E9 -- De linea brevissima in superficie quacunque duo quaelibet puncta jungente

(On the shortest line joining two points on a surface)


This article arose out of a homework assignment that Euler did for Johann Bernoulli. Bernoulli asked Euler to find "the shortest line between two points on a surface." Together with a paper that Euler later published based on this homework assignment, this laid the first analytical foundations for the calculus of variations. For a more detailed look at this paper, see Ed Sandifer's notes.

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