Introductio in analysin infinitorum

170 DE REALI FUNCTIONUM LIB. I. $ \frac{\mathrm{A}+\mathrm{A}z}{(pp-2pqz\cos.\Phi+qqzz)^2} + \frac{\mathrm{B}+\mathrm{B}z}{pp-2pqz\cos.\Phi+qqzz} $, ubi litteras constantes $A$, $\mathrm{A}$, $B$, $\mathrm{B}$ determinari oportet. 207. His positis, debebit ista expressio $ \frac{M-(\mathrm{A}+\mathrm{A}z)Z-(\mathrm{B}+\mathrm{B}z)Z(pp-2pqz\cos.\Phi+qqzz)}{(pp-2pqz\cos.\Phi+qqzz)^2} $ esse Functio integra, & hanc ob rem numerator divisibilis erit per denominatorem. Primum ergo haec expressio $ M - AZ - \mathrm{A}zZ $ divisibilis esse debet per $ pp - 2pqz\cos.\Phi + qqzz $; qui cum sit casus praecedens, codem quoque modo litterae $A$ & $\mathrm{A}$ determinabuntur. Quare, posito $ z^n = \frac{p^n}{q^n}\cos.n\phi $, fit $ M=\mathrm{P} $, & $ Z=\mathrm{N} $: &, posito $ z^n = \ [TRUNCATED]