Constructive Geometry and the Parallel postulate

@article{Beeson2016ConstructiveGA,
  title={Constructive Geometry and the Parallel postulate},
  author={Michael Beeson},
  journal={Bull. Symb. Log.},
  year={2016},
  volume={22},
  pages={1-104}
}
  • Michael Beeson
  • Published 2016
  • Mathematics, Computer Science
  • Bull. Symb. Log.
  • Euclidean geometry consists of straightedge-and-compass constructions and reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. We consider three versions of Euclid's parallel postulate: Euclid's own formulation in his Postulate 5; Playfair's 1795 version, and a new version we call the strong parallel postulate. These differ in that Euclid's version and the new version both assert the existence of a point where two… CONTINUE READING
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