Introductio in analysin infinitorum

208 DE MULTIPLICATIONE LIB. I. 245. Quod ad productum ex omnibus attinet, variæ quidem prodeunt expressiones, prout $n$ fuerit numerus vel impar, vel impariter par, vel pariter par: omnes autem comprehenduntur in expressione generali (§. 242.) inventa, si singuli Sinus in Cosinus transmutentur: Erit scilicet $cos. z = 1 cos. z$ $cos. 2z = 2 cos.(\frac{\pi}{4}+z).cos.(\frac{\pi}{4}-z)$ $cos. 3z = 4 cos.(\frac{2\pi}{6}+z).cos.(\frac{2\pi}{6}-z).cos.z$ $cos. 4z = 8 cos.(\frac{3\pi}{8}+z).cos.(\frac{3\pi}{8}-z).cos.(\frac{\pi}{8}+z)\times cos.(\frac{\pi}{8}-z)$ $cos. 5z = 16 cos.(\frac{4\pi}{8}+z).cos.(\frac{4\pi}{8}-z).cos.(\frac{2\pi}{8}+z)\times cos.(\frac{2\pi}{8}-z) cos.z$ & generaliter $cos. nz = 2^{n-1} cos.(\frac{n-1}{n}\pi+z).cos.(\frac{n-1}{n}\pi-z)\times cos.(\frac{n-3}{n}\pi+z).cos.(\frac{n-3}{n}\pi-z)\times cos.(\frac{n-5}{n}\pi+z).cos.(\frac{n-5}{n}\pi-z)\times cos.(\frac{n-7}{n}\pi+z) \&c.,$ sumtis tot Factoribus, quot numerus $n$ continet unitares. 246. [TRUNCATED]