Commentary on the Difficulties of Certain Postulates of Euclid
E131567
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.
All labels observed (2)
How this entity was disambiguated
This entity first appeared as the object of triple T1148806 — 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: Commentary on the Difficulties of Certain Postulates of Euclid Context triple: [Omar Khayyam, notableWork, Commentary on the Difficulties of Certain Postulates of Euclid]
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A.
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.
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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.
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C.
Ethica, ordine geometrico demonstrata
Ethica, ordine geometrico demonstrata is Baruch Spinoza’s major philosophical work, a systematic treatise that presents his metaphysics, ethics, and theory of mind in a rigorous, geometrical style.
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D.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
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E.
Grundgesetze der Arithmetik, Volume II
Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
- 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: Commentary on the Difficulties of Certain Postulates of Euclid Target entity description: 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.
-
A.
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.
-
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.
Ethica, ordine geometrico demonstrata
Ethica, ordine geometrico demonstrata is Baruch Spinoza’s major philosophical work, a systematic treatise that presents his metaphysics, ethics, and theory of mind in a rigorous, geometrical style.
-
D.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
-
E.
Grundgesetze der Arithmetik, Volume II
Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical treatise
ⓘ
work on geometry ⓘ |
| addresses |
consistency of Euclid's axioms
ⓘ
independence of the parallel postulate ⓘ |
| aimsTo | resolve difficulties in Euclid's postulates ⓘ |
| analyzes | logical structure of Euclid's postulates ⓘ |
| associatedWith | medieval Islamic mathematics ⓘ |
| author | Omar Khayyam ⓘ |
| contributesTo |
early studies of the parallel postulate
ⓘ
foundations of geometry ⓘ |
| critiques |
Playfair's axiom
ⓘ
surface form:
Euclid's fifth postulate
|
| examines | equivalent formulations of the parallel postulate ⓘ |
| field |
geometry
ⓘ
history of mathematics ⓘ |
| focusesOn | parallel postulate ⓘ |
| genre | mathematical commentary ⓘ |
| hasAuthorOccupation |
astronomer
ⓘ
mathematician ⓘ philosopher ⓘ |
| historicalPeriod | Islamic Golden Age ⓘ |
| influenced | later work on the foundations of geometry ⓘ |
| influencedBy |
Euclid's Elements
ⓘ
surface form:
Elements (Euclid)
|
| language | Arabic ⓘ |
| mainSubject |
Euclid's postulates
ⓘ
Euclidean geometry ⓘ |
| notableFor |
early attempt to strengthen Euclid's axiomatic system
ⓘ
systematic critique of the parallel postulate ⓘ |
| originalTitleLanguage | Arabic ⓘ |
| philosophicalAspect |
nature of mathematical proof
ⓘ
status of axioms in geometry ⓘ |
| prefigures | later investigations of non-Euclidean geometry ⓘ |
| preservedIn | manuscript tradition ⓘ |
| regionOfOrigin | Persia ⓘ |
| relatedWork | Treatise on the Division of Quadrants (Omar Khayyam) ⓘ |
| seeksTo | derive the parallel postulate from other axioms ⓘ |
| studiedBy |
historians of mathematics
ⓘ
scholars of Islamic philosophy ⓘ |
| studiedIn |
history of Islamic science
ⓘ
history of geometry ⓘ |
| timeOfComposition |
11th century
ⓘ
12th century ⓘ |
| tradition | Islamic commentary tradition on Greek mathematics ⓘ |
| uses |
geometric constructions
ⓘ
logical argumentation ⓘ |
| writtenBy | Omar Khayyam ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Commentary on the Difficulties of Certain Postulates of Euclid Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Treatise on Demonstration of Problems of Algebra
→
alsoKnownAs
→
Commentary on the Difficulties of Certain Postulates of Euclid
ⓘ
this entity surface form:
Risāla fī sharḥ mā ashkala min muṣādarāt kitāb Uqlīdis (contextually related work / tradition)