Book III of Geometry (Descartes)
E203774
Book III of Geometry (Descartes) is the concluding section of René Descartes’ seminal work "La Géométrie," where he further develops his analytic methods and applies them to more advanced problems in algebraic geometry.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Book III of Geometry (Descartes) canonical | 3 |
| Livre III de La Géométrie | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1783758 — 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 III of Geometry (Descartes) Context triple: [Geometry (Descartes), hasPart, Book III of Geometry (Descartes)]
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A.
Book II of Geometry (Descartes)
Book II of Geometry (Descartes) is the section of René Descartes’ seminal work where he develops and applies his new algebraic methods to solve classical geometric problems, helping to lay the foundations of analytic geometry.
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B.
Book I of Geometry (Descartes)
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.
-
C.
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.
-
D.
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.
-
E.
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.
- 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 III of Geometry (Descartes) Target entity description: Book III of Geometry (Descartes) is the concluding section of René Descartes’ seminal work "La Géométrie," where he further develops his analytic methods and applies them to more advanced problems in algebraic geometry.
-
A.
Book II of Geometry (Descartes)
Book II of Geometry (Descartes) is the section of René Descartes’ seminal work where he develops and applies his new algebraic methods to solve classical geometric problems, helping to lay the foundations of analytic geometry.
-
B.
Book I of Geometry (Descartes)
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.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
book section
ⓘ
mathematical treatise section ⓘ |
| aim | to demonstrate the power of algebraic methods in solving complex geometric problems ⓘ |
| associatedPhilosopher | René Descartes ⓘ |
| author | René Descartes ⓘ |
| contains | advanced applications of Descartes’ analytic methods ⓘ |
| contribution |
development of analytic geometry
ⓘ
extension of algebraic methods introduced in earlier books of La Géométrie ⓘ systematic treatment of algebraic curves ⓘ |
| countryOfOrigin | Kingdom of France ⓘ |
| field |
algebraic geometry
ⓘ
analytic geometry ⓘ geometry ⓘ mathematics ⓘ |
| firstPublishedIn |
Discours de la méthode
ⓘ
surface form:
Le Discours de la méthode
|
| follows | Book II of Geometry (Descartes) ⓘ |
| genre |
mathematical exposition
ⓘ
scientific literature ⓘ |
| historicalPeriod | 17th century ⓘ |
| historicalSignificance | helped establish the foundations of modern algebraic geometry ⓘ |
| influenced |
later developments in analytic geometry
ⓘ
subsequent work in algebraic geometry ⓘ |
| languageFamily | Romance languages ⓘ |
| mainTheme |
application of analytic methods to advanced geometric problems
ⓘ
classification of curves by algebraic equations ⓘ solution of geometric problems using algebra ⓘ study of algebraic curves ⓘ |
| originalLanguage | French ⓘ |
| originalPublicationFormat | appendix to a philosophical discourse ⓘ |
| originalTitle |
Book III of Geometry (Descartes)
self-linksurface differs
ⓘ
surface form:
Livre III de La Géométrie
|
| partOf | La Géométrie ⓘ |
| positionInWork |
final book
ⓘ
third book ⓘ |
| precedes | none (concluding section) ⓘ |
| publicationYear | 1637 ⓘ |
| relatedConcept |
Cartesian coordinates
ⓘ
algebraic equation of a curve ⓘ |
| relatedWork |
Book I of Geometry (Descartes)
ⓘ
Book II of Geometry (Descartes) ⓘ |
| usesMethod |
Cartesian coordinate method
ⓘ
algebraic representation of geometric curves ⓘ |
| workType | appendix to Discours de la méthode ⓘ |
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 III of Geometry (Descartes) Description of subject: Book III of Geometry (Descartes) is the concluding section of René Descartes’ seminal work "La Géométrie," where he further develops his analytic methods and applies them to more advanced problems in algebraic geometry.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
Book III of Geometry (Descartes)
→
originalTitle
→
Book III of Geometry (Descartes)
self-linksurface differs
ⓘ
this entity surface form:
Livre III de La Géométrie