JMifcellanea Cur i of a. 255 



AB -=^y 1 the Ordinate BD = the Arc of 

 the Parabola AC = v. And let the General 

 Equation expreffing the Nature of Infinite 

 irrational Curves be this, Z = rvy\ in which 

 r denotes a given and determinate Quantity, 

 and n an indefinite Exponent of the indeter- 

 min'd Quantity^. 1 fay the Area 



ABD = ~* V — qv 4 \]%*y -\-y*x — 



ra 



yH-x ^=-^ 4 



*4 2X^| .l «u|-2X»4i| 



— i — a / *"""* y 1 



^x^lax^-r 11 * — 1 



aB% i x — 3 _ aC% n _ ± , & ^ 



#~2 » — 3 



In this Series 'tis to be noted : (1.) That 

 the Capital Letters A, B, C, &c. denote the 

 Coefficients of the Term preceding them. 

 (2.) That if the Exponent n be an Integer 

 a id Pofitive, or equal to nothing, or if in be 

 an odd Number, then the Quadrature may 

 be exhibited by a finite Number of Terms ; 

 the Series in thefe Cafes breaking off. (3.) 

 That 4 ls equal to the Term laft breaking 

 off. (4.) That of the Terms multiplying the 



Quantity V lay -|- y 2 , the laft breaking off is 

 to be doubl'd. (5.) That all thofe Figures 

 in which n is an Integer, Pofitive and an odd 

 Number, or more generally, all thofe Fi- 

 gures in which the laft Term breaking off 



has 



