Book XIII of Euclid's Elements
E190162
Book XIII of Euclid's Elements is the concluding book of Euclid’s mathematical treatise, focusing on the construction and properties of the five regular Platonic solids within the framework of classical Greek geometry.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Book XIII of Euclid's Elements canonical | 2 |
| Book XIII of the Elements | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1686032 — 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: Book XIII of Euclid's Elements Context triple: [Platonic solids, describedIn, Book XIII of Euclid's Elements]
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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.
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.
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C.
The Method of Mechanical Theorems
The Method of Mechanical Theorems is a treatise by Archimedes in which he uses heuristic mechanical arguments, involving balances and centers of mass, to discover and justify results in geometry and calculus-like area and volume calculations.
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D.
On the Measurement of the Circle
On the Measurement of the Circle is a mathematical treatise by Archimedes in which he rigorously approximates the value of π and explores properties of circles.
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E.
On the Sphere and Cylinder
On the Sphere and Cylinder is a foundational mathematical treatise by Archimedes in which he develops key results in geometry, including the relationships between the surface areas and volumes of spheres and cylinders.
- 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: Book XIII of Euclid's Elements Target entity description: Book XIII of Euclid's Elements is the concluding book of Euclid’s mathematical treatise, focusing on the construction and properties of the five regular Platonic solids within the framework of classical Greek 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.
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.
The Method of Mechanical Theorems
The Method of Mechanical Theorems is a treatise by Archimedes in which he uses heuristic mechanical arguments, involving balances and centers of mass, to discover and justify results in geometry and calculus-like area and volume calculations.
-
D.
On the Measurement of the Circle
On the Measurement of the Circle is a mathematical treatise by Archimedes in which he rigorously approximates the value of π and explores properties of circles.
-
E.
On the Sphere and Cylinder
On the Sphere and Cylinder is a foundational mathematical treatise by Archimedes in which he develops key results in geometry, including the relationships between the surface areas and volumes of spheres and cylinders.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
book of Euclid's Elements
ⓘ
mathematical treatise ⓘ |
| author | Euclid ⓘ |
| concludes | there are no other regular convex polyhedra besides the five Platonic solids ⓘ |
| contains |
propositions on inscribing regular solids in a sphere
ⓘ
propositions on ratios of edges of Platonic solids ⓘ propositions on relationships between different Platonic solids ⓘ |
| field | geometry ⓘ |
| focusesOn |
construction of the five regular Platonic solids
ⓘ
properties of the five regular Platonic solids ⓘ |
| geometricSetting | three-dimensional Euclidean space ⓘ |
| historicalPeriod | Hellenistic period ⓘ |
| includes |
constructions of Platonic solids in a given sphere
ⓘ
proofs of commensurability relations among edges and diagonals of solids ⓘ results involving the golden ratio ⓘ |
| influenced |
Renaissance geometry
ⓘ
foundations of three-dimensional Euclidean geometry ⓘ later studies of polyhedra ⓘ |
| isFinalBookOf | Euclid's Elements ⓘ |
| isPrecededBy | Book XII of Euclid's Elements ⓘ |
| languageOfComposition | Ancient Greek ⓘ |
| mainTopic | Platonic solids ⓘ |
| numberOfPlatonicSolidsConstructed | 5 ⓘ |
| partOf | Euclid's Elements ⓘ |
| positionInSeries | 13 ⓘ |
| preservedIn |
Arabic translations of the Elements
ⓘ
Latin translations of the Elements ⓘ medieval Greek manuscripts of the Elements ⓘ |
| relates | Platonic solids to the sphere ⓘ |
| shows | existence of exactly five regular convex polyhedra ⓘ |
| significance | classical source for the theory of regular polyhedra ⓘ |
| studiedIn | history of mathematics ⓘ |
| studies |
cube
ⓘ
regular dodecahedron ⓘ regular icosahedron ⓘ regular octahedron ⓘ regular tetrahedron ⓘ |
| subjectOf | commentaries by ancient Greek mathematicians ⓘ |
| tradition | classical Greek geometry ⓘ |
| uses |
golden ratio in constructing the dodecahedron
ⓘ
golden ratio in constructing the icosahedron ⓘ properties of circles ⓘ properties of regular polygons ⓘ properties of triangles ⓘ results from earlier books of the Elements ⓘ theory of proportion ⓘ |
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: Book XIII of Euclid's Elements Description of subject: Book XIII of Euclid's Elements is the concluding book of Euclid’s mathematical treatise, focusing on the construction and properties of the five regular Platonic solids within the framework of classical Greek geometry.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.