### Abstract:

A set of axioms of incidence and order for geometry was formulated
by David Hilbert in 1898. In this paper these axioms are reformulated
and particular care is taken with the two relations of order
and incidence. Such phrases as " point P lies on line [cursive small letter L]" are
defined in terms of the incidence relation. A set of models is developed
which illustrates and clarifies the axioms and establishes their
independence.
A major portion of the paper is devoted to the implications of
these axioms. Hilbert gave a list of theorems in his book Foundations
of Geometry which he believed were provable on the basis of only
these axioms. Some of the proofs were sketched and some were not
given. The three major theorems which are a consequence of these
axioms are
The ordering of a finite number of points on a line.The ordering of angles with a common side.
The Jordan Theorem for polygons.
A full proof is given of each of these theorems based upon elementary
and not metric concepts. Some consequences of the theorems are
investigated. Special attention is payed to the significance of Pasch's
Axiom in the proof of these theorems.