ROBERT HEATH v. JOHN TURNER 219 



are exactly such finite Ouantities, proportional to 

 the Velocities as Sir Isaac Newton here ^ speaks of ; 

 since it is well known that the Quantities produced, 

 or the Distances described, in any given Time, by 

 Motions uniformly continued, are, accurately, as 

 the Velocities of the said Motions." 



193. In No. V (1752) of the Mathematical 

 Exercises appears another article in the contro- 

 versy, written by John Turner. There is little in 

 it requiring our attention. It is a reply to two 

 pamphlets, the Lady's Philosopher and a new 

 Pal/admm, both publications from , the pen of 

 Robert Heath. 



Ladies' Diary^ 175 1, 1752 



194. The Ladies' Diary iox 175 i has an article on 

 The Nature and Use of the Algebraic Cypher^ or 

 Quantity o, *' by Fluxioniensis " ; o / o is proved to 

 signify ''any Value at Pleasure by considering 

 {cT — X'') ^ {a — x) {orn= I, 2, 3, 4, etc. , when x = a.'' 

 This "confutes the Notion of some Mathematicians" 

 that o / o expresses " a Ratio of Equality." Next 

 it is argued that o°=i. " Hence," says a second 

 anonymous critic, "ali Cypher-Paradoxes, and 

 Mysteries of Ultimate Ratios, or Ratios of Least 

 Increments or Decrements of Quantities, vanish and 

 Day appears. ..." 



" Waltoniensis, making a Distinction between 

 signifying some Quantity, and o signifying no 

 Quantity, or absolute Nothing, says that when x 



* Principia^ Bk. II, Lemma 2. See our §§ 16-19. 



