Book V
E162578
Book V is a section of Carl Friedrich Gauss’s seminal number theory work *Disquisitiones Arithmeticae*, focusing on advanced properties and structures within arithmetic.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Book V canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1381988 — 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 V Context triple: [Disquisitiones Arithmeticae, hasPart, Book V]
-
A.
Book V
Book V is a major section of John Stuart Mill’s "Principles of Political Economy" that focuses on the role and functions of government within an economic system.
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B.
Book V
Book V is one of the later sections of Washington Irving’s satirical work *A History of New York*, continuing its mock-historical narrative of the early Dutch settlement of the city.
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C.
Book V
Book V is a section of Nicolaus Copernicus’s seminal astronomical work "De revolutionibus orbium coelestium," contributing to his formulation of the heliocentric model.
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D.
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.
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E.
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.
- 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 V Target entity description: Book V is a section of Carl Friedrich Gauss’s seminal number theory work *Disquisitiones Arithmeticae*, focusing on advanced properties and structures within arithmetic.
-
A.
Book V
Book V is one of the later sections of Washington Irving’s satirical work *A History of New York*, continuing its mock-historical narrative of the early Dutch settlement of the city.
-
B.
Book V
Book V is a major section of John Stuart Mill’s "Principles of Political Economy" that focuses on the role and functions of government within an economic system.
-
C.
Book V
Book V is a section of Nicolaus Copernicus’s seminal astronomical work "De revolutionibus orbium coelestium," contributing to his formulation of the heliocentric model.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
book section
ⓘ
mathematics text ⓘ |
| aimsTo |
classify quadratic forms of given discriminant
ⓘ
determine representation of integers by forms ⓘ |
| author | Carl Friedrich Gauss ⓘ |
| contributesTo |
algebraic number theory
ⓘ
class field theory foundations ⓘ |
| field | number theory ⓘ |
| focusesOn |
class groups of quadratic forms
ⓘ
classification of quadratic forms ⓘ composition law for quadratic forms ⓘ composition of forms ⓘ discriminants of quadratic forms ⓘ equivalence of forms ⓘ forms and quadratic forms ⓘ reduction of quadratic forms ⓘ representation of integers by quadratic forms ⓘ theory of binary quadratic forms ⓘ |
| follows |
Disquisitiones Arithmeticae
ⓘ
surface form:
Book IV (Disquisitiones Arithmeticae)
|
| hasMathematicalConcept |
composition of classes
ⓘ
improper equivalence of forms ⓘ indefinite forms ⓘ positive definite forms ⓘ primitive forms ⓘ principal form ⓘ proper equivalence of forms ⓘ reduced form ⓘ |
| hasMathematicalObjects |
binary quadratic forms
ⓘ
class number ⓘ discriminant ⓘ equivalence classes of forms ⓘ |
| historicalSignificance |
foundational treatment of binary quadratic forms
ⓘ
precursor to modern class group theory ⓘ |
| influenced |
development of ideal class groups
ⓘ
later theory of quadratic forms ⓘ |
| introduces | systematic theory of binary quadratic forms ⓘ |
| language | Latin ⓘ |
| originalPublicationYear | 1801 ⓘ |
| partOf | Disquisitiones Arithmeticae ⓘ |
| positionInWork | 5 ⓘ |
| precedes |
Disquisitiones Arithmeticae
ⓘ
surface form:
Book VI (Disquisitiones Arithmeticae)
|
| usesMethod |
arithmetical transformations of variables
ⓘ
composition of equivalence classes ⓘ |
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 V Description of subject: Book V is a section of Carl Friedrich Gauss’s seminal number theory work *Disquisitiones Arithmeticae*, focusing on advanced properties and structures within arithmetic.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.