1 4 $ Mifcellanea Cur to fa . 



COROL Hi 



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

 lowing Series, i , 2, 3, 4, 5, 6, 7, &c. Every 



— n 



x 



Curve whofe Ordinate is 



— w 



\/ dx-\-xx 

 Terms. 



\] dx xx 

 is fquared by this Series in finite 



COROL. III. 



If m be expounded by any Term of the 

 following Series, o, 1, 2, 3, 4, 5, 6, 7? &c. 



m 

 x 



the Gurve whofe Ordinate is — , de- 



\l dx~*xx 



pends upon the Quadrature of the Circle. 



But the Curve whofe Ordinate is 



m 



x 



\ldxA 



t 'XX 



depends upon the Quadrature of the Hy- 

 perbola. 



For if on the Center C, (Fig.20.) the Diame- 

 ter AB t=J d^ the Circle AEB be defcribed, and 

 AD be taken s=s x, alfo erecting the Perpendi- 

 cular DEj the Line CE be drawn. Then the 



Se-r 



