On Divisions of Figures
E537784
On Divisions of Figures is an ancient mathematical treatise attributed to Euclid that systematically studies how geometric figures can be divided into parts with specified ratios or properties.
All labels observed (2)
| Label | Occurrences |
|---|---|
| On Divisions of Figures canonical | 1 |
| Peri diaireseōs schēmatōn | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5658065 — 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 Divisions of Figures Context triple: [Euclid, notableWork, On Divisions of Figures]
-
A.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
-
B.
“Solutio problematis ad geometriam situs pertinentis”
“Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
-
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.
Checkerboard Division
The Checkerboard Division is the nickname of the U.S. Army’s 99th Infantry Division, a World War II unit noted for its distinctive shoulder patch and its role in the Battle of the Bulge.
-
E.
The Beauty of Geometry
The Beauty of Geometry is a classic mathematical book by H. S. M. Coxeter that explores elegant geometric ideas and configurations through clear exposition and rich illustrations.
- 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 Divisions of Figures Target entity description: On Divisions of Figures is an ancient mathematical treatise attributed to Euclid that systematically studies how geometric figures can be divided into parts with specified ratios or properties.
-
A.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
-
B.
“Solutio problematis ad geometriam situs pertinentis”
“Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
-
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.
Checkerboard Division
The Checkerboard Division is the nickname of the U.S. Army’s 99th Infantry Division, a World War II unit noted for its distinctive shoulder patch and its role in the Battle of the Bulge.
-
E.
The Beauty of Geometry
The Beauty of Geometry is a classic mathematical book by H. S. M. Coxeter that explores elegant geometric ideas and configurations through clear exposition and rich illustrations.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
ancient mathematical treatise
ⓘ
geometrical treatise ⓘ work on Euclidean geometry ⓘ |
| aimsTo |
provide general methods for dividing figures with given conditions
ⓘ
systematically classify division problems for plane figures ⓘ |
| associatedWith | Hellenistic mathematics ⓘ |
| attributedTo | Euclid ⓘ |
| authorshipStatus | attribution to Euclid is not fully certain ⓘ |
| concerns |
construction of dividing lines
ⓘ
geometric optimization under constraints ⓘ loci arising from division conditions ⓘ proportional division of areas ⓘ |
| field |
geometry
ⓘ
mathematics ⓘ |
| focusesOn |
dividing figures by lines at given angles
ⓘ
dividing figures by lines parallel to given lines ⓘ dividing figures by lines through given points ⓘ dividing figures into equal areas ⓘ dividing figures into parts satisfying geometric constraints ⓘ dividing figures into parts with specified areas ⓘ dividing figures into parts with specified ratios ⓘ dividing figures into similar parts ⓘ |
| genre | mathematical problem collection ⓘ |
| hasAlternativeName |
De Divisionibus Figurarum
ⓘ
Peri diaireseōs schēmatōn ⓘ
linked to:
On Divisions of Figures
|
| hasStatus | surviving in later manuscript traditions ⓘ |
| influenced |
later Islamic mathematical tradition
ⓘ
medieval European geometry ⓘ |
| mainSubject |
area division problems
ⓘ
division of geometric figures ⓘ geometric constructions ⓘ partition of figures with given properties ⓘ ratio and proportion in geometry ⓘ |
| relatedTo |
Data
ⓘ
Elements ⓘ ancient Greek treatises on geometric problems ⓘ |
| studiesFigureType |
circles
ⓘ
polygons ⓘ quadrilaterals ⓘ segments of circles ⓘ triangles ⓘ |
| timePeriod | ancient Greek mathematics ⓘ |
| tradition | Euclidean corpus ⓘ |
| typeOfProblem |
area partition problems
ⓘ
construction problems ⓘ locus problems ⓘ ratio problems ⓘ |
| usesMethod | classical ruler-and-compass construction ⓘ |
| writtenIn | Ancient Greek ⓘ |
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 Divisions of Figures Description of subject: On Divisions of Figures is an ancient mathematical treatise attributed to Euclid that systematically studies how geometric figures can be divided into parts with specified ratios or properties.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: On Divisions of Figures