488 SIMSON. 



question, which we thus have his own authority for say- 

 ing he never had previously entertained any intention of 

 composing. It is much to be lamented that he never 

 did give such a work to the world. His thoughts had 

 often been very profoundly directed to the subject ; 

 and no one was so well fitted to handle it with the 

 learning and with the judgment which its execution 

 required. 



That he 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 ' 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 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 de- 

 votion. 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 



* Book i. oh. ii. prop. 3. 



