Desargues' Conflguration in a Special Layout

In the paper a special case of Desargues' conflguration will be dis- cussed, 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 De- sargues 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. Difierent cases are dis- cussed. In the case of a base circle the center of the collineation KD coincides with the Gergonne point.