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.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
book of a mathematical treatise
ⓘ
part of Euclid's Elements ⓘ |
| author | Euclid NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| studiedIn |
foundations of geometry
ⓘ
history of mathematics ⓘ philosophy of mathematics ⓘ |
| traditionallyNumberedAs | Book V NERFINISHED ⓘ |
| usedIn |
Book VI of the Elements
NERFINISHED
ⓘ
Book XII of the Elements NERFINISHED ⓘ |
| workForm | geometrical treatise section ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.