On Conoids and Spheroids
E160226
"On Conoids and Spheroids" is a mathematical treatise by Archimedes in which he investigates the geometry, volumes, and surface areas of solids generated by rotating conic sections.
All labels observed (2)
| Label | Occurrences |
|---|---|
| De Sectionibus Conicis | 1 |
| On Conoids and Spheroids canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1358769 — 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 Conoids and Spheroids Context triple: [Archimedes, notableWork, On Conoids and Spheroids]
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
Elementa curvarum linearum
Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
-
E.
On the Equilibrium of Planes
On the Equilibrium of Planes is a foundational treatise by Archimedes that systematically develops the principles of statics and the law of the lever in classical mechanics.
- 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 Conoids and Spheroids Target entity description: "On Conoids and Spheroids" is a mathematical treatise by Archimedes in which he investigates the geometry, volumes, and surface areas of solids generated by rotating conic sections.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
Elementa curvarum linearum
Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
-
E.
On the Equilibrium of Planes
On the Equilibrium of Planes is a foundational treatise by Archimedes that systematically develops the principles of statics and the law of the lever in classical mechanics.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical treatise
ⓘ
work by Archimedes ⓘ |
| approximateDate | 3rd century BCE ⓘ |
| author | Archimedes ⓘ |
| fieldOfWork | geometry ⓘ |
| focusesOn |
conoids
ⓘ
ellipsoids ⓘ hyperboloids ⓘ paraboloids ⓘ spheroids ⓘ |
| genre | ancient Greek mathematics ⓘ |
| hasForm | geometrical propositions and proofs ⓘ |
| hasInfluenceOn |
early ideas of integration
ⓘ
geometric methods for volume computation ⓘ |
| hasTopic |
centers of gravity of solids
ⓘ
quadrature and cubature ⓘ relations between areas and volumes ⓘ |
| historicalPeriod | Hellenistic period ⓘ |
| influenced |
development of infinitesimal methods
ⓘ
later work in integral calculus ⓘ |
| investigates |
solids generated by rotating conic sections
ⓘ
surface areas of conoids ⓘ surface areas of spheroids ⓘ volumes of conoids ⓘ volumes of spheroids ⓘ |
| mainSubject |
conic sections
ⓘ
solid geometry ⓘ surface areas of solids of revolution ⓘ volumes of solids of revolution ⓘ |
| mathematicalDomain |
conic geometry
ⓘ
solid of revolution ⓘ |
| originalLanguage | Ancient Greek ⓘ |
| partOf | corpus of Archimedes ⓘ |
| preservedIn | medieval manuscript tradition ⓘ |
| relatedWork |
On Spirals
ⓘ
Quadrature of the Parabola ⓘ
surface form:
On the Quadrature of the Parabola
On the Sphere and Cylinder ⓘ |
| studiedIn | history of mathematics ⓘ |
| studiesProperty |
ratios of volumes of related solids
ⓘ
relationships between cross-sectional areas and volumes ⓘ |
| tradition | Greek classical geometry ⓘ |
| 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 Conoids and Spheroids Description of subject: "On Conoids and Spheroids" is a mathematical treatise by Archimedes in which he investigates the geometry, volumes, and surface areas of solids generated by rotating conic sections.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
De Sectionibus Conicis