Quadrature of the Parabola
E160225
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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| On the Quadrature of the Parabola | 2 |
| Quadrature of the Parabola canonical | 2 |
| Quadratura parabolae | 1 |
| The Quadrature of the Parabola | 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 |
Ancient Greece
ⓘ
linked to:
Greek Antiquity
|
| 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 ⓘ |
| hasTitleInLatin |
Quadratura parabolae
ⓘ
linked to:
Quadrature of the Parabola
|
| 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 |
corpus of Archimedes
ⓘ
linked to:
The Method of Mechanical Theorems
|
| proves | area of parabolic segment equals 4/3 of reference triangle ⓘ |
| relatedTo |
On the Measurement of a Circle
ⓘ
linked to:
On the Measurement of the 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
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: Quadrature of the Parabola Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Quadrature of the Parabola
linked to: Quadrature of the Parabola
linked to: Quadrature of the Parabola
linked to: Quadrature of the Parabola