On the Equilibrium of Planes
E156209
On the Equilibrium of Planes is a foundational treatise by Archimedes that systematically develops the principles of statics and the law of the lever in classical mechanics.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Book I of On the Equilibrium of Planes | 1 |
| Book II of On the Equilibrium of Planes | 1 |
| De planorum aequilibris | 1 |
| On the Equilibrium of Planes canonical | 1 |
| law of the lever | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1358764 — 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 Equilibrium of Planes Context triple: [Archimedes, notableWork, On the Equilibrium of Planes]
-
A.
The Science of Mechanics
The Science of Mechanics is Ernst Mach’s influential treatise that critically examines the foundations of classical mechanics and helped shape the development of modern physics and the philosophy of science.
-
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.
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.
-
D.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
-
E.
Philosophiæ Naturalis Principia Mathematica
Philosophiæ Naturalis Principia Mathematica is Isaac Newton’s foundational work that formulated the laws of motion and universal gravitation, becoming a cornerstone of classical physics and the Scientific Revolution.
- 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 Equilibrium of Planes Target entity description: On the Equilibrium of Planes is a foundational treatise by Archimedes that systematically develops the principles of statics and the law of the lever in classical mechanics.
-
A.
The Science of Mechanics
The Science of Mechanics is Ernst Mach’s influential treatise that critically examines the foundations of classical mechanics and helped shape the development of modern physics and the philosophy of science.
-
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.
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.
-
D.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
-
E.
Philosophiæ Naturalis Principia Mathematica
Philosophiæ Naturalis Principia Mathematica is Isaac Newton’s foundational work that formulated the laws of motion and universal gravitation, becoming a cornerstone of classical physics and the Scientific Revolution.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical text
ⓘ
scientific work ⓘ treatise ⓘ work on statics ⓘ |
| approximateCentury | 3rd century BCE ⓘ |
| associatedWithPerson | Eutocius of Ascalon ⓘ |
| author | Archimedes ⓘ |
| developsConcept |
center of gravity of plane figures
ⓘ
conditions for balance of weights ⓘ law of the lever ⓘ principles of statics ⓘ |
| field |
classical mechanics
ⓘ
mathematics ⓘ physics ⓘ statics ⓘ |
| genre |
mathematical treatise
ⓘ
scientific treatise ⓘ |
| hasPart |
On the Equilibrium of Planes
self-linksurface differs
ⓘ
surface form:
Book I of On the Equilibrium of Planes
On the Equilibrium of Planes self-linksurface differs ⓘ
surface form:
Book II of On the Equilibrium of Planes
|
| hasTitleInGreek | Περὶ ἐπιπέδων ἱσορροπιῶν ⓘ |
| hasTitleInLatin |
On the Equilibrium of Planes
self-linksurface differs
ⓘ
surface form:
De planorum aequilibris
|
| historicalSignificance |
foundational work in the history of statics
ⓘ
one of the earliest systematic treatments of mechanical equilibrium ⓘ |
| influenced |
Galileo Galilei
ⓘ
Renaissance science ⓘ classical statics ⓘ early modern physics ⓘ later mechanics ⓘ |
| mainSubject |
center of gravity
ⓘ
conditions of mechanical equilibrium ⓘ equilibrium of planar figures ⓘ On the Equilibrium of Planes self-linksurface differs ⓘ
surface form:
law of the lever
|
| notableFor |
early axiomatic treatment of statics
ⓘ
rigorous geometric proofs in mechanics ⓘ systematic derivation of the law of the lever ⓘ |
| originalLanguage | Ancient Greek ⓘ |
| originallyWrittenIn | Syracuse ⓘ |
| partOf |
The Method of Mechanical Theorems
ⓘ
surface form:
Archimedes' works on mechanics
|
| proves |
conditions for equilibrium of weights on a lever
ⓘ
positions of centers of gravity of plane figures ⓘ |
| relatedWork |
On Floating Bodies
ⓘ
On the Sphere and Cylinder ⓘ |
| survivesAs | medieval manuscript tradition ⓘ |
| timePeriod | Hellenistic period ⓘ |
| topic |
levers and balances
ⓘ
moments of forces ⓘ |
| usesMethod |
Greek geometric method
ⓘ
axiomatic-deductive reasoning ⓘ |
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 Equilibrium of Planes Description of subject: On the Equilibrium of Planes is a foundational treatise by Archimedes that systematically develops the principles of statics and the law of the lever in classical mechanics.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
On the Equilibrium of Planes
→
mainSubject
→
On the Equilibrium of Planes
self-linksurface differs
ⓘ
this entity surface form:
law of the lever
this entity surface form:
Book I of On the Equilibrium of Planes
this entity surface form:
Book II of On the Equilibrium of Planes
On the Equilibrium of Planes
→
hasTitleInLatin
→
On the Equilibrium of Planes
self-linksurface differs
ⓘ
this entity surface form:
De planorum aequilibris