Introductio in analysin infinitorum

94 DE QUANTITATIBUS TRANSCENDENT. LIB. I. tinentur. Erit autem porro $cof. z = fin. (\frac{1}{2}\pi - z)$, & $fin. z = cof. (\frac{1}{2}\pi - z)$, atque $(fin. z)^2 + (cof. z)^2 = 1$. Præter has denominationes notandæ sunt quoque hæ: tang. z, quæ denotat Tangentem Arcus z; cot. z Cotangentem Arcus z; constatque esse $tang. z = \frac{fin. z}{cof. z}$ & $cot. z = \frac{cof. z}{fin. z} = \frac{1}{tang. z}$; quæ omnia ex Trigonometria sunt nota. 128. Hinc vero etiam constat si habeantur duo Arcus y & z, fore $fin. (y+z) = fin. y. cof. z + cof. y. fin. z$, & $cof. (y+z) = cof. y. cof. z - fin. y. fin. z$, itemque $fin. (y-z) = fin. y. cof. z - cof. y. fin. z$ & $cof. (y-z) = cof. y. cof. z + fin. y. fin. z$. Hinc loco y substituendo Arcus $\frac{1}{2}\pi; \pi; \frac{3}{2}\pi, \&c.$, erit $fin. (\frac{1}{2}\pi + z) = + cof. z$ | $fin. (\frac{1}{2}\pi - z) = + cof. z$ $cof. (\frac{1}{2}\pi + z) = - fin. z$ | $cof. (\frac{1}{2}\pi - z) = + fin. z$ $fin. (\pi + z) = - fin. z$ | $fin. (\pi - z) = + fin. z$ $cof. (\pi + z) = - cof. z$ | $cof. (\pi - z) = - cof. z$ $fin. (\frac{3}{2}\pi + z) = - cof. z$ | $fin. (\frac{3}{2}\pi - z) = - cof. z$ $cof. (\frac{3}{2}\pi + z) = + fin. z$ | $cof. (\frac{3}{2}\pi - z) = - fin. z$ $fin. (2\pi + z) = + fin. z$ | $fin. (2\pi - z) = - fin. z$ $cof. (2\pi + z) = + cof. z$ | $cof. (2\pi - z) = + cof. z$ Si