Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
geometric axiom
|
| gptkbp:alsoKnownAs |
fifth postulate
|
| gptkbp:alternativeTo |
Through a point not on a given line, there is exactly one line parallel to the given line.
|
| gptkbp:category |
gptkb:Titan
gptkb:geometry |
| gptkbp:debatedBy |
mathematicians for centuries
|
| gptkbp:formedBy |
gptkb:Euclid
gptkb:Elements circa 300 BCE |
| https://www.w3.org/2000/01/rdf-schema#label |
Euclid's parallel postulate
|
| gptkbp:influenced |
development of elliptic geometry
development of hyperbolic geometry |
| gptkbp:logicalStatus |
independent of other Euclidean postulates
|
| gptkbp:relatedTo |
gptkb:Playfair's_axiom
parallel lines |
| gptkbp:state |
If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
|
| gptkbp:subjectOf |
noncommutative geometry
|
| gptkbp:bfsParent |
gptkb:Non-Euclidean_geometry
|
| gptkbp:bfsLayer |
5
|