Introductio in analysin infinitorum

EVOLUTIONE FACTORUM ORTIS. 247 291. Possunt etiam innumerabiles hujusmodi Series exhiberi, quarum summa fit $= 0$. Cum enim fit C A P. X V. $0 = \frac{2}{3} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot \frac{7}{8} \cdot \frac{11}{12} \cdot \frac{13}{14} \cdot \frac{17}{18} \cdot \&c.,$ erit $0 = \frac{1}{(1+\frac{1}{2})(1+\frac{1}{3})(1+\frac{1}{5})(1+\frac{1}{7})(1+\frac{1}{11})(1+\frac{1}{13}) \&c.,}$ unde, ut supra vidimus, oritur $0 = 1 - \frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \frac{1}{5} + \frac{1}{6} - \frac{1}{7} - \frac{1}{8} + \frac{1}{9} + \frac{1}{10} \&c.,$ ubi omnes numeri primi signum habent —; compositorumque numerorum signa regulam multiplicationis sequuntur. Multiplicemus autem illam expressionem per [TRUNCATED]