Introductio in analysin infinitorum

FRACTARUM EVOLUTIONE 169 CAP. XII. posito $z^n = \frac{p^n}{q^n} . \cos. n\Phi$, fit $M = P$, & $Z = Q;$ & posito $z^n = \frac{p^n}{q^n} . \sin. n\Phi$, fit $M = P$, & $Z = Q:$ ubi notandum est Functiones $M$ & $Z$, antequam haec substitutio fiat, omnino evolvi debere, ut hujusmodi habeant formas $M = A+Bz+Cz^2+Dz^3+Ez^4+\&c.,$ & $Z = \alpha + \mathfrak{b}z + \gamma z^2 + \delta z^3 + \varepsilon z^4 + \&c.;$ eritque ideo $P = A+B\frac{p}{q}.\cos.\Phi+C\frac{p^2}{q^2}.\cos.2\Phi+D\frac{p^3}{q^3}.\cos.3\Phi+\&c.$ $P = B\frac{p}{q}.\sin.\Phi+C\frac{p^2}{q^2}.\sin.2\Phi+D\frac{p^3}{q^3}.\sin.3\Phi+\&c.$ $Q = \alpha+\mathfrak{b}\ [TRUNCATED]