Home Geometry Euclid's Elements Post a comment Proposition 2        By Antonio Gutierrez
Euclid's Elements Book I, Proposition 1: On a given finite line to construct an equilateral triangle.

Let AB be the given finite straight line. Thus it is required to construct an equilateral triangle on the straight line AB.
 
Given a finite straight line
 

Construction

Euclid's Elements Book I, Proposition 1: Equilateral triangle

 

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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