David Hilbert
Foundations of Geometry
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notions, including the essential concepts of point, line, and plane, along with relations such as Betweenness, Lies on, and Congruence. This monograph, which was inspired by Hilberts own lectures for a memo...
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017 - Proportion and the theorems of similitude 04.03.2026 6:00
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
016 - An algebra of segments based upon Pascal's theorem 04.03.2026 7:03
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
015 - Demonstrations of Pascal's theorem 04.03.2026 14:51
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
014 - Complex number-systems 04.03.2026 6:34
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
013 - Independence of the axiom of continuity Non-archimedean geometry 04.03.2026 6:25
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
012 - Independence of the axioms of congruence 04.03.2026 6:26
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
011 - Independence of the axioms of parallels Non-euclidean geometry 04.03.2026 4:59
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
010 - Compatibility of the axioms 04.03.2026 6:37
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
009 - Group V Axiom of Continuity Archimedes's axiom 04.03.2026 4:20
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
008 - Consequences of the axioms of congruence 04.03.2026 20:39
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
007 - Group IV Axioms of congruence 04.03.2026 8:38
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
006 - Group III Axioms of Parallels Euclid's axiom 04.03.2026 2:33
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
005 - Consequences of the axioms of connection and order 04.03.2026 7:01
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
004 - Group II Axioms of Order 04.03.2026 3:23
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
003 - Group I Axioms of connection 04.03.2026 3:55
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
002 - The elements of geometry and the five groups of axioms 04.03.2026 2:31
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
001 - Preface Contents and Introduction 04.03.2026 11:45
Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notion...
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