290 LIMITS AND FLUXIONS 



vvhat I had formerly published on this Head in the 

 first Edition of this Work." 



Cheyne uses in Part II, p. 20, the notation ± io 

 denote a distance B^ when he supposes " b infinitely 

 near to B." In § 58 we pointed out that in 1704 

 Cheyne wrote once x= i, but nowhere in the present 

 hook does x denote a finite quantity. He argues 

 that I / i'= co I, that i / o=co ; hence thati-=^, or 

 "relative nothing," which is ** the least Part of the 

 Finite, to which it is related or compared. " On 

 p. 21 he calls x " an infinitely little Part of x." On 

 p. 12 he speaks of the " absolute infinite" as " ad- 

 mitting of neither Increase, nor Diminution, or of 

 any Operation that mathematica! Quantity is sub- 

 jected to," while (p. 13) " absolute nothing" is 

 ''neither capable of increasing nor diminishing, nor 

 of any wise altering any Mathematica! Quantity to 

 which it is apply'd, but stands in full opposition to 

 absolute Infinite. " On the other band, "indefinite" 

 or ' ' relative infinite " quantities (p. 29") ' ' are not 

 properly either Finite or Infinite, but between both. " 

 The " relative nothing " (p. 8) " is an infinitely little 

 Quantity, as it stands related to a given Finite, 

 by the perpetuai Subtraction of which from it self 

 it is generated. Let stand for relative nothing. 

 Thus <?i is a relative infinitely little Quantity, as it 

 stands related to Unity, by the perpetuai Subtrac- 

 tion of which from it self, it is generated ; that is 

 £?i = i — i + i — i + i — i-f-i — I ec, and oa is an 

 infinitely little Quantity, as it stands related to 

 the given F'niite a^ by the perpetuai Subtraction 



