Introductio in analysin infinitorum

RECURRENTIBUS. 181 CAP. XIII. $\frac{A+Bpz}{1-2pz.\cos.\Phi+ppzz}$; $(\frac{A+Bpz}{1-2pz.\cos.\Phi+ppzz})^k$, ex quarum evolutione cujusmodi Series nascantur videndum est. Ac primo quidem, ob $\cos.n\Phi = 2\cos.\Phi.\cos.(n-1)\Phi - \cos.(n-2)\Phi$, fractio $\frac{A}{1-2pz.\cos.\Phi+ppzz}$ evoluta dabit $A+2Apz.\cos.\Phi+2Appzz.\cos.2\Phi+2Ap^3z^3.\cos.3\Phi+2Ap^4z^4.\cos.4\Phi$ $+Appzz, +2Ap^3z^3.\cos.\Phi+2Ap^4z^4.\cos.2\Phi$ &c. cujus Seriei terminus generalis non tam facile apparet. 218. Quo igitur ad scopum perveniamus, consideremus has duas Series $Ppz.\sin.\Phi+Pp^2z^2.\sin.2\Phi+Pp^3z^3.\sin.3\Phi+Pp^4z^4.\sin.4\Phi+\&c.$ $Q+Qpz.\cos.\Phi+Qp [TRUNCATED]