Introductio in analysin infinitorum

164 DE REALI FUNCTIONUM LIB. I. posito $z^n = f^n \cos n\phi$, fit $M=P$ ..... $z^n = f^n \sin n\phi$, fit $M=p$ ..... $z^n = f^n \cos n\phi$, fit $Z=Q$ ..... $z^n = f^n \sin n\phi$, fit $Z=q$ ..... $z^n = f^n \cos n\phi$, fit $zZ=R$ ..... $z^n = f^n \sin n\phi$, fit $zZ=r$ Inventis hoc modo valoribus $P, Q, R, p, q, r$ erit $A = \frac{PR-pR}{QR-qR}$, & $A = \frac{PQ-pQ}{QR-qR}$. EXEMPLUM I. Si fuerit proposita hæc Functio fracta $\frac{zz}{(1-z+zz)(1+z^4)}$ ex qua partem a denominatoris Factore $1-z+zz$ oriundam definire oporteat, quæ fit $\frac{A+Az}{1-z+zz}$. Ac primo quidem hic Factor, cum forma generali $pp-2pqz \cos \phi + qqzz$ comparatus, dat $p=1, q=1$ & $\cos \phi = \frac{1 [TRUNCATED]