On a theorem about projectivities

The main result of this paper is a theorem about projectivities in then-dimensional complex projective spaceP ⁿ (n 2). Puttingn = 2, we showed in 3] that the theorem of Desargues inP ⁿ is a special case of this theorem. And not only the theorem of Desargues but also the converse of the theorem of Pascal, the theorem of Pappus-Pascal, the theorem of Miquel, the Newton line, the Brocard points and a lot of lesser known results in the projective, the affine and the Euchdean plane were obtained from this theorem as special cases without any further proof. Many extensions of classical theorems in the projective, affine and Euclidean plane to higher dimensions can be found in the literature and probably some of these are special cases of this theorem inP ⁿ. We only give a few examples and leave it as an open problem which other special cases could be found.