Book V of the Elements
E537787
Book V of the Elements is the section of Euclid’s mathematical treatise that rigorously develops the general theory of proportion, foundational for real number and magnitude theory in geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Book V of the Elements canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5658088 — 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 V of the Elements Context triple: [Euclid, hasPart, Book V of the Elements]
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A.
Aristotle’s On the Heavens
Aristotle’s On the Heavens is an influential ancient Greek treatise that presents Aristotle’s cosmology and theories about the structure and motions of the universe.
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B.
Book VI
Book VI is the concluding section of Nicolaus Copernicus’s seminal astronomical work *De revolutionibus orbium coelestium*, in which he further develops and applies his heliocentric model.
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C.
Book VI
Book VI is a section of Augustine’s theological and philosophical work *The City of God* that continues his critique of pagan religion and Roman culture.
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D.
Book VI
Book VI is the final section of Carl Friedrich Gauss’s *Disquisitiones Arithmeticae*, focusing on the theory of binary quadratic forms and their composition.
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E.
Book VI
Book VI is a section of Leonardo Bruni’s historical work "History of the Florentine People," continuing his humanist narrative of Florence’s political and civic development.
- 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 V of the Elements Target entity description: Book V of the Elements is the section of Euclid’s mathematical treatise that rigorously develops the general theory of proportion, foundational for real number and magnitude theory in geometry.
-
A.
Aristotle’s On the Heavens
Aristotle’s On the Heavens is an influential ancient Greek treatise that presents Aristotle’s cosmology and theories about the structure and motions of the universe.
-
B.
Book VI
Book VI is the concluding section of Nicolaus Copernicus’s seminal astronomical work *De revolutionibus orbium coelestium*, in which he further develops and applies his heliocentric model.
-
C.
Book VI
Book VI is a section of Augustine’s theological and philosophical work *The City of God* that continues his critique of pagan religion and Roman culture.
-
D.
Book VI
Book VI is a section of Leonardo Bruni’s historical work "History of the Florentine People," continuing his humanist narrative of Florence’s political and civic development.
-
E.
Book VI
Book VI of Aristotle’s Nicomachean Ethics is the section that analyzes the intellectual virtues, especially practical wisdom (phronesis), and their role in ethical decision-making.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
book of a mathematical treatise
ⓘ
part of Euclid's Elements ⓘ |
| author | Euclid ⓘ |
| basedOn | Eudoxus of Cnidus' theory of proportion ⓘ |
| canonicalStatus | standard part of the Euclidean corpus ⓘ |
| conceptualRole |
early rigorous treatment of incommensurable magnitudes
ⓘ
precursor to modern real analysis (historically) ⓘ |
| contains |
axioms about magnitudes and ratios
ⓘ
definition of equal ratios ⓘ definition of greater ratio ⓘ definition of less ratio ⓘ definition of proportional magnitudes ⓘ propositions about addition of proportional magnitudes ⓘ propositions about alternation of ratios ⓘ propositions about compounding of ratios ⓘ propositions about conversion of ratios ⓘ propositions about equality of multiple ratios ⓘ propositions about inversion of ratios ⓘ propositions about properties of proportional magnitudes ⓘ propositions about proportionality in series of magnitudes ⓘ propositions about subtraction of proportional magnitudes ⓘ |
| describedAs | rigorous development of the general theory of proportion ⓘ |
| field |
geometry
ⓘ
mathematics ⓘ |
| hasStructure | sequence of definitions followed by propositions ⓘ |
| historicalPeriod | Hellenistic mathematics ⓘ |
| influenced |
Eudoxian theory of proportion
ⓘ
foundations of classical geometry ⓘ magnitude theory in geometry ⓘ real number theory (historical development) ⓘ |
| languageOfOriginal | Ancient Greek ⓘ |
| logicalRole |
foundational for later books of the Elements
ⓘ
provides general theory of proportion independent of number ⓘ |
| mainSubject |
magnitudes
ⓘ
proportionality ⓘ ratio ⓘ theory of proportion ⓘ |
| method |
axiomatic
ⓘ
geometric ⓘ |
| partOf | Euclid's Elements ⓘ |
| studiedIn |
foundations of geometry
ⓘ
history of mathematics ⓘ philosophy of mathematics ⓘ |
| traditionallyNumberedAs | Book V ⓘ |
| usedIn |
Book VI of the Elements
ⓘ
Book XII of the Elements ⓘ
linked to:
Book XII of Euclid's Elements
|
| workForm | geometrical treatise section ⓘ |
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 V of the Elements Description of subject: Book V of the Elements is the section of Euclid’s mathematical treatise that rigorously develops the general theory of proportion, foundational for real number and magnitude theory in geometry.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.