Methodus inveniendi lineas curvas

90 DE METHODO MAX. ET MIN. $+\frac{[T]d^4L' + 5d[T]d^3L' + 10dd[T]ddL' + 10d^3[T]dL' + 5d^4[T]L'}{dx^4})$ in qua expressione, quia omnes termini inter se sunt homogenei, jam indices numerici negligi poterunt. Sequentium autem terminorum $L^v dx + L^{vi} dx + \&c.$ omnium incrementum erit= $nv. dx([N'] - \frac{d[P'']}{dx} + \frac{dd[Q''']}{dx^2} - \frac{d^3[R'''']}{dx^3} + \frac{d^4[S''''']}{dx^4} - \frac{d^5[T'''''']}{dx^5})$ ($L''dx + L'''dx + L''''dx + L'''''dx + \&c.$ usque in Z). Hic autem posterior factor definictur per integrationem formulæ $\int Ldx$, quæ respondet abscissæ indefinitæ $AH=x$; ponatur in hac formula post integrationem $x=a$, abeatque ea in $H$, erit $H$ valor formulæ $\int Ldx$ abscissæ toti propositæ AZ respondens; a qua ergo si [TRUNCATED]