PRINTED BOOKS, ETC, BEFORE 1734 45 



The Reason of that [difference], is this. Because 

 there is (speaking strictly and accurately) an Infinity 

 of Velocities to be consider'd, in the Generation and 

 Production of a Real hicrernent ; ... So that if we 

 conceiv'd the Fluxion, to be the Velocity of the 

 Increment, as actually Generateci ; we must conceive 

 it to be an Infinite Variety or Series of Velocities. 

 Whereas the Velocity, with which any sort of In- 

 crement arises, or begins to be generateli ; is a thing 

 that one may form a very clear and distinct Idea of, 

 and leaves the Mind in no Ambiguity or Confusion 

 at ali. . . . However, if we take those Particles 

 of time exceeding small indeed, and Neglect the 

 Acceleration of the Velocity as inconsiderable, we 

 may say the Fluxions are proportional to those In- 

 crements ; remembering at the same time, that they 

 are but nearly, and not accurately so. . . . If in the 

 Differential Calculus, some Terms are reìected and 

 thrown out of an Equation, because they are nothing 

 Comparatively, or with respect to other Terms in the 

 same Equation ; that is, because they are infinitely 

 small in proportion to those other Terms, and so may 

 be neglected upon that Score: On the other band, in 

 the Method of Fluxions, those same Terms go out 

 of the- Equation, because they are multiplied into a 

 Ouantity, which . . . does at last really vanish. . . . 

 N.B. Speaking bere of Infinitely small Quantities, 

 or Infinitesimals as some Authors (and particularly 

 Mr. Neiwentiit) chuse to term them, I cannot but 

 take notice of a notion, which that Excellent and In- 

 genious Ferson advances in bis Analysis htjìnitorum. 



