TEXT-BOOKS, 1736-1741 169 



We are tempted to make the remark that in 

 1737 Smith left the subject even more mysterious 

 than he found it. 



Thomas Siinpson^ ^72)7 



156. Thomas Simpson, the son of a vveaver, was 

 a self-taught mathematician, and acquired a know- 

 ledge of fluxions through Stone's translation of De 

 L'Hospital's A^ialysc des infinimcnt pctits. Simpson 

 was a mathematician of marked power, and influenced 

 considerably the teaching of mathematics in England. 

 In 1737 he broughtout his New Treatise of Fluxions ,'^ 

 which contains some novel features. 



** The Fluxions of variable Ouantities are always 

 measured by their Relation to each other ; and are 

 ever expressed by the finite Spaces that would be 

 uniformly described in equal Times, with the Veloci- 

 ties by which those Quantities are generated." 



He finds it easy to show that the fluxion of a 

 rectangular area of Constant height and uniformly 

 variable base is as the height drawn into the 

 velocity with which the base changes ; also that 

 the fluxion of a curvilinear area generated by an 

 abscissa moving with uniform velocity is at a given 

 point, as the ordinary y for this point, multiplied 

 by that velocity. This last result is applied to 

 finding the fluxion of ,tT. 



Avoiding infinitely small quantities, Simpson finds 



^ A Ne7v Treatise of Fluxions: whercin the direct and ifiverse 

 Method are demonstrated after a new, clear and concise Manner, with 

 their Application to Physics and Astronomy, By Thomas Simpson, 

 London, 1737. 



