The development of projective geometry

Egbert Brieskorn and Horst Knörrer
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Egbert Brieskorn: Universität Bonn, Mathematisches Institut
Horst Knörrer: Universität Bonn, Mathematisches Institut

Chapter 3 in Plane Algebraic Curves, 1986, pp 102-171 from Springer

Abstract: Abstract We have seen how the methods of perspective representation of spatial objects, which had their beginnings in antiquity, were developed into a fine art during the Renaissance in the work of artists, architects and inventors. In the 16th and 17th century this art became a geometric theory, which at the end of the 18th century unfolded into a mature system, descriptive geometry. This theory is concerned with generating planar pictures of spatial or planar objects by projec-tion. We have already seen how Newton used this projection method to unify the classification of cubic curves. As descriptive geometry itself unfolded, geometers realised that the consistent introduction of the “projective” viewpoint made possible a far-reaching unification and generalisation of geometric methods. This led to the development of projective geometry, in which the synthetic and analytic methods developed alternately. In what follows we shall look more closely at some essential steps in this development.

Keywords: Riemann Surface; Projective Plane; Projective Geometry; Projective Line; Central Projection (search for similar items in EconPapers)
Date: 1986
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DOI: 10.1007/978-3-0348-5097-1_3

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