PREFACE. XI 



papers in the British Museum that he was well ac- 

 quainted with Pappus and other geometrical works 

 which had then been recently published abroad. 

 There is a remarkable note of Sir Charles Cavendish 

 at p. 84, who says, " Dr. Jungius prefers the analitics 

 of the ancients before Vieta's by letters, which he saies 

 is more subject to errors or mistakes, though more 

 facile and quick of dispatch, but I conceive not yet 

 whye." This serves to show that the ro^og avaXvopwog 

 of the Alexandrian school still held its sway in the 

 minds of foreign mathematicians, notwithstanding the 

 writings of Vieta and Descartes ; but we find no traces 

 in this country of its influence over the new analysis 

 before the time of Robert Simson, that is, nearly a 

 century afterwards. 



The science of the seventeenth century possessed 

 one feature which is now obsolete, and which pro- 

 bably contributed, in a great measure, to preserve 

 and foster a taste for analytics. We allude to the 

 practice of publicly proposing problems for solution 

 a kind of challenge from individuals to the science 

 of all Europe and thus exciting an emulation which, 

 perhaps, would otherwise not have been felt. The 

 superiority of the new analysis over the ancient geo- 

 metry was soon acknowledged, and although some 

 questions were required to be solved geometrically, 

 yet mathematicians soon evinced their dislike to a 

 system of attaining by a long and tedious method 

 that which was often capable of speedy and easy re- 

 solution by another analysis. Specimens of these 

 challenges are preserved among Pell's papers in the 



