2o8 LIMITS AND FLUXIONS 



Fluxions. And hence, whether we cali those finite 

 Ratios, Pluxions, or Increments, their Idea, Nature, 

 and Originai appear to be the very same thing. 

 For ali Things are relative. ..." 



He argues that while we consider a line or piane, 

 generating an area or solid, as of no thickness in the 

 mind, in our notation we represent them as of unit 

 thickness, **and consequently each Line or Piane 

 should be express'd by ^ x L, and o x P, to denote 

 them as they are in the Mind. But L x ^ to o, 

 and P X <? to 0^ are in the same Ratio with L to i, 

 and P to I , by equal Division by o ; and those again 

 in the same Ratio with Li- to i-, and Yx to i', by 

 equal Multiplication by i-, for the Ratio of Fluxions. 

 But, this finite Notation of Line or Plane^ which we 

 consider of no Breadth, or Thickness, and yet denote 

 by Unity, each, at the same Time, makes the Practice 

 and our Comprehension disagree. ... So that it will 

 be an Error to conclude that the Ratio of the 

 Fluxions of Quantities generated by the Motion of 

 Lines, or Planes, is arrived at this Way, without 

 the previous Consideration of an Increment ; for the 

 very Lines and Planes must be Increments, or Some- 

 things next to Notkings themselves, before they 

 were what we finitely express them by Notation, 

 or Quantities could never increase or be generated 

 thereby : For to carry a Line or Piane of no Breadth 

 or Thickness forward, is the same in Terms as to 

 carry Nothing forward. And therefore the Dis- 

 tinction between the Ratio of Increments, and that 

 of Fluxions, is only what the Conception of the 



