MifceUaneoL Curio fa. 153 



a&ly fquar'd, nor does it depend upon the 

 Circle or the Hpperbola, but is reduced to 

 a more ample Curve. 



T H E O R. V. 



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



x m 



fcifle is x r and its Ordinate *, let B be 



d'—'X 



the Area of a Curve, whofe Abfcifle alfo is 

 x m — n 



■ x y and its Ordinate • — — Then will A= 



d\ — *x N 



x ™ dx m ~ l ddx m ~ 2 



rf»B— — — — « — &c. 



m — »i m — 2 



m 



Let the Ordinate be — and then the 



^ dx m ~ l ddx m ~ 2 

 Area A will == -~ - 1 — — — &c ;± 



d n B. 



C O R Q L 



If w be expounded by any Term of the 

 following Series, i, 2, 3, 4> 5? ^ & c - the 

 Quadrature of the Curve, whofe Ordinate 



x m x m ' 

 is — . or ' — ■ — , depends upon the Quadra- 

 d*—~x d-\-x 



ture 



