Hilbert’s Axioms

  • Robin Hartshorne
Part of the Undergraduate Texts in Mathematics book series (UTM)


Our purpose in this chapter is to present (with minor modifications) a set of axioms for geometry proposed by Hilbert in 1899. These axioms are sufficient by modern standards of rigor to supply the foundation for Euclid's geometry. This will mean also axiomatizing those arguments where he used intuition, or said nothing. In particular, the axioms for betweenness, based on the work of Pasch in the 1880s, are the most striking innovation in this set of axioms.


Line Segment Euclidean Plane Axiom System Isosceles Triangle Affine Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Robin Hartshorne 2000

Authors and Affiliations

  • Robin Hartshorne
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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