Its first known usage in this was in 1645. Pons asinorum is also used metaphorically for a problem or challenge which acts as a test of critical thinking in a field, separating capable and incapable reasoners it represents a test of ability or understanding. The term is also applied to the Pythagorean theorem. Its converse is also true: if two angles of a triangle are equal, then the sides opposite them are also equal. This statement is Proposition 5 of Book 1 in Euclid's Elements, and is also known as the isosceles triangle theorem. In geometry, the statement that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum ( Latin:, English: / ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m/ PONZ ass-i- NOR-əm), typically translated as "bridge of asses".
The pons asinorum in Byrne's edition of the Elements showing part of Euclid's proof.
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