Introductio in analysin infinitorum

214 DE MULTIPLICATIONE LIB. I. $t - tang. z = 0$ $t^3 - 3t^2 tang. 3z - 3t + tang. 3z = 0$ $t^5 - 10t^3 + 10t^2 tang. 5z + 5t - tang. 5z = 0$ & generaliter $t^n - nt^{n-1} tang. nz - \dots \mp tang. nz = 0$ ubi signum superius — valet, si m fit numerus par, inferius + si m fit numerus impar. Erit ergo ex coëfficiente secundi termini $tang. z = tang. z$ $3tang. 3z = tang. z + tang.(\frac{\pi}{3}+z) + tang.(\frac{2\pi}{3}+z)$ $5tang. 5z = tang. z + tang.(\frac{\pi}{5}+z) + tang.(\frac{2\pi}{5}+z) + tang.(\frac{3\pi}{5}+z) + tang.(\frac{4\pi}{5}+z)$. &c. 253. Cum igitur sit $tang. v = -tang.(\pi - v)$, Anguli recto majores ad Angulos recto minores reducuntur, eritque $tang. z = tang. z$ $3 [TRUNCATED]