians, to Cotes, to himself, and, perhaps, one or two more. 

 The selection, nevertheless, was abundantly injudicious ; 

 for Bernoulli, as long ago as 1702, had explained the 

 method of integrating this, and such like formulas, both in 

 the Paris Memoirs and in the Leipsic Acts. The ques- 

 tion, accordingly, was no sooner proposed than it was an- 

 swered in a manner the most clear and satisfactory ; so 

 the defiance of Taylor only served to display the address 

 and augment the triumph of his adversary. 



The last and most unsuccessful of these challenges was 

 that of Keill, of whose former appearance in this contro- 

 versy we have already had so much more reason to com- 

 mend the zeal than the discretion. Among the problems 

 in the mixt mathematics which had excited most attention, 

 and which seemed best calculated to exercise the resour- 

 ces of the new analysis, was the determination of the path 

 of a projectile in a medium which resists proportionally 

 to the square of the velocity, that being nearly the law 

 of the resistance which the air opposes to bodies moving 

 with great velocity. The resistance of fluids had been 

 treated of by Newton in the second book of the Princi- 

 pia, and he had investigated a great number of curious 

 and important propositions relative to its effects. He had 

 considered some of the simpler laws of resistance, but of 

 the case just mentioned he had given no solution, and, 

 after approaching as near as possible to it on all sides, 

 had withdrawn without making an attack. A problem so 

 formidable was not likely to meet with many who, even 

 in the more improved state at which the calculus had 

 now arrived, could hope to overcome its difficulties. — • 

 Whether Keill had flattered himself that he could resolve 

 the problem, or had forgotten, that when a man proposes 

 a question of defiance to another, he ought to be sure 

 that he can answer it himself, may be doubted ; but this 



