Methodus inveniendi lineas curvas

ELASTICIS. 269 per tantum deprimatur; tum erit $c$ quantitas valde magna, ideoque erit proxime $1/\sqrt{(cc-xx)(cc-2gg+xx)} = (c^4-2ccgg+2ggxx-x^4)^{-\frac{1}{2}} = \frac{1}{cc} + \frac{gg}{c^4} - \frac{ggxx}{c^6} + \frac{x^4}{2c^6}$, ideoque integrando quoque proxime: $s = \frac{(cc-gg)x}{cc} + \frac{(cc-gg)ggx}{c^4} - \frac{(cc-gg)ggx^3}{3c^6} + \frac{(cc-gg)x^5}{10c^6}$ & $y = \frac{ggx}{cc} + \frac{x^4}{3c^4} - \frac{ggx^3}{3c^6} + \frac{ggx^5}{10c^6} - \frac{x^3}{3cc} - \frac{ggx^3}{3c^4} + \frac{ggx^5}{5c^6} - \frac{x^7}{14c^6}$. Sit nunc $x=g$, fietque $f=g-\frac{37g^5}{3 [TRUNCATED]