Introductio in analysin infinitorum

244 DE SERIEBUS EX LIB. I. ubi ratio signorum ita est comparata, ut binarius habeat $-$; numeri primi formæ $4m-1$ signum $-$; & numeri primi formæ $4m+1$ signum $+$; numeri autem compositi ea habent signa, quæ ipsis ratione multiplicationis ex primis conveniunt. Sic patebit signum fractionis $\frac{1}{60}$, ob $60 = 2 \cdot 2 \cdot 3 \cdot 5$, quod erit $-$. Simili modo porro erit $\frac{\pi}{2} = \frac{1}{(1-\frac{1}{2})(1+\frac{1}{3})(1-\frac{1}{5})(1+\frac{1}{7})(1+\frac{1}{11})(1-\frac{1}{13}) \&c.}$, unde orietur hæc Series $\frac{\pi}{2} = 1 + \frac{1}{2} - \frac{1}{3} + \frac{1}{4} + \frac{1}{5} - \frac{1}{6} - \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} \&c.$, ubi binarius habet signum $+$; numeri primi formæ $4m-1$ signum $-$; numeri primi formæ $4m [TRUNCATED]