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...

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...

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...

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

notes on Euclid's Elements, which he had with great pains drawn up and digested. Afterwards our author Billingsley translated the said Elements into English...

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...

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...

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

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

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...

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,...

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...

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

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...

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...

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...

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"...

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...

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...

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...

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...

depends upon Euclid's parallel postulate will be referred to as the "High school exterior angle theorem" (HSEAT) to distinguish it from Euclid's exterior...

of Euclid's Elements (Cambridge: Cambridge University Press, 1908) Aristarchus of Samos, the Ancient Copernicus Oxford: Clarendon Press, 1913) Euclid in...

by Proclus (AD 412 to 485) in his commentary on the first book of Euclid's Elements: one pair of parallel sides – a trapezium (τραπέζιον), divided into...

dimensions is the lemon. This figure appears in the first proposition of Euclid's Elements, where it forms the first step in constructing an equilateral triangle...

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...

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