Varignon’s theorem in statics
E923660
Varignon’s theorem in statics is a fundamental principle stating that the moment of a force about a point equals the sum of the moments of its components about that point, simplifying the analysis of mechanical systems.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Varignon’s principle of moments | 1 |
| Varignon’s theorem in statics canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11398855 — 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: Varignon’s theorem in statics Context triple: [Pierre Varignon, notableIdea, Varignon’s theorem in statics]
-
A.
On the Equilibrium of Planes
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.
-
B.
On the Principles of Geometry
"On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
-
C.
Inventional Geometry
Inventional Geometry is an educational work by William George Spencer that introduces geometric concepts through intuitive, discovery-based learning rather than formal proofs.
-
D.
Application de l’analyse à la géométrie
Application de l’analyse à la géométrie is a foundational mathematical treatise by Gaspard Monge that helped establish descriptive geometry by systematically applying analytical methods to geometric problems.
-
E.
A Parallelogram
A Parallelogram is a darkly comic play by Bruce Norris that explores questions of fate, free will, and alternate realities through the story of a woman visited by a future version of herself.
- 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: Varignon’s theorem in statics Target entity description: Varignon’s theorem in statics is a fundamental principle stating that the moment of a force about a point equals the sum of the moments of its components about that point, simplifying the analysis of mechanical systems.
-
A.
On the Equilibrium of Planes
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.
-
B.
On the Principles of Geometry
"On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
-
C.
Inventional Geometry
Inventional Geometry is an educational work by William George Spencer that introduces geometric concepts through intuitive, discovery-based learning rather than formal proofs.
-
D.
Application de l’analyse à la géométrie
Application de l’analyse à la géométrie is a foundational mathematical treatise by Gaspard Monge that helped establish descriptive geometry by systematically applying analytical methods to geometric problems.
-
E.
A Parallelogram
A Parallelogram is a darkly comic play by Bruce Norris that explores questions of fate, free will, and alternate realities through the story of a woman visited by a future version of herself.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
principle of statics
ⓘ
theorem in mechanics ⓘ |
| alternativeName |
Varignon’s principle of moments
ⓘ
linked to:
Varignon’s theorem in statics
principle of moments ⓘ |
| appliesTo |
concurrent force systems
ⓘ
coplanar force systems ⓘ nonconcurrent force systems ⓘ three-dimensional force systems ⓘ |
| assumes |
force additivity
ⓘ
rigid body model ⓘ |
| category |
engineering principle
ⓘ
physical law (approximate, classical) ⓘ |
| coreStatement | The moment of a force about a point equals the sum of the moments of its components about that point. ⓘ |
| expressedAs | The moment of a force about a point equals the algebraic sum of the moments of its rectangular components about that point. ⓘ |
| field |
classical mechanics
ⓘ
engineering mechanics ⓘ statics ⓘ |
| hasApplication |
aerospace engineering
ⓘ
civil engineering ⓘ machine design ⓘ structural analysis ⓘ |
| historicalPeriod | late 17th century ⓘ |
| implies | moment of a resultant equals sum of moments of component forces ⓘ |
| mathematicalForm |
M_O(F) = r × F
ⓘ
M_O(F) = Σ M_O(F_i) ⓘ |
| namedAfter | Pierre Varignon ⓘ |
| relatedTo |
Newtonian mechanics
ⓘ
equilibrium conditions ΣM = 0 ⓘ parallelogram law of forces ⓘ |
| relatesConcept |
force components
ⓘ
moment of a force ⓘ position vector ⓘ resultant force ⓘ vector cross product ⓘ |
| requires | vector decomposition of forces ⓘ |
| taughtIn |
engineering statics textbooks
ⓘ
mechanical engineering curricula ⓘ undergraduate engineering courses ⓘ |
| usedFor |
analysis of beams
ⓘ
analysis of frames ⓘ analysis of trusses ⓘ computation of resultant moments ⓘ equilibrium analysis ⓘ simplifying moment calculations ⓘ |
| validIn |
three-dimensional vector mechanics
ⓘ
two-dimensional vector mechanics ⓘ |
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: Varignon’s theorem in statics Description of subject: Varignon’s theorem in statics is a fundamental principle stating that the moment of a force about a point equals the sum of the moments of its components about that point, simplifying the analysis of mechanical systems.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Varignon’s theorem in statics