Introductio in analysin infinitorum

AC DIVISIONE ANGULORUM. 213 $5\cot 5z = \cot z + \cot(\frac{\pi}{5}+z) + \cot(\frac{2\pi}{5}+z) + \cot(\frac{3\pi}{5}+z) + \cot(\frac{4\pi}{5}+z).$ CAP. XIV. 251. Quia vero est $\cot v = -\cot(\pi-v)$, erit $\cot z = \cot z$ $2\cot 2z = \cot z - \cot(\frac{\pi}{2}-z)$ $3\cot 3z = \cot z - \cot(\frac{\pi}{3}-z) + \cot(\frac{\pi}{3}+z)$ $4\cot 4z = \cot z - \cot(\frac{\pi}{4}-z) + \cot(\frac{\pi}{4}+z) - \cot(\frac{2\pi}{4}-z)$ $5\cot 5z = \cot z - \cot(\frac{\pi}{5}-z) + \cot(\frac{\pi}{5}+z) - \cot(\frac{2\pi}{5}-z) + \cot(\frac{2\pi}{5}+z)$ & generaliter $n \cdot \cot nz = \cot z - \cot(\frac{\pi}{n}-z) + \cot(\frac{\pi}{n}+z) - \cot(\frac{2\pi}{n}-z) + \cot(\frac{2\pi}{n}+z) - \cot(\frac{3\pi}{n}-z) + \cot(\frac{3\pi}{n}+z) - \text{\&c.}$ donec tot habeantur termini, quot numerus $n$ continet unitates. 252. Incipiamus aequationem inventam a Potestate summa, ubi primum distingendi sunt casus, quibus $n$ est vel numerus par, vel impar. Sit $n$ numerus impar, $n = 2m+1$ erit Dd 3 —