On the Sphere and Cylinder

E156206

mathematical treatise work of geometry

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.

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All labels observed (6)

Label	Occurrences
On the Sphere and Cylinder canonical	12
Archimedes in On the Sphere and Cylinder	1
On the Sphere and Cylinder (two‑book treatise)	1
On the Sphere and Cylinder by Archimedes	1
On the Sphere and Cylinder, Book I	1
On the Sphere and Cylinder, Book II	1

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]

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
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 of Syracuse ⓘ linked to: Archimedes
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	Archimedean corpus ⓘ linked to: The Method of Mechanical Theorems
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	Method of Mechanical Theorems ⓘ linked to: The 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

Referenced by (17)

Full triples — surface form annotated when it differs from this entity's canonical label.

Archimedes → notableWork → On the Sphere and Cylinder ⓘ

On the Equilibrium of Planes → relatedWork → On the Sphere and Cylinder ⓘ

On Spirals → relatedTo → On the Sphere and Cylinder ⓘ

Quadrature of the Parabola → relatedTo → On the Sphere and Cylinder ⓘ

On Conoids and Spheroids → relatedWork → On the Sphere and Cylinder ⓘ

The Method of Mechanical Theorems → relatedWork → On the Sphere and Cylinder ⓘ

Hellenistic mathematics → notableWork → On the Sphere and Cylinder ⓘ

Book II (On the Sphere and Cylinder) → partOf → On the Sphere and Cylinder ⓘ

subject linked to: Book II

Book II (On the Sphere and Cylinder) → workSeries → On the Sphere and Cylinder (two‑book treatise) ⓘ

subject linked to: Book II