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The 56 pages that link to Euclid's Elements, each with the reason it gives.

• Euclidean geometryBroader topic: It preserved and organized the propositions that became classical Euclidean geometry.

• EuclidBroader topic: This is Euclid’s best-known work and the main source of his lasting mathematical influence.

• Mathematical proofBroader topic: Its axiomatic organization became a lasting model for mathematical exposition.

• AxiomBroader topic: Its geometric postulates became a lasting model for axiomatic mathematics.

• Euclidean algorithmRelated: Book VII presents the procedure for finding the greatest common measure of two numbers.

• History of mathematicsBroader topic: Its axiomatic structure shaped mathematical teaching and proof for centuries.

• Synthetic geometryBroader topic: Its axiomatic presentation became the enduring model for synthetic geometric proof.

• Eudoxus of CnidusRelated: Books V and XII preserve major results associated with Eudoxus.

• Golden ratioRelated: Its construction of division in extreme and mean ratio gives the classical geometric definition.

• Greek mathematicsBroader topic: It exemplifies the tradition’s chain of definitions, axioms, and demonstrated theorems.

• Foundations of mathematicsBroader topic: Its axiomatic presentation became a lasting model for deductive mathematics.

• Axiomatic methodBroader topic: Its systematic derivation of propositions became the model case for axiomatic organization.

• Geometric constructionRelated: Its propositions helped establish construction as a standard method of geometric proof.

• Thales' theoremRelated: Its circle theorems provide a formal framework for proving this result.

• Euclid's lemmaBroader topic: Book VII contains the proposition traditionally identified with Euclid's lemma.

• Method of exhaustionRelated: Book XII uses exhaustion to prove results about circles, pyramids, cones, and spheres.

• HypatiaRelated: Theon’s edition and commentary belonged to the mathematical scholarship associated with Hypatia’s family.

• Latin translations of the 12th centuryBroader topic: Latin versions transmitted Greek mathematical knowledge to medieval scholars.

• Sieve of EratosthenesRelated: Its treatment of primes and divisibility provides an earlier context for the sieve’s subject.

• Gerard of CremonaRelated: Gerard’s Latin version helped make this foundational mathematical text accessible to Western scholars.

• Graeco-Arabic translation movementBroader topic: Its Arabic versions transmitted Greek mathematical reasoning and supported later mathematical work.

• Platonic solidRelated: Its final book constructs the five regular convex polyhedra.

• ProclusRelated: Proclus’s commentary explains the foundations and historical origins of this influential work.

• QuadriviumRelated: Its geometry became a major source for teaching the quadrivium’s spatial mathematics.

• Straightedge and compass constructionRelated: Its first book sets out basic constructions using a straightedge and compass.

• Archimedean propertyRelated: Book V's common notion on repeated multiples anticipates the comparison underlying the property.

• DemonstrationBroader topic: Its organized proofs became a lasting model of demonstrative mathematical knowledge.

• Foundations of GeometryBroader topic: Its axiomatic presentation shaped the foundational ideal that later mathematicians examined.

• Geometric proofRelated: Its propositions provide a foundational collection of classical geometric arguments.

• Philosophy of mathematicsBroader topic: Its axiomatic presentation became a lasting model for foundational organization.

• Hilbert's axiomsRelated: Hilbert's formulation made explicit assumptions that Euclid's presentation left implicit.

• Icosahedral symmetryRelated: Its final book constructs the regular icosahedron and establishes classical results about it.

• Mary SomervilleRelated: Studying Euclid gave Somerville a foundation in formal mathematics.

• Perfect numberBroader topic: Book IX contains the construction later recognized as producing even perfect numbers.

• History of geometryBroader topic: Its axiomatic structure became the most influential model of geometry for centuries.

• Pure mathematicsBroader topic: Its axiomatic presentation shaped mathematical exposition for more than two millennia.

• Theon of AlexandriaRelated: Theon’s edition helped transmit this foundational mathematical text.

• BetweennessRelated: Its geometric arguments use point order intuitively, before betweenness was axiomatized separately.

• Regular dodecahedronRelated: Book XIII culminates in the construction and classification of the five regular solids.

• Formal scienceBroader topic: Its axiomatic presentation became a durable model of mathematical exposition.

• Hyperbolic triangleRelated: Its parallel postulate became the point of departure for the geometry of these triangles.

• Pasch's axiomCompared with: Euclid's development relies on intuitive order facts that Pasch's axiom states explicitly.

• Tarski's axiomsRelated: Tarski's formal system recasts the tradition of Euclidean geometry in modern logic.

• Poncelet–Steiner theoremRelated: Its constructions established straightedge-and-compass methods as a classical geometric standard.

• Square root of 2Related: Book X classifies incommensurable magnitudes, including the relation between a square's side and diagonal.

• Mohr–Mascheroni theoremNarrower topic: Classical Euclidean construction problems supplied the setting for the theorem.

• Segment Addition PostulateRelated: Its axiomatic tradition provides the model for treating geometric relations as postulates.

• Six circles theoremNarrower topic: The theorem extends the synthetic tradition of proving geometric incidence from elementary relations.

• Axiom (mathematics and logic)Broader topic: Its geometric postulates became a lasting model for axiomatic mathematics.

• Barrow's inequalityRelated: Its triangle principles provide background for classical geometric inequalities.