50 LIMITS AND FLUXIONS 



whereof the first or finite Ouantities themselves, viz. 

 X, V, z, may be conceiv'd as Fluxions.'' And again, 

 "a Point . . . may be consider'd as the Fluxion of 

 a Line, a Line as the Fluxion of a Piane, and a 

 Piane as the Fluxion of a Solid, and a finite Solid 

 as the Fluxion of a (parfially) infinite one, and that 

 again as the Fluxion of one of an higher Gender of 

 Infinity, and so on ad inf. which we shall further 

 illustrate in some Dissertations at the end of this 

 Treatise." 



68. Brook Taylor brought out at London in 17 15 

 his Methodus incrementonim dire età et inversa, in 

 which he looks upon fluxions strictly from the stand- 

 point of the Newtonian exposition in the Quadrature 

 of Curves, 1704. 



69. James Stirling uses x and y as infinitesimals 

 in his LinecE tertii ordinis, Oxford, 17 17. He draws 

 the inftnitely small right triangle at the contact 

 of a curve with its asymptote, the horizontal side 

 being " quam minima" and equal to i-, the vertical 

 side being y. In the appendix to this booklet of 

 17 17, X and y are again infinitely small. In his 

 Methodus differentialis, London, 1730, there is no 

 direct attempt to explain fundamentals, any more 

 than there was in 17 17, but on p. 80 he puts the 

 fluxion of an independent variable equal to unity, 

 from which we infer that a fluxion is with him now 

 a finite velocity. 



70. For twenty-four years after Ditton no new 

 text appeared. In 1730 Edmund Stone, a self- 

 taught mathematician who had studied De l'Hospital, 



