MtjceUanea Curiofa. 141 



Series exprefled by P, is to be multiplied in*- 

 to as many Terms as there are Unities in ri« 

 3. That as many of the following Series ex- 

 prefled by-a,^R^S,-T, &c. are -to be 

 taken, as there are Unities in n. Which to il- 

 luftrate by an Example or two \ If »' s=s i , the 



I fay that A m *B- mo ~ ^ * 



2tfI-Vt . 



and if n^i, then A m dm into into 



5HFT " 5+3 * J ' 7 2j^t 



x™~*y 3 . 4. That if y be put « V f dx - 

 then A will £ Q,- R + S - T, &c- ± P> 



COROL I. 



If w be put pis to any Term of the follow- 

 ing Series - i, i, i, I, |, f, &c. then the 

 Quadrature of the Curve whofe Ordinate is 



m - . . m r 



x Vdx~*xx y or x ydx-y-xx, will be ex- 

 prefled in finite Terms, and be found by 

 our Series. To illuftrate which by^ an Ex- 

 ample or two ; Let it be required to 

 find the Area of a Curve whofe Ordinate is 



x •— xx. Let us imagine this Curve 



to be compar'd with another Curve whofe 



-* / 



Ordinate is at V dx *-* xx. Now becaufe in 

 this cafe «?=ii, therefore will Ass^B -into 



?Hfcf I JL- /~y but w ~ there- 



' 1 £r\ r- « 



