LATER BOOKS AND ARTICLES 343 



doctrine of indivisibles there *'has been introduced 

 into mathematica! reasoning ali that absurd jargon 

 concerning quantities infinitely great, and infinitely 

 little, which has been so much objected to by mathe- 

 maticians. And, though it has often been elegantly 

 applied by some able geometers to the demonstra- 

 tion of many noble theorems ; yet in the hands of 

 less accurate reasoners, it has often led to false 

 conclusions" (p. 71). 



F. Holliday, 1777 



210. In a somewhat lengthy preface to his Intro- 

 duction to Fluxions^ the author tells that, when in 

 1745 he was in London, in company with W. Jones 

 and De Moivre, they expressed great approbation 

 of Emerson's Fluxions^ with regard to the method 

 of treatment, but thought his book too high for 

 beginners. The author tries to be more diffuse in 

 the laying down of first principles. He derives the 

 fundamental results in two ways : first, by the aid 

 of nascent or evanescent quantities, as suggested by 

 Newton's Principia; second, ''without using any 

 infinitely small quantities, or vanescent Parallelo- 

 grams, which perhaps will be more acceptable to 

 many of my Readers. " Holliday explains at great 

 length the Scholium (see our §§ 10-15) on prime 

 and ultimate ratios, and gives a short account of 

 the invention of fluxions as given in the review of 



^ An hitroduction to Fluxions^ Designedfor the Use, and Adapted to 

 the Capacities of Beginners. By the Reverend F. Holliday, Vicar of 

 West Markham and Bothamsall, Nott's. London, 1777. 



