Methodus inveniendi lineas curvas

304 DE CURVIS. $ = \frac{1+\sqrt{\text{cof. }\frac{a}{c}}}{2 \text{ cof. }\frac{a}{2c}} = \frac{1}{2}\text{fec. }\frac{a}{2c} + \frac{1}{2}\text{fec. }\frac{a}{2c}\sqrt{\text{cof. }\frac{a}{c}} $. At est $ \text{cof. }\frac{a}{c} = \text{fin. }1^\circ, 0', 39'' $ & $ \text{cof. }\frac{a}{2c} = \text{fin. }45^\circ, 30', 19'' $. Hinc reperitur $ \frac{Cc}{Aa} = 0,607815 $. Deinde si ponatur $ y=0 $, reperientur puncta E & F quibus curva axem intersecat. Erit ergo $ e^{\frac{z}{c}} + e^{-\frac{z}{c}} = \frac{\text{cof. }\frac{z}{c}}{\text{cof. }\frac{a}{2c}}(e^{\frac{a}{2c}} + e^{-\frac{a}{2c}}) = \frac{2 \text{ cof. }\frac{z}{c}}{\sqrt{\text{cof. }\frac{a}{c}}} $ [TRUNCATED]