Introductio in analysin infinitorum

FRACTARUM EVOLUTIONE. 165 $\frac{1+z+zz}{1+z^4}$, cujus denominator $1+z^4$ cum habeat Factores $1+z\sqrt{2}+zz$ & $1-z\sqrt{2}+zz$, resolutio denuo suscipi potest; fit autem $\Phi = \frac{\pi}{4}$ & priori casu $f = -1$ posteriori $f = +1$. CAP. XII. EXEMPLUM. II. Sit igitur proposita hæc fractio resolvenda $\frac{1+z+zz}{(1+z\sqrt{2}+zz)(1-z\sqrt{2}+zz)}$ & erit $M = 1+z+zz$; & pro priore Factore habebitur $f = -1$; $\Phi = \frac{\pi}{4}$, & $Z = 1-z\sqrt{2}+zz$, unde erit $P = 1 - \cos.\frac{\pi}{4} + \cos.\frac{2\pi}{4} = \frac{\sqrt{2}-1}{\sqrt{2}}$ $P = - \sin.\frac{\pi}{4} + \sin.\frac{2\pi}{4} = \frac{\sqrt{2}-1}{\sqrt{2}}$ $Q = 1 + \sqrt{2}.\cos.\frac{\pi}{4} + \cos.\frac [TRUNCATED]