Pons asinorum
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Pons Asinorum (Latin for "Bridge of Asses") is the name given to Euclid's fifth proposition in Book 1 of his Elements of geometry, namely that
- in an isosceles triangle, the angles at the base are equal, and if the equal length sides are extended then the angles beyond the base are equal.
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 will show that two sides and the included angle at A are the same, so by the fourth proposition the angles at B and C are the same. Euclid's proof was longer and involved the construction of more 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.
