CRITICI SMS BY BRITISH WRITERS 271 



Lacroix's '■^ Elementary Treatise,'' 18 16 



230. The translation of Lacroix's Elementary 

 Trenti se on the Differential and Integrai Calculus ^ 

 in 18 16 marks an important period of transition. 



From the '* Advertisement " we quote : 



This work of Lacroix '' may be considered as an 

 abridgement of his great work on the Differential 

 and Integrai Calculus, although in the demonstra- 

 tion of the first principles, he has substituted the 

 method of limits of D'Alembert, in the place of the 

 more correct and naturai method of Lagrange, 

 which was adopted in the former. The first part 

 of this Treatise, which is devoted to the exposition 

 of the principles of the Differential Calculus, was 

 translated by Mr. Babbage. The translation of the 

 second part, which treats of the Integrai Calculus, 

 was executed by Mr. G. Peacock, of Trinity College, 

 and by Mr. Herschel, of St. John's College, in nearly 

 equal proportions." 



On p. 2 the process of differentiation of u^ax^ 

 is explained, so that 2ax " is the Hmit " of the ratio 

 {u' — u) I h, or it is **the value towards which 

 this ratio tends in proportion as the quantity // 

 diminishes, and to which it may approach as near 

 as we choose to make it. " 



Thus Lacroix's definition, like D'Alembert's, does 

 not prohibit the limit to be reached. In Note A, 

 added by the translators, we read : 



^ Alt Elementary Treatise on the Diffei ential and Integrai Calculus. 

 By S. F. Lacroix. Translated from me French. Cambridge. 1816. 



