On Spirals
E156211
On Spirals is a mathematical treatise by Archimedes in which he systematically studies the properties and applications of spiral curves, especially the Archimedean spiral.
All labels observed (1)
| Label | Occurrences |
|---|---|
| On Spirals canonical | 5 |
How this entity was disambiguated
This entity first appeared as the object of triple T1358767 — 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 Spirals Context triple: [Archimedes, notableWork, On Spirals]
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A.
The Pisa Lectures
The Pisa Lectures are a series of influential talks by Noam Chomsky that laid out the core ideas of his Government and Binding theory in generative grammar.
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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.
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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D.
Mysterium Cosmographicum
Mysterium Cosmographicum is Johannes Kepler’s early astronomical treatise in which he proposes a geometric model of the solar system based on nested Platonic solids to explain the spacing of the planets.
-
E.
The Cobweb
The Cobweb is a 1955 American drama film directed by Vincente Minnelli, set in a psychiatric clinic and known for its focus on interpersonal tensions symbolized through a dispute over new drapes.
- 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 Spirals Target entity description: On Spirals is a mathematical treatise by Archimedes in which he systematically studies the properties and applications of spiral curves, especially the Archimedean spiral.
-
A.
The Pisa Lectures
The Pisa Lectures are a series of influential talks by Noam Chomsky that laid out the core ideas of his Government and Binding theory in generative grammar.
-
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.
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.
-
D.
Mysterium Cosmographicum
Mysterium Cosmographicum is Johannes Kepler’s early astronomical treatise in which he proposes a geometric model of the solar system based on nested Platonic solids to explain the spacing of the planets.
-
E.
The Cobweb
The Cobweb is a 1955 American drama film directed by Vincente Minnelli, set in a psychiatric clinic and known for its focus on interpersonal tensions symbolized through a dispute over new drapes.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical treatise
ⓘ
work by Archimedes ⓘ |
| aim |
to apply spirals to classical geometric problems
ⓘ
to explore properties and applications of spiral curves ⓘ |
| approximateDate | 3rd century BCE ⓘ |
| associatedWith | Syracuse ⓘ |
| author | Archimedes ⓘ |
| contribution |
early work on circle quadrature
ⓘ
early work on curve rectification ⓘ systematic study of Archimedean spiral ⓘ |
| defines |
Archimedean spiral
ⓘ
linked to:
Archimedes' spiral
|
| field |
geometry
ⓘ
mathematics ⓘ |
| genre | mathematical work ⓘ |
| hasConcept |
area between spiral turns
ⓘ
construction of tangents to spirals ⓘ use of spirals for angle trisection ⓘ |
| hasForm |
geometric proofs
ⓘ
propositions and theorems ⓘ |
| hasImpact | foundational work on Archimedean spiral in geometry ⓘ |
| historicalPeriod | Hellenistic mathematics ⓘ |
| influenced |
development of infinitesimal methods
ⓘ
later studies of plane curves ⓘ |
| language | Ancient Greek ⓘ |
| latinTitle | De spiralibus ⓘ |
| mainSubject |
Archimedean spiral
ⓘ
spiral curves ⓘ |
| originalTitle | Περὶ ἑλίκων ⓘ |
| partOf | corpus of works of Archimedes ⓘ |
| preservedIn | medieval manuscript tradition ⓘ |
| relatedTo |
Measurement of a Circle
ⓘ
linked to:
On the Measurement of the Circle
On the Sphere and Cylinder ⓘ |
| studiedIn | history of mathematics ⓘ |
| studiesObject |
intersections of spirals with lines
ⓘ
points on the Archimedean spiral ⓘ radii and angles of spiral curves ⓘ |
| studiesProperty |
areas bounded by spirals and lines
ⓘ
geometric properties of spirals ⓘ quadrature of the circle by spirals ⓘ rectification of curves using spirals ⓘ tangents to spiral curves ⓘ |
| usesMethod |
classical Greek geometric methods
ⓘ
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 Spirals Description of subject: On Spirals is a mathematical treatise by Archimedes in which he systematically studies the properties and applications of spiral curves, especially the Archimedean spiral.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.