Introductio in analysin infinitorum

212 DE MULTIPLICATIONE LIB. I. & generaliter $tang. nz = \frac{nt - \frac{n(n-1)(n-2)}{1 \cdot 2 \cdot 3}t^3 + \frac{n(n-1)(n-2)(n-3)(n-4)}{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5}t^5 - \&c.}{1 - \frac{n(n-1)}{1 \cdot 2}t^2 + \frac{n(n-1)(n-2)(n-3)}{1 \cdot 2 \cdot 3 \cdot 4}t^4 - \&c.}$ Cum jam fit $tang. nz = tang. (\pi+nz) = tang.(2\pi+nz) = tang. (3\pi+nz) \&c.$, erunt valores ipsius $t$, seu radices aequationis, hae, $tang.z$; $tang.(\frac{\pi}{n}+z)$; $tang.(\frac{2\pi}{n}+z)$; $tang.(\frac{3\pi}{n}+z)$; $\&c.$, quarum numerus est $n$. 250. Quod si aequatio ab unitate incipiat, erit $0 = 1 - \frac{nt}{tang. nz} - \frac{n(n-1)t^2}{1 \cdot [TRUNCATED]