Introductio in analysin infinitorum

LIB. I. 134 DE USU FACTORUM INVENTORUM do Series notatu dignas suppeditabunt. Cum enim sit cos. $\frac{1}{2} v +$ tang. $\frac{1}{2} g$. sin. $\frac{1}{2} v = (1 + \frac{v}{\varpi - g})(1 - \frac{v}{\varpi + g})$ $(1 + \frac{v}{3\varpi - g})$ &c., si ponamus $v = \frac{x\varpi}{n}$ & $g = \frac{m\varpi}{n}$ erit $(1 + \frac{x}{n-m})(1 - \frac{x}{n+m})(1 + \frac{x}{3n-m})(1 - \frac{x}{3n+m})$ $(1 + \frac{x}{5n-m})(1 - \frac{x}{5n+m})$ &c. = cos. $\frac{x\varpi}{2n}$ + tang. $\frac{m\varpi}{2n}$ sin. $\frac{x\varpi}{2n}$ $= 1 + \frac{\varpi x}{2n}$ tang. $\frac{m\varpi}{2n} - \frac{\varpi\varpi xx}{2.4 nn} - \frac{\varpi^3 x^3}{2.4.6 n^3 [TRUNCATED]