LATER BOOKS AND ARTICLES 253 



and quotes Newton's Scholium, Sect. i, in the Prin- 

 cipia. He points out, also, that if x increases uni- 

 formly, x'^ increases with accelerateci velocity, and 

 the part of the increment x'^ is the efifect of the 

 acceleration, and therefore, by his definition of 

 fluxion, to be " omitted in taking the fluxions " 

 (P. 8). 



New Editions, 1 801- 1809 



218. William Davis, who was a bookseller in 

 London and editor of the Companion to the Gentle- 

 man' s Diaryy appears also as the editor of new 

 editions of three dififerent texts on fluxions. In 

 1801 he saw through the press the second edition 

 of Maclaurin's Treatise of Fluxions \ in 1805 the 

 third edition of Thomas Simpson's Doctrine and 

 Application of Fluxions. In 1809 appeared the fourth 

 edition of John Rowe's Doctrine of Fluxions^ revised 

 **by the late William Davis." 



Remarks 



219. Among some of the authors of this period 

 there is less concern than among writers of former 

 years about the attainment of the rigour of the 

 ancients. Perhaps the effects of the revival of the 

 ideals of Euclid and Archimedes which followed the 

 publication of the Analyst were gradually subsiding. 

 It would not be fair to this age to judge its mathe- 

 matical status altogether by the authors which we 

 bave selected. There was a movement under way 



