Introductio in analysin infinitorum

NUMERORUM. 259 $(1+x^2z)(1+x^3z)(1+x^4z) \&c. = \frac{Z}{1+xz}$ CAP. XVI. ergo, posito $xz$ loco $z$, valor producti, qui erat $Z$, abibit in $\frac{Z}{1+xz}$; sicque, cum fit $Z = 1 + Pz + Qz^2 + Rz^3 + Sz^4 + \&c.$ erit $\frac{Z}{1+xz} = 1 + Pxz + Qx^2z^2 + Rx^3z^3 + Sx^4z^4 + \&c.,$ multiplicetur ergo actu per $1+xz$, atque prodibit $Z = 1 + Pxz + Qx^2z^2 + Rx^3z^3 + Sx^4z^4 + \&c.$ $+ xz + Px^2z^2 + Qx^3z^3 + Rx^4z^4 + \&c.,$ qui valor ipsius $Z$ cum superiori comparatus dabit $P = \frac{x}{1-x}$; $Q = \frac{Px^2}{1-x^2}$; $R = \frac{Qx^3}{1-x^3}$; $S = \frac{Rx^4}{1-x^4}$ \& [TRUNCATED]