Abstract
In non-commutative projective geometry there exist Pappus' configurations whose diagonal points are not collinear. In this paper, we consider two lines r, s in a projective plane and the points A, B on r, A ′, B ′, C ′ on s, and we investigate which points X on r lead to collinear diagonal points in the corresponding Pappus' configuration. A geometric interpretation of this result is given, showing that these are exactly all the fixed points of a projectivity of the line r. Finally, we show that the system of fixed points of a large class of projectivities of the line r may be considered as the set of points X on r such that the diagonal points of a suitable Pappus' configuration defined by X and other points, are collinear.
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