Book I
E157375
Book I is the opening section of Carl Friedrich Gauss’s seminal work *Disquisitiones Arithmeticae*, laying foundational concepts in number theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Book I canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1381984 — 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 I Context triple: [Disquisitiones Arithmeticae, hasPart, Book I]
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A.
Book I
Book I is the opening section of Washington Irving’s satirical work *A History of New York*, introducing the mock-historical tone and humorous narrative that characterize the rest of the book.
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B.
Book I
Book I is the opening section of Jean-Jacques Rousseau’s political treatise *The Social Contract*, where he lays the philosophical groundwork for his theory of legitimate political authority and the social pact.
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C.
Book I
Book I is the opening section of Nicolaus Copernicus’s "De revolutionibus orbium coelestium," where he lays out the foundational principles of his heliocentric model of the cosmos.
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D.
Book I
Book I is the opening section of John Locke’s "An Essay Concerning Human Understanding," in which he challenges the doctrine of innate ideas and lays the groundwork for his empiricist theory of knowledge.
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E.
Book I
Book I is the first section of Isaac Newton’s *Philosophiæ Naturalis Principia Mathematica*, laying out the mathematical foundations of classical mechanics and the laws of motion.
- 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 I Target entity description: Book I is the opening section of Carl Friedrich Gauss’s seminal work *Disquisitiones Arithmeticae*, laying foundational concepts in number theory.
-
A.
Book I
Book I is the opening section of Washington Irving’s satirical work *A History of New York*, introducing the mock-historical tone and humorous narrative that characterize the rest of the book.
-
B.
Book I
Book I is the opening section of Jean-Jacques Rousseau’s political treatise *The Social Contract*, where he lays the philosophical groundwork for his theory of legitimate political authority and the social pact.
-
C.
Book I
Book I is the opening section of John Locke’s "An Essay Concerning Human Understanding," in which he challenges the doctrine of innate ideas and lays the groundwork for his empiricist theory of knowledge.
-
D.
Book I
Book I is the opening section of Nicolaus Copernicus’s "De revolutionibus orbium coelestium," where he lays out the foundational principles of his heliocentric model of the cosmos.
-
E.
Book I
Book I is the first section of Isaac Newton’s *Philosophiæ Naturalis Principia Mathematica*, laying out the mathematical foundations of classical mechanics and the laws of motion.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf | book section ⓘ |
| aimsTo | establish basic arithmetic properties rigorously ⓘ |
| author | Carl Friedrich Gauss ⓘ |
| contains |
definitions
ⓘ
proofs ⓘ propositions ⓘ |
| coversTopic |
basic properties of congruence classes
ⓘ
congruences ⓘ divisibility ⓘ greatest common divisor ⓘ least common multiple ⓘ prime numbers ⓘ properties of integers ⓘ residues modulo n ⓘ |
| describedAs | opening section of Disquisitiones Arithmeticae ⓘ |
| field | number theory ⓘ |
| hasAuthorRole | Gauss as sole author ⓘ |
| hasInfluenceOn |
notation and methods of modular arithmetic
ⓘ
rigorous axiomatic treatment of arithmetic ⓘ |
| historicalPeriod | early 19th century mathematics ⓘ |
| influenced | development of modern number theory ⓘ |
| introducesConcept |
congruence notation a ≡ b (mod m)
ⓘ
systematic use of modular arithmetic ⓘ |
| isFoundationFor | Gauss’s later work in number theory ⓘ |
| isStudiedIn |
advanced undergraduate number theory courses
ⓘ
graduate courses in number theory ⓘ |
| language | Latin ⓘ |
| laysFoundationFor |
elementary number theory
ⓘ
later books of Disquisitiones Arithmeticae ⓘ |
| mathematicalDiscipline | arithmetic ⓘ |
| originalPublicationYear | 1801 ⓘ |
| originalPublisher | Friedrich Vieweg und Sohn ⓘ |
| partOf | Disquisitiones Arithmeticae ⓘ |
| positionInWork | first book ⓘ |
| relatedWork |
Disquisitiones Arithmeticae
ⓘ
surface form:
Book II (Disquisitiones Arithmeticae)
Disquisitiones Arithmeticae ⓘ
surface form:
Book III (Disquisitiones Arithmeticae)
Disquisitiones Arithmeticae ⓘ
surface form:
Book IV (Disquisitiones Arithmeticae)
Disquisitiones Arithmeticae ⓘ
surface form:
Book V (Disquisitiones Arithmeticae)
Disquisitiones Arithmeticae ⓘ
surface form:
Book VI (Disquisitiones Arithmeticae)
Disquisitiones Arithmeticae ⓘ
surface form:
Book VII (Disquisitiones Arithmeticae)
|
| workType | theoretical mathematics ⓘ |
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 I Description of subject: Book I is the opening section of Carl Friedrich Gauss’s seminal work *Disquisitiones Arithmeticae*, laying foundational concepts in number theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.