Treatise on Demonstration of Problems of Algebra
E131566
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Treatise on Demonstration of Problems of Algebra canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T1148805 — 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: Treatise on Demonstration of Problems of Algebra Context triple: [Omar Khayyam, notableWork, Treatise on Demonstration of Problems of Algebra]
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A.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
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B.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
C.
The Mathematical Analysis of Logic
The Mathematical Analysis of Logic is George Boole’s pioneering 1847 work that laid the foundations of symbolic logic and helped initiate the algebraic treatment of logical reasoning.
-
D.
Begriffsschrift
Begriffsschrift is Gottlob Frege’s groundbreaking 1879 work that introduced a formal logical notation and is widely regarded as the foundation of modern 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
- 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: Treatise on Demonstration of Problems of Algebra Target entity description: Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
-
A.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
B.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
C.
The Mathematical Analysis of Logic
The Mathematical Analysis of Logic is George Boole’s pioneering 1847 work that laid the foundations of symbolic logic and helped initiate the algebraic treatment of logical reasoning.
-
D.
Begriffsschrift
Begriffsschrift is Gottlob Frege’s groundbreaking 1879 work that introduced a formal logical notation and is widely regarded as the foundation of modern 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 (38)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical treatise ⓘ work on algebra ⓘ |
| alsoKnownAs |
Commentary on the Difficulties of Certain Postulates of Euclid
ⓘ
surface form:
Risāla fī sharḥ mā ashkala min muṣādarāt kitāb Uqlīdis (contextually related work / tradition)
|
| approach |
geometric demonstration
ⓘ
systematic classification of equation types ⓘ |
| author | Omar Khayyam ⓘ |
| authorNationality | Persian ⓘ |
| authorOccupation |
astronomer
ⓘ
mathematician ⓘ philosopher ⓘ |
| contributedTo |
history of algebra
ⓘ
history of cubic equations ⓘ |
| field |
algebra
ⓘ
geometry ⓘ |
| genre | mathematics ⓘ |
| hasPart |
classification of cubic equations
ⓘ
geometric constructions using conic sections ⓘ |
| historicalSignificance | one of the earliest systematic treatments of cubic equations ⓘ |
| influenced |
development of algebra in Europe
ⓘ
later Islamic algebraists ⓘ |
| influencedBy |
Greek geometry
ⓘ
earlier Islamic mathematics ⓘ |
| mainSubject |
algebra
ⓘ
cubic equations ⓘ geometric solutions of equations ⓘ |
| notableFor |
early development of algebraic geometry ideas
ⓘ
geometric solutions of cubic equations ⓘ systematic analysis of cubic equations ⓘ |
| originalLanguage | Arabic ⓘ |
| period | Islamic Golden Age ⓘ |
| relatedTo |
Al-Khwarizmi's Al-jabr wa-l-muqabala
ⓘ
surface form:
al-Khwarizmi's algebra
history of conic sections ⓘ |
| timeOfCreation |
11th century
ⓘ
12th century ⓘ |
| title | Treatise on Demonstration of Problems of Algebra self-link ⓘ |
| uses |
conic sections
ⓘ
geometric methods ⓘ |
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: Treatise on Demonstration of Problems of Algebra Description of subject: Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Treatise on Demonstration of Problems of Algebra
→
title
→
Treatise on Demonstration of Problems of Algebra
self-link
ⓘ