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Accolineation in the \(P\)-projection. (English) Zbl 1188.51012

Let \(S\) and \(N\) be two opposite points of a sphere \(\Phi\). The plane \(\pi\) is tangent to \(\Phi\) in the point \(S\). A \(P\)-projection is the superposition of a central projection onto \(\Phi\) from \(S\) and a stereographic projection onto \(\pi\) from \(N\). It is discussed general and specific properties of the \(P\)-projection. It is given the tranformation of an arbitrary circle into a parabola.
The paper is dedicated to Professor Marian Palej.

MSC:

51N05 Descriptive geometry
51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)
51M15 Geometric constructions in real or complex geometry
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