Euclid's postulates

E555119
axiomatic system foundational assumptions of Euclidean geometry geometric axiom set

Euclid's postulates are the foundational axioms of classical Euclidean geometry, defining basic properties of points, lines, and planes from which the rest of the geometry is logically derived.

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Observed surface forms (5)

Surface form Occurrences
Fifth postulate 0
First postulate 0
Third postulate 0

Statements (49)

Predicate Object
instanceOf axiomatic system ⓘ
foundational assumptions of Euclidean geometry ⓘ
geometric axiom set ⓘ
alsoKnownAs parallel postulate NERFINISHED ⓘ
appliesTo plane geometry ⓘ
two-dimensional space ⓘ
approximateDate 3rd century BCE ⓘ
assume comparability of right angles ⓘ
existence of circles ⓘ
existence of straight lines ⓘ
author Euclid NERFINISHED ⓘ
basedOn intuitive geometric notions ⓘ
characterizedBy independence from proof ⓘ
intended self-evidence ⓘ
concerns circles ⓘ
intersecting lines ⓘ
line segments ⓘ
parallel lines ⓘ
points ⓘ
right angles ⓘ
straight lines ⓘ
distinguishedFrom Euclid's common notions NERFINISHED ⓘ
theorems of Euclidean geometry ⓘ
domain flat space ⓘ
field geometry ⓘ
mathematics ⓘ
formalizationOf basic properties of points, lines, and planes ⓘ
hasPostulate Fifth postulate ⓘ
First postulate ⓘ
Fourth postulate ⓘ
Second postulate ⓘ
Third postulate ⓘ
historicalPeriod Hellenistic period NERFINISHED ⓘ
influenced axiomatic method in mathematics ⓘ
foundations of classical geometry ⓘ
languageOfOriginal Ancient Greek ⓘ
ledTo development of non-Euclidean geometries ⓘ
logicalRole axioms ⓘ
notValidIn general curved spaces ⓘ
numberOfElements 5 ⓘ
partOf Euclidean geometry NERFINISHED ⓘ
roleInHistory starting point for non-Euclidean geometry ⓘ
statedIn Elements NERFINISHED ⓘ
statement A straight line segment can be drawn joining any two points. ⓘ
All right angles are equal to one another. ⓘ
Any straight line segment can be extended indefinitely in a straight line. ⓘ
Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. ⓘ
If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles. ⓘ
usedFor deriving theorems of Euclidean geometry ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Commentary on the Difficulties of Certain Postulates of Euclid → mainSubject → Euclid's postulates ⓘ