also **Eu·clid·i·an**

adjective

also **Eu·clid·i·an**

adjective

Of or relating to Euclid's geometric principles.

THE AMERICAN HERITAGE® DICTIONARY OF THE ENGLISH LANGUAGE, FIFTH EDITION by the Editors of the American Heritage Dictionaries. Copyright © 2016, 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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**MLA Style**

"Euclidean." YourDictionary, n.d. Web. 20 January 2019. <https://www.yourdictionary.com/Euclidean>.

**APA Style**

Euclidean. (n.d.). Retrieved January 20th, 2019, from https://www.yourdictionary.com/Euclidean

Relating to geometry of plane figures based on the five postulates (axioms) of Euclid, involving the derivation of theorems from those postulates. The five postulates are: **1. **Any two points can be joined by a straight line. **2. **Any straight line segment can be extended indefinitely in a straight line. **3. **Given any straight line segment, a circle can be drawn having the line segment as radius and an endpoint as center. **4. **All right angles are congruent. **5. **(Also called the *parallel postulate.*) If two lines are drawn that intersect a third in such a way that the sum of inner angles on one side is less than the sum of two right triangles, then the two lines will intersect each other on that side if the lines are extended far enough.

Compare non-Euclidean

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**MLA Style**

"Euclidean." YourDictionary, n.d. Web. 20 January 2019. <https://www.yourdictionary.com/Euclidean>.

**APA Style**

Euclidean. (n.d.). Retrieved January 20th, 2019, from https://www.yourdictionary.com/Euclidean

Adjective

(*not comparable*)

- (rare) Alternative spelling of
*Euclidean*.

English Wiktionary. Available under CC-BY-SA license.

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**MLA Style**

"Euclidean." YourDictionary, n.d. Web. 20 January 2019. <https://www.yourdictionary.com/Euclidean>.

**APA Style**

Euclidean. (n.d.). Retrieved January 20th, 2019, from https://www.yourdictionary.com/Euclidean

- Reference should be made to the article Geometry:
**Euclidean**, for a detailed summary of the**Euclidean**treatment, and the elementary properties of the circle. - A much less wise class than the 7r-computers of modern times are the pseudo-circle-squarers, or circle-squarers technically so called, that is to say, persons who, having obtained by illegitimate means a
**Euclidean**construction for the quadrature or a finitely expressible value for 7r, insist on using faulty reasoning and defective mathematics to establish their assertions. - At the same time, it delights the pure theorist by the simplicity of the logic with which the fundamental theorems may be established, and by the elegance of its mathematical operations, insomuch that hydrostatics may be considered as the
**Euclidean**pure geometry of mechanical science. - The problem of finding a square equal in area to a given circle, like all problems, may be increased in difficulty by the imposition of restrictions; consequently under the designation there may be embraced quite a variety of geometrical problems. It has to be noted, however, that, when the " squaring " of the circle is especially spoken of, it is almost always tacitly assumed that the restrictions are those of the
**Euclidean**geometry. - Since the area of a circle equals that of the rectilineal triangle whose base has the same length as the circumference and whose altitude equals the radius (Archimedes, KIKXou A ir, prop.i), it follows that, if a straight line could be drawn equal in length to the circumference, the required square could be found by an ordinary
**Euclidean**construction; also, it is evident that, conversely, if a square equal in area to the circle could be obtained it would be possible to draw a straight line equal to the circumference.

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