Pascal's theorem and its closest analogues on the plane and in space
Abstract
Pascal's theorem lies at the foundation of the theory of conoprimas, expressing their fundamental property of being completely and uniquely determined by five elements. In its modern generalized form, it can be expressed as follows: if six elements ABCDEF of one linear second belong to one conoprim, then, finding the intersection elements of the linear primas AB with DE, BC with EF, and CD with FA, we obtain that all three belong to one linear prima. (see the article). This expression clearly testifies to the deep organic connection of each sixth element with the five remaining ones that determine the conoprima. A simpler analogue of this theorem can be found in the well-known theorems expressing the fundamental properties of spheroprims and spheroseconds.
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