Diagram of flat conoprimes

Abstract

The numerous and useful results that came from drawing up a diagram of spherical conoprimes prompted me to take up, as a simpler case, drawing up a diagram of flat conoprimes. Of course, in both cases the difference is enormous. There we are dealing with the second of conoprime; here only with prima, since the totality of all similar conoprims has to be considered as one single one. There, each conoprim is characterized by the angular magnitude of two axes, which are always real; here only the main (major) axis is always real, while the minor axis in hyperbolas is the imaginary axis. The diagram is based on combining all similar conoprims into one. But in the composition of hyperbolas there is a striking exception in relation to similarity, namely the extreme difference of hyperbolas with equal angles between asymptotes, that is, the pair of asymptotes itself, like a hyperbola, cannot be called similar to all the others. For this reason, the diagram does not include special hyperbolas consisting of a pair of rays.