Some corollaries from a theorem similar to Pascal's theorem

Abstract

Let us turn to similar constructions in space, which are a consequence of a theorem similar to Pascal’s theorem. Since the basis of the construction according to this theorem is the structure of two hyperboloids of a linear prime, to which the desired conosecond belongs, and for this it is necessary to construct two hexaprimes, it is clear that the data can be such tangents together with the points of tangency on them, which are sufficient for the construction of hexaprimes. To understand why Pascal’s theorem, and therefore its analogues, has fundamental significance, it is enough to point out that these theorems are only partial expressions of the deepest and most important fundamental theorem of new geometry, according to which in two projective systems linear collections correspond to linear, quadratic, quadratic, in general, aggregates of the n-th order are aggregates of the same order. In this case, intersections correspond to intersections, tangents to tangents, and involutions to involution.