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pons asinorum∗
Wkbj79†
2013-03-21 23:18:38
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 ω̃ν ισoσκελω̃ν τ ριγ ώνων αι πρòς τ η̃ β άσει γωνίαι ισαι αλλήλαις
εισίν, καὶ πρoσεκβληθεισ ω̃ν τ ω̃ν ισων ευθειω̃ν αι υπò τ ὴν β άσιν
γωνίαι ισαι αλλήλαις εσoντ αι.
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 a post written by rspuzio and a post written by
Wkbj79.
References
[1] Mourmouras, Dimitrios. The Elements: The original Greek text. URL:
http://www.physics.ntua.gr/Faculty/mourmouras/euclid
[2] Wikipedia. Pons asinorum. URL: http://en.wikipedia.org/wiki/PonsA sinorum
∗ hPonsAsinorumi
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h1i hTopici h51M04i h51-03i h51-00i h01A20i h01A35i
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