Affine and Projective Geometry

  • K. W. Gruenberg
  • A. J. Weir
Part of the Graduate Texts in Mathematics book series (GTM, volume 49)


In this chapter we shall introduce two different (but closely related) geometrical languages. The first of these, the language of affine geometry, is the one which appeals most closely to our intuitive ideas of geometry. In this language the subspaces of a vector space of dimensions 0, 1 and 2 are called “points”, “lines” and “planes”, respectively. But we cannot limit these words to describe only subspaces: otherwise V would have only one point, namely the zero subspace, and every line and plane in V would contain this point. Our intuition suggests that we introduce the concept of “translated” subspace.


Projective Plane Vector Space Versus Projective Geometry Division Ring Projective Dimension 


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  1. Except where we state the contrary, all vector spaces considered in the remainder of this book are assumed to be finite dimensional.Google Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • K. W. Gruenberg
    • 1
  • A. J. Weir
    • 2
  1. 1.Department of Pure Mathematics, Queen Mary CollegeUniversity of LondonEngland
  2. 2.School of Mathematical and Physical SciencesUniversity of SussexEngland

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