Cognate geometric systems

Abstract

When dualism was recognized in the New Geometry, only two geometric systems were adopted the system of points and the correlative to it system of planes. This note aims to show the special significance of such a particular case, which is expressed by the following theorem, if we attribute as cognate two such correlative systems, in which the spheroprims of one are correlative to the spheroprims of the other. "Absolutely all graphic constructions, and therefore all theorems, of one cognate system are transferable to the other." In addition, I mean to show that in general case it is possible to establish such systems where for each of its linear seconds, it is possible to reproduce a cognate system of points on the plane.

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