SEQUEL TO THE GENERALIZATION. 99 



proposition to which we have referred, gave only 

 an indirect view of the nature of the curve de- 

 scribed by a projectile in the air; and it is probable 

 that Newton, when he wrote the Principia, did not 

 see his way to any direct and complete solution 

 of this problem. At a later period, in 1718, when 

 the quarrel had waxed hot between the admirers 

 of Newton and Leibnitz, Keill, who had come for- 

 ward as a champion on the English side, proposed 

 this problem to the foreigners as a challenge. Keill 

 probably imagined that what Newton had not dis- 

 covered, no one of his time would be able to 

 discover. But the sedulous cultivation of analysis 

 by the Germans had given them mathematical 

 powers beyond the expectation of the English ; who, 

 whatever might be their talents, had made little 

 advance in the effective use of general methods ; 

 and for a long period seemed to be fascinated to 

 the spot, in their admiration of Newton's excel- 

 lence. Bernoulli speedily solved the problem ; and 

 reasonably enough, according to the law of honour 

 of such challenges, called upon the challenger to 

 produce his solution. Keill was unable to do this ; 

 and after some attempts at procrastination, was 

 driven to very paltry evasions. Bernoulli then 

 published his solution, with very just expressions 

 of scorn towards his antagonist. And this may, 

 perhaps, be considered as the first material addi- 

 tion which was made to the Principia by subse- 

 quent writers. 



