Introductio in analysin infinitorum

246 DE SERIEBUS EX LIB. I. Multiplicetur hæc expressio per $\frac{1+\frac{1}{3}}{1-\frac{1}{3}} = 2$, crit $\pi = \frac{1}{(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{5})(1+\frac{1}{7})(1+\frac{1}{11}) \text{ \&c.}},$ $\pi = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} - \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} - \frac{1}{11} \text{ \&c.}},$ ubi binarius signum habet $+$; ternarius $+$; reliqui numeri primi omnes formæ $4m-1$ signum $-$; at numeri primi formæ $4m+1$ signum $+$; & unde pro numeris compositis ratio signorum intelligitur. Simili modo, cum fit $\pi = \frac{1}{(1-\frac{1}{2})(1-\frac{1}{3})(1+\frac{1}{5})(1-\frac{1}{7})(1-\frac{1}{11}) \text{ \&c [TRUNCATED]