Treatise on the Division of Quadrants (Omar Khayyam)
E555120
Treatise on the Division of Quadrants is a mathematical work by Omar Khayyam in which he investigates geometric constructions and the division of arcs and quadrants, contributing to the development of geometry beyond Euclid.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Treatise on the Division of Quadrants (Omar Khayyam) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5915433 — 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.
Target entity: Treatise on the Division of Quadrants (Omar Khayyam) Context triple: [Commentary on the Difficulties of Certain Postulates of Euclid, relatedWork, Treatise on the Division of Quadrants (Omar Khayyam)]
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A.
Al-Farghani's Elements of Astronomy
Al-Farghani's Elements of Astronomy is a foundational 9th-century Arabic treatise that systematically summarizes and explains Ptolemaic astronomy and became highly influential in both the Islamic world and medieval Europe.
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B.
Al-Khwarizmi's Al-jabr wa-l-muqabala
Al-Khwarizmi's *Al-jabr wa-l-muqabala* is a foundational 9th-century mathematical treatise that systematically introduced and developed algebra as an independent discipline.
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C.
Ulugh Beg's Zij-i Sultani
Ulugh Beg's Zij-i Sultani is a 15th-century astronomical star catalogue and set of planetary tables compiled at the Samarkand observatory, renowned for its remarkably accurate measurements and lasting influence on later astronomy.
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D.
Treatise on Astronomy
Treatise on Astronomy is a 19th-century textbook by American mathematician and astronomer Elias Loomis that systematically presents the fundamental principles and observations of astronomy for students and general readers.
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E.
Al-Zarqali's Toledan Tables
Al-Zarqali's Toledan Tables are a highly influential set of medieval astronomical tables, compiled in Toledo, that provided precise planetary positions and were widely used across the Islamic world and later in Europe.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Treatise on the Division of Quadrants (Omar Khayyam) Target entity description: Treatise on the Division of Quadrants is a mathematical work by Omar Khayyam in which he investigates geometric constructions and the division of arcs and quadrants, contributing to the development of geometry beyond Euclid.
-
A.
Al-Farghani's Elements of Astronomy
Al-Farghani's Elements of Astronomy is a foundational 9th-century Arabic treatise that systematically summarizes and explains Ptolemaic astronomy and became highly influential in both the Islamic world and medieval Europe.
-
B.
Al-Khwarizmi's Al-jabr wa-l-muqabala
Al-Khwarizmi's *Al-jabr wa-l-muqabala* is a foundational 9th-century mathematical treatise that systematically introduced and developed algebra as an independent discipline.
-
C.
Ulugh Beg's Zij-i Sultani
Ulugh Beg's Zij-i Sultani is a 15th-century astronomical star catalogue and set of planetary tables compiled at the Samarkand observatory, renowned for its remarkably accurate measurements and lasting influence on later astronomy.
-
D.
Treatise on Astronomy
Treatise on Astronomy is a 19th-century textbook by American mathematician and astronomer Elias Loomis that systematically presents the fundamental principles and observations of astronomy for students and general readers.
-
E.
Al-Zarqali's Toledan Tables
Al-Zarqali's Toledan Tables are a highly influential set of medieval astronomical tables, compiled in Toledo, that provided precise planetary positions and were widely used across the Islamic world and later in Europe.
- F. None of above. chosen
Statements (32)
| Predicate | Object |
|---|---|
| instanceOf |
geometrical work
ⓘ
mathematical treatise ⓘ |
| approximateCentury |
11th century
ⓘ
12th century ⓘ |
| associatedPerson | Omar Khayyam NERFINISHED ⓘ |
| associatedWith | Persian mathematical tradition ⓘ |
| author | Omar Khayyam NERFINISHED ⓘ |
| authorNationality | Persian ⓘ |
| buildsUpon | Elements by Euclid NERFINISHED ⓘ |
| contextOfCreation | medieval Islamic science ⓘ |
| contributionTo | development of geometry beyond Euclid ⓘ |
| employs | rigorous geometric proofs ⓘ |
| field | mathematics ⓘ |
| focusesOn |
construction of arcs
ⓘ
geometric solution of problems ⓘ subdivision of circular quadrants ⓘ |
| genre | scientific treatise ⓘ |
| hasAuthor | Omar Khayyam NERFINISHED ⓘ |
| historicalPeriod | Islamic Golden Age NERFINISHED ⓘ |
| influenced | later Islamic geometers ⓘ |
| influencedBy | Greek mathematics ⓘ |
| language | Arabic ⓘ |
| mainSubject |
division of arcs
ⓘ
division of quadrants ⓘ geometric constructions ⓘ geometry ⓘ |
| originalTitleLanguage | Arabic ⓘ |
| relatedTo |
Islamic mathematics
ⓘ
history of geometry ⓘ |
| studies |
properties of circular arcs
ⓘ
subdivision of angles ⓘ |
| usesMethod | classical Euclidean geometry ⓘ |
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.
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.
Subject: Treatise on the Division of Quadrants (Omar Khayyam) Description of subject: Treatise on the Division of Quadrants is a mathematical work by Omar Khayyam in which he investigates geometric constructions and the division of arcs and quadrants, contributing to the development of geometry beyond Euclid.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.