Absolute Geometry » geometry that doesn’t (assume the) Playfair (axiom)

 

Absolute Geometry (wiki)

“Absolute geometry is a geometry that does not assume the parallel postulate or any of its   alternatives.”

 

Playfair's Axiom  (MathWorld)

Through any point in space, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.”