Methodus inveniendi lineas curvas

ELASTICIS. 303 Unde fit $e^{\frac{a}{c}} = e^{\frac{a}{2c}} e^{\frac{a}{2c}} = e^{\frac{a}{2c}} \sqrt{\frac{1-\sin\frac{a}{c}}{\cos\frac{a}{c}}}$, & $e^{-\frac{a}{c}} = e^{-\frac{a}{2c}} \sqrt{\frac{\cos\frac{a}{c}}{1-\sin\frac{a}{c}}}$; ex quo erit $\frac{A e^{\frac{x}{c}} + B e^{-\frac{x}{c}}}{b} = \frac{(e^{\frac{x}{c}} + e^{-\frac{x}{c}}) \sqrt{\cos\frac{a}{c}(1-\sin\frac{a}{c})}}{2(1-\sin\frac{a}{c}+\cos\frac{a}{c})} = \frac{e^{\frac{x}{c}}+e^{-\frac{x}{c}}}{2(e^{\frac{a}{2c}}+e^{-\frac{a}{2c}})}$. Tum vero erit $(1-\cos\frac{a}{c})\sin\frac{x}{c} + \sin\frac{a}{c}\cos\frac{x}{c} = \sin\frac{x}{c} + \sin\frac{a-x}{c} = \sin(\frac{a}{2c}-\ [TRUNCATED]