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Projective Geometry

In: An Axiomatic Approach to Geometry

Author

Listed:
  • Francis Borceux

    (Université catholique de Louvain)

Abstract

The attempts to formalize the rules of perspective representation lead the mathematicians of the seventeenth century to consider seriously “points at infinity”. This is the birth of projective geometry which, in a first approach, proves to often unify in a single statement various bunches of similar Euclidean results. The study of conics and polar lines leads to the recognition of the duality principle in projective geometry. During the nineteenth century, an elegant system of axioms for projective geometry is individualized and the close connection with projective spaces over a field is established.

Suggested Citation

  • Francis Borceux, 2014. "Projective Geometry," Springer Books, in: An Axiomatic Approach to Geometry, edition 127, chapter 0, pages 197-241, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-01730-3_6
    DOI: 10.1007/978-3-319-01730-3_6
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