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(yo͞o`klĭd), fl. 300 B.C., Greek mathematician. Little is known of his life other than the fact that he taught at Alexandria, being associated with the school that grew up there in the late 4th cent. B.C. He is famous for his Elements, a presentation in thirteen books of the geometry and other mathematics known in his day. The first six books cover elementary plane geometry and have served since as the basis for most beginning courses on this subject. The other books of the Elements treat the theory of numbers and certain problems in arithmetic (on a geometric basis) and solid geometry, including the five regular polyhedra, or Platonic solids. A few modern historians have questioned Euclid's authorship of the Elements, but he is definitely known to have written other works, most notably the Optics.

The great contribution of Euclid was his use of a deductive system for the presentation of mathematics. Primary terms, such as point and line, are defined; unproved assumptions, or postulates, regarding these terms are stated; and a series of statements are then deduced logically from the definitions and postulates. Although Euclid's system no longer satisfies modern requirements of logical rigor, its importance in influencing the direction and method of the development of mathematics is undisputed.

One consequence of the critical examination of Euclid's system was the discovery in the early 19th cent. that his fifth postulate, equivalent to the statement that one and only one line parallel to a given line can be drawn through a point external to the line, can not be proved from the other postulates; on the contrary, by substituting a different postulate for this parallel postulate two different self-consistent forms of non-Euclidean geometrynon-Euclidean geometry,
branch of geometry in which the fifth postulate of Euclidean geometry, which allows one and only one line parallel to a given line through a given external point, is replaced by one of two alternative postulates.
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 were deduced, one by Nikolai I. LobachevskyLobachevsky, Nikolai Ivanovich
, 1793–1856, Russian mathematician. A pioneer in non-Euclidean geometry, he challenged Euclid's fifth postulate that one and only one line parallel to a given line can be drawn through a fixed point external to the line; he developed,
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 (1826) and independently by János BolyaiBolyai
, family of Hungarian mathematicians. The father, Farkas, or Wolfgang, Bolyai, 1775–1856, b. Bolya, Transylvania, was educated in Nagyszeben from 1781 to 1796 and studied in Germany during the next three years at Jena
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 (1832) and another by Bernhard RiemannRiemann, Bernhard
(Georg Friedrich Bernhard Riemann) , 1826–66, German mathematician. He studied at the universities of Göttingen and Berlin and was professor at Göttingen from 1859.
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See D. Berlinski, The King of Infinite Space: Euclid and His Elements (2013).


city (1990 pop. 54,875), Cuyahoga co., NE Ohio, a suburb adjoining Cleveland, on Lake Erie; settled 1798, inc. 1848. Named for the famous Greek mathematician, the industrial city manufactures metal goods, electrical supplies and equipment, airplane and automobile parts, and machinery. The National American Shrine of Our Lady of Lourdes is there.


1. 3rd century bc, Greek mathematician of Alexandria; author of Elements, which sets out the principles of geometry and remained a text until the 19th century at least
2. the works of Euclid, esp his system of geometry


(Named after the Greek geometer, fl ca 300 BC.) A Pascal descendant for development of verifiable system software. No goto, no side effects, no global assignments, no functional arguments, no nested procedures, no floats, no enumeration types. Pointers are treated as indices of special arrays called collections. To prevent aliasing, Euclid forbids any overlap in the list of actual parameters of a procedure. Each procedure gives an imports list, and the compiler determines the identifiers that are implicitly imported. Iterators.

Ottawa Euclid is a variant.

["Report on the Programming Language Euclid", B.W. Lampson et al, SIGPLAN Notices 12(2):1-79, Feb 1977].
References in periodicals archive ?
Based on Euclides da Cunha's Os Sertoes, a first-hand account of a violent rebellion in the backlands of late-19th century Brazil against the newly established national government, The War of the End of the World has proven to be an unusually prescient work of political fiction.
Doug Mientkiewicz, former owner of the ball that won the 2004 World Series, is managing the Twins' Florida State League (Class A) team in Fort Myers; reliever Carlos Reyes is a pitching coach in the Royals' farm system; and one-time Sox bullpen coach Euclides Rojas has the same job with the Pirates.
Leao TP, Silva AP, Macedo MCM, Imhoff S, Euclides VPB (2006) Least limiting water range: A potential indicator of changes in nearsurface soil physical quality after the conversion of Brazilian Savanna into pasture.
Right now the state has no money to move people from here, but they should at least provide us with minimum conditions," said Euclides Fernandes, 33.
Euclides Diaz, secretary at Anagan, said the main market for Panamanian meat was Taiwan, to which it sends about 50% of its exports, while Costa Rica absorbs exports of live cattle for fattening.
Aqui no Brasil, no inicio do seculo XX, o servidor publico Euclides da Cunha foi enviado pelo jornal O Estado de S.
Euclides da Cunha, the author of Backlands who witnessed portions of the battle provides a detailed description of the clash between these unlikely enemies and even "draws on anthropology, psychology, and social Darwinism to explain the popular interest in the Canudos religious community and its relationship with the whole of Brazil" (39).
In addition to Plato, students Xenophon, Euclides, Aeschines, Simon the Cobbler and others wrote about the Master; from Xenophon we have substantial extant texts (e.
Vargas Llosa's treatment of this story is a fictionalized version of a famous account of the rebellion written by Euclides da Cunha ([1902] 1944), a journalist who accompanied the fourth and final expedition.
Contudo, varios autores concordam que o uso de cruzamentos bem delineados pode melhorar os indices produtivos dos rebanhos e caracteristicas de carcaca e carne (PEROTTO, 2001; EUCLIDES FILHO et al.
Euclides reads the transcript of that conversation long after Socrates and Theaetetus are dead.
Leao TP, da Silva AP, Macedo MCM, Imhoff S, Euclides VPB (2006) Least limiting water range: A potential indicator of changes in near-surface soil physical quality after the conversion of Brazilian Savanna into pasture.