A theorem analogous to Pascal's theorem, but relating to space
Abstract
Since on a plane the analogous problem is solved very simply on the basis of Pascal's theorem, it is quite natural that the thoughts of geometers have been persistently directed toward finding a simple solution to the problem for space, and the lack of success has elevated this question to the status of a difficult problem. Pascal's theorem can be formulated in various ways, but, especially from the point of view of modern geometry, for which it served as one of the first foundations, this formulation must be connected with collineation, specifically one that transforms the conoprima determined by five points into itself. The construction based on a theorem analogous to that of Pascal is carried over into all geometric systems, particularly into the system of planes. However, the latter theorem, being of a non-positional character, is carried over only to related systems; for example, it is not carried over to the system of planes, just as the theorem of a non-positional character just cited is not applicable to the system of lines in a plane.
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