On the Sphere and Cylinder
E156206
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| On the Sphere and Cylinder canonical | 6 |
How this entity was disambiguated
This entity first appeared as the object of triple T1358761 — 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 the Sphere and Cylinder Context triple: [Archimedes, notableWork, On the Sphere and Cylinder]
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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.
Aristotle’s On the Heavens
Aristotle’s On the Heavens is an influential ancient Greek treatise that presents Aristotle’s cosmology and theories about the structure and motions of the universe.
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D.
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.
-
E.
De revolutionibus orbium coelestium
De revolutionibus orbium coelestium is Nicolaus Copernicus’s seminal 1543 work that introduced the heliocentric model of the universe, fundamentally transforming astronomy and natural philosophy.
- 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 the Sphere and Cylinder Target entity description: 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.
-
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.
Aristotle’s On the Heavens
Aristotle’s On the Heavens is an influential ancient Greek treatise that presents Aristotle’s cosmology and theories about the structure and motions of the universe.
-
D.
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.
-
E.
De revolutionibus orbium coelestium
De revolutionibus orbium coelestium is Nicolaus Copernicus’s seminal 1543 work that introduced the heliocentric model of the universe, fundamentally transforming astronomy and natural philosophy.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical treatise
ⓘ
work of geometry ⓘ |
| attributedTo |
Archimedes
ⓘ
surface form:
Archimedes of Syracuse
|
| author | Archimedes ⓘ |
| commemoratedBy | inscription on Archimedes' tomb as reported in antiquity ⓘ |
| compares | sphere and circumscribed cylinder ⓘ |
| contains |
Book I
ⓘ
Book II ⓘ |
| demonstrates |
early integral-like reasoning via exhaustion
ⓘ
use of rigorous deductive reasoning in geometry ⓘ |
| derivesFormula |
A_cylinder = 2 π r h + 2 π r^2
ⓘ
A_sphere = 4 π r^2 ⓘ V_cylinder = π r^2 h ⓘ V_sphere = 4/3 π r^3 ⓘ |
| dimension | three-dimensional solids ⓘ |
| field | classical geometry ⓘ |
| focusesOn |
surface area of the cylinder
ⓘ
surface area of the sphere ⓘ volume of the cylinder ⓘ volume of the sphere ⓘ |
| genre | ancient Greek mathematical text ⓘ |
| geometricConfiguration | sphere inscribed in right circular cylinder ⓘ |
| historicalImportance | foundational work in solid geometry ⓘ |
| influenced |
Renaissance mathematicians
ⓘ
later Greek mathematicians ⓘ medieval Islamic mathematicians ⓘ |
| isPartOf |
The Method of Mechanical Theorems
ⓘ
surface form:
Archimedean corpus
|
| keyResult |
ratio of sphere surface area to cylinder surface area including bases is 1:1
ⓘ
ratio of sphere volume to cylinder volume is 2:3 ⓘ |
| language | Ancient Greek ⓘ |
| mainSubject |
cylinder
ⓘ
geometry ⓘ sphere ⓘ |
| originallyWrittenIn | manuscript form ⓘ |
| period | Hellenistic period ⓘ |
| proves |
surface area of a sphere is equal to the lateral surface area of its circumscribed cylinder including bases
ⓘ
surface area of a sphere is four times the area of its great circle ⓘ volume of a sphere is two-thirds the volume of its circumscribed cylinder ⓘ |
| relatedTo |
The Method of Mechanical Theorems
ⓘ
surface form:
Method of Mechanical Theorems
On the Measurement of the Circle ⓘ |
| studiedIn | history of mathematics ⓘ |
| survivesThrough | medieval manuscript tradition ⓘ |
| usesMethod |
geometric proof
ⓘ
method of exhaustion ⓘ |
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 the Sphere and Cylinder Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.