|
|
|
Geometry which depends only on the first four of Euclid's Postulates and not on the Parallel Postulate.
Euclid 
himself used only the first four postulates for the first 28 propositions of the Elements, but
was forced to invoke the Parallel Postulate on the 29th.
See also Affine Geometry, Elements, Euclid's Postulates, Geometry, Ordered Geometry, Parallel Postulate
References
Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid.
New York: Vintage Books, pp. 90-91, 1989.