TEXT-BOOKS, 1736-1741 179 



From the notion of absolute space springs that of 

 absolute motion ..." He continues in a foot- 

 note : " Our judgment in these matters is not to be 

 overborne by a presumed evidence of mathematica! 

 notions and reasonings, since it is plain the mathe- 

 maticians of this age embrace obscure notions, and 

 uncertain opinions, and are puzzled about them, 

 contradicting each other and disputing like other 

 men : witness their doctrine of Fluxions, about 

 which, within these ten years, I bave seen published 

 about twenty tracts and dissertations, whose authors 

 being utterly at variance, and inconsistent with each 

 other, instruct by-standers what to think of their 

 pretensions to evidence." 



Remarks 



162. In these publications no reference is made 

 to the Jurin-Robins controversy, though Berkeley's 

 Analyst is frequently discussed. Excepting only in 

 Benjamin Martin, the definition of a fluxion as a 

 '' differential " nowhere appears. Therein we see 

 a step in advance. 



The influence of Newton's Quadrature of Curvcs 

 (1704) is evident almost everywhere. An improve- 

 ment in the mode of deriving the fluxion of a 

 *' product " appears in the anonymous Explanation of 

 Fluxions and in the revised text by John Rowe 

 (our §§ 158, 160). 



Noteworthy is Thomas Simpson's new definition 

 of fluxions ; this new definition plays an important 

 ròle during the rest of the century. 



