One of Euclid's axioms is that parallel lines do not intersect. This is true on a plane, so Euclidean's axioms describe planar geometry. In non-euclidian geometry you relax this requirement, giving rise to things like hyperbolic spaces and elliptical spaces.
Not sure what OP is going on about though, as this doesn't seem particularly on topic.
https://en.wikipedia.org/wiki/Non-Euclidean_geometry