On the Principles of Geometry
E838599
"On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
All labels observed (1)
| Label | Occurrences |
|---|---|
| On the Principles of Geometry canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10055803 — 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: On the Principles of Geometry Context triple: [Nikolai Lobachevsky, notableWork, On the Principles of Geometry]
-
A.
The Foundations of Geometry
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.
-
B.
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.
-
C.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
-
D.
Commentary on Euclid's Elements
Commentary on Euclid's Elements is a late antique philosophical and mathematical treatise by Proclus that analyzes and interprets Euclid’s foundational geometry text while preserving valuable information about earlier Greek mathematics.
-
E.
Neue Geometrie des Raumes
Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
- 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: On the Principles of Geometry Target entity description: "On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
-
A.
The Foundations of Geometry
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.
-
B.
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.
-
C.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
-
D.
Commentary on Euclid's Elements
Commentary on Euclid's Elements is a late antique philosophical and mathematical treatise by Proclus that analyzes and interprets Euclid’s foundational geometry text while preserving valuable information about earlier Greek mathematics.
-
E.
Neue Geometrie des Raumes
Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
scientific work ⓘ treatise ⓘ |
| author | Nikolai Lobachevsky ⓘ |
| authorNationality | Russian ⓘ |
| authorOccupation | mathematician ⓘ |
| contribution |
demonstrated consistency of a geometry where multiple parallels through a point exist
ⓘ
introduced new trigonometric relations in hyperbolic geometry ⓘ provided alternative axioms to Euclidean geometry ⓘ showed that the sum of angles in a triangle can be less than 180 degrees ⓘ |
| countryOfOrigin | Russian Empire ⓘ |
| field |
geometry
ⓘ
hyperbolic geometry ⓘ non-Euclidean geometry ⓘ |
| genre | academic monograph ⓘ |
| hasKeyConcept |
geometric consistency independent of Euclid’s fifth postulate
ⓘ
models of hyperbolic space ⓘ parallel lines diverging ⓘ |
| historicalPeriod | 19th century ⓘ |
| impact |
contributed to the eventual acceptance of multiple geometries in mathematics
ⓘ
helped establish non-Euclidean geometry as a legitimate branch of mathematics ⓘ |
| influenced |
differential geometry
ⓘ
foundations of mathematics ⓘ theory of relativity ⓘ |
| influencedBy |
Euclid’s Elements
ⓘ
linked to:
Euclid's Elements
classical Euclidean geometry ⓘ |
| language | Russian ⓘ |
| mainSubject |
Euclid’s parallel postulate
ⓘ
linked to:
Playfair's axiom
angle sum of a triangle ⓘ foundations of geometry ⓘ geometric axioms ⓘ hyperbolic plane ⓘ parallel lines ⓘ |
| notableFor |
challenging the universality of Euclid’s parallel postulate
ⓘ
introducing non-Euclidean geometry ⓘ systematic development of hyperbolic geometry ⓘ |
| relatedConcept |
Lobachevskian geometry
ⓘ
linked to:
Non-Euclidean Geometry
curvature of space ⓘ hyperbolic trigonometry ⓘ |
| relatedWork |
Elements
ⓘ
Foundations of Geometry ⓘ
linked to:
The Foundations of Geometry
|
| topic |
axiomatic method in geometry
ⓘ
logical structure of geometric theories ⓘ |
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: On the Principles of Geometry Description of subject: "On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.