Euclid is the most prominent mathematician of antiquity best known for his treatise on geometry The Elements . The long lasting nature ofThe Elements must make Euclid the leading mathematics teacher of all time.Little is known of Euclid's life except that he taught at Alexandria in Egypt.
Euclid's most famous work is his treatise on geometry The Elements . The book was a compilation of geometrical knowledge that became the centre of mathematical teaching for 2000 years. Probably no results in The Elements were first proved by Euclid but the organisation of the material and its exposition are certainly due to him.
The Elements begins with definitions and axioms, including the famous fifth, or parallel, postulate that one and only one line can be drawn through a point parallel to a given line. Euclid's decision to make this an axiom led to Euclidean geometry. It was not until the 19th century that this axiom was dropped and non-euclidean geometries were studied.
Zeno of Sidon, about 250 years after Euclid wrote the Elements , seems to have been the first to show that Euclid's propositions were not deduced from the axioms alone, and Euclid does make other subtle assumptions.
The Elements is divided into 13 books. Books 1-6, plane geometry: books 7-9, number theory: book 10, Eudoxus's theory of irrational numbers: books 11-13, solid geometry. The book ends with a discussion of the properties of the five regular polyhedra and a proof that there are precisely five. Euclid's Elements is remarkable for the clarity with which the theorems are stated and proved. The standard of rigour was to become a goal for the inventors of the calculus centuries later.
More than one thousand editions ofThe Elements have been published since it was first printed in 1482.
Euclid also wrote Data (with 94 propositions), On Divisions ,Optics and Phaenomena which have survived. His other books Surface Loci , Porisms , Conics , Book of Fallacies and Elements of Music have all been lost.
Euclid may not have been a first class mathematician but the long lasting nature ofThe Elements must make him the leading mathematics teacher of antiquity.
The picture of Euclid above is from the 18th Century and must be regarded as entirely fanciful.
References (91 books/articles)
Some pages from works by Euclid:
The first page of The Elements in the translation by Campanus. This edition was published in 1482.
The five postulates taken from this edition.
Another page from the edition of The Elements, Book V published in 1482
The first page of The Elements published in 1505. (This was the first Latin translation directly from the Greek.)
Propositions 1 and 2 from The Elements, Book I (1536)
Propositions 2 and 3 from The Elements, Book I (1536)
Propositions 6 and 7 from The Elements, Book I (The Campanus translation 1482)
Propositions 27 and 28 from The Elements, Book I (The Campanus translation 1482)
A page from Optics (an edition of 1557)
Proposition 2 of Elements (Campani edition of 1482) and its continuation
References elsewhere in this archive:
Tell me about Euclid's axioms
Show me Euclid's geometric solution of a quadratic equation
Tell me about the five regular polyhedra
There is a Crater Euclides on the moon. You can see a list of lunar features named after mathematicians.
Other Web sites:
Clarke University, USA
Library of Congress, USA
More links at Yahoo, California, USA
New Jersey, USA
Texas A and M, USA
University of Virginia, USA
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