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Euclid's Elements, Book I
Euclid's Elements is a mathematical and geometric
treatise, consisting of 13 books, written by the Hellenistic mathematician
Euclid in Alexandria circa 300 BC. It comprises a collection of definitions,
postulates (axioms), propositions (theorems and constructions), and proofs of
the theorems. The 13 books cover Euclidean geometry and the ancient Greek
version of elementary number theory.
The Elements form one of the most beautiful and influential works of science in
the history of humankind. Its beauty lies in its logical development of geometry
and other branches of mathematics. It has influenced all branches of science but
none so much as mathematics and the exact sciences. The Elements have been
studied 24 centuries in many languages starting, of course, in the original
Greek, then in Arabic, Latin, and many modern languages.
Euclid's Book I begins with 23 definitions — such as point, line, and surface —
followed by five postulates and five "common notions" (both of which are today
called axioms). These are the foundation of all that follows.
The frontispiece of Sir Henry Billingsley's first
English version of Euclid's Elements, 1570

The Elements: Books IXIII (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 (427347
BC) and the birth of Archimedes (287212 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. 
