Methodus inveniendi lineas curvas

AD CURVAS INVENIENDAS ABSOLUTA. 111 $[L'']dx + L'dx ([L''']dx + [L''''']dx) + \&c.$ Sumatur valor sequens $S' = S+dS$, erit $S+dS = L'dx + [L'']dx + L'dx([L''']dx + [L''''']dx) + \&c.$ qui ab illo subtractus relinquet, $-dS = [L'']dx(L'dx + L''dx + L'''dx + \&c.)$ ideoque $-dS = [L'']dx(H - \int Ldx)$, & integrando $S = G - \int [L'']dx(H - \int Ldx)$, constante G ita assumta, ut fiat $S=0$ si ponatur $x=a$. His inventis fiet valor differentialis formulæ propositæ $\int Zdx =$ $nv. dx (N - \frac{dP}{dx} + \frac{ddQ}{dx^2} + L[P] - \frac{[Q]dL + 2Ld[Q]}{dx} + L[L][q]$ $+ (H - \int Ldx) ([L][p] - \frac{[q]d[L] + 2[L]d[q]}{dx})$ $+ ([N] - \frac{d[P]}{dx} + \frac{dd[Q]}{dx [TRUNCATED]