Cycles of collineation and linear primas of conoprimas and conosecunds
Abstract
In any given conoprima, we can arbitrarily take two groups of points, four in each, and establish a general collinearity based on them (see the article). A cycle can consist of a different number of points, up to infinity. If, for example, a point is self-homologous in the collineation, then the entire cycle consists of a single point; if we have a double homology of points A and A', then the entire cycle reduces to two points, and so on. In the general case, the cycle encompasses a significant number of points, or even an infinite number, and it may happen that all points of the conoprima form part of a single cycle. If the collineation, established in some way from the given points, makes a conosecund self-homologous, then the problem of constructing the points of the latter reduces to a simple problem of collinear constructions.
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