On Divisions of Figures
E537784
On Divisions of Figures is an ancient mathematical treatise attributed to Euclid that systematically studies how geometric figures can be divided into parts with specified ratios or properties.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
ancient mathematical treatise
ⓘ
geometrical treatise ⓘ work on Euclidean geometry ⓘ |
| aimsTo |
provide general methods for dividing figures with given conditions
ⓘ
systematically classify division problems for plane figures ⓘ |
| associatedWith | Hellenistic mathematics NERFINISHED ⓘ |
| attributedTo | Euclid NERFINISHED ⓘ |
| authorshipStatus | attribution to Euclid is not fully certain ⓘ |
| concerns |
construction of dividing lines
ⓘ
geometric optimization under constraints ⓘ loci arising from division conditions ⓘ proportional division of areas ⓘ |
| field |
geometry
ⓘ
mathematics ⓘ |
| focusesOn |
dividing figures by lines at given angles
ⓘ
dividing figures by lines parallel to given lines ⓘ dividing figures by lines through given points ⓘ dividing figures into equal areas ⓘ dividing figures into parts satisfying geometric constraints ⓘ dividing figures into parts with specified areas ⓘ dividing figures into parts with specified ratios ⓘ dividing figures into similar parts ⓘ |
| genre | mathematical problem collection ⓘ |
| hasAlternativeName |
De Divisionibus Figurarum
NERFINISHED
ⓘ
Peri diaireseōs schēmatōn NERFINISHED ⓘ |
| hasStatus | surviving in later manuscript traditions ⓘ |
| influenced |
later Islamic mathematical tradition
ⓘ
medieval European geometry ⓘ |
| mainSubject |
area division problems
ⓘ
division of geometric figures ⓘ geometric constructions ⓘ partition of figures with given properties ⓘ ratio and proportion in geometry ⓘ |
| relatedTo |
Data
ⓘ
Elements NERFINISHED ⓘ ancient Greek treatises on geometric problems ⓘ |
| studiesFigureType |
circles
ⓘ
polygons ⓘ quadrilaterals ⓘ segments of circles ⓘ triangles ⓘ |
| timePeriod | ancient Greek mathematics ⓘ |
| tradition | Euclidean corpus NERFINISHED ⓘ |
| typeOfProblem |
area partition problems
ⓘ
construction problems ⓘ locus problems ⓘ ratio problems ⓘ |
| usesMethod | classical ruler-and-compass construction ⓘ |
| writtenIn | Ancient Greek ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.