A theorem similar to Pascal's theorem, but related to space

Abstract

Since on the plane a similar problem is solved very simply on the basis of Pascal’s theorem, it is very natural that the thought of geometers was persistently directed towards finding a simple solution to the problem for space, and failure raised this question to the level of a difficult problem. Pascal's theorem can be formulated in various ways, but, especially from the point of view of modern rheometry, for which it served as one of the first foundations, this formulation must be associated with collineation, namely one that transforms the conoprime defined by five points into itself. The construction according to a theorem similar to Pascal's is transferred to all geometric systems, in particular, to the system of planes, but the last theorem, as a theorem of a non-positional nature, is transferred only to related systems, and for example, it is not transferred to a system of planes, just as for a system of rays on plane, the non-positional theorem just given is not applicable.