Introductio in analysin infinitorum

210 DE MULTIPLICATIONE LIB. I. $7\sec{7z} = \sec{(\frac{3\pi}{7}+z)} + \sec{(\frac{3\pi}{7}-z)} - \sec{(\frac{2\pi}{7}+z)} - \sec{(\frac{2\pi}{7}-z)} + \sec{(\frac{\pi}{7}+z)} + \sec{(\frac{\pi}{7}-z)} - \sec{(\frac{0\pi}{7}+z)}$ & generaliter, posito $n=2m+1$, crit $n \sec{nz} = \sec{(\frac{m}{n}\pi+z)} + \sec{(\frac{m}{n}\pi-z)} - \sec{(\frac{m-1}{n}\pi+z)} - \sec{(\frac{m-1}{n}\pi-z)} + \sec{(\frac{m-2}{n}\pi+z)} + \sec{(\frac{m-2}{n}\pi-z)} - \sec{(\frac{m-3}{n}\pi+z)} - \sec{(\frac{m-3}{n}\pi-z)} + \sec{(\frac{m-4}{n}\pi+z)} + \dots \pm \sec{z}.$ 248. Pro Cosecantibus autem erit ex §. 237. $\mathrm{cosec.}\,z = \mathrm{cosec.}\, [TRUNCATED]