Abstract
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.
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© 2000 Robin Hartshorne
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Hartshorne, R. (2000). Hilbert’s Axioms. In: Geometry: Euclid and Beyond. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22676-7_3
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DOI: https://doi.org/10.1007/978-0-387-22676-7_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3145-0
Online ISBN: 978-0-387-22676-7
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