18 DISSERTATION SECOND. [part ij. 



met with the attention it was supposed to deserve, but 

 John Bernoulli having resumed the consideration of it, 

 found out what appeared a very perfect and very gene- 

 ral solution; and the question was then (1716) proposed 

 anew by Leibnitz, for the avowed purpose of trying the 

 skill of the English mathematicians. The question is, a 

 system of curves described according to a known law be- 

 ing given (all the hyperbolas, for instance, that are de- 

 scribed between the same assymptotes ; or all the parabo- 

 las that have the same directrix, and that pass through 

 the same point, &c), to describe a curve which shall cut 

 them all at right angles. This may be considered as the 

 first defiance professedly aimed at the English mathemati- 

 cians. The problem was delivered to Newton on his re- 

 turn from the Mint, when he was much fatigued with the 

 business of the day ; he resolved it, however, the same 

 evening, and his solution, though without a name, is given 

 in the Philosophical Transactions for 1716. 1 



This solution, however, only gave rise to new quarrels, 

 for hardly any thing so excellent could come from the 

 one side, that it could meet with the entire approbation 

 of the other. Newton's, indeed, was rather the plan or 

 projet of an investigation, than an actual solution ; and, in 

 the general view which it took of the question, could 

 hardly provide against all the difficulties that might occur 

 in the application to particular cases. This was what Ber- 

 noulli objected to, and affected to treat the solution as of 

 no value. Brook Taylor, secretary of the Royal Society, 

 and well known as one of the ablest geometers of the 

 time, undertook the defence of it, but concluded with 

 using language very reprehensible, and highly improper to 

 be directed by one man of science against another. Hav- 



1 Vol. XXIX. p. 399. 



