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The eight of Hilbert's Axioms which concern collinearity and intersection; they include the first four of Euclid's Postulates.
See also Absolute Geometry, Congruence Axioms, Continuity Axioms, Euclid's Postulates, Hilbert's Axioms, Ordering Axioms, Parallel Postulate
References
Hilbert, D. The Foundations of Geometry, 2nd ed. Chicago, IL: Open Court, 1980.
Iyanaga, S. and Kawada, Y. (Eds.). ``Hilbert's System of Axioms.'' §163B in
Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 544-545, 1980.