Book IV
E160780
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Book IV canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1381987 — 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 IV Context triple: [Disquisitiones Arithmeticae, hasPart, Book IV]
-
A.
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.
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B.
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.
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C.
Book III
Book III is the section of Jean-Jacques Rousseau’s political treatise *The Social Contract* that focuses on the nature, forms, and functioning of government in relation to the sovereign people.
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D.
Book III
Book III is the section of John Locke’s "An Essay Concerning Human Understanding" that focuses on the nature, use, and limitations of language in human knowledge.
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E.
Book III
Book III is one of the sections of Nicolaus Copernicus’s seminal astronomical work *De revolutionibus orbium coelestium*, which laid the foundations of the heliocentric model of the solar system.
- 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 IV Target entity description: 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.
-
A.
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.
-
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 III
Book III is a section of Washington Irving’s satirical work *A History of New York*, continuing its humorous mock-historical narrative of the city’s early days.
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D.
Book III
Book III is the section of John Locke’s "An Essay Concerning Human Understanding" that focuses on the nature, use, and limitations of language in human knowledge.
-
E.
Book III
Book III is one of the sections of Nicolaus Copernicus’s seminal astronomical work *De revolutionibus orbium coelestium*, which laid the foundations of the heliocentric model of the solar system.
- F. None of above. chosen
Statements (26)
| Predicate | Object |
|---|---|
| instanceOf | book section ⓘ |
| author | Carl Friedrich Gauss ⓘ |
| containedIn | original 1801 Latin edition of Disquisitiones Arithmeticae ⓘ |
| field | number theory ⓘ |
| focusesOn |
arithmetic of residues modulo primes
ⓘ
conditions for solvability of quadratic congruences ⓘ congruences ⓘ properties of quadratic residues ⓘ quadratic residues ⓘ residue classes ⓘ |
| hasInfluenceOn |
classical algebraic number theory
ⓘ
development of quadratic reciprocity theory ⓘ modern treatments of congruences ⓘ |
| includedIn | English translations of Disquisitiones Arithmeticae ⓘ |
| isFollowedBy |
Disquisitiones Arithmeticae
ⓘ
surface form:
Book V (Disquisitiones Arithmeticae)
|
| isPartOf | Gauss’s foundational work in arithmetic theory ⓘ |
| isPrecededBy |
Disquisitiones Arithmeticae
ⓘ
surface form:
Book III (Disquisitiones Arithmeticae)
|
| language | Latin ⓘ |
| originalTitle |
Disquisitiones Arithmeticae
ⓘ
surface form:
Disquisitiones Arithmeticae, Liber Quartus
|
| partOf | Disquisitiones Arithmeticae ⓘ |
| publicationYear | 1801 ⓘ |
| subject |
criteria for quadratic residuosity
ⓘ
distribution of quadratic residues and non-residues ⓘ quadratic congruences modulo primes ⓘ structure of the multiplicative group modulo a prime ⓘ |
| workTitle | Liber Quartus ⓘ |
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 IV Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.