### Abstract

We formalize the basics of projective geometry. In particular, we give a proof of the so-called Hessenberg's theorem in projective plane geometry. We also provide a proof of the so-called Desargues's theorem based on an axiomatization of (higher) projective space geometry using the notion of rank of a matroid. This last approach allows to handle incidence relations in an homogeneous way dealing only with points and without the need of talking explicitly about lines, planes or any higher entity.

### License

BSD License

### Topics

- Mathematics/Geometry

### Session Projective_Geometry

- Projective_Plane_Axioms
- Pappus_Property
- Pascal_Property
- Desargues_Property
- Pappus_Desargues
- Higher_Projective_Space_Rank_Axioms
- Matroid_Rank_Properties
- Desargues_2D
- Desargues_3D
- Projective_Space_Axioms
- Higher_Projective_Space_Axioms

## Cite

×

Projective_Geometry-AFP

    @article{Projective_Geometry-AFP,
      author  = {Anthony Bordg},
      title   = {Projective Geometry},
      journal = {Archive of Formal Proofs},
      month   = {June},
      year    = {2018},
      note    = {\url{https://isa-afp.org/entries/Projective_Geometry.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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