Introductio in analysin infinitorum

LIB. I. 126 DE INVESTIGATIONE $(1 - \frac{2gv-vv}{16\varpi\varpi-gg})$ &c. $= (1 - \frac{v}{g})(1 + \frac{v}{g})(1 + \frac{v}{2\varpi-g})$ $(1 - \frac{v}{2\varpi+g})(1 - \frac{v}{2\varpi-g})$ $(1 - \frac{v}{4\varpi+g})$ &c. $= (1 - \frac{vv}{gg})(1 - \frac{vv}{(2\varpi-g)^2})$ $(1 - \frac{vv}{(2\varpi+g)^2})(1 - \frac{vv}{(4\varpi-g)^2})(1 - \frac{vv}{(4\varpi+g)^2})$ &c.. Secunda combinatio dat $\frac{fin. g+fin. v}{fin. g} = 1 + \frac{v}{fin. g} - \frac{v^3}{1.2.3 fin. g} + \frac{v^5}{1.2...5 fin. g}$ &c. $= (1+\frac{v}{g})(1+\frac{2gv-vv}{\varpi\varpi-gg})(1-\frac{2gv-vv}{4\varpi\varpi-gg})(1+\frac{2gv [TRUNCATED]