On imaginary conoprimas and conosecunds

Abstract

At the very foundations of the new geometry lies the concept of involution, and two cases are distinguished: involution with a pair of real (hyperbolic) and a pair of imaginary (elliptical) double elements. In particular, just as for points on a line we can pass from one type of involution to another, if we invert one of the the systems of points constituting the involution so that the points that were self-conjugate (double) become conjugate to one another, so in the involution in the plane (a polar system), the conoprima that determines the involution becomes imaginary (see the article). The distinction between a real and an imaginary conoprima, as well as between a real and an imaginary conosecund, is elucidated. The example illustrating polar relations for all imaginary conoprimas and conosecunds is presented.

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