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...

These include Pythagorean theorem, Thales' theorem, the Euclidean algorithm for greatest common divisors, Euclid's theorem that there are infinitely many...

The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and...

never ends. This statement is referred to as Euclid's theorem in honor of the ancient Greek mathematician Euclid, since the first known proof for this statement...

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

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...

They are named after the ancient Greek mathematician Euclid, in connection with Euclid's theorem that there are infinitely many prime numbers. For example...

propositions (theorems) from these. One of those is the parallel postulate which relates to parallelism on a Euclidean plane. Although many of Euclid's results...

Euclidean division is based on the following result, which is sometimes called Euclid's division lemma. Given two integers a and b, with b ≠ 0, there exist unique...

The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than...

Company. p. 435. ISBN 0-393-04002-X. Heiberg, J.L. "Euclid's Elements of Geometry" (PDF). pp. 46–47. "Euclid's Elements, Book I, Proposition 47". See also a...

Euclidean theorem may refer to: Any theorem in Euclidean geometry Any theorem in Euclid's Elements, and in particular: Euclid's theorem that there are...

\ } and Dirichlet's theorem states that this sequence contains infinitely many prime numbers. The theorem extends Euclid's theorem that there are infinitely...

Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements...

which is exactly what the theorem of the gnomon states. The theorem of the gnomon was described as early as in Euclid's Elements (around 300 BC), and...

is arguably closer to and in the same spirit as Euclid's original formulation. In this case Euclid's proof applies refutation by contradiction at one...

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

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

The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry...

greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime...

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

Euclid in 1795 in which he proposed replacing Euclid's fifth postulate by his own axiom. Today, over two thousand two hundred years later, Euclid's fifth...

called Legendre's theorem. The existence of at least one triangle with angle sum of 180 degrees in absolute geometry implies Euclid's parallel postulate...

natural number greater than 1 with no divisors other than 1 and itself. Euclid's theorem proves that for any given prime number, there will always be a higher...

associated circle. This result is found as Proposition 36 in Book 3 of Euclid's Elements. Given a secant g intersecting the circle at points G1 and G2...

In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created...

Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result in plane geometry which cannot be derived from Euclid's postulates...

mathematicians active in the 4th century BC. Euclid's Elements is also believed to contain many theorems that are attributed to mathematicians in the...

theorem (algebraic number theory) Equidistribution theorem (ergodic theory) Erdős–Kac theorem (number theory) Euclid's theorem (number theory) Euclid–Euler...

absolutely evident were called postulates or axioms; for example Euclid's postulates. All theorems were proved by using implicitly or explicitly these basic...