2i8 LIMITS AND FLUXIONS 



express'd in infinite Time ; in which Sense the 

 algebraic Increases being again diminish'd, are said 

 never to converge to the Limits of their geometrical 

 Magnitudes in Motion, but will stili have sensible 

 Value ; yet supposing the geometrie Increases, and 

 their algebraic Values to flow and decrease alike, 

 to something determinate, then o^ and <?, and it's 

 Powers into a Variable Quantity, and it's Powers, 

 will accurately express the Limits of variable Quan- 

 tities, or Beginnings of their Increases ; which 

 Limits^ or Beginnings of Increases of Ouantities, 

 are accurately, as the Fluxions of those Ouantities 

 in general." 



" Visionarius " closes with a philosophic vision in 

 which four candidates for honors appear before the 

 Goddess of Science. Rejected are the first three, 

 viz. the author of M atheinatical Exercises (John 

 Turner), the one holding to the motto ** A cypher 

 is no Algebraic Quantity " (Bishop Berkeley), and 

 a Grand Magnifier of Fluxions (Thomas Simpson) ; 

 crowned is the author of the incomparable treatises 

 of Fluxions and Trigonometry (William Emerson), 

 in whose interests Truth Triuniphant appears to be 

 mainly written. 



192. The probability is that the **scurrilous 

 pamphlet " to which John Turner made reply in 

 an issue of his Mathematical Exercises was only a 

 part of what is given in Truth Triuniphant. The 

 latter is probably a later and enlarged publication. 

 In that reply Turner argues that ** it must appear to 

 everyone that, what Mr. Simpson defines as Fluxions, 



