Introductio in analysin infinitorum

AC DIVISIONE ANGULORUM. 211 CAP. XIV. $n.cosec.nz = cosec.z + cosec.(\frac{\pi}{n} - z) - cosec.(\frac{\pi}{n} + z) -$ $cosec.(\frac{2\pi}{n} - z) + cosec.(\frac{2\pi}{n} + z) +$ $cosec.(\frac{3\pi}{n} - z) - cosec.(\frac{3\pi}{n} + z) -$ $............ \mp cosec.(\frac{m\pi}{n} - z) \pm cosec.(\frac{m\pi}{n} + z)$ ubi signa superiora valent si m fuerit numerus par, inferiora si m fit impar. 249. Cum fit, uti supra vidimus, $cos.nz \pm \sqrt{-1}.sin.nz = (cos.z \pm \sqrt{-1}.sin.z)^n$, erit $cos.nz =$ $\frac{(cos.z + \sqrt{-1}.sin.z)^n + (cos.z - \sqrt{-1}.sin.z)^n}{2}, \& sin.nz =$ $\frac{(cos.z + \sqrt{-1}.sin.z)^n - (cos.z - \sqrt{-1}.sin.z)^n}{2\sqrt{-1}}$, erit $tang.nz = \frac [TRUNCATED]