Book VI
E164170
Book VI is the final section of Carl Friedrich Gauss’s *Disquisitiones Arithmeticae*, focusing on the theory of binary quadratic forms and their composition.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Book VI canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1381989 — 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: Book VI Context triple: [Disquisitiones Arithmeticae, hasPart, Book VI]
-
A.
Book VI
Book VI is the concluding section of Nicolaus Copernicus’s seminal astronomical work *De revolutionibus orbium coelestium*, in which he further develops and applies his heliocentric model.
-
B.
Book IV
Book IV is the concluding section of John Locke’s "An Essay Concerning Human Understanding," in which he develops his influential theory of knowledge, including the nature, extent, and limits of human understanding.
-
C.
Book IV
Book IV is a section of Carl Friedrich Gauss’s seminal number theory work *Disquisitiones Arithmeticae*, focusing on properties of quadratic residues and related arithmetic concepts.
-
D.
Book IV
Book IV is the concluding section of Jean-Jacques Rousseau’s political treatise *The Social Contract*, where he further develops his ideas on sovereignty, civil religion, and the functioning of a legitimate political community.
-
E.
Book V
Book V is a section of Carl Friedrich Gauss’s seminal number theory work *Disquisitiones Arithmeticae*, focusing on advanced properties and structures within arithmetic.
- 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: Book VI Target entity description: Book VI is the final section of Carl Friedrich Gauss’s *Disquisitiones Arithmeticae*, focusing on the theory of binary quadratic forms and their composition.
-
A.
Book VI
Book VI is the concluding section of Nicolaus Copernicus’s seminal astronomical work *De revolutionibus orbium coelestium*, in which he further develops and applies his heliocentric model.
-
B.
Book IV
Book IV is the concluding section of John Locke’s "An Essay Concerning Human Understanding," in which he develops his influential theory of knowledge, including the nature, extent, and limits of human understanding.
-
C.
Book IV
Book IV is a section of Carl Friedrich Gauss’s seminal number theory work *Disquisitiones Arithmeticae*, focusing on properties of quadratic residues and related arithmetic concepts.
-
D.
Book IV
Book IV is the concluding section of Jean-Jacques Rousseau’s political treatise *The Social Contract*, where he further develops his ideas on sovereignty, civil religion, and the functioning of a legitimate political community.
-
E.
Book V
Book V is a section of Carl Friedrich Gauss’s seminal number theory work *Disquisitiones Arithmeticae*, focusing on advanced properties and structures within arithmetic.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
book section
ⓘ
mathematical text ⓘ |
| author | Carl Friedrich Gauss ⓘ |
| authorNationality | German ⓘ |
| contribution |
connection between binary quadratic forms and ideal class groups of quadratic fields
ⓘ
systematic theory of equivalence classes of binary quadratic forms ⓘ |
| era | 19th-century mathematics ⓘ |
| field | number theory ⓘ |
| focus |
classification of binary quadratic forms by discriminant
ⓘ
composition law on classes of forms ⓘ structure of the class group of binary quadratic forms ⓘ |
| hasEnglishTranslation |
Disquisitiones Arithmeticae
ⓘ
surface form:
Disquisitiones Arithmeticae (English translation)
|
| hasInfluentialReader |
David Hilbert
ⓘ
Ernst Eduard Kummer ⓘ
surface form:
Ernst Kummer
Richard Dedekind ⓘ |
| historicalSignificance |
foundational work on the composition of quadratic forms
ⓘ
introduced Gauss’s composition law for binary quadratic forms ⓘ |
| influenced |
development of class field theory
ⓘ
modern algebraic number theory ⓘ theory of quadratic number fields ⓘ |
| language | Latin ⓘ |
| mainTopic |
binary quadratic forms
ⓘ
composition of binary quadratic forms ⓘ |
| originalLanguageOfWholeWork | Latin ⓘ |
| originalPublicationYear | 1801 ⓘ |
| originalPublisher | Friedrich Vieweg und Sohn ⓘ |
| originalTitleOfWholeWork | Disquisitiones Arithmeticae ⓘ |
| partOf | Disquisitiones Arithmeticae ⓘ |
| placeOfPublication | Brunswick ⓘ |
| positionInWork |
final section
ⓘ
sixth book ⓘ |
| relatedConcept |
binary quadratic form
ⓘ
class number ⓘ composition law ⓘ discriminant of a quadratic form ⓘ equivalence of quadratic forms ⓘ |
| relatedWork |
Disquisitiones Arithmeticae
ⓘ
surface form:
Book V (Disquisitiones Arithmeticae)
|
| subjectArea |
algebraic number theory (proto-formulation)
ⓘ
arithmetic of quadratic forms ⓘ |
| workContainedIn |
Disquisitiones Arithmeticae
ⓘ
surface form:
Disquisitiones Arithmeticae Book I–VI
|
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: Book VI Description of subject: Book VI is the final section of Carl Friedrich Gauss’s *Disquisitiones Arithmeticae*, focusing on the theory of binary quadratic forms and their composition.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.