Journal for Geometry and Graphics 7 (2003), No. 2, 191--200
Copyright Heldermann Verlag 2003
Desargues' Configuration in a Special Layout
DG&EG Division A-9, Dept. of Architecture, Cracow University of Technology, Warszawska 24, 31-155 Krakow, Poland, firstname.lastname@example.org
A special case of Desargues' configuration will be discussed, where one triangle is inscribed into a conic and the other is circumscribed about the same conic. These two triangles are in a correspondence called a Desargues collineation KD. Three theorems have been formulated and proved. One of them characterizes the central collineation KD. In a Desargues collineation the base conic will be transformed into another conic. Different cases are discussed. In the case of a base circle the center of the collineation KD coincides with the Gergonne point.
Keywords: Desargues configuration, collineation.
MSC: 51M35; 51M05.
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