and INFINITE SERIES,

185 bx^p* _ ab ^ab 1 , &c. ~a^b t &c. +TT* , &c. Make ax 1 -f- bx* the firfl Term of 2/>, then will frf.v l -f- f &v "be the firfl Term of /. Therefore abx* b*x* will be the firfl Term of 2bx*p, and ^a*x* -f- -^abx* -f- -^bx* will be the firfl Term of/*. Thefe being collected, and their Signs changed, muil be made the fecond Term of 2/, which will give abx* -f- |J*A %a*x* for the fecond Term of/. Then the fecond Term of 2bx*p will be -^ab^x 6 l>*x 6 -f- ^a i bx 6 > and the fecond Term of p* (by fquaring) will be found f a l bx 6 +- ab*x 6 j-aX 6 -{- $frx 6 , and the firfl Term of bx*p l will be ^a^bx 6 -^ab'-x 6 f^'AT 4 ; which being collected and the Signs changed, will make the third Term of 2p, half which will be the third Term of p ; and fo on as far as you pleafe. And thus if we were to extract the Cube-root of a* 4- x*, or the Root y of this Equation 7' = a 3 4- tf 3 j make y = a -f-/, then by Subflitution a 3 -f- 3d 1 / -f- ^ap 1 -+- p> = & -+- x*, or 3 i / -f = A: S , which fupplemental Equation may be thus refolved. 243 l B b The