Introductio in analysin infinitorum

LIB. I. 168 DE REALI FUNCTIONUM Fractio ergo proposita $\frac{1+2z+zz}{(1-\frac{8}{5}z+zz)(1+2z+3zz)}$ resolvitur in $\frac{9(17-5z):178}{1-\frac{8}{5}z+zz} + \frac{5(5+27z):178}{1+2z+3zz}$. 204. Possunt autem valores litterarum $R$ & $\mathfrak{R}$ ex litteris $Q$ & $\mathfrak{Q}$ definiri, cum enim fit $Q = a + \epsilon f.\text{cof.}\Phi + \gamma f^2.\text{cof.}2\Phi + \delta f^3.\text{cof.}3\Phi \text{ \&c.}$ $\mathfrak{Q} = \epsilon f.\text{sin.}\Phi + \gamma f^2.\text{sin.}2\Phi + \delta f^3.\text{sin.}3\Phi \text{ \&c.}$ erit $Q.\text{cof.}\Phi - \mathfrak{Q}.\text{sin.}\Phi = a.\text{cof.}\Phi + \epsilon f.\text{cof.}2\Phi + \gamma f^2.\text{cof.}3\Phi + \text{\&c.}$ ideoque $\mathfrak{R} = f(Q.\text [TRUNCATED]