38 DISSERTATION SECOND. Jpart ». 



Another very original and profound writer of this period 

 was Brook Taylor, who has already been often mentioned, 

 and who, in his Method of Increments, published in 1715, 

 added a new branch to the analysis of variable quantity. 

 According to this method, quantities are supposed to change, 

 not by infinitely small, but by finite increments, or such as 

 may be of any magnitude whatever. There are here, there- 

 fore, as in the case of fluxions or differentials, two general 

 questions : A function of a variable quantity being given, 

 to find the expression for the finite increment of that function, 

 the increment of the variable quantity itself being a finite 

 magnitude. This corresponds to the direct method of flux- 

 ions ; the other question corresponds to the inverse, viz. A 

 function being given containing variable quantities, and their 

 increments any how combined, to find the function from 

 which it is derived. The author has considered both these 

 problems, and in the solution of the second, particularly, has 

 displayed much address. He has also made many ingenious 

 applications of this calculus both to geometrical and physical 

 questions, and, above all, to the summation of series, a pro- 

 blem for the solution of which it is peculiarly adapted. 



Taylor, however, was more remarkable for the ingenuity 

 and depth, than for the perspicuity of his writings ; even a 

 treatise on Perspective, of which he is the author, though in 

 other respects excellent, has always been complained of as 

 obscure ; and it is no wonder if, on a new subject, and one 

 belonging to the higher geometry, his writings should be still 

 more exposed to that reproach. This fault was removed, 

 and the whole theory explained with great clearness, by M. 

 Nicol, of the Academy of Sciences of Paris, in a series of 

 Memoires from the year 1717 to 1727. 



A single analytical formula in the Method of Increments 

 has conferred a celebrity on its author, which the most 

 voluminous works have not often been able to bestow. It 



