Methodus inveniendi lineas curvas

302 DE CURVIS quam lamina inter oscillandum format, hactenus indeterminata poterit determinari. Cum enim fit $e^{\frac{a}{c}} = \frac{1-\text{fin.}\frac{a}{c}}{\text{cof.}\frac{a}{c}}$, erit $B = \frac{1-\text{fin.}\frac{a}{c}}{\text{cof.}\frac{a}{c}}A, \& C=A-B$ $= \frac{A(\text{cof.}\frac{a}{c} + \text{fin.}\frac{a}{c} - 1)}{\text{cof.}\frac{a}{c}}, \& D=A+B$ $= \frac{A(\text{cof.}\frac{a}{c} - \text{fin.}\frac{a}{c} + 1)}{\text{cof.}\frac{a}{c}}$. Jam est $b=A+B+D=2D=2A(\text{cof.}\frac{a}{c}-\text{fin.}\frac{a}{c}+1):\text{cof.}\frac{a}{c}$; unde fit $A = \frac{b \text{cof.}\frac{a}{c}}{2(\text{cof.}\frac{a}{c} - \text{fin.}\frac{a}{c} + 1)} = \frac{b(1+\text{fin.}\frac{a}{c}-\text{cof.}\frac{a}{ [TRUNCATED]