272 LIMirS AND FLUXIONS 



** A limit, according to the notions of the 

 ancients, is some fixed quantity, to which another 

 of variable magnitude can never become equal, 

 though in the course of its variation it may approach 

 nearer to it than any difìference that can be 

 assigned. " Thus, the method of limits is bere 

 ascribed by the translators to the ancients, which 

 is an act of reading into the ancient expositions a 

 theory not actually there. The ancient * ' Method 

 of Exhaustions " is merely a prelude to the theory 

 of limits. Peacock gives in Note A a history of 

 the theory of limits, in which researches on the 

 Continent are dwelled upon and the contribution 

 made by Newton is explained, but no reference is 

 made to Jurin, Robins, and Maclaurin. In Note B 

 Peacock states that the method used by Lacroix in 

 this treatise " was first given by D'Alembert, in 

 \}[i^ Encyclopédie'' z.xWq\q '* Différentiel. " Evidently 

 Peacock was not altogether friendly toward this 

 method, for in Note B he proceeds " directly to 

 show in what manner this calculus may be estab- 

 lished upon principles which are entirely indepen- 

 dent of infinitesimals or limits," and then informs 

 the reader **that we are indebted for the principal 

 part of the contents of this note, to the Calcul des 

 P'onctions of Lagrange and the large treatise by our 

 author, on the Differential and Integrai Calculus." 

 Peacock proceeds to give an account of Lagrange's 

 calculus of functions and of the method of fluxions. 

 Attention is called to ''the difìfìculty of denoting 

 the operations of finding the difìferent orders of 



