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Euclid's Elements Book I, Proposition 5: (Pons Asinorum)
In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines are produced further, then the angles under the base will be equal to one another.

Let ABC be an isosceles triangle having the side AB equal to the side BC, and let the straight lines BD, CE be produced further in a straight line with AB and BC.

I say that the angle BAC is equal to the angle ACB, and the angle CAD to the angle ACE.
 

Euclid's Elements Book I,1 Proposition 5
 


Pons Asinorum (Latin for "bridge of asses")

Pons asinorum is the name given to Euclid's fifth proposition in Book 1 of his Elements of geometry because this proposition is the first real test in the Elements of the intelligence of the reader and as a bridge to the harder propositions that follow.
 


The Elements: Books I-XIII (Barnes & Noble Library of Essential Reading)
 

by Euclid, Thomas L. Heath (Translator), Andrew Aberdein (Introduction)
(Paperback - Complete and Unabridged)

Euclid's Elements is a fundamental landmark of mathematical achievement. Firstly, it is a compendium of the principal mathematical work undertaken in classical Greece, for which in many cases no other source survives. Secondly, it is a model of organizational clarity which has had a deep influence on the way almost all subsequent mathematical research has been conducted. Thirdly, it is the most successful textbook ever written, only seriously challenged as an account of elementary geometry in the nineteenth century, more than two thousand years after its first publication.

Euclid reportedly lived some time between the death of Plato (427-347 BC) and the birth of Archimedes (287-212 BC). He most likely learned mathematics at Plato's Academy in Athens and taught at Alexandria in Egypt. Scholars believe Euclid was hired as one of the original faculty at a school of advanced study, patterned after those in Athens, and known as the Museum.


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In its broad sense, education refers to any act or experience that has a formative effect on the mind, character, or physical ability of an individual...In its technical sense education is the process by which society, through schools, colleges, universities, and other institutions, deliberately transmits its cultural heritage--its accumulated knowledge, values, and skills--from one generation to another. George F. Kneller, Introduction to the Philosophy of Education (New York: John Wiley and Sons, 1971.) 

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