ROBERT HEATH v. JOHN TURNER 221 



passed over together by those instantaneous Veloci- 

 ties^ uniformly continued ; but are not the Spaces or 

 Ouantities themselves that would be described by 

 them according to Mr. SimpsorCs new Theory, and 

 Application. See Emerson' s Doctrine and Applica- 

 tion of Fluxions. Price 6s. only." 



195. In the Ladies' Diary for 1752 the reader 

 is amused by satirical remarks on mathematicians. 

 There is also a continuation of the discussion ** Of 

 the Cypher-Value and Office of the Algebraic 

 Quantity ^." *' Nihil Maximus says that -9999, 

 etc. ad inf. will never converge to i, nor yet 

 I / (10,000, etc. ad inf.) to o\ because any Quantity 

 infinitely increased or diminished will be stili greater 

 or less, and never numerically arrive at Infinity, and 

 Value. . . . That a Distinction should be care- 

 fully made between what are called infinite and 

 indefinite great and small Quantities {the former of 

 which being impossible) ; for what is of indefinite 

 Value has Equality, tho' it may be sometimes un- 

 assignable ; while what is infinite is never determin- 

 able, and has never Equality. Hence the numerical 

 Value of and i / (1000, etc), will be for ever 

 different ; one being a Quantity of no sensible 

 Value, but yet significant, and the other of indefi- 

 nite small Value. . . . Infinite Quantity, or in- 

 finite numerical Value, expressed by Authors, is 

 neither practicable nor comprehensible. . . . An 

 infinite Series can never precisely converge to a 

 finite or determinate Value ; because it for ever ì-uns 

 on. The finite Value, taken for that of an infinite 



