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.
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.