Book I of Geometry (Descartes)
E198133
Book I of Geometry (Descartes) is the opening section of René Descartes’ seminal work where he introduces his method of applying algebra to geometry, laying the foundations of analytic geometry.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Cartesian method | 5 |
| Book I of Geometry (Descartes) canonical | 3 |
| Book I (La Géométrie) | 1 |
| La Géométrie | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1783756 — 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 of Geometry (Descartes) Context triple: [Geometry (Descartes), hasPart, Book I of Geometry (Descartes)]
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A.
Euclides adauctus et methodicus
Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
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B.
Commentary on the Difficulties of Certain Postulates of Euclid
Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
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C.
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.
-
D.
Ethica, ordine geometrico demonstrata
Ethica, ordine geometrico demonstrata is Baruch Spinoza’s major philosophical work, a systematic treatise that presents his metaphysics, ethics, and theory of mind in a rigorous, geometrical style.
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E.
Principles of Cartesian Philosophy
Principles of Cartesian Philosophy is Baruch Spinoza’s early systematic exposition and critique of René Descartes’ philosophy, presented in a geometric, axiomatic style that anticipates his later work.
- 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 of Geometry (Descartes) Target entity description: Book I of Geometry (Descartes) is the opening section of René Descartes’ seminal work where he introduces his method of applying algebra to geometry, laying the foundations of analytic geometry.
-
A.
Euclides adauctus et methodicus
Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
-
B.
Commentary on the Difficulties of Certain Postulates of Euclid
Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
-
C.
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.
-
D.
Ethica, ordine geometrico demonstrata
Ethica, ordine geometrico demonstrata is Baruch Spinoza’s major philosophical work, a systematic treatise that presents his metaphysics, ethics, and theory of mind in a rigorous, geometrical style.
-
E.
Principles of Cartesian Philosophy
Principles of Cartesian Philosophy is Baruch Spinoza’s early systematic exposition and critique of René Descartes’ philosophy, presented in a geometric, axiomatic style that anticipates his later work.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
book section
ⓘ
mathematical treatise ⓘ |
| aim | to provide a general method for solving geometric problems ⓘ |
| associatedWith |
Cartesian coordinates
ⓘ
linked to:
Cartesian coordinate system
Cartesian geometry ⓘ
linked to:
Cartesian coordinate system
|
| author | René Descartes ⓘ |
| contribution | foundation of analytic geometry ⓘ |
| countryOfOrigin | France ⓘ |
| explains |
how to solve geometric problems using algebraic manipulation
ⓘ
how to translate geometric constructions into algebraic equations ⓘ |
| field |
algebra
ⓘ
analytic geometry ⓘ geometry ⓘ |
| genre | mathematics text ⓘ |
| hasPartOfSeries |
Book II of Geometry (Descartes)
ⓘ
Book III of Geometry (Descartes) ⓘ |
| historicalPeriod |
Early modern period
ⓘ
linked to:
Early Modern period
|
| impact |
integration of algebra and geometry into a unified framework
ⓘ
transformation of classical Euclidean geometry ⓘ |
| inCollection | appendix to Discours de la méthode ⓘ |
| influenced |
development of coordinate geometry
ⓘ
later work in algebraic geometry ⓘ |
| introducedMethod | application of algebra to geometry ⓘ |
| language | French ⓘ |
| methodology | reduction of geometry to algebra ⓘ |
| notableFor |
early use of modern algebraic notation
ⓘ
systematic use of algebraic symbolism in geometry ⓘ |
| originalTitle |
La Géométrie, Livre I
ⓘ
linked to:
La Géométrie
|
| partOf | La Géométrie ⓘ |
| philosophicalContext | Descartes’ program of methodical reasoning ⓘ |
| publishedIn | 1637 ⓘ |
| publishedWith | Discours de la méthode ⓘ |
| relatedWork |
Discours de la méthode
ⓘ
Meditationes de prima philosophia ⓘ
linked to:
Meditations on First Philosophy
|
| topic |
algebraic solution of geometric problems
ⓘ
classification of curves by equations ⓘ notation for powers and exponents ⓘ representation of geometric problems by equations ⓘ use of coordinates in geometry ⓘ use of letters to denote known and unknown quantities ⓘ |
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 of Geometry (Descartes) Description of subject: Book I of Geometry (Descartes) is the opening section of René Descartes’ seminal work where he introduces his method of applying algebra to geometry, laying the foundations of analytic geometry.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.