Introductio in analysin infinitorum

LIB. I. 200 DE MULTIPLICATIONE funt $ \sin z $; $ \sin(\frac{2\pi}{n}+z) $; $ \sin(\frac{4\pi}{n}+z) $; $ \sin(\frac{6\pi}{n}+z) $; $ \sin(\frac{8\pi}{n}+z) $; &c., quarum numerus est $ n $. 237. Hujus ergo aequationis $ 0 = 1 - \frac{nx}{\sin nz} + \frac{n(n^2-1)x^3}{1 \cdot 2 \cdot 3 \sin nz} - \frac{n(n^2-1)(n^2-9)x^5}{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \sin nz} \dots \pm $ $ \frac{x^{\frac{n-1}{2}}}{\sin nz} $, (ubi signum superius valet si $ n $ unitate deficiat a multiplo quaternarii, contra inferius,) Factores sunt $ (1-\frac{x}{\sin z}) $ $ (1-\frac{x}{\sin(\frac{2\pi}{n}+z)}) $ &c., ex quibus concluditur fore $ \frac{n}{\sin nz} = \frac{1}{\sin z} + \frac{1}{\sin(\frac [TRUNCATED]