On the Equilibrium of Planes

E156209

mathematical text scientific work treatise work on statics

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.

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All labels observed (8)

Label	Occurrences
On the Equilibrium of Planes canonical	2
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 by Archimedes	1
On the Equilibrium of Planes, Book I	1
On the Equilibrium of Planes, Book II	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	Book I of On the Equilibrium of Planes ⓘ linked to: On the Equilibrium of Planes Book II of On the Equilibrium of Planes ⓘ linked to: On the Equilibrium of Planes
hasTitleInGreek	Περὶ ἐπιπέδων ἱσορροπιῶν ⓘ
hasTitleInLatin	De planorum aequilibris ⓘ linked to: On the Equilibrium of Planes
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 ⓘ law of the lever ⓘ linked to: On the Equilibrium of Planes
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	Archimedes' works on mechanics ⓘ linked to: The Method of Mechanical Theorems
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