distance." Euclid, Elements, Book I, Postulates 1 & 3. Euclid's axiomatic approach and constructive methods were widely influential. Many of Euclid's propositions...

to the Elements, Euclid wrote a central early text in the optics field, Optics, and lesser-known works including Data and Phaenomena. Euclid's authorship...

In algebra and number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers: Euclid's lemma — If a prime p divides the...

the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean...

attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small...

Commentary on the First Book of Euclid's "Elements" Proclus (1970). A Commentary on the First Book of Euclid's Elements. Princeton, N.J.: Princeton University...

g_{k}} and derived a contradiction. Euclid's theorem states that there are infinitely many primes. In Euclid's Elements the theorem is stated in Book IX...

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid...

"Euclid's Elements, Book XII, Proposition 2". aleph0.clarku.edu. "Euclid's Elements, Book XII, Proposition 5". aleph0.clarku.edu. "Euclid's Elements,...

received their training from Euclid's students and his Elements and were able to solve many open problems at the time of Euclid. It is a prime example of...

become so popular that it is often referred to as Euclid's parallel axiom, even though it was not Euclid's version of the axiom. Proclus (410–485 A.D.) clearly...

written—the Elements (Stoichia) of Euclid. Considering the fame of the author and of his best seller, remarkably little is known of Euclid's life. So obscure...

Conceptual Development. Kluwer. ISBN 0-7923-5972-0. Euclid (1956). The Thirteen Books of Euclid's Elements, Translated from the Text of Heiberg, with Introduction...

mathematician Euclid, which he described (although non-rigorously by modern standards) in his textbook on geometry: the Elements. Euclid's method consists...

to the Elements, Euclid wrote a central early text in the optics field, Optics, and lesser-known works including Data and Phaenomena. Euclid's authorship...

Mathematics: From Thales to Euclid. New York: Dover Publications. p. 1. ISBN 978-0-486-24073-2. Mueller, I. (1969). "Euclid's Elements and the Axiomatic Method"...

arithmetic can also be proved without using Euclid's lemma. The proof that follows is inspired by Euclid's original version of the Euclidean algorithm...

explained by the side-side-angle congruence ambiguity. Book II of Euclid's Elements, compiled c. 300 BC from material up to a century or two older, contains...

of each of the other pairs are also congruent. Proposition 1.27 of Euclid's Elements, a theorem of absolute geometry (hence valid in both hyperbolic and...

an integral Euclid's Elements, a mathematical treatise on geometry and number theory An entry, or element, of a matrix. Classical elements, ancient beliefs...

until the 16th century. Book V of Euclid's Elements has 18 definitions, all of which relate to ratios. In addition, Euclid uses ideas that were in such common...

also equal. Euclid's proof involves drawing auxiliary lines to these extensions. But, as Euclid's commentator Proclus points out, Euclid never uses the...

VII Euclid, On Divisions of Figures Euclid, On Weights Heron, Catoptrica Heron, Mechanica Menelaus, Sphaerica Pappus, Commentary on Euclid's Elements book...

alternative symbol for a right angle. Right angles are fundamental in Euclid's Elements. They are defined in Book 1, definition 10, which also defines perpendicular...

to m and n from Euclid's formula is referenced throughout the rest of this article. Despite generating all primitive triples, Euclid's formula does not...

of Euclid, we do not know." Hypsicles letter was a preface of the supplement taken from Euclid's Book XIV, part of the thirteen books of Euclid's Elements...

introduced to Western Europe. The oldest surviving Latin translation of Euclid's Elements is a 12th-century translation by Adelard from an Arabic version. He...

mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. It is generally attributed to Thales of Miletus, but it is sometimes...

Demonstrations of Euclid's algorithm Weisstein, Eric W. "Euclidean Algorithm". MathWorld. Euclid's Algorithm at cut-the-knot Euclid's algorithm at PlanetMath...

defined in Book One of Euclid's Elements. The names used for modern classification are either a direct transliteration of Euclid's Greek or their Latin...