E732 -- Solutio facilior problematis Diophantei circa triangulum, in quo rectae ex angulis latera opposita bisecantes rationaliter exprimantur

(An easier solution of a Diophantine problem about triangles, in which those lines from the vertices which bisect the opposite sides may be expressed rationally)

Summary:

(based on Jordan Bell's abstract)

Euler proves that there are triangles with integer side lengths such that the length of the bisectors of the sides to the opposite angles are integers. He also provides a general method to make a certain class of such triangles.

This is part of the Memoires, a follow-up on that earlier paper on triangles, E713. Euler gives a couple more such triangles.

Publication:

Originally published in Memoires de l'academie des sciences de St.-Petersbourg 2, 1810, pp. 10-16
Opera Omnia: Series 1, Volume 4, pp. 399 - 405
Reprinted in Commentat. arithm. 2, 1849, pp. 362-365 [E732a]

Documents Available:

Original publication: E732
English translation (Jordan Bell): E732

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