Introductio in analysin infinitorum

CONTINUIS. 305 CAP. XVIII. $\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \&c.,$ ubi $π$ denotat peripheriam circuli, cujus diameter $= 1$, in fractionem continuam. Substitutis loco $A, B, C, D, \&c.,$ numeris $1, 3, 5, 7, \&c.,$ orietur $\frac{\pi}{4} = \frac{1}{1+\frac{1}{2+\frac{9}{2+\frac{25}{2+\frac{49}{2+\&c.}}}}}$ hincque, invertendo fractionem, erit $\frac{4}{\pi} = 1 + \frac{1}{2+\frac{9}{2+\frac{25}{2+\frac{49}{2+\&c.}}}}$ quae est expressio, quam BROUNCKERUS primum pro quadratura circuli protulit. EXEMPLUM III. Sit proposita ista Series infinita $x = \frac{1}{m} - \frac{1}{m+n} + \frac{1}{m+2n} - \frac{1}{m+3n} + \&c.,$ quae, ob $A=m; [TRUNCATED]