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

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