Collineation cycles and linear primes of conoprimes and conoseconds

Abstract

On a conoprime we can arbitrarily take two groups of points, four in each, and use them to establish collinearity of a general nature (see article). A cycle can consist of a different number of points, up to infinity. If, for example, a point in a collineation is self-homologous , then the entire cycle consists of one single point; if we have double homology of points A and A', then the entire cycle is reduced to two points, etc. In the general case, a cycle embraces a significant number of points or even an infinite number, and it may happen that all the points of a conoprime are part of one cycle. If collineation, somehow established from these points, makes the conosecond self-homologous, then the problem of constructing the points of the latter is reduced to a simple problem of collinear constructions.