Leonhard Euler · 1744 · Internet Archive
Methodus inveniendi lineas curvas
All 336 leaves · leaf 115
Transcription
108 DE METHODO MAX. ET MIN.
Erit autem
$d.[z]dx = nv.dx \frac{[q]}{dx^2}$
$d.[z']dx = nv.dx(\frac{[p']}{dx} - \frac{2[q']}{dx^2})$
$d.[z'']dx = nv.dx([n''] - \frac{[p'']}{dx} + \frac{[q'']}{dx^2})$
$d.[z''']dx = 0$
$d.[z^{iv}]dx = 0$
&c.
Ex his itaque obtinebitur
$d.\pi = 0$
$d.\pi' = nv.dx.\frac{[q]}{dx^2}$
$d.\pi'' = nv.dx(\frac{[p']}{dx} - \frac{[q]}{dx^2} - \frac{2d[q]}{dx^3})$
$d.\pi''' = nv.dx([n''] - \frac{d[p']}{dx^2} + \frac{dd[q]}{dx^4})$
$d.\pi^{iv} = nv.dx([n''] - \frac{d[p']}{dx^2} + \frac{dd[q]}{dx^4})$
$d.\pi^v = nv.dx([n''] - \frac{d[p']}{dx^2} +
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