Mtfcellanea Curio [a. 131 



Area. Put VaHVss hence .v :S zz, ~* a, 



xx 



and Therefore « fes izSz,*-* 



\^ x-Va 



and confequently | — 2^, or \ r f 



V f x\a will be the Area fought. 



But it often happens that we meet with 

 fome Curves (fuch as the Circle and Hyper- 

 bola) which are of fuch a Nature, that 'tis 

 in vain to attempt the freeing the Fluxions 

 of them from Surds. And then reducing 

 the Value of the ordinate into an infi- 

 nite Series, and multiplying the feveral 

 Terms of the Series into the Fluxion of 

 the AbfcilFe (as before) let the Fluent of 

 each of thofe Terms be found, and fo there 

 will arife a new Series^ which will exhibit 

 the Quadrature of the Curve. 



This Method is with the iaine cafe appli- 

 ed to the MenfuratUn of the Solids generated 

 by the Rotation o c a Plane j<viz,. taking for 

 their Fluxions, the Product of the Fluxion 

 of die Abfcifie into the circular Bafts. Let 

 the Proportion of a Square to the inferib'd 

 n 



Circle be'—. The Equation expreffing the 

 1 



Nature of a Circle is yy ~ dx ~* xx - 0 there- 

 fore 4 dxx — x^x is the Fluxion of a Portion 

 K 2 of 



