Linked from

The 137 pages that link to Euclidean geometry, each with the reason it gives.

• Doubling the cubeNarrower topic: The original challenge belongs to the geometric tradition that defined its construction rules.

• Euclidean planeNarrower topic: The plane is the basic two-dimensional setting for this geometry.

• QuadrilateralNarrower topic: Standard quadrilateral angle and parallel-side properties assume a Euclidean plane.

• Elliptic geometryCompared with: Its parallel postulate is replaced by elliptic geometry's claim that no parallels exist.

• ParallelogramRelated: The usual parallelogram properties assume the flat geometry of Euclidean space.

• Piero della FrancescaNarrower topic: Piero’s mathematical investigations draw on the geometric principles established in this tradition.

• Right angleNarrower topic: Its familiar rules define right angles through perpendicular lines and equal quarter-turns.

• Complete quadrilateralCompared with: Metric properties are not intrinsic to the quadrilateral’s projective incidence structure.

• Geometric inequalityNarrower topic: Many classical inequalities compare lengths, angles, and areas in Euclidean figures.

• Nikolai LobachevskyCompared with: Its parallel postulate was the assumption Lobachevsky challenged.

• Point (geometry)Narrower topic: Its axioms describe how points relate to lines and planes.

• Projective dualityCompared with: Those metric properties are not what projective duality preserves.

• Angle bisector theoremNarrower topic: The familiar theorem and its standard parallel-line proof belong to Euclidean geometry.

• Circle packingNarrower topic: Ordinary circle tangency is defined using Euclidean distance.

• Constructible numberNarrower topic: Classical straightedge-and-compass constructions are formulated within this geometric setting.

• Hyperbolic planeCompared with: Its unique-parallel rule is the alternative that hyperbolic geometry rejects.

• Leon Battista AlbertiRelated: Geometry supplied tools for Alberti’s account of proportion and perspective.

• Miquel's theoremNarrower topic: Miquel's theorem is a classical incidence result in the Euclidean plane.

• Straightedge and compass constructionNarrower topic: The classical construction rules are formulated within this geometric framework.

• Foundations of GeometryBroader topic: It provides the canonical example of a geometry organized around explicit postulates.

• Geometric proofNarrower topic: Its postulates provide the familiar framework for many classical geometric proofs.

• Intersecting chords theoremNarrower topic: The theorem belongs to classical circle geometry in the Euclidean plane.

• Pappus of AlexandriaNarrower topic: Its propositions and constructions form much of the geometry surveyed in the Collection.

• Roman surveyingNarrower topic: Geometric constructions made right angles, parallels, and measured plots reproducible.

• Simson lineNarrower topic: The construction and its classical proof use perpendiculars, circles, and angle relations.

• Spherical law of cosinesCompared with: Its triangle identities omit the curvature corrections present in the spherical formula.

• Axiomatic systemBroader topic: Its parallel postulate illustrates how changing one axiom can produce a different theory.

• Hilbert's axiomsNarrower topic: Hilbert's system formalizes this geometry while making its assumptions explicit.

• János BolyaiNarrower topic: Bolyai’s work departed from this geometric system by rejecting its parallel postulate.

• Spherical excessCompared with: Its triangle angle sum of 180 degrees supplies the baseline for the excess.

• Egyptian mathematicsCompared with: It highlights the difference between Egyptian practical procedures and later axiomatic presentation.

• Erlangen programBroader topic: Its transformations preserve distances and angles, illustrating Klein’s classification method.

• Euclid's theoremCompared with: It is the better-known subject of the same work, distinct from its number theory.

• Hippocrates of ChiosNarrower topic: His area arguments belong to the geometric tradition later organized by Euclid.

• History of geometryBroader topic: It became the central framework inherited from ancient Greek geometry.

• Ray (geometry)Narrower topic: Rays are standard objects in Euclidean constructions and proofs.

• Theon of AlexandriaBroader topic: Theon’s editorial work helped preserve the text that became geometry’s standard foundation.

• TransversalNarrower topic: The standard transversal angle theorems are stated in Euclidean geometry.

• BetweennessRelated: Euclidean geometry uses betweenness to express how points are ordered along a line.

• Skew linesNarrower topic: Its three-dimensional setting supplies the basic objects used to define skewness.

• Napoleon's theoremNarrower topic: The theorem is a classical result within the geometry of triangles and Euclidean constructions.

• Tangent–secant theoremNarrower topic: The theorem is a metric relation within classical plane geometry.

• Van Aubel's theoremNarrower topic: The theorem is a classical plane-geometric result built from squares and perpendicularity.

• Viviani's theoremNarrower topic: Perpendicular distances, triangle altitudes, and the area argument are Euclidean notions.

• Intercept theoremNarrower topic: The standard intercept theorem is a result within Euclidean geometry.

• Morley's trisector theoremNarrower topic: The result belongs to the classical geometry of triangles and their angle lines.

• Tarski's axiomsNarrower topic: Tarski's system formalizes this geometry through relations on points.

• Axiom (general principle)Broader topic: Its parallel postulate became a famous example of a geometric axiom.

• Exterior angle theoremNarrower topic: The theorem follows from Euclidean triangle angle sums.

• Intersecting secants theoremNarrower topic: The theorem is a metric result within classical plane geometry.