Introductio in analysin infinitorum

FRACTARUM EVOLUTIONE. 167 CAP. XII. $A = \frac{1836}{2136} = \frac{153}{178}$ ; $A = \frac{540}{2136} = \frac{45}{178}$. Quare fractio ex Factore $1 - \frac{8}{5}z + zz$ oriunda erit $\frac{9(17-5z):178}{1 - \frac{8}{5}z + zz}$. Quæramus simili modo fractionem alteri Factori respondentem; erit $p=1, q=-\sqrt{3}$ & $cof. \Phi = \frac{1}{\sqrt{3}}$, ergo $f = -\frac{1}{\sqrt{3}}$, $M = 1+2z+zz$ & $Z = 1 - \frac{8}{5}z + zz$. Fiet autem, ob $cof. \Phi = \frac{1}{\sqrt{3}}$, $sin. \Phi = \frac{\sqrt{2}}{\sqrt{3}}$ $cof. 2\Phi = -\frac{1}{3}$, $sin. 2\Phi = \frac{2\sqrt{2}}{3}$ $cof. 3\Phi = -\frac{5}{3\sqrt{3}}$, $sin. 3\Phi = \frac{\sqrt{ [TRUNCATED]