Methodus inveniendi lineas curvas

ELASTICIS. 199 contenta reperietur, si ejusmodi tantum curvas admittamus, quae rectam Cc habeant diametrum, seu in quibus valor ipsius y prodeat idem, si loco $x$ scribatur $a-x$. Ponamus ergo in aequatione generali $a-x$ loco $x$: atque prodibit $y=A e^{\frac{a}{c}-\frac{x}{c}}+B e^{-\frac{a}{c}+\frac{x}{c}}+C \sin.\frac{x}{c} \cdot \cos.\frac{a}{c}-C \cos.\frac{x}{c} \cdot \sin.\frac{a}{c}$ $+D \cos.\frac{x}{c} \cdot \cos.\frac{a}{c}+D \sin.\frac{x}{c} \cdot \sin.\frac{a}{c}$ quae cum congruere debeat cum aequatione $y=A e^{\frac{x}{c}}+B e^{-\frac{x}{c}}+C \sin.\frac{x}{c}+D \cos.\frac{x}{c}$; fiet $A e^{\frac{a}{c}}=B$, $C(1+\cos.\frac{a}{c})=D \sin.\frac{a}{c}$, & $C \sin.\frac{a}{c}$ $=D(1-\cos.\frac [TRUNCATED]