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Archimedes and consequences

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@jnarboux jnarboux released this 10 Dec 13:45
· 173 commits to master since this release

This new release brings mainly:

  • some results about Archimedes' postulates contributed by Charly Gries,
  • equivalences between about 30 versions of the parallel postulate by Charly Gries and Pierre Boutry,
  • a study of the bisector and incenter contributed by Dan Song,
  • a justification of the area method axioms contributed by Julien Narboux

Changelog:

  • Add compatibility with Coq 8.5.
  • Definition of Archimedes' postulate (geometric version).
  • Definition of Archimedes' postulate for angles.
  • Archimedes' postulate implies Aristotle's postulate.
  • Legendre's theorems.
  • Szmielew's theorem about parallel postulates: every proposition which is true in Euclidean geometry and not in Hyperbolic geometry is equivalent to the parallel postulate.
  • Predicate TS (Two Sides) cleared of a redundant condition.
  • Definition of the interior bisector and related properties.
  • Proof of the existence of the incenter of a triangle.
  • Proof of the existence of an equilateral triangle build on a given base without any continuity axiom (in any Pythagorean field).
  • Justification of the axioms of the area method.