NEWTON 17 



ing the remainder by 0, he remarks (page 393) : 

 ''Destroy the terms multipUed by as infinitely 

 small, and there will remain the equation 2)^x^—^yy 

 — 2X}'y + aaà = o. " 



III. Quadratura Curvarum,^ 1704 

 '' Introductio 



27. " Quantitates Mathematicas non ut ex parti- 

 bus quam minimis constantes, sed ut motu con- 

 tinuo descriptas hic considero. Lineae describuntur 

 ac describendo generantur non per appositionem 

 partium sed per motum continuum punctorum, 

 superficies per motum Hnearum, soHda per motum 

 superficierum, anguli per rotationem laterum, tem- 

 pora per fluxum continuum, et sic in ca^teris. Hse 

 Geneses in rerum natura locum vere habent et in 

 motu corporum quotidie cernuntur. Et ad hunc 

 modum Veteres ducendo rectas mobiles in longi- 

 tudinem rectarum immobilium genesin docuerunt 

 rectangulorum. 



28. "Considerando igitur quod quantitates aequa- 

 libus temporibus crescentes et crescendo genita^, 

 prò velocitate majori vel minori qua crescunt ac 



^ Tractatus de Quadratura Curvarum, published in 1704 in London, 

 as an appendix to Newton's Opiicks. It was reprinted under the 

 editorship of William Jones in London in ihe year 171 1, in a volume 

 containing also three other papers of Newton, viz., the De analysi per 

 ceguationes infinifas, Enumcratio Hnearum tertii ordinis, and Methodus 

 differentialis. An English translation of the Qìiadratura Curvarum, 

 made by John Stewart, was brought out in 1745 at London, in a volume 

 containing also Newton's Analysis hy Equations of an Infinite Ntiinber 

 of Ternis. A German translation of the Quadratura Curvarum by 

 Gerhard Kowalewski appeared at Leipzig in 1908 in OsiwalcP s Klassiker 

 der exakten Wissenschaften, Nr. 164. 



2 



