tip jMifcetlaneA Curio fa. 

 fore 2 wt i ttOy and therefore A w 



- ^ 2 ^ 

 ^3 »— i 



It is here to be obfervM, that the Area 

 thus found, is fometimes deficient from the 

 true Area, by a given Quantity, or exceeds 

 it by that fame given Quantity. And in or- 

 der to find that Defett or £xcefs y let the 

 Area found be fuppos'd to be encreas'd or 

 diminiftVd, by a given Quantity and then 

 putting x r=3 0, let the Area increased or di- 

 niiniih'd, be fuppos'd 5=3 0. Thus in the pre- 

 fent cafe, we mail find ^s=sf ds/d, and con- 

 fequently Aw f — 27* 



COROL II. 



If # be put equal to any Term of the 

 following Series, 3, 4, 5, <5, 7, &c. then the 

 Quadrature of the Curve whofe Ordinate is 



—* xx? or x \l dx -\-xx, is exprcf- 

 fed in finite Terms, and is found by our Se- 

 ries. 



Let the Area of the Curve be to be 



found, whofe Ordinate is ~ x V dx XX. 

 Suppofe it to be compared with the Area of 

 a Circle, which call A. Then will mmo^ 

 3, and fo A t=i.P ^ Q_~* R §. But 

 fince, in the Denominator of the third Term 

 by which d n B is multiplied, there is found 



