NEWTON 31 



the Principia (17 13) is a letter of May 15, 17 14, 

 from Newton to KeilV from which we quote the 

 foUowing : — 



51. ". . . altho I use prickt Letters in the first 

 Proposition of the hook of Quadratures, yet I do 

 not there make them necessary to the method. 

 For in the Introduction to that hook I describe 

 the method at large & illustrate it w"' various 

 examples without making any use of such letters. 

 And it cannot be said that when I wrote that 

 Preface I did not understand the method of fluxions 

 because I did not there make use of prickt letters 

 in solving of Problems.^ The book of Quadratures 

 is ancient, many things being cited out of it by me 

 in my Letter of 24 Octob. 1676. . . . 



52. ''ffluxions & moments are quantities of 

 a different kind. ffluxions are finite motions, 

 moments are infinitely little parts. 1 put letters 

 with pricks for fìiuxions, & multiply fluxions by the 

 letter to make them become infinitely little and 

 the rectangles I put for moments. And wherever 

 prickt letters represent moments & are without the 

 letter o this letter is always understood. Wherever 

 •^> j) y^ 7) ^tc, are put for moments they are put for 

 xo^ yo^ j/00, yo^. In demonstrating Propositions I 

 always write down the letter & proceed by the 

 Geometry of Euclide and ApoUonius without any 



^ J. Edleston, Correspondence of Sir Isaac A/ewlon and Professor 

 CoUs, London, 1850, pp. 176, 177. 



yji^ John Bernoulii, in tlie Ada Ertiditorum for February and March, 

 17 13, had critici-sed a passage in the Principia^ and claimed ihal Newton 

 did not understand the second fluxions when writinij that passagc. 



