NE WTON 29 



primce quantitatum nascentiuin rationes, which have 

 a Being in Geometry, whilst Indivisibles, upon 

 which the Differential Method is founded, have no 

 Being either in Geometry or in Nature. There are 

 rationes primce quantitatum nascentium, but not 

 quantitates prinicB nascentes. Nature generates 

 Quantities by continuai Flux or Increase ; and the 

 ancient Geometers admitted such a Generation of 

 Areas and Solids " (p. 205). 



Front Newton' s Correspondence and Manuscripts 

 not in print in 1734 



48. Manuscripts of Newton, some of them stili 

 unpublished, show that he first thought of fluents 

 and fluxions in 1665 and 1666, when he was in 

 his twenty-third and twenty-fourth years.^ The 

 notation by dots occurs as early as 1665. As 

 pointed out by De Morgan,- these early papers are 

 infinitesimal in character. They were first published 

 in 1838.^ A manuscript, dated Nov. 13, 1665, 

 gives rules for finding the velocities p, q, ;-, etc. , 

 of two or more lines x, y, z, etc, described by bodies 

 A, B, C, etc, the lines being related to each other 



^ See a list of Newton's manuscripts and publications on fiuxional 

 calculus prepared by Philip E. B. Jouidain, in his edition of Augtistus 

 De Morgati's Essays on the Life and Work of Nezvton, The Open 

 Court Publishing Co., 1914, pp. 107- 1 12. 



" Augustus De Morgan, "On the Early History of Infinitesimals 

 in England," 7'he London, Edinburgh, and Duhlin Philosophical 

 Magazine, 4th S., voi. iv, 1852, pp. 321-330. This article is an 

 important historical contribution, of which extensive use is made in the 

 present history. 



^ See S. P. Rigaud, Historical Essay on the first Public ation of Sir 

 Isaac Newton's Principia, Oxford, 1838, Appendix, pp. 20-24. 



