236 NEW MODE OF REPRESENTING 



y — f (.r), for explicit functions of cV (1). 



f (_y, x) = for implicit functions of x ...(2). 



This convenient and powerful notation was 

 first used, I believe, by Lagrange, whose powers, 

 to create symmetrical symbols designed to repre- 

 sent groups of ideas, were almost unlimited. 



Fig. 2. 



(2). If, as in Fig. 2, when x becomes equal to 

 AB ~ a, the function of x be changed to some 

 other function of x represented by ^\{x)\, and 

 when X becomes equal AB'=6, the function of x 

 be changed to ii{x) ; and so on, that is, if we take 



xj=i{x);y = f,(a-) ; y = U{,v) &c. &c. 



the first to exist for all values of x between the 

 limits .r = and .r rr a ; the second to exist for all 

 values of x between the limits x = a and .r r: i ; 

 the third between the limits x = h and x — c, &c. 

 &c. Then these functions are denominated by 



