PRINTED BOOKS, ETC, BEFORE 1734 55 



*'The infinitely small Part generateci by the con- 

 tinuai increasing or decreasing of the Fluxion of a 

 variable Quantity, is called the Fluxion of the 

 Fluxion of that Quantity, or second Fluxion.'' In 

 like manner he defines third Fluxion ; ' ' fluxion of 

 the second fluxion" taking the place of " différence 

 de la différence seconde." 



In the appendix, containing Stone's Inverse 

 Method of Fluxions, a fluent is defined thus : 



' ' The fluent or flowing Quantity of a given 

 fluxionary Expression, is that Quantity whereof 

 the given fluxionary Expression is the Fluxion." 



Remarks 



73. The earliest treatment of the new analysis 

 which became current in England was that of 

 Leibniz. The Scotsman Craig used it for over 

 a quarter of a century before rejecting it in favour 

 of fluxions. Harris, Hayes, and Stone drew their 

 inspiration from French writers who followed 

 Leibniz. A hopeless confusion arose in the use of 

 the term ''fluxion." Newton always took it to be 

 a velocity, but many writers, including Newton's 

 friends who prepared the Corniate rcium Episiolicum, 

 simply said "fluxion" instead of " differential, " 

 thus putting a home label upon goods of foreign 

 manufacture. A strict foUower of the Newton of 

 1704 was Ditton ; fluxions are taken as infinitesimals 

 by Fatio de Duillier, Cotes (in 1701), Harris, Hayes, 

 Raphson, Stirlìng (in 17 17), and Stone. 



Stone Comes out strongly with the view that a 



