28 LIMirS AND FLUXIONS 



forbears to write it down, and uses ali manner of 

 Approximations which he conceives will produce 

 no Error in the Conclusion. " In ^^yN\.ovC^ Principia 

 " he frequently considers Lines as Fluents described 

 by Points, whose Velocities increase or decrease, 

 the Velocities are the first Fluxions, and their 

 Increase the second. " The Compendium of his 

 Analysis was written ''in or before the year 1669" 

 (p. 180). ''And the same Way of working he used 

 in his Book of Quadratures, and stili uses to this 

 day"(p. 182). On p. 204 we read : '*Mr. Newton 

 used the letter in his Analysis written in or before 

 the Years 1669, and in his Book of Quadratures, 

 and in his Principia PhilosophicB, and stili uses it 

 in the very same Sense as at first. . . . These 

 Symbols and i' are put for things of a different kind. 

 The one is a Moment, the other a Fluxion or 

 Velocity as has been explained above. . . . Prickt 

 Letters never signify Moments, unless when they 

 are multiplied by the Moment either exprest or 

 understood to make them infinitely little, and then 

 the Rectangles are put for the Moments " (p. 204). 

 Further on we read : " It [the method of fluxions] 

 is more elegant [than the Differential Method of 

 Leibniz], because in his Calculus there is but one 

 infinitely little Quantity represented by a symbol, 

 the symbol 0. We bave no Ideas of infinitely little 

 Ouantities, and therefore Mr. Newton introduced 

 Fluxions into his Method, that it might proceed by 

 finite Ouantities 'as much as possible. It is more 

 Naturai and Geometrical, because founded upon the 



