ANCIENT ANALYSIS. POEISMS. 67 



which it has given rise, appears from, many circumstances 

 among others, from, what has already been stated ; it appears 

 also from this, that in many of his manuscripts there are 

 found algebraical formulas for propositions which he had 

 investigated geometrically. Maclaurin consulted him on the 

 preparation of his admirable work, the 'Fluxions,' and re- 

 ceived from him copious suggestions and assistance. Indeed, 

 he adopted from him the celebrated demonstration of the 

 fluxion (or differential) of a rectangle.* But Simson's whole 

 mind, when left to its natural bent, was given to the beauties 

 of the Greek Geometry ; and he had not been many months 

 settled in his academical situation when he began to follow 

 the advice which Halley had given him, as both calculated, 

 he said, to promote his own reputation, and to confer a lasting 

 benefit upon the science cultivated by them both with an 

 equal devotion. It is even certain that the obscure and most 

 difficult subject of Porisms very early occupied his thoughts, 

 and was the field of his researches, though to the end of his 

 life he never had made such progress in the investigation as 

 satisfied himself. Before 1715, three years after he began his 

 course of teaching, he was deeply engaged in this inquiry ; 

 but he only regarded it as one branch of the great and dark 

 subject which Halley had recommended to his care. After he 

 had completely examined, corrected, and published, with most 

 important additions, the Conies of Apollonius, which happily 

 remain entire, but which, as we have seen, had been most 

 inelegantly and indeed algebraically given by De la Hire, 

 L'Hopital, and others, to restore the lost books was his great 

 desire, and formed the grand achievement which he set 

 before his eyes. 



We have already shown how scanty the light was by which 

 his steps in this path must be guided. The introduction to 

 the Seventh book of Pappus contained the whole that had 

 reached our times to let us know the contents of the lost 

 works. Some of the summaries which that valuable discourse 



* Book i. chap. ii. prop. 3. 



F 2 



