The Book of Lemmas or Book of Assumptions (Arabic Maʾkhūdhāt Mansūba ilā Arshimīdis) is a book attributed to Archimedes by Thābit ibn Qurra, though the...

altitudes of a triangle concur (at the orthocenter) is not directly stated in surviving Greek mathematical texts, but is used in the Book of Lemmas (proposition...

earliest known reference to this figure is in Archimedes's Book of Lemmas, where some of its mathematical properties are stated as Propositions 4 through...

Archimedes' Book of Lemmas or Liber Assumptorum is a treatise with 15 propositions on the nature of circles. The earliest known copy of the text is in...

Greek) is a geometrical figure that consists of four semicircles. It was first introduced in the Book of Lemmas, a work attributed to Archimedes. Let A, D...

appeared in the Book of Lemmas, which showed (Proposition V) that the two circles are congruent. Thābit ibn Qurra, who translated this book into Arabic,...

on Archimedes's Book of Lemmas and Menelaus's theorem (Kitab al-ishba, or "satiation"), where he made corrections to the Book of Lemmas as translated into...

Archimedean circle was first constructed by Archimedes in his Book of Lemmas. In his book, he constructed what is now known as Archimedes' twin circles...

Conics books V to VII Apollonius, Cutting Off of a Ratio Archimedes, Book of Lemmas Archimedes, Construction of the Regular Heptagon Diocles, On Burning Mirrors...

On Floating Bodies Book of Lemmas The Method Treating of Mechanical Problems Apollonius of Perga On Conic Sections Nicomachus of Gerasa Introduction to...

semicircle with radius r2. According to Proposition 5 of Archimedes' Book of Lemmas, the common radius of Archimedes' twin circles is: r 1 ⋅ r 2 r . {\displaystyle...

Pseudo-Archimedes, the Book of Lemmas, is an Arabic treatise not listed among Archimedes' works. Donald Routledge Hill is of the opinion that the original...

Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma, or the orbit-counting theorem, is a result in group theory...

In mathematics, Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says...

q1 and q2. Then (the first equality is Proposition 11 in Archimedes' Book of Lemmas) D 2 = p 1 2 + p 2 2 + q 1 2 + q 2 2 = a 2 + c 2 = b 2 + d 2 {\displaystyle...

Zorn's lemma, also known as the Kuratowski–Zorn lemma, is a proposition of set theory. It states that a partially ordered set containing upper bounds...

create another continuous function. The lemma is implicit in the use of piecewise functions. For example, in the book Topology and Groupoids, where the condition...

In mathematics, the Yoneda lemma is a fundamental result in category theory. It is an abstract result on functors of the type morphisms into a fixed object...

Euclid's lemma is a lemma that captures a fundamental property of prime numbers: Euclid's lemma — If a prime p divides the product ab of two integers...

lemma, named after Hermann Amandus Schwarz, is a result in complex analysis about holomorphic functions from the open unit disk to itself. The lemma is...

Terrae, epitome of Aristarchus of Samos's On the Sizes and Distances Lemmata Archimedis, translation by John Greaves of the Book of Lemmas, attributed to...

Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who...

Shephard's lemma is a major result in microeconomics having applications in the theory of the firm and in consumer choice. The lemma states that if indifference...

In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a univariate...

Between the ages of 20 and 60, people learn about 6,000 more lemmas, or one every other day. An average 20-year-old knows 42,000 lemmas coming from 11,100...

q1 and q2. Then (the first equality is Proposition 11 in Archimedes' Book of Lemmas) D 2 = p 1 2 + p 2 2 + q 1 2 + q 2 2 = a 2 + c 2 = b 2 + d 2 {\displaystyle...

Laurence A (1977-07-01). "Cubical sperner lemmas as applications of generalized complementary pivoting". Journal of Combinatorial Theory. Series A. 23 (1):...

The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have...

of Sidon (Stoic) Boios Boium Bolbe Bolina Bolina (Achaea) Bomolochus Book of Lemmas Boreads Boreas Borghese Gladiator Borghese Vase Bormus Borus Borysthenes...

Titu's lemma, Bergström's inequality, Engel's form or Sedrakyan's inequality, respectively, referring to the article About the applications of one useful...