Abstract
The conjugacy mapping rel. to a complete quadrangle in a Pappian projective plane of characteristic ≠2 is constructed by using a bijection of the line set onto the bundle of conics through the diagonal points of the quadrangle. The inversion with center O of the inversion circle going through the point P in the Euclidean plane proves to be the product of the reflection at OP and the affine restriction of the conjugacy mapping rel. to the quadrangle having P as one of its vertices and O together with the circular points at infinity as diagonal points.
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