Euclid


Also found in: Dictionary, Thesaurus, Acronyms, Wikipedia.
Related to Euclid: Euclid elements

Euclid,

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.

Euclid

(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.
..... Click the link for more information.
 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,
..... Click the link for more information.
 (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
..... Click the link for more information.
 (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.
..... Click the link for more information.
 (1854).

Bibliography

See D. Berlinski, The King of Infinite Space: Euclid and His Elements (2013).

Euclid

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

Euclid

(language)
(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 classic literature ?
They took De Foe to their bosoms, instead of Euclid, and seemed to be on the whole more comforted by Goldsmith than by Cocker.
In her desire to be in all things his companion, she would have set herself with equal zeal to master Algebra, or Euclid, if he had divided his soul between her and either.
His conclusions were as infallible as so many propositions of Euclid.
Stelling set to work at his natural method of instilling the Eton Grammar and Euclid into the mind of Tom Tulliver.
said Tom, in such high spirits at this announcement that he quite enjoyed the idea of confounding Maggie by showing her a page of Euclid.
what I've got to do," said Tom, drawing Maggie toward him and showing her his theorem, while she pushed her hair behind her ears, and prepared herself to prove her capability of helping him in Euclid.
She knew she could do Euclid, for she had looked into it again, and she saw what A B C meant; they were the names of the lines.
Stelling," she said, that same evening when they were in the drawing-room, "couldn't I do Euclid, and all Tom's lessons, if you were to teach me instead of him?
The ribbon has been cut on Stemilt Growers' new, state-of-the-art cherry packing line at the company's Euclid Street facility in Wenatchee.
The Euclid clutch catalog has been updated to include the self-adjusting clutch and features the specification and ordering process for customers, visuals with component descriptions, flywheel gauge and adjustment tool instructions and current cross reference details.
He begins by interpreting signs from Euclid about the meaning of geometry as it applies to Berkinski, observes an abstraction, gives common beliefs about Euclid and his work, shows that the work is actually darker by definition, gives the axioms an backs them up in a new way with visible and invisible proof, explains "the devil's offer, "exercises the Euclidian joint stock company, and elucidates Euclid's triumphant management of the elements of plane geometry.
The European Space Agency yesterday said Euclid was ready for construction after announcing that Italian company Thales will be the prime contractor.