On the Measurement of the Circle
E156207
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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| On the Measurement of the Circle canonical | 2 |
| Measurement of a Circle | 1 |
| On the Measurement of a Circle | 1 |
| Περὶ μέτρου κύκλου | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1358762 — 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 Measurement of the Circle Context triple: [Archimedes, notableWork, On the Measurement of the Circle]
-
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.
Almagest
The Almagest is an influential 2nd-century astronomical treatise by Claudius Ptolemy that systematically presents the geocentric model of the cosmos and provides mathematical tools for predicting planetary motions.
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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.
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E.
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.
- 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 Measurement of the Circle Target entity description: 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.
-
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.
Almagest
The Almagest is an influential 2nd-century astronomical treatise by Claudius Ptolemy that systematically presents the geocentric model of the cosmos and provides mathematical tools for predicting planetary motions.
-
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.
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.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical treatise
ⓘ
work on geometry ⓘ |
| approximateDate | 3rd century BCE ⓘ |
| author | Archimedes ⓘ |
| citedFor | classical bounds on pi ⓘ |
| contains | three propositions ⓘ |
| demonstrates |
early use of limit-like reasoning
ⓘ
rigorous geometric proof techniques ⓘ |
| field |
geometry
ⓘ
mathematics ⓘ |
| focusesOn |
approximation of pi
ⓘ
area of a circle ⓘ circumference of a circle ⓘ ratio of circumference to diameter ⓘ |
| genre | mathematical text ⓘ |
| givesLowerBoundForPi | 223/71 ⓘ |
| givesUpperBoundForPi | 22/7 ⓘ |
| historicalPeriod | Hellenistic period ⓘ |
| influenced |
classical geometry
ⓘ
later studies of pi ⓘ |
| languageOfWork | Ancient Greek ⓘ |
| mainSubject |
circle
ⓘ
geometry ⓘ pi ⓘ |
| numberOfPropositions | 3 ⓘ |
| originalTitle |
On the Measurement of the Circle
self-linksurface differs
ⓘ
surface form:
Περὶ μέτρου κύκλου
|
| partOf | Archimedes' works on geometry ⓘ |
| polygonSidesUsed | 96 ⓘ |
| preservedIn | medieval manuscript traditions ⓘ |
| proposition |
Proposition 1
ⓘ
Proposition 2 ⓘ Proposition 3 ⓘ |
| proposition1States | the area of a circle equals that of a right triangle with legs equal to the radius and the circumference ⓘ |
| proposition2States | the area of a circle is proportional to the square of its diameter ⓘ |
| proposition3States | gives upper and lower bounds for pi using inscribed and circumscribed polygons ⓘ |
| proves | inequalities for pi ⓘ |
| relatedTo |
Archimedes
ⓘ
Method of Exhaustion ⓘ |
| significance | one of the earliest rigorous approximations of pi ⓘ |
| states | 3 1/7 > pi > 3 10/71 ⓘ |
| studiedIn | history of mathematics ⓘ |
| title | On the Measurement of the Circle self-link ⓘ |
| typeOfResult | geometric proof of circle area formula ⓘ |
| uses |
circumscribed polygons
ⓘ
inscribed polygons ⓘ |
| usesMethod | 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 Measurement of the Circle Description of subject: 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.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
On the Measurement of the Circle
→
originalTitle
→
On the Measurement of the Circle
self-linksurface differs
ⓘ
this entity surface form:
Περὶ μέτρου κύκλου
this entity surface form:
Measurement of a Circle
this entity surface form:
On the Measurement of a Circle