Section: Axioms of Connection and Their Consequences
As mentioned above, David Hilbert (1862  1943) proposed an axiomatic system dealing with geometrical objects like "points", "straight lines", and "planes", detaching them from their specific meaning. Hilbert wanted to avoid any attempt to define exactly what a point, a straight line, or a plane is. He rather focussed on the relationships between these objects. The following definitions and axioms demonstrate this approach.
Table of Contents
 Definition: Points, Straight Lines, and Planes
 Definition: "Lies on" Relation
 Axiom: Axioms of Connection
 Proposition: Common Points of Two Distinct Straight Lines in a Plane
 Proposition: Common Points of a Plane and a Straight Line Not in the Plane
 Proposition: Plane Determined by a Straight Line and a Point not on the Straight Line
 Proposition: Plane Determined by two Crossing Straight Lines
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References
Bibliography
 Lee, John M.: "Axiomatic Geometry", AMC, 2013
 Berchtold, Florian: "Geometrie", Springer Spektrum, 2017
 Klotzek, B.: "Geometrie", Studienbücherei, 1971
 Hilbert, David: "Grundlagen der Geometrie", Leipzig, B.G. Teubner, 1903