Lectures on Quaternions
E455350
Lectures on Quaternions is a foundational 19th-century mathematical treatise in which William Rowan Hamilton systematically develops and expounds his theory of quaternions.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Elements of Quaternions | 2 |
| Lectures on Quaternions canonical | 2 |
| Elementary Treatise on Quaternions | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4585420 — 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: Lectures on Quaternions Context triple: [William Rowan Hamilton, notableWork, Lectures on Quaternions]
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A.
Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
-
B.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
-
C.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
-
D.
On Conoids and Spheroids
"On Conoids and Spheroids" is a mathematical treatise by Archimedes in which he investigates the geometry, volumes, and surface areas of solids generated by rotating conic sections.
-
E.
Elements of Analytical Geometry and of the Differential and Integral Calculus
Elements of Analytical Geometry and of the Differential and Integral Calculus is a 19th-century mathematics textbook that systematically introduces analytic geometry alongside the fundamentals of differential and integral calculus.
- 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: Lectures on Quaternions Target entity description: Lectures on Quaternions is a foundational 19th-century mathematical treatise in which William Rowan Hamilton systematically develops and expounds his theory of quaternions.
-
A.
Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
-
B.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
-
C.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
-
D.
On Conoids and Spheroids
"On Conoids and Spheroids" is a mathematical treatise by Archimedes in which he investigates the geometry, volumes, and surface areas of solids generated by rotating conic sections.
-
E.
Elements of Analytical Geometry and of the Differential and Integral Calculus
Elements of Analytical Geometry and of the Differential and Integral Calculus is a 19th-century mathematics textbook that systematically introduces analytic geometry alongside the fundamentals of differential and integral calculus.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
19th-century book
ⓘ
book ⓘ mathematical treatise ⓘ nonfiction book ⓘ |
| author | William Rowan Hamilton ⓘ |
| availableAt |
Google Books
ⓘ
Internet Archive ⓘ |
| basedOn | Hamilton’s earlier papers on quaternions ⓘ |
| centuryOfPublication | 19th century ⓘ |
| countryOfOrigin | Ireland ⓘ |
| describes |
lines and planes represented by quaternions
ⓘ
quaternion conjugation ⓘ quaternion multiplication ⓘ rotation in three-dimensional space ⓘ scalar part of a quaternion ⓘ vector part of a quaternion ⓘ |
| field |
mathematical physics
ⓘ
mathematics ⓘ |
| genre |
mathematics textbook
ⓘ
scientific literature ⓘ |
| hasEdition |
later reprints
ⓘ
original 1853 edition ⓘ |
| hasFormat |
digital scan
ⓘ
print ⓘ |
| hasNotation | Hamiltonian quaternion notation ⓘ |
| hasPart |
algebraic theory of quaternions
ⓘ
geometrical applications ⓘ introductory lectures ⓘ |
| historicalSignificance |
first systematic exposition of Hamilton’s quaternion theory
ⓘ
foundational work in the history of quaternions ⓘ |
| influenced |
development of vector analysis
ⓘ
later work on noncommutative algebra ⓘ |
| intendedAudience |
advanced students of mathematics
ⓘ
mathematicians ⓘ |
| isPartOf | Hamilton’s works on quaternions ⓘ |
| language | English ⓘ |
| libraryOfCongressSubject | Quaternions ⓘ |
| mainSubject |
algebra
ⓘ
quaternions ⓘ vector analysis ⓘ |
| placeOfPublication | Dublin ⓘ |
| precedes |
Elements of Quaternions
ⓘ
linked to:
Lectures on Quaternions
|
| publicationYear | 1853 ⓘ |
| publisher | Hodges and Smith ⓘ |
| timePeriodDescribed | mid-19th century mathematics ⓘ |
| title | Lectures on Quaternions ⓘ |
| usesConcept |
imaginary units i, j, k
ⓘ
noncommutative multiplication ⓘ |
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: Lectures on Quaternions Description of subject: Lectures on Quaternions is a foundational 19th-century mathematical treatise in which William Rowan Hamilton systematically develops and expounds his theory of quaternions.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Lectures on Quaternions
linked to: Lectures on Quaternions
linked to: Lectures on Quaternions