Euclid's Elements is a mathematical
and geometric treatise consisting of 13 books written by the Greek
mathematician Euclid in Alexandria circa 300 BC. It comprises a
collection of definitions, postulates (axioms), propositions
(theorems and constructions), and mathematical proofs of the
Book 1 contains Euclid's 10 axioms (5 named postulates - including the parallel postulate
- and 5 named axioms) and the basic propositions of geometry: the pons asinorum (proposition 5) , the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area).
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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.