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

Leonhard Euler

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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

Leonhard Euler

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Abstract

This is an English translation from the Latin original of Leonhard Euler's ``Solutio facilior problematis Diophantei circa triangulum, in quo rectae ex angulis latera opposita bisecantes rationaliter exprimantur''. In this paper, Euler proves that there exist triangles with integer length sides such that the length of the bisectors of the sides to the opposite angles are integer valued, and he gives a general method for making a certain class of such triangles.

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Leonhard Euler. 2005-03-03. 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. https://arxiv.org/abs/math/0503052

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