Steps / Historical AI

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} + [TRUNCATED]
confidence 0.85 10 expressions source scan at the Internet Archive

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