Introductio in analysin infinitorum

182 DE SERIEBUS LIB. I. 219. Ad terminum generalem inveniendum, si denominator fractionis fuerit Potestas, ut $(1 - 2pz \cos \Phi + ppzz)^k$, conveniet hanc fractionem resolvi in duas etsi imaginarias $\frac{a}{(1 - (\cos \Phi + \sqrt{-1} \sin \Phi) pz)^k} + \frac{b}{(1 - (\cos \Phi - \sqrt{-1} \sin \Phi) pz)^k}$ quarum simul sumtarum terminus generalis Seriei ex ipsis ortae erit $\frac{(n+1)(n+2)(n+3)\dots(n+k-1)}{1 \cdot 2 \cdot 3 \dots (k-1)} (\cos n\Phi + \sqrt{-1} \sin n\Phi) ap^n z^n + \frac{(n+1)(n+2)(n+3)\dots(n+k-1)}{1 \cdot 2 \cdot 3 \dots (k-1)} (\cos n\Phi - \sqrt{-1} \sin n\Phi) bp^n z^n$. Sit $a+b=f$; $a-b = \frac{g}{\sqrt{-1}}$, ut fit $a = \frac{f\sqrt{-1}+g}{2\sqrt{-1}}$ & $b = \frac{f\sqrt{- [TRUNCATED]