Foundation of Geometry in Planes, and Some Complements: Excluding the Parallel Axioms

Fumiya Iwama

22 November 2021

Abstract

"Foundations of Geometry" is a mathematical book written by Hilbert in 1899. This entry is a complete formalization of "Incidence" (excluding cubic axioms), "Order" and "Congruence" (excluding point sequences) of the axioms constructed in this book. In addition, the theorem of the problem about the part that is treated implicitly and is not clearly stated in it is being carried out in parallel.
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@article{Foundation_of_geometry-AFP,
  author  = {Fumiya Iwama},
  title   = {Foundation of geometry in planes, and some complements: Excluding the parallel axioms},
  journal = {Archive of Formal Proofs},
  month   = November,
  year    = 2021,
  note    = {\url{http://isa-afp.org/entries/Foundation_of_geometry.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
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