Generalization of quadrics: quadratic sets It is not reasonable to formally extend the definition of quadrics to spaces over genuine skew fields (division rings). Because one would obtain secants bearing more than 2 points of the quadric which is totally different from usual quadrics.R. Artzy: The Conic in Moufang Planes, Aequat.Mathem. 6 (1971), p. 31-35E. Berz: Kegelschnitte in Desarguesschen Ebenen, Math. Zeitschr. 78 (1962), p. 55-8external link E. Hartmann: Planar Circle Geometries, p. 123 The reason is the following statement.
Generalization of quadrics: quadratic sets It is not. reasonable to formally extend the definition of quadrics to spaces over genuine skew fields (division rings). Because one would obtain secants bearing more than 2 points of the quadric which is totally different from usual quadrics.R. Artzy: ?The Conic in Moufang Planes, Aequat.Mathem. 6 (1971), p. 31-35E. Berz: Kegelschnitte in Desarguesschen Ebenen, Math. Zeitschr. 78 (1962), p. 55-8external link E. Hartmann: Planar Circle Geometries, p. 123 The reason is the following statement.