Methodus inveniendi lineas curvas

86 DE METHODO MAX. ET MIN. $d.Π = 0$ $d.Π' = nν.dx.[T]$ $d.Π'' = nν.dx ( \frac{[S']}{dx^4} - \frac{4[T]+5d[T]}{dx^3} )$ $d.Π''' = nν.dx ( \frac{[R'']}{dx^5} - \frac{3[S']+4d[S']}{dx^4} + \frac{6[T]+15d[T]+10dd[T]}{dx^3} )$ $d.Π'''' = nν.dx ( \frac{[Q''']}{dx^6} - \frac{2[R'']+3d[R'']}{dx^5} + \frac{3[S']+8d[S']+6dd[S']}{dx^4} - \frac{4[T]+15d[T]+20dd[T]+10d^3[T]}{dx^3} )$ $d.Π''''' = nν.dx ( \frac{[P'''']}{dx^7} - \frac{[Q''']+2d[Q''']}{dx^6} + \frac{[R'']+3d[R'']+3dd[R'']}{dx^5} - \frac{[S']+5d[S']+6dd[S']+4d^3[S']}{dx^4} + \frac{[T]+5d[T]+10dd[T]+10d^3[T]+5d^4[T]}{dx^3} )$ $dΠ'''''' = nν.dx ( [N'''''] - \frac{d[P'''']}{dx} + \frac{dd[Q''']}{dx^2} - \frac{d^3[R'']}{dx^3} + \frac{d^4[S']}{dx^4} - \frac{d^5[T]}{dx^5} )$ cui sequentium valorum omnium incrementa sunt æqualia. Q. E. I. COROLL. I. 2. Si ergo Π fuerit hujusmodi quantitas indeterminata, seu formula integralis indefinite integrationem non admittens, tum ejus omnes valores post locum abscissae, ubi una applicata augeri concipitur, mutationem patientur, & aliquot ejus etiam valores ante illum locum, quorum numerus pendet a gradu differentialium, quae in ea formula Π insunt. COROLL. II. 3. Quod si ergo istiusmodi quantitas insit in maximi minimive formula $\int Z dx$, tum ejus valor differentialis non solum ab aliquot abscissae elementis, verum a tota abscissa, cui maximum minimumve respondere debet, pendebit. Co-