LA TER BOOKS AND ARTICLES 249 



which is otherwise called the Differential Calculus^ 

 or the Method of Fluxions^ is that which is con- 

 versant about the differences of variable quantities, 

 of whatever order those differences may be. " 



"Any infiiiitely little portion of a variable quantity 

 is called it's Difference or Fluxion ; when it is so 

 small, as that it has to the variable itself a less pro- 

 portion than any that can be assigned ; and by 

 which the same variable being either increased or 

 diminished, it may stili be conceived the same as 

 at first." 



On p. 3 we read that certain lines in a figure 

 " will be quantities less than any that can be given, 

 and therefore will be inassignable ^ or differentials^ or 

 infinitesimals^ or, finally, fluxions. Thus, by the 

 common Geometry alone, we are assured that not 

 only these infinitely little quantities, but infinite 

 others of inferior orders, really enter the composi- 

 tion of geometrical extension." 



"These propositions," says a reviewer^ of the 

 translation, '*may appear exceptionable, in point of 

 language, to the rigorists in geometry ; but they are 

 nevertheless founded on good principles, and furnish 

 rules for the comparison of evanescent quantities, 

 which will prove safe guides in investigation. The 

 demonstrations appear to us to be perfectly sound 

 (if the word infinite be taken in its true sense, as 

 denoting merely the absence of any limit), with the 

 exception, perhaps, of the first theorem, which 

 (as is not a little curious to remark) is liable to the 



* Edinburgh Review^ voi. iii, 1805, p. 405, 



