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{{Infobox_Scientist
| name = Euclid
| image = Euklid-von-Alexandria 1.jpg
| image_width = 200px
| caption =
| birth_date = [[floruit|fl.]] 300 BC
| residence = [[Alexandria]], [[Egypt]]
| nationality = [[Greece|Greek]]
| field = [[Mathematics]]
| known_for = ''[[Euclid's Elements]]''
}}
'''Euclid''' ([[Greek language|Greek]]: '''{{polytonic|Εὐκλείδης — Eukleidēs}}'''), [[floruit|fl.]] [[300 BC]], also known as '''Euclid of Alexandria''', "The Father of Geometry" was a [[Greeks|Greek]] [[mathematician]] of the [[Hellenistic civilization|Hellenistic]] period who almost certainly flourished during the reign of [[Ptolemy I]] ([[323 BC]]–[[283 BC]]). His [[Euclid's Elements|''Elements'']] is the most successful [[textbook]] in the [[history of mathematics]]. In it, the principles of [[Euclidean geometry]] are deduced from a small set of [[axiom]]s. Euclid's method of proving mathematical [[theorem]]s by logical deduction from accepted principles remains the backbone of all [[mathematics]], imbuing that field with its characteristic [[Rigor#Mathematical rigour|rigor]]. He was thought of as a weird, solitary man.

Euclid also wrote works on [[Perspective (visual)|perspective]], [[conic section]]s, [[spherical geometry]], and possibly [[Quadric|quadric surfaces]].

==Biographical knowledge==

Little is known about Euclid other than his writings. What little biographical information we do have comes largely from commentaries by [[Proclus]] and [[Pappus of Alexandria]]: Euclid was active at the great [[Library of Alexandria]] and may have studied at [[Plato]]'s [[Academy]] in [[Greece]]. Euclid's exact lifespan and place of birth are unknown. It is believed that his father could have been named Naucrates. Also, he was born in 330 B.C. and died in 260 B.C., and lived to be about 70 years old.

Some writers in the [[Middle Ages]] confused him with [[Euclid of Megara]], a Greek [[Socrates|Socratic]] [[philosopher]] who lived approximately one century earlier.

==The ''Elements''==
{{main|Euclid's Elements}}
[[Image:Oxyrhynchus papyrus with Euclid's Elements.jpg|left|thumb|A fragment of Euclid's ''Elements'' found at [[Oxyrhynchus]], which is dated to circa AD [[100]]. The diagram accompanies Book II, Proposition 5.]]
Although many of the results in ''Elements'' originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.

Although best-known for its geometric results, the ''Elements'' also includes [[number theory]]. It considers the connection between [[perfect numbers]] and [[Mersenne primes]], the infinitude of [[prime number]]s, [[Euclid's lemma]] on factorization (which leads to the [[fundamental theorem of arithmetic]] on uniqueness of [[integer factorization|prime factorizations]]), and the [[Euclidean algorithm]] for finding the [[greatest common divisor]] of two numbers.

The geometrical system described in the ''Elements'' was long known simply as ''[[geometry]]'', and was considered to be the only geometry possible. Today, however, that system is often referred to as ''[[Euclidean geometry]]'' to distinguish it from other so-called [[Non-Euclidean geometry|''Non-Euclidean geometries'']] that mathematicians discovered in the [[19th century]].

==Other works==
[[Image:Euclid.jpg|right|thumb|200px|Euclid, as imagined by [[Raphael]] in this detail from ''[[The School of Athens]]''.<ref>No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art depends on the artist's imagination.</ref>]]

In addition to the ''Elements'', at least five works of Euclid have survived to the present day.

* ''[[Data (Euclid)|Data]]'' deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the ''Elements''.
* ''On Divisions of Figures'', which survives only partially in [[Arabic language|Arabic]] translation, concerns the division of geometrical figures into two or more equal parts or into parts in given [[ratio]]s. It is similar to a [[third century]] AD work by [[Heron of Alexandria]].
* ''[[Catoptrics]]'', which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. This work is of doubtful authenticity, being perhaps by [[Autolycus of Pitane|Theon]] of Alexandria.
* [[Phaenomena]], is a treatise on spherical Astronomy, it survives in Greek and is quite similar to "On the Moving Sphere", by Autolycus of Pitane, who flourished around 310 B.C.
* [[Optics]], is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: ``Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal.'' In the 36 propositions which follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. [[Pappus]] believed such results to be important in astronomy and included Euclid's Optics, along with the previous work, Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy.

All of these works follow the basic logical structure of the ''Elements'', containing definitions and proved propositions.

There are works credibly attributed to Euclid which have been lost.
* ''Conics'' was a work on [[conic section]]s that was later extended by [[Apollonius of Perga]] into his famous work on the subject. It is likely that the first four books of Apollonius' work come directly from Euclid. [[Pappus]] states that ``Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics.'' The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclid's work was already lost.
* ''[[Porism]]s'' might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial.
* ''Pseudaria'', or ''Book of Fallacies'', was an elementary text about errors in [[reasoning]].
* ''Surface Loci'' concerned either [[Locus (mathematics)|loci]] (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with [[Quadric|quadric surfaces]].
* Several works on [[Mechanics]] are attributed to Euclid by Arabic sources. "On the Heavy and the Light" contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. A book "On the Balance" treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions. These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on [[Mechanics]] written by Euclid.

==See also==
* [[Euclidean geometry]]
* [[Axiomatic method]]
* [[Euclidean algorithm]]

==Footnotes==
<references/>
==References==
* Artmann, Benno (1999). ''Euclid: The Creation of Mathematics''. New York: Springer. ISBN 0-387-98423-2.
*{{cite book
| first=Carl B.
| last=Boyer
| authorlink=Carl Benjamin Boyer
| title=A History of Mathematics
| edition=2d ed.
| publisher=John Wiley & Sons, Inc.
| year=1991
| isbn=0-47154397-7
}}
* [[Ivor Bulmer-Thomas|Bulmer-Thomas, Ivor]] (1971). "Euclid". ''Dictionary of Scientific Biography.''
* Heath, Thomas L. (1956). ''The Thirteen Books of Euclid's Elements'', Vol. 1 (2nd ed.). New York: Dover Publications. ISBN 0-486-60088-2: includes extensive commentaries on Euclid and his work in the context of the history of mathematics that preceded him.
* Heath, Thomas L. (1981). ''A History of Greek Mathematics'', 2 Vols. New York: Dover Publications. ISBN 0-486-24073-8 / ISBN 0-486-24074-6.
* Kline, Morris (1980). ''Mathematics: The Loss of Certainty''. Oxford: Oxford University Press. ISBN 0-19-502754-X.
* {{MacTutor Biography|id=Euclid}}

==External links==
{{wikiquote}}
{{Commonscat}}
*[http://aleph0.clarku.edu/~djoyce/java/elements/elements.html Euclid's elements], All thirteen books, with interactive diagrams using Java. [[Clark University]]
*[http://farside.ph.utexas.edu/euclid.html Euclid's elements], with the original Greek and an English translation on facing pages (includes PDF version for printing) (only the first ten books). [[University of Texas]].
* [[:Image:Euclid-Elements.pdf|Euclid's Elements]] in ancient Greek (typeset in PDF format, public domain, available in print at [[Lulu.com]] as [http://www.lulu.com/content/829379 "Euclid's Elements"].)
*[http://euclides.org Euclid's elements], All thirteen books, in Spanish and Catalan.
*[http://www.rarebookroom.org/Control/eucgeo/index.html ''Elementa Geometriae''] 1482, Venice. From [[Rare Book Room]].
*[http://www.rarebookroom.org/Control/eucmsd/index.html ''Elementa''] 888 AD, Byzantine. From [[Rare Book Room]].
* [http://www.mathopenref.com/euclid.html Euclid biography by Charlene Douglass] With extensive bibliography.
* [http://www.wilbourhall.org Euclid's Elements.] Heiberg's edition of the Greek with Latin translation (public domain). PDF scans of all 13 books.
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{{Greek mathematics}}

{{Persondata
|NAME=Euclid
|ALTERNATIVE NAMES=Euclid of Alexandria; Εὐκλείδης (Greek)
|SHORT DESCRIPTION=Greek mathematician
|DATE OF BIRTH=325 BCE
|PLACE OF BIRTH=
|DATE OF DEATH=265 BCE
|PLACE OF DEATH=
}}
[[Category:Ancient Greek mathematicians]]
[[Category:Ancient Alexandrians]]
[[Category:Hellenistic Egyptians]]
[[Category:Geometers]]
[[Category:4th century BC births]]
[[Category:3rd century BC deaths]]
[[Category:Number theory]]

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Revision as of 01:33, 19 March 2008

this guy was terrible at math and was wicked cool. born in jamaica he live in l yal peace.