Methodus inveniendi lineas curvas

112 DE METHODO MAX. ET MIN. COROLL. I. 32. Inventus igitur est valor differentialis pro formula $\int Zdx$ latius patente, quam quidem in Propositione est assumta: scilicet si fuerit $dZ = Ld\pi + Mdx + Ndy + Pdp + Qdq + RdR + \&c.$ atque existente $d\Pi = [Z]dx$, fit $d[Z] = [L]d\pi + [M]dx + [N]dy + [P]dp + [Q]dq + [R]dr + \&c.$ itemque si posito $d\pi = [z]dx$ fuerit $d[z] = [m]dx + [n]dy + [p]dp + [q]dq + [r]dr + \&c.$ Quoticunque nimirum gradus differentialia insint in quantitatibus $Z$, $[Z]$, & $[z]$ solutio data inserviet. COROLL. II. 33. Quod si ponatur $H - \int Ldx = T$, & $G - \int [L]dx$ $(H - \int Ldx) = V$, erit valor differentialis $= \eta v.dx(N - \frac{dP}{dx} + \frac{ddQ}{dx^2} - \frac{d^3 R}{dx^3} + \&c.)$ [TRUNCATED]