Introductio in analysin infinitorum

304 DE FRACTIONIBUS LIB. I. $α = \frac{b}{A}$; $β = \frac{Abc}{B-A}$; $γ = \frac{B^2cd}{(B-A)(C-B)}$; $δ = \frac{C^2de}{(C-B)(D-C)}$; $ε = \frac{D^2ef}{(D-C)(E-D)}$; &c. Ponatur ergo ut sequitur $b = A$; $c = B - A$; $d = C - B$; $e = D - C$; $α = 1$ $β = AA$ $γ = BB$ $δ = CC$ &c., eritque per fractionem continuam $x = \frac{1}{A+\frac{AA}{B-A+\frac{BB}{C-B+\frac{CC}{D-C+\text{&c.}}}}}$ EXEMPLUM I. Transformetur hac Series infinita $1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \text{&c.},$ in fractionem continuam. Erit ergo $A=1$, $B=2$, $C=3$, $D=4$, &c., atque, cum Seriei propositae valor fit $=l2$, [TRUNCATED]