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Journal for Geometry and Graphics 7 (2003), No. 2, 191--200
Copyright Heldermann Verlag 2003

Desargues' Configuration in a Special Layout

Barbara Wojtowicz
DG&EG Division A-9, Dept. of Architecture, Cracow University of Technology, Warszawska 24, 31-155 Krakow, Poland,

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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