Introductio in analysin infinitorum

AC DIVISIONE ANGULORUM. 207 244. Primum igitur patet, ob terminum secundum deficientem excepto casu $n=1$, fore summam harum radicum omnium $=0$. Erit ergo CAP. XIV. $0 = cos.z + cos.(\frac{2\pi}{n} - z) + cos.(\frac{2\pi}{n} + z) + cos.(\frac{4\pi}{n} - z) +$ $cos.(\frac{4\pi}{n} + z) + \&c.,$ sumendo tot terminos quot $n$ continet unitates: Hæc autem æqualitas sponte se offert si $n$ fit numerus par, cum quivis terminus ab alio sui negativo destruatur. Contemplemur ergo numeros impares, unitate exclusa, eritque, ob $cos.v = -cos.(\pi - v)$ $0 = cos.z - cos.(\frac{\pi}{3} - z) - cos.(\frac{\pi}{3} + z)$ $0 = cos.z - cos.(\frac{\pi}{5} - z) - cos.(\frac{\pi}{5} + z) + cos.(\frac{2\pi}{5} - z) +$ $cos.(\frac{2\pi}{5} + z)$ $0 = cos.z - cos.(\frac{\pi}{7} - z) - cos [TRUNCATED]