Methodus inveniendi lineas curvas

AD CURVAS INVENIENDAS ABSOLUTA. 65 A tang. $p = \frac{ap+bp^2+cp^3}{1+pp} - \int \frac{(a+cpp)dp}{1+pp}$, ob $b \int dp \text{ A tang. } p$ $= bp \text{ A tang. } p - b \int \frac{pdp}{1+pp}$. Hinc erit $y = f + \frac{ap+bp^2+cp^3}{1+pp}$ $x = c + (c-a) \text{ A tang. } p - cp$ $y = f + \frac{(a-c)p+(b+f)pp}{1+pp}$ $x = c + (c-a) \text{ A tang. } p$. Atque ex his quidem ipsarum $x$ & $y$ valoribus per $p$ inventis, curva quaesita per data quatuor puncta duci atque construi potest. Verum ut ipsa curva qualis sit cognoscatur, eliminetur A tang. $p$; eritque A tang. $p = \frac{x}{b} - \frac{a}{b} - \frac{c}{b}p - \frac{f}{b}pp$ $= \frac{y}{c-a} - \frac{f}{c-a} + p - \frac{(b+f)}{c- [TRUNCATED]