Elements of Arithmetic
E428889
Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Elements of Arithmetic canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4290526 — 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: Elements of Arithmetic Context triple: [Augustus De Morgan, notableWork, Elements of Arithmetic]
-
A.
The Higher Arithmetic
The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
-
B.
Die Grundlagen der Arithmetik
Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
-
C.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
-
D.
Philosophy and Fun of Algebra
Philosophy and Fun of Algebra is an accessible, imaginative book that introduces algebraic ideas and mathematical thinking to children and lay readers through stories, puzzles, and philosophical reflections.
-
E.
Arithmetic, Algebra, Analysis
"Arithmetic, Algebra, Analysis" is a foundational mathematics text that systematically develops core topics in number theory, algebraic structures, and real analysis from a rigorous, advanced perspective.
- 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: Elements of Arithmetic Target entity description: Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
-
A.
The Higher Arithmetic
The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
-
B.
Die Grundlagen der Arithmetik
Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
-
C.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
-
D.
Philosophy and Fun of Algebra
Philosophy and Fun of Algebra is an accessible, imaginative book that introduces algebraic ideas and mathematical thinking to children and lay readers through stories, puzzles, and philosophical reflections.
-
E.
Arithmetic, Algebra, Analysis
"Arithmetic, Algebra, Analysis" is a foundational mathematics text that systematically develops core topics in number theory, algebraic structures, and real analysis from a rigorous, advanced perspective.
- F. None of above. chosen
Statements (33)
| Predicate | Object |
|---|---|
| instanceOf |
19th-century book
ⓘ
arithmetic textbook ⓘ mathematics textbook ⓘ |
| author | Augustus De Morgan ⓘ |
| contributedTo |
development of mathematical pedagogy
ⓘ
formalization of arithmetic ⓘ |
| countryOfOrigin | United Kingdom ⓘ |
| field |
arithmetic
ⓘ
mathematics ⓘ number theory ⓘ |
| focusesOn |
logical foundations of arithmetic
ⓘ
rigorous treatment of number concepts ⓘ systematic development of arithmetic principles ⓘ |
| genre |
educational book
ⓘ
textbook ⓘ |
| hasNotableAuthor | Augustus De Morgan ⓘ |
| historicalPeriod | 19th century ⓘ |
| influencedBy | British mathematical tradition ⓘ |
| intendedAudience |
students of mathematics
ⓘ
teachers of mathematics ⓘ |
| language | English ⓘ |
| mainSubject |
basic number theory
ⓘ
fractions ⓘ fundamental operations of arithmetic ⓘ integers ⓘ natural numbers ⓘ proportions ⓘ |
| publicationCentury | 19th century ⓘ |
| teaches |
addition
ⓘ
division ⓘ multiplication ⓘ subtraction ⓘ |
| usedIn | mathematics education ⓘ |
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: Elements of Arithmetic Description of subject: Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.