Grundlagen der Geometrie
E41776
Grundlagen der Geometrie is David Hilbert’s foundational 1899 treatise that rigorously axiomatizes Euclidean geometry and helped shape modern mathematical logic and the axiomatic method.
Observed surface forms (2)
| Surface form | As subject | As object |
|---|---|---|
| Foundations of Geometry (English translations) | 0 | 1 |
| Hilbert's axioms | 0 | 1 |
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
axiomatic work
→
mathematics book → treatise → |
| aim |
to clarify the logical structure of geometry
→
to provide a rigorous axiomatization of Euclidean geometry → |
| author | David Hilbert → |
| contains |
axioms of congruence
→
axioms of continuity → axioms of incidence → axioms of order → axioms of parallels → |
| countryOfOrigin | German Empire → |
| feature |
explicit separation of undefined terms and axioms
→
formal treatment of consistency and independence of axioms → systematic analysis of Euclid's postulates → use of models to study axiom systems → |
| field |
foundations of mathematics
→
geometry → mathematics → |
| genre | scientific monograph → |
| hasEdition |
fourth edition
→
later revised editions → second edition → third edition → |
| historicalSignificance |
contributed to the emergence of mathematical logic as a discipline
→
helped shape the formalist program in mathematics → milestone in the development of modern axiomatic geometry → |
| influenced |
20th-century mathematical logic
→
Hilbert-style proof systems → formal axiomatizations of mathematics → modern axiomatic method → |
| influencedBy | Euclid's Elements → |
| language | German → |
| originalTitle | Grundlagen der Geometrie self-link → |
| placeOfPublication | Leipzig → |
| publicationYear | 1899 → |
| publisher |
B. G. Teubner Verlag
→
surface form:
Teubner
|
| relatedConcept |
Grundlagen der Geometrie
self-linksurface differs
→
surface form:
Hilbert's axioms
formal system → |
| relatedWork |
Grundlagen der Geometrie
self-linksurface differs
→
surface form:
Foundations of Geometry (English translations)
Principia Mathematica → |
| subject |
Euclid's Elements
→
surface form:
Euclidean geometry
axiomatic method → foundations of geometry → mathematical logic → |
| topic |
axiomatization of geometry
→
logical foundations → |
| translatedInto |
English
→
French → other languages → |
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hilbert's axioms
this entity surface form:
Foundations of Geometry (English translations)