pons asinorum
Pons asinorum^{} is Latin for “bridge of asses”. During medieval times, this name was given to the fifth proposition^{} in the first book of Euclid’s The Elements. In the original Greek, this proposition reads:
$T\stackrel{~}{\omega}\nu $ $\iota \sigma o\sigma \kappa \epsilon \lambda \stackrel{~}{\omega}\nu $ $\tau \rho \iota \gamma \stackrel{\xb4}{\omega}\nu \omega \nu $ $\alpha \iota $ $\pi \rho \stackrel{`}{o}\varsigma $ $\tau \stackrel{~}{\eta}$ $\beta \stackrel{\xb4}{\alpha}\sigma \epsilon \iota $ $\gamma \omega \nu \stackrel{\xb4}{\iota}\alpha \iota $ $\iota \sigma \alpha \iota $ $\alpha \lambda \lambda \stackrel{\xb4}{\eta}\lambda \alpha \iota \varsigma $ $\epsilon \iota \sigma \stackrel{\xb4}{\iota}\nu ,$ $\kappa \alpha \stackrel{`}{\iota}$ $\pi \rho o\sigma \epsilon \kappa \beta \lambda \eta \theta \epsilon \iota \sigma \stackrel{~}{\omega}\nu $ $\tau \stackrel{~}{\omega}\nu $ $\iota \sigma \omega \nu $ $\epsilon \upsilon \theta \epsilon \iota \stackrel{~}{\omega}\nu $ $\alpha \iota $ $\upsilon \pi \stackrel{`}{o}$ $\tau \stackrel{`}{\eta}\nu $ $\beta \stackrel{\xb4}{\alpha}\sigma \iota \nu $ $\gamma \omega \nu \stackrel{\xb4}{\iota}\alpha \iota $ $\iota \sigma \alpha \iota $ $\alpha \lambda \lambda \stackrel{\xb4}{\eta}\lambda \alpha \iota \varsigma $ $\epsilon \sigma o\nu \tau \alpha \iota .$
A translation^{} of this proposition is:
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.
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 geometry^{}. 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.
References
 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  20130322 17:17:31 
Last modified on  20130322 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 5103 
Classification  msc 5100 
Classification  msc 01A20 
Classification  msc 01A35 
Related topic  AnglesOfAnIsoscelesTriangle 