JVlifceUanea Curiofd. 14.3 



im, a Quantity infinitely fmall, or rather 

 nothing j the Quantity exprefs'd by P is In- 

 finite and for the fame reafon the Quan- 

 tity exprefs'd by — « S is Infinite, and fa the 

 Quantities A, -^O^ -'R, do vanifh. There- 

 fore P»S, and dividing the Equation by 



2m-\~i . 2m — 1 , „ 7m— 2 

 into — r-f we have d n B into ■ 



2ra-\~4. 2m-\-2 %m 



dd m—i . . . 2wi— 3 w— .3 

 53 — # y 3 or #B into — — si <sw# y 5 • 



and putting 0 and 3 for and there will 

 be dB into - i or B= 



x 3 3** 



COROL. III. 



If m be put equal to any Term of the fol- 

 lowing Series, 2, 1, o, 1, 2, 3, 4, 5, &c. 

 the Quadrature of the Curve, whofe Ordi- 



m > : — 



nate is * Vdx^xx, depends upon the Qua- 

 drature of the Circle. But the Area of the 



m i~ • 



Curve, whofe Ordinate is x ydx~\~xx 7 de- 

 pends upon the Quadrature of the Hyper- 

 bola \ and the relation of that Curve to the 

 Circle of the Hyperbola, is exhibited by our 

 Series in finite Terms. 



coro l: 



