Liber Quartus
E631881
Liber Quartus is the fourth book of Carl Friedrich Gauss’s *Disquisitiones Arithmeticae*, focusing on the theory of quadratic forms and related foundational topics in number theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Liber Quartus canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T6945252 — 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: Liber Quartus Context triple: [Book IV (Disquisitiones Arithmeticae), workTitle, Liber Quartus]
-
A.
Liber Tertius
Liber Tertius is the third book of Nicolaus Copernicus’s seminal work *De revolutionibus orbium coelestium*, in which he develops key mathematical and astronomical arguments for the heliocentric model.
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B.
Summus Poeninus
Summus Poeninus is the Latin name for the Great St Bernard Pass, a historic Alpine route linking Switzerland and Italy that has served as a key transalpine crossing since antiquity.
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C.
Liber Continens
Liber Continens is a monumental medical encyclopedia by the Persian polymath Al-Razi, compiling and critically evaluating the medical knowledge and clinical observations of his time.
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D.
Tertia Pars
Tertia Pars is the third and final major section of Thomas Aquinas’s Summa Theologiae, focusing primarily on Christology and the sacraments.
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E.
Utrinque Paratus
Utrinque Paratus is the Latin motto of the British Army’s Parachute Regiment, meaning “Ready for Anything” or “Ready on Both Sides,” reflecting its airborne readiness and versatility.
- 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: Liber Quartus Target entity description: Liber Quartus is the fourth book of Carl Friedrich Gauss’s *Disquisitiones Arithmeticae*, focusing on the theory of quadratic forms and related foundational topics in number theory.
-
A.
Liber Tertius
Liber Tertius is the third book of Nicolaus Copernicus’s seminal work *De revolutionibus orbium coelestium*, in which he develops key mathematical and astronomical arguments for the heliocentric model.
-
B.
Summus Poeninus
Summus Poeninus is the Latin name for the Great St Bernard Pass, a historic Alpine route linking Switzerland and Italy that has served as a key transalpine crossing since antiquity.
-
C.
Liber Continens
Liber Continens is a monumental medical encyclopedia by the Persian polymath Al-Razi, compiling and critically evaluating the medical knowledge and clinical observations of his time.
-
D.
Tertia Pars
Tertia Pars is the third and final major section of Thomas Aquinas’s Summa Theologiae, focusing primarily on Christology and the sacraments.
-
E.
Utrinque Paratus
Utrinque Paratus is the Latin motto of the British Army’s Parachute Regiment, meaning “Ready for Anything” or “Ready on Both Sides,” reflecting its airborne readiness and versatility.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
book section
ⓘ
mathematics book ⓘ |
| author | Carl Friedrich Gauss ⓘ |
| contributesTo |
foundations of algebraic number theory
ⓘ
theory of binary quadratic forms ⓘ |
| field | number theory ⓘ |
| focusesOn |
binary quadratic forms
ⓘ
class number of quadratic forms ⓘ classes of quadratic forms ⓘ classification of quadratic forms ⓘ composition of quadratic forms ⓘ discriminant of quadratic forms ⓘ equivalence of quadratic forms ⓘ genus of quadratic forms ⓘ integral quadratic forms ⓘ quadratic forms ⓘ reduction of quadratic forms ⓘ representation of integers by quadratic forms ⓘ |
| follows | Liber Tertius ⓘ |
| hasKeyConcept |
class group of binary quadratic forms
ⓘ
composition law for forms ⓘ discriminant invariance ⓘ improper equivalence of forms ⓘ proper equivalence of forms ⓘ reduced form ⓘ |
| hasKeyResult |
conditions for representation of integers by forms
ⓘ
finiteness of class number for given discriminant ⓘ law of composition of classes of forms ⓘ structure of classes of forms with given discriminant ⓘ |
| hasModernTranslations |
English
ⓘ
French ⓘ German ⓘ |
| hasOrderInWork | 4 ⓘ |
| hasOriginalLanguage | Latin ⓘ |
| historicalRole |
early systematic treatment of binary quadratic forms
ⓘ
foundational text on quadratic forms ⓘ |
| influenced |
19th-century number theory
ⓘ
development of class field theory ⓘ work of Dedekind on ideals ⓘ work of Dirichlet on quadratic forms ⓘ |
| isContainedIn | original 1801 edition of Disquisitiones Arithmeticae ⓘ |
| language | Latin ⓘ |
| originalTitleOfWork | Disquisitiones Arithmeticae ⓘ |
| partOf | Disquisitiones Arithmeticae ⓘ |
| partOfWorkBy | Carl Friedrich Gauss ⓘ |
| precedes | Liber Quintus ⓘ |
| publicationYear | 1801 ⓘ |
| publishedIn | Brunswick ⓘ |
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: Liber Quartus Description of subject: Liber Quartus is the fourth book of Carl Friedrich Gauss’s *Disquisitiones Arithmeticae*, focusing on the theory of quadratic forms and related foundational topics in number theory.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.