Book X of the Elements
E539694
Book X of the Elements is a section of Euclid’s mathematical treatise that systematically develops the theory of irrational magnitudes and incommensurability.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Book X of the Elements canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5658089 — 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 X of the Elements Context triple: [Euclid, hasPart, Book X of the Elements]
-
A.
Book V of the Elements
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.
-
B.
Book XIII of Euclid's Elements
Book XIII of Euclid's Elements is the concluding book of Euclid’s mathematical treatise, focusing on the construction and properties of the five regular Platonic solids within the framework of classical Greek geometry.
-
C.
Proclus' Chrestomathy
Proclus' Chrestomathy is a lost ancient Greek work, known through later summaries, that provided prose epitomes of the early epic poems of the Trojan cycle and other pre-Homeric epics.
-
D.
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.
-
E.
Euclid's Elements
Euclid's Elements is an ancient Greek mathematical treatise that systematically presents the foundations of geometry, number theory, and mathematical proof.
- 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 X of the Elements Target entity description: Book X of the Elements is a section of Euclid’s mathematical treatise that systematically develops the theory of irrational magnitudes and incommensurability.
-
A.
Book V of the Elements
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.
-
B.
Book XIII of Euclid's Elements
Book XIII of Euclid's Elements is the concluding book of Euclid’s mathematical treatise, focusing on the construction and properties of the five regular Platonic solids within the framework of classical Greek geometry.
-
C.
Proclus' Chrestomathy
Proclus' Chrestomathy is a lost ancient Greek work, known through later summaries, that provided prose epitomes of the early epic poems of the Trojan cycle and other pre-Homeric epics.
-
D.
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.
-
E.
Euclid's Elements
Euclid's Elements is an ancient Greek mathematical treatise that systematically presents the foundations of geometry, number theory, and mathematical proof.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
book of a mathematical treatise
ⓘ
section of Euclid's Elements ⓘ |
| aim |
to classify different kinds of irrational magnitudes
ⓘ
to formalize incommensurability within geometry ⓘ |
| author | Euclid NERFINISHED ⓘ |
| basedOn | earlier Greek work on incommensurability ⓘ |
| canonicalStatus | standard part of the 13‑book corpus of Euclid's Elements ⓘ |
| epistemicStatus | attributed to Euclid in the mathematical tradition ⓘ |
| field |
Greek mathematics
ⓘ
geometry ⓘ number theory ⓘ |
| follows | Book IX of the Elements NERFINISHED ⓘ |
| genre | mathematical treatise ⓘ |
| hasForm | geometric exposition ⓘ |
| hasPart |
definitions
ⓘ
geometric proofs ⓘ propositions ⓘ |
| historicalContext | development of Greek theory of irrationals ⓘ |
| influenced |
Renaissance mathematics
ⓘ
later number theory ⓘ medieval mathematics ⓘ theory of irrational numbers ⓘ |
| language | Ancient Greek ⓘ |
| mainSubject |
classification of irrational lines
ⓘ
incommensurability ⓘ irrational magnitudes ⓘ |
| method | synthetic geometry ⓘ |
| notableFor |
geometric approach to irrationality
ⓘ
rigorous treatment of incommensurable magnitudes ⓘ systematic theory of irrational magnitudes ⓘ |
| partOf | Euclid's Elements NERFINISHED ⓘ |
| positionInSeries | 10 ⓘ |
| precedes | Book XI of the Elements NERFINISHED ⓘ |
| relatedTo | Eudoxus' theory of proportion ⓘ |
| usesConcept |
commensurable magnitudes
ⓘ
geometric construction ⓘ incommensurable magnitudes ⓘ proportion ⓘ ratio ⓘ |
| workPeriod | Hellenistic period ⓘ |
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 X of the Elements Description of subject: Book X of the Elements is a section of Euclid’s mathematical treatise that systematically develops the theory of irrational magnitudes and incommensurability.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.