The Foundations of Geometry
E255570
The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
All labels observed (1)
| Label | Occurrences |
|---|---|
| The Foundations of Geometry canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2314441 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: The Foundations of Geometry Context triple: [Oswald Veblen, notableWork, The Foundations of Geometry]
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A.
Commentary on the Difficulties of Certain Postulates of Euclid
Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
-
B.
Über die Hypothesen, welche der Geometrie zu Grunde liegen
"Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
-
C.
Grundlagen der Geometrie
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.
-
D.
Book I of Geometry (Descartes)
Book I of Geometry (Descartes) is the opening section of René Descartes’ seminal work where he introduces his method of applying algebra to geometry, laying the foundations of analytic geometry.
-
E.
Euclides adauctus et methodicus
Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: The Foundations of Geometry Target entity description: The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
-
A.
Commentary on the Difficulties of Certain Postulates of Euclid
Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
-
B.
Über die Hypothesen, welche der Geometrie zu Grunde liegen
"Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
-
C.
Grundlagen der Geometrie
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.
-
D.
Book I of Geometry (Descartes)
Book I of Geometry (Descartes) is the opening section of René Descartes’ seminal work where he introduces his method of applying algebra to geometry, laying the foundations of analytic geometry.
-
E.
Euclides adauctus et methodicus
Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
geometry textbook
ⓘ
mathematics book ⓘ non‑fiction book ⓘ |
| academicDiscipline | pure mathematics ⓘ |
| aim | to provide a rigorous axiomatic basis for geometry ⓘ |
| author | Oswald Veblen ⓘ |
| bibliographicCategory | monograph ⓘ |
| countryOfOrigin |
United States of America
ⓘ
surface form:
United States
|
| field |
axiomatic set theory
ⓘ
geometry ⓘ mathematical logic ⓘ |
| hasEdition | reprinted editions in the 20th century ⓘ |
| hasInfluenced |
modern treatments of axiomatic geometry
ⓘ
research in mathematical logic and foundations ⓘ |
| hasPart |
system of axioms for congruence
ⓘ
system of axioms for continuity ⓘ system of axioms for incidence ⓘ system of axioms for order ⓘ system of axioms for parallels ⓘ |
| influencedBy |
David Hilbert
ⓘ
Euclid ⓘ Giuseppe Peano ⓘ |
| language | English ⓘ |
| mainConcept |
logical derivation of geometric theorems from axioms
ⓘ
primitive geometric notions such as point and line ⓘ |
| notableFor |
influence on 20th‑century foundations of mathematics
ⓘ
modern axiomatic treatment of geometric concepts ⓘ rigorous logical development of geometry ⓘ |
| publicationYear | 1904 ⓘ |
| publisher | Cambridge University Press ⓘ |
| relatedWork |
Grundlagen der Geometrie
ⓘ
surface form:
Foundations of Geometry by David Hilbert
|
| structure | organized into axioms theorems and proofs ⓘ |
| subject |
affine geometry
ⓘ
axiomatic foundations of geometry ⓘ logical foundations of mathematics ⓘ metric geometry ⓘ projective geometry ⓘ |
| targetAudience |
advanced students of mathematics
ⓘ
mathematical researchers ⓘ |
| timePeriod | early 20th century ⓘ |
| uses |
axiomatic method
ⓘ
symbolic logic ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: The Foundations of Geometry Description of subject: The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.