Some corollaries of a theorem analogous to Pascal's theorem
Abstract
Let us turn to analogous constructions in space, which are a consequence of a theorem analogous to Pascal's theorem. Since the construction based on this theorem involves the construction of two hyperboloids of a linear prima, to which the required conosecund also belongs, and for this it is necessary to construct two hexaprimas, it is clear that the given data may consist of such tangents, together with their points of contact, as are sufficient for the construction of the hexaprimas.To understand why Pascal's theorem, and consequently its analogue, is of fundamental importance, it suffices to point out that these theorems are merely particular expressions of the deepest and most important fundamental theorem of new geometry, according to which, in two projective systems, linear aggregates correspond to linearaggregates, quadratic to quadratic, and, in general, aggregates of the n-th order correspond to aggregates of the same order. Moreover, intersections correspond to intersections, tangencies to tangencies, and involutions to involutions.
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