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

2007/10/21 by Leonhard Euler, Euler, Leonhard
Mathematics · #01A50 #49-03 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications #math.CA #math.HO #msc:01A50 #msc:49-03

paper · pdf · doi:10.48550/arxiv.0710.3956

5 pages, 2 figures

arxiv created 2007/10/21 · openalex publication_date 2007/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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