40 LIMITS AND FLUXIONS 



''infinitely little."' In 1702-3 Humphry Ditton, 

 in voi. xxiii of the Transactions ^ used the fluxional 

 notation, without explanation. 



58. Other vvritings that do not define their terms 

 are the Fluxionum rnethodus inversa, 1704, by the 

 London physician, George Cheyne, and De Moivre's 

 Animadvei'siones in D. Georgii Cheynai Tractaium, 

 London, 1704. However, Cheyne lets x— i, from 

 which we infer that, with him, x was finite. [See 

 Addenda, p. 289.] 



59. The next writer on fluxions was John Harris, 

 a voluminous author of books on various subjects. 

 He was at one time Secretary of the Royal Society. 

 In 1702 he published at London A New Short 

 Treatise of Algebra, which devotes the last 22 

 pages, out of a total of 136 pages, to fluxions. It 

 is the first hook in the English language in which 

 this subject is treated. The doctrine of fluxions is 

 the " Arithmetick of the I n finii e ly s mail Increments 

 or Decrements of Indeterminate or Variable Qua?i- 

 tities, or as some cali them the Moments or hifin- 

 itely small Differences of such Variable Ouantities. 

 These Infinitely small Increments or Decrements, 

 our incomparable Mr. Isaac Newton calls very pro- 

 perly by this name of Fluxions " (p. 115). A few 

 lines further on it says that Newton ''calls the 

 celerity or Velocity of the Augmentation of Diminu- 

 tion of these Flowing Quantities, by the name of 

 Fluxions.'' A second edition of this hook appeared 

 in 1705. As authors on fluxions, Harris in 1705 



^ J. Edleston, Correspondence of Sir Isaac Newton and Professor 

 Cotes, London, 1850, p. 196. 



