srasoN. 141 



That lie did not undervalue algebra and the calculus 

 to which it has given rise, appears from many circum- 

 stances 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 4 Fluxions,' and received 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 situ- 

 ation 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 occu- 

 pied 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. Be- 

 fore 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 inele- 

 gantly 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 



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



