Methodus inveniendi lineas curvas

AD CURVAS INVENIENDAS APPLICATA. 25 COROLL. III. 51. Cum deinde valor ipsius $p$ sit $\frac{dy}{dx}=\frac{Nn-Mm}{dx}$; erit $p=\frac{y'-y}{dx}$; sequentes autem pariter ac antecedentes ipsius $p$ valores ita se habebunt: $p = \frac{y'-y}{dx}$ | $p = \frac{y'-y}{dx}$ $p' = \frac{y''-y'}{dx}$ | $p_i = \frac{y-y_i}{dx}$ $p'' = \frac{y'''-y''}{dx}$ | $p_{ii} = \frac{y_i-y_{ii}}{dx}$ $p''' = \frac{y''''-y'''}{dx}$ | $p_{iii} = \frac{y_{ii}-y_{iii}}{dx}$ &c. | &c. COROLL. IV. 52. Deinde, quia est $q=\frac{dp}{dx}=\frac{p'-p}{dx}$; erit $q=\frac{y''-2y'+y}{dx^2}$; ex quo quantitatis $q$ valores, cum sequentes tum antecedentes, ita se habebunt: $q = \frac{y''-2y'+y}{dx^2}$ | $q = \frac{y'' [TRUNCATED]