Cours d’Analyse
E239299
Cours d’Analyse is a foundational 19th-century mathematics textbook by Augustin-Louis Cauchy that rigorously developed the theory of functions, limits, and continuity, helping to formalize modern analysis.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Cours d’Analyse canonical | 2 |
| Cours d’Analyse de l’École Royale Polytechnique | 1 |
| Résumé des leçons sur le calcul infinitésimal | 1 |
| foundations of real analysis | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2171680 — 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: Cours d’Analyse Context triple: [Augustin-Louis Cauchy, notableWork, Cours d’Analyse]
-
A.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
B.
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
-
C.
Recherches sur les fonctions elliptiques
Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
-
D.
A Course of Pure Mathematics
A Course of Pure Mathematics is a classic early 20th-century textbook that rigorously introduces the foundations of mathematical analysis and helped shape modern university-level mathematics education.
-
E.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
- 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: Cours d’Analyse Target entity description: Cours d’Analyse is a foundational 19th-century mathematics textbook by Augustin-Louis Cauchy that rigorously developed the theory of functions, limits, and continuity, helping to formalize modern analysis.
-
A.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
B.
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
-
C.
Recherches sur les fonctions elliptiques
Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
-
D.
A Course of Pure Mathematics
A Course of Pure Mathematics is a classic early 20th-century textbook that rigorously introduces the foundations of mathematical analysis and helped shape modern university-level mathematics education.
-
E.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
mathematician
ⓘ
mathematics textbook ⓘ treatise on mathematical analysis ⓘ |
| approach | epsilon-style rigor precursor ⓘ |
| author | Augustin-Louis Cauchy ⓘ |
| authorInstanceOf | Augustin-Louis Cauchy ⓘ |
| citedAs | one of the first rigorous analysis textbooks ⓘ |
| containsTopic |
continuity of functions
ⓘ
differential calculus ⓘ integral calculus ⓘ limits of functions ⓘ series ⓘ theory of functions of a real variable ⓘ |
| countryOfOrigin | France ⓘ |
| field |
calculus
ⓘ
mathematical analysis ⓘ mathematical analysis ⓘ real analysis ⓘ |
| firstPublicationYear | 1821 ⓘ |
| hasPart |
volume on algebraic analysis
ⓘ
volume on infinitesimal calculus ⓘ |
| historicalPeriod | early 19th century mathematics ⓘ |
| historicalSignificance | helped formalize the foundations of analysis in the 19th century ⓘ |
| impactOnEducation | standard reference for analysis instruction in 19th-century Europe ⓘ |
| influenced |
development of modern analysis
ⓘ
later textbooks in analysis ⓘ rigorous foundations of calculus ⓘ |
| intendedAudience |
advanced mathematics students
ⓘ
students of the École Polytechnique ⓘ |
| methodologicalFeature | definition-based treatment of fundamental concepts ⓘ |
| notableFor |
early formalization of real analysis
ⓘ
rigorous development of limits ⓘ rigorous treatment of continuity ⓘ systematic use of infinitesimal calculus with rigor ⓘ |
| originalLanguage | French ⓘ |
| placeOfPublication | Paris ⓘ |
| publicationCentury | 19th century ⓘ |
| publisher | Debure frères ⓘ |
| shortTitle | Cours d’Analyse ⓘ |
| title |
Cours d’Analyse de l’École Royale Polytechnique
ⓘ
linked to:
Cours d’Analyse
|
| usedAt | École Polytechnique ⓘ |
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: Cours d’Analyse Description of subject: Cours d’Analyse is a foundational 19th-century mathematics textbook by Augustin-Louis Cauchy that rigorously developed the theory of functions, limits, and continuity, helping to formalize modern analysis.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Cours d’Analyse
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
→
contributedTo
→
foundations of real analysis
ⓘ
linked to: Cours d’Analyse
linked to: Cours d’Analyse