154 Mijcellanea Curiofa. 



ture of the Hyperbola. For (See ftg* 22.) 

 drawing DE, EF at right Angles, take EG 

 -=r~d, and draw GH at right Angles to EF, 

 and equal to it. Within the Afymptotes 

 DE, EF, let an Hyperbola be defcrib'd, 

 pafling through the point H ; which done, 

 take GR=a', towards E in the firft Cafe, and 

 towards F in the fecond ; and draw the Or- 

 dinate KL. Then the Area HGKL divided 

 by dd 7 is equal to the Area of the Curve, 



x° x° 



whofe Ordinate is — ■ — or — < % Hence the 



d<— *x d-\-x 

 Solid generated by a Portion of the Cijfold^ 

 while it turns about the Diameter of the 

 Generating Circle, is exhibited in finite 

 Terms, fuppofing the Quadrature of the Hy- 

 perbola. 



THEOR. VI. 



Let A be the Area of a Curve, whofe Ab* 



x m 



fcilfe is at, and Ordinate — ; let B be 



rr~\-xx 



the Area of a Curve, whofe Abfciffe is alio 



— . Then will the 



rr-\-xx 



rrx m ~l r+x* 1 -! 



1- &C, 



1 ^ 3 5 



COROL 



