1 48 Mifcellanea Cufiofa. 



T H E O R. III. 



Let A be the Area of a Curve whofe 

 Abfciffe is *, and its Ordinate Applicate 



x* \)rr~-xxy let B be the Area of a Curve 

 whofe Abfciffe is alfo x, and its Ordinate 



m~-2n >— — -™ 

 x V rr—xx. 



Let V rr—xx—y. Then will A— r n2 B in- 



to 5^ mto — into — into j^&c-P. 



-~ — into — ~ at y 3 — — H. 



— — mto -v- mt ° — x y 



&c \ 

 COROL I. 



If m be expounded by any Term of the 

 following Series, 1, 3, 5, 7? 9, &c the Qua- 

 drature of the Curve whofe Ordinate is 



pi 1— — — - m i- — 



x yrr—xx^ or x V rr^-xx, is had in finite 

 Terms, and that by the help of this Theo- 

 rem* 



COROL, 



