26 LIMITS AND FLUXIONS 



Let the quantity o be diminished infinitely, and 

 neglecting the terms which vanish, there will remain 

 ^xx^ — xyy — 2xyy + aaz = o. Q. E. D. " 



IV. An Account of the '*Commercium 

 Epistolicum " 



46. It is now generally accepted that the account ^ 

 of the Commeixium Epistolicum^ published in the 

 Philosophical Transactions, London, 17 17, was 

 written by Newton. The reasons for attributing it 

 to him are stated by De Morgan^ and by Brewster.^ 

 In abstract the account is as follows : — 



47. (Pp. 177-178.) In a letter of October 24, 

 1676, to Oldenburgh, Newton explained that in 

 deducing areas he considered the area as growing 

 "by continuai Flux"; ''from the Moments of Time 

 he gave the Name of Moments to the momentaneous 

 Increases, or infinitely small Parts of the Abscissa 

 and Area generated in Moments of Time. The 

 Moment of a Line he called a Point, in the Sense 

 of Cavalerius, tho' it be not a geometrical Point, 

 but a Line infinitely short, and the Moment of an 

 Area or Superficies he called a Line, in the sense 

 of Cavalerius, tho' it be not a geometrical Line, 



^ Philosophical Transactions, voi. xxix, for the years 17 14, 17 15, 

 1716. Li)ndon, 1717. " An Account of the Hook entituled Commer- 

 ciimi Epistolicum Collimi et aliorum, De Analysi promoia . . .," 

 pp. 173-224. This account was translated into Latin and inserted in 

 the edilion of the Commerciiim Epistolicum of 1725. 



2 See De Morgan's articles in the Philosophical Magazine, S. 4, 

 voi. iii, June, 1852, pp. 440-444; v )1. iv, November 1652, p. 323. 



^ Sir David V>tcvi^\.ttx, Memoirs of the Life, Writings,and Discoveries 

 of Sir Isaac Newton, 2nd ed., voi. ii, Edinburgh, 1860, pp. 35, 36. 



