Géométrie de position
E144233
Géométrie de position is a foundational 1803 treatise by Lazare Carnot that helped establish projective geometry and modern geometric reasoning about position and transformation.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Geometry of Position | 1 |
| Géométrie de position canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1260571 — 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: Géométrie de position Context triple: [Lazare Carnot, notableWork, Géométrie de position]
-
A.
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.
-
B.
Lie sphere geometry
Lie sphere geometry is a branch of differential geometry that studies the properties and transformations of spheres (and related objects like planes and points) using the methods of Lie groups and projective geometry.
-
C.
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.
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D.
Dioptrique
Dioptrique is a scientific treatise by René Descartes that lays out his pioneering theories on light and optics, including the law of refraction.
-
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: Géométrie de position Target entity description: Géométrie de position is a foundational 1803 treatise by Lazare Carnot that helped establish projective geometry and modern geometric reasoning about position and transformation.
-
A.
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.
-
B.
Lie sphere geometry
Lie sphere geometry is a branch of differential geometry that studies the properties and transformations of spheres (and related objects like planes and points) using the methods of Lie groups and projective geometry.
-
C.
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.
-
D.
Dioptrique
Dioptrique is a scientific treatise by René Descartes that lays out his pioneering theories on light and optics, including the law of refraction.
-
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 |
book
ⓘ
mathematical treatise ⓘ work on geometry ⓘ |
| approach | synthetic geometry ⓘ |
| author | Lazare Carnot ⓘ |
| contributedTo |
development of projective geometry
ⓘ
modern geometric reasoning about position ⓘ modern geometric reasoning about transformation ⓘ |
| countryOfOrigin | France ⓘ |
| field |
geometry
ⓘ
mathematics ⓘ projective geometry ⓘ |
| focus |
incidence relations between points and lines
ⓘ
invariance under geometric transformations ⓘ |
| hasAuthor | Lazare Carnot ⓘ |
| hasAuthorRole | Lazare Carnot ⓘ |
| hasGenre |
mathematical literature
ⓘ
scientific literature ⓘ |
| hasKeyConcept |
geometric transformation
ⓘ
invariance ⓘ positional geometry ⓘ projective properties ⓘ synthetic methods in geometry ⓘ |
| historicalPeriod | early 19th century ⓘ |
| influenced |
19th‑century projective geometry
ⓘ
Jean‑Victor Poncelet ⓘ development of synthetic geometry ⓘ |
| mainSubject |
geometric properties invariant under projection
ⓘ
geometry of position ⓘ transformations in geometry ⓘ |
| notableFor |
early systematic treatment of projective methods
ⓘ
emphasis on positional relationships over metric properties ⓘ foundational role in projective geometry ⓘ |
| originalLanguage | French ⓘ |
| partOf |
history of mathematics
ⓘ
history of projective geometry ⓘ |
| publicationCentury | 19th century ⓘ |
| publicationYear | 1803 ⓘ |
| relatedTo |
foundations of geometry
ⓘ
projective geometry ⓘ synthetic projective geometry ⓘ |
| titleTranslation |
Géométrie de position
self-linksurface differs
ⓘ
surface form:
Geometry of Position
|
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: Géométrie de position Description of subject: Géométrie de position is a foundational 1803 treatise by Lazare Carnot that helped establish projective geometry and modern geometric reasoning about position and transformation.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Geometry of Position