Introductio in analysin infinitorum

216 LIB. I. DE MULTIPLICATIONE & generaliter, si $n = 2m$, erit $t^n + n t^{n-1} \cot nz - \dots \mp 1 = 0$ ubi signum superius — valet si $m$ fit numerus impar, inferius + si $m$ fit par. Comparando ergo radices cum coefficiente secundi termini, erit $- 2 \cot 2z = \tan z + \tan (\frac{\pi}{2} + z)$ $- 4 \cot 4z = \tan z + \tan (\frac{\varpi}{4} + z) + \tan (\frac{2\varpi}{4} + z) + \tan (\frac{3\varpi}{4} + z)$ $- 6 \cot 6z = \tan z + \tan (\frac{\varpi}{6} + z) + \tan (\frac{2\varpi}{6} + z) + \tan (\frac{3\varpi}{6} + z) + \tan (\frac{4\varpi}{6} + z) + \tan (\frac{5\varpi}{6} + z)$. &c. 256. Cum sit $\tan v = -\tan (\varpi - v)$, sequentes formabuntur aequationes $2 \cot 2z = -\tan z + \tan (\frac{\varpi}{2} - z)$ $4 \cot 4z = -\tan z + \tan (\frac{\varpi}{4} - z) - \tan (\frac{\varpi}{4} + z) + \tan (\frac{2\varpi}{4} - z)$ $6 \cot 6z = -\tan z + \tan (\frac{\varpi}{6} - z) - \tan (\frac{\varpi}{6} + z) + \tan (\frac{2\varpi}{6} - z) - \tan (\frac{2\varpi}{6} + z) + \tan (\frac{3\varpi}{6} - z)$ &