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arXiv · 0710.3956

The solution of a memorable problem by a special artifice of calculation

Leonhard Euler
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Abstract

E731 in the Enestrom index. Originally published as "Solutio problematis ob singularia calculi artificia memorabilis", Memoires de l'academie des sciences de St-Petersbourg 2 (1810), 3-9. For $z$ the distance from the origin, and $v$ a given function of $z$, Euler wants to find a curve $s$ such that the integral of $z$ over $s$ is a maximum or a minimum. He starts with the Euler-Lagrange equation, and does a lot of manipulations with polar coordinates.

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Leonhard Euler. 2007-10-21. The solution of a memorable problem by a special artifice of calculation. https://arxiv.org/abs/0710.3956

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