Verify the interpretations of the incidence axioms the betwe

Verify the interpretations of the incidence axioms, the betweeness axioms, and Dedekind\'s axiom (if hte Euclidean plane is real) for the Klein model.

K-4) Given chords l and m, of gamma, that are not diameteres. Suppose the line extending m passes through the pole of l. Prove that the line extending l passes through the pole of m.

Solution

solution:

hilbert axiom\'s:

are a set of 20 assumptions proposed by david hilbert.
The axioms[edit]
Hilbert\'s axiom system is constructed with six primitive notions: three primitive terms:

point;
line;
plane;
and three primitive relations:Betweenness, a ternary relation linking points;

Lies on (Containment), three binary relations, one linking points and straight lines, one linking points and planes, and one linking straight lines and planes;
Congruence, two binary relations, one linking line segments and one linking angles, each denoted by an infix
Note that line segments, angles, and triangles may each be defined in terms of points and straight lines, using the relations of betweenness and containment. All points, straight lines, and planes in the following axioms are distinct unless otherwise stated.