490 . SIMSON. 



useless in the solution of problems, the great purpose 

 of Apollonius, as of all the authors of the TOTTO? 

 avaXvopevov the thirty-three ancient books. As for 

 the analysis, it was given by neither, unless, indeed, 

 Schooten's algebra is to be so termed : Fermat's de- 

 monstrations were all synthetical. His treatise, though 

 written as early as 1629, was only published among 

 his collected works in 1670. Schooten's was published 

 among his ' Exercitationes Mathematics' in 1657. Of 

 the field thus left open Dr. Simson took possession, 

 and he most successfully cultivated every corner 

 of it. Nothing is left without the most full discus- 

 sion ; all the cases of each proposition are thoroughly 

 investigated. Many new truths of great importance 

 are added to those which had been unfolded by the 

 Greek philosopher. The whole is given with the per- 

 fect precision and the pure elegance of the ancient 

 analysis ; and the universal assent of the scientific 

 world has even confessed that there is every reason to 

 consider the restored work as greatly superior to the 

 lost original. 



The history of this excellent treatise shows in a 

 striking manner the cautious and modest nature of its 

 author. He had completed it in 1738 ; but, unsatisfied 

 with it, he kept it by him for eight years. He could 

 not bring himself to think that he had given the 

 " ipsissimee propositiones of Apollonius in the very 

 order and spirit of the original work." He was then 

 persuaded to let the book appear, and it was published 

 in 1746. His former scruples and alarms recurred; 

 he stopped the publication ; he bought up the copies 

 that had been sold ; he kept them three years longer 



