pons asinorum

Pons asinorumMathworldPlanetmath is Latin for “bridge of asses”. During medieval times, this name was given to the fifth propositionPlanetmathPlanetmath in the first book of Euclid’s The Elements. In the original Greek, this proposition reads:

Tω~ν ισoσκελω~ν τριγω´νων αι πρo`ς τη~ βα´σει γωνι´αι ισαι αλλη´λαις εισι´ν, και` πρoσεκβληθεισω~ν τω~ν ισων ευθειω~ν αι υπo` τη`ν βα´σιν γωνι´αι ισαι αλλη´λαις εσoνται.

A translationMathworldPlanetmathPlanetmath of this proposition is:

In isosceles trianglesMathworldPlanetmath, 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.

There are a couple of reasons why this proposition was named pons asinorum:

  • Euclid’s diagram for this proposition looks like a bridge.

  • This is the first nontrivial proposition in The Elements and thus tests a student’s ability to understand more advanced concepts in Euclidean geometryMathworldPlanetmath. Therefore, this proposition serves as a bridge from from the trivial portion of Euclidean geometry to the nontrivial portion, and the people who cannot cross this bridge are considered to be unintelligent.

For more details, please see http://planetmath.org/?op=getmsg&id=15847a post written by rspuzio and http://planetmath.org/?op=getmsg&id=15849a post written by Wkbj79.


  • 1 Mourmouras, Dimitrios. The Elements: The original Greek text. URL: http://www.physics.ntua.gr/Faculty/mourmouras/euclidhttp://www.physics.ntua.gr/Faculty/mourmouras/euclid
  • 2 Wikipedia. Pons asinorum. URL: http://en.wikipedia.org/wiki/Pons_Asinorumhttp://en.wikipedia.org/wiki/Pons_Asinorum
Title pons asinorum
Canonical name PonsAsinorum
Date of creation 2013-03-22 17:17:31
Last modified on 2013-03-22 17:17:31
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 6
Author Wkbj79 (1863)
Entry type Topic
Classification msc 51M04
Classification msc 51-03
Classification msc 51-00
Classification msc 01A20
Classification msc 01A35
Related topic AnglesOfAnIsoscelesTriangle