Introductio in analysin infinitorum

302 DE FRACTIONIBUS LIB. I. $\frac{B}{A} = \frac{\mathfrak{G}}{Q}$; $\mathfrak{G} = \frac{B Q}{A}$ $\frac{C}{B} = \frac{\gamma P}{R}$; $\gamma = \frac{C R}{B P}$ $\frac{D}{C} = \frac{\delta Q}{S}$; $\delta = \frac{D S}{C Q}$ $\frac{E}{D} = \frac{\epsilon R}{T}$; $\epsilon = \frac{E T}{D R}$ \&c. \&c. Porro vero differentiis sumendis habebitur $A-B = \frac{a(Q - \mathfrak{G})}{PQ} = \frac{ac}{Q} = \frac{A P c}{Q}$ $B-C = \frac{a\mathfrak{G}(R - \gamma P)}{PQR} = \frac{a\mathfrak{G}d}{PR} = \frac{B Q d}{R}$ $C-D = \frac{a\mathfrak{G}\gamma(S - \delta Q)}{QRS} = \frac{a\mathfrak{G}\gamma e}{QS} = \frac{C R e}{S}$ $D-E = \frac{a\mathfrak{G}\gamma\delta(T - \epsilon R)}{RST} = \frac{a\mathfrak{G}\gamma\delta f}{RT} = \frac{D S f}{T}$, \&c. \&c. \&c. Si bini igitur in se invicem ducantur, fiet $(A-B)(B-C) = ABcd \cdot \frac{P}{R}$; \& $\frac{R}{P} = \frac{A Bcd}{(A-B)(B-C)}$ $(B-C)(C-D) = BCde \cdot \frac{Q}{S}$; \& $\frac{S}{Q} = \frac{B Ced}{(B-C)(C-D)}$ $(C-D)(D-E) = CDef \cdot \frac{R}{T}$; \& $\frac{T}{R} = \frac{C Def}{(C-D)(D-E)}$ \&c. Unde, cum sit $P=b$; $Q = \frac{ac}{A-B} = \frac{Abc}{A-B}$, erit $a = Ab$ $\mathfrak{G} = \frac{Bbc}{A-B}$ $\gamma = \frac{ACcd}{(A-B)(B-C)}$ $\delta =$