Introductio in analysin infinitorum

AC DIVISIONE ANGULORUM. 215 CAP. XIV. & generaliter, si $n = 2m+1$, erit $n\tan nz = \tan z - \tan(\frac{\pi}{n}-z)+\tan(\frac{\pi}{n}+z)-\tan(\frac{2\pi}{n}-z)+\tan(\frac{2\pi}{n}+z)-\tan(\frac{3\pi}{n}-z)+\dots-\tan(\frac{m\pi}{n}-z)+\tan(\frac{m\pi}{n}+z).$ 254. Tum vero productum ex his Tangentibus omnibus erit $= \tan nz$, propterea quod per signorum negativorum numerum alternatim parem & imparem, superior signorum ambiguitas tollitur. Sic erit $\tan z = \tan z$ $\tan 3z = \tan z \tan(\frac{\pi}{3}-z)\tan(\frac{\pi}{3}+z)$ $\tan 5z = \tan z \tan(\frac{\pi}{5}-z)\tan(\frac{\pi}{5}+z)\tan(\frac{2\pi}{5}-z)\times \tan(\frac{2\pi}{5}+z)$ & generaliter, si $n = 2m+1$, erit $\tan nz = \tan z \tan(\frac{\pi}{n}-z)\tan(\frac{\pi}{n}+z)\tan(\frac [TRUNCATED]