Introductio in analysin infinitorum

184 DE SERIEBUS LIB. I. Deinde Seriei ex fractione $\frac{a+bz}{(1-2pz.cof.\Phi+ppzz)}$, seu ex hac $\frac{a-2apz.cof.\Phi+appzz+bpz-2bppzz.cof.\Phi+bp^3z^3}{(1-2pz.cof.\Phi+ppzz)^2}$ ortae terminus generalis est $\frac{(n+3)fin.(n+1)\Phi - (n+1)fin.(n+3)\Phi}{4(fin.\Phi)^3} ap^n z^n + \frac{(n+2)fin.n\Phi - n.fin.(n+2)\Phi}{4(fin.\Phi)^3} bp^n z^n$. Addantur hae fractiones ac ponatur numerator $= A$, erit $a+f = A$. $3f.cof.\Phi - 3g.fin.\Phi + 2a.cof.\Phi - b = 0$, $3f.cof.2\Phi - 3g.fin.2\Phi + a - 2b.cof.\Phi = 0$; & $b = f.cof.3\Phi - g.fin.3\Phi$, hinc erit $a = \frac{f.cof.3\Phi - g.fin.3\Phi - 3f.cof.\Phi + 3g.fin.\Phi [TRUNCATED]