Introductio in analysin infinitorum

RECURRENTIBUS. 183 $\frac{a-2apz\cos\Phi+appzz}{(1-2pz\cos\Phi+ppzz)^2}$ ortae terminus generalis est = $\frac{a\sin(n+1)\Phi}{\sin\Phi} p^n z^n$. Addantur hae fractiones invicem, ac ponatur $a+f=A$; $2a\cos\Phi+2f\cos\Phi-2g\sin\Phi=B$ & $a+f\cos2\Phi-g\sin2\Phi=0$, hinc erit $g=\frac{B+2A\cos\Phi}{2\sin\Phi}$, $a=\frac{A+B\cos\Phi}{1-\cos2\Phi}=\frac{A+B\cos\Phi}{2(\sin\Phi)^2}$ & $f=\frac{A\cos2\Phi-B\cos\Phi}{2(\sin\Phi)^2}$, & $g=\frac{B\sin\Phi+A\sin2\Phi}{2(\sin\Phi)^2}$. Hanc ob rem Seriei ex hac fractione $\frac{A+Bpz}{(1-2pz\cos\Phi+ppzz)^2}$, ortae terminus generalis est $\frac{A+B\cos\Phi}{2(\sin\Phi)^3}\sin(n+1)\Phi \cdot p^n z^n [TRUNCATED]