Quadrature of the Parabola

E160225

mathematical treatise work by Archimedes

Quadrature of the Parabola is a treatise by Archimedes in which he determines the area of a parabolic segment using an early form of infinite series and geometric summation.

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All labels observed (3)

Label	Occurrences
On the Quadrature of the Parabola	2
Quadrature of the Parabola canonical	2
Quadratura parabolae	1

How this entity was disambiguated

This entity first appeared as the object of triple T1358768 — 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: Quadrature of the Parabola
Context triple: [Archimedes, notableWork, Quadrature of the Parabola]

A. 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.
B. 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.
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. The Sand Reckoner
The Sand Reckoner is a treatise by Archimedes in which he develops a system for expressing extremely large numbers to estimate the quantity of sand that could fit in the universe.
E. 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.
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: Quadrature of the Parabola
Target entity description: Quadrature of the Parabola is a treatise by Archimedes in which he determines the area of a parabolic segment using an early form of infinite series and geometric summation.

A. 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.
B. 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.
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. The Sand Reckoner
The Sand Reckoner is a treatise by Archimedes in which he develops a system for expressing extremely large numbers to estimate the quantity of sand that could fit in the universe.
E. 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.
F. None of above. chosen

Statements (40)

Predicate	Object
instanceOf	mathematical treatise ⓘ work by Archimedes ⓘ
approximateDate	3rd century BCE ⓘ
author	Archimedes ⓘ
concernsConcept	area ⓘ geometric progression ⓘ infinite series ⓘ
concernsCurve	parabola ⓘ
conclusion	area of a parabolic segment is four-thirds the area of a certain inscribed triangle ⓘ
countryOfOrigin	Greek Antiquity ⓘ surface form: Ancient Greece
demonstrates	early use of limit processes ⓘ summation of an infinite geometric series ⓘ
field	geometry ⓘ mathematics ⓘ
focusesOn	area determination ⓘ parabolic segment ⓘ quadrature ⓘ
genre	ancient Greek mathematical text ⓘ
hasForm	axiomatic argument ⓘ geometric proof ⓘ
hasTitleInEnglish	Quadrature of the Parabola self-link ⓘ
hasTitleInLatin	Quadrature of the Parabola self-linksurface differs ⓘ surface form: Quadratura parabolae
historicalPeriod	Hellenistic period ⓘ
influenced	development of integral calculus ⓘ later theories of area and integration ⓘ
keyResult	infinite geometric series with ratio 1/4 sums to 1/3 of the initial triangle ⓘ sum of areas of successively inscribed triangles forms a geometric series ⓘ
mainSubject	area of a parabolic segment ⓘ
mathematicalTechnique	exhaustion by inscribed polygons ⓘ reductio ad absurdum ⓘ
originalLanguage	Ancient Greek ⓘ
partOf	The Method of Mechanical Theorems ⓘ surface form: corpus of Archimedes
proves	area of parabolic segment equals 4/3 of reference triangle ⓘ
relatedTo	On the Measurement of the Circle ⓘ surface form: On the Measurement of a Circle On the Sphere and Cylinder ⓘ The Method of Mechanical Theorems ⓘ
uses	geometric series ⓘ infinite summation ⓘ method of exhaustion ⓘ
workLocation	Syracuse ⓘ

How these facts were elicited

Referenced by (5)

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

Archimedes → notableWork → Quadrature of the Parabola ⓘ

Quadrature of the Parabola → hasTitleInEnglish → Quadrature of the Parabola self-link ⓘ

Quadrature of the Parabola → hasTitleInLatin → Quadrature of the Parabola self-linksurface differs ⓘ

this entity surface form: Quadratura parabolae

On Conoids and Spheroids → relatedWork → Quadrature of the Parabola ⓘ

this entity surface form: On the Quadrature of the Parabola

The Method of Mechanical Theorems → relatedWork → Quadrature of the Parabola ⓘ