pons asinorum

Pons Asinorum (Latin for "Bridge of Asses") is the name given to Euclid's fifth proposition in Book 1 of his Elements of geometry:

In isosceles triangles the angles at the base equal one another, and, if the equal straight lines are produced further, then the angles under the base equal one another.

Pappus provided the shortest proof of the first part, that if the triangle is ABC with AB being the same length as AC, then comparing it with the triangle ACB (the mirror image of triangle ABC) will show that two sides and the included angle at A of one are equal to the corresponding parts of the other, so by the fourth proposition (on congruent triangles) the angles at B and C are equal. Euclid's proof was longer and involved the construction of additional triangles.

It takes its name as the first real test in the Elements of the intelligence of the reader and as a bridge to the harder propositions that followed. Its location in that text is much more advanced than where the problem is posed in present-day geometry textbooks for high-school students.

External link

• D.E.Joyce's presentation of Euclid's Elements

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