Elements of Analytical Geometry and of the Differential and Integral Calculus
E288299
Elements of Analytical Geometry and of the Differential and Integral Calculus is a 19th-century mathematics textbook that systematically introduces analytic geometry alongside the fundamentals of differential and integral calculus.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Elements of Analytical Geometry and of the Differential and Integral Calculus canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2667156 — 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 Analytical Geometry and of the Differential and Integral Calculus Context triple: [Elias Loomis, notableWork, Elements of Analytical Geometry and of the Differential and Integral Calculus]
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A.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
-
B.
Elementa curvarum linearum
Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
-
C.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
-
D.
Cours d’Analyse
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.
-
E.
Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
- 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 Analytical Geometry and of the Differential and Integral Calculus Target entity description: Elements of Analytical Geometry and of the Differential and Integral Calculus is a 19th-century mathematics textbook that systematically introduces analytic geometry alongside the fundamentals of differential and integral calculus.
-
A.
Treatise on Demonstration of Problems of Algebra
Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
-
B.
Elementa curvarum linearum
Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
-
C.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
-
D.
Cours d’Analyse
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.
-
E.
Disquisitiones Generales Circa Superficies Curvas
Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
19th-century book
ⓘ
educational work ⓘ mathematics textbook ⓘ |
| documentType | printed book ⓘ |
| educationalLevel |
advanced secondary level
ⓘ
university level ⓘ |
| educationalObjective |
systematic introduction to analytic geometry
ⓘ
systematic introduction to differential calculus ⓘ systematic introduction to integral calculus ⓘ |
| fieldOfWork | mathematics ⓘ |
| genre | textbook ⓘ |
| hasPart |
applications of differential calculus
ⓘ
applications of integral calculus ⓘ fundamentals of differentiation ⓘ fundamentals of integration ⓘ introduction to coordinate geometry ⓘ problems and exercises ⓘ treatment of curves in the plane ⓘ |
| hasTopic |
Cartesian coordinate system
ⓘ
surface form:
Cartesian coordinates
areas under curves ⓘ derivatives ⓘ equations of conic sections ⓘ equations of lines ⓘ geometric interpretation of algebraic equations ⓘ integrals ⓘ limits ⓘ maxima and minima ⓘ series expansions ⓘ tangents to curves ⓘ |
| historicalContext | development of modern mathematical education in the 19th century ⓘ |
| intendedUse |
self-study
ⓘ
university instruction ⓘ |
| language | English ⓘ |
| mainSubject |
analytic geometry
ⓘ
differential calculus ⓘ integral calculus ⓘ |
| teachesSkill |
applying calculus to geometry
ⓘ
computing derivatives ⓘ computing integrals ⓘ solving geometric problems using algebraic methods ⓘ |
| timePeriod | 19th century ⓘ |
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 Analytical Geometry and of the Differential and Integral Calculus Description of subject: Elements of Analytical Geometry and of the Differential and Integral Calculus is a 19th-century mathematics textbook that systematically introduces analytic geometry alongside the fundamentals of differential and integral calculus.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
Elias Loomis
→
notableWork
→
Elements of Analytical Geometry and of the Differential and Integral Calculus
ⓘ