Introductio in analysin infinitorum

AC DIVISIONE ANGULORUM. 209 CAP. XIV. $+ \frac{1}{\cos.z} = \frac{1}{\cos.z}$ $- \frac{3}{\cos.3z} = \frac{1}{\cos.z} - \frac{1}{\cos.(\frac{\pi}{3}-z)} - \frac{1}{\cos.(\frac{\pi}{3}+z)}$ $+ \frac{5}{\cos.5z} = \frac{1}{\cos.z} - \frac{1}{\cos.(\frac{\pi}{5}-z)} - \frac{1}{\cos.(\frac{\pi}{5}+z)} + \frac{1}{\cos.(\frac{2\pi}{5}-z)} + \frac{1}{\cos.(\frac{2\pi}{5}+z)}$ & generaliter, posito $n = 2m+1$, erit $\frac{n}{\cos.nz} = \frac{2m+1}{\cos.(2m+1)z} = \frac{1}{\cos.(\frac{m}{n}\pi+z)} + \frac{1}{\cos.(\frac{m}{n}\pi-z)} - \frac{1}{\cos.(\frac{m-1}{n}\pi+z)} - \frac{1}{\cos.(\frac{m-1}{n}\pi-z)} + \frac{1}{\cos.(\frac{m-2}{n}\pi+z [TRUNCATED]