Possibility of different geometric systems with one and the same complete set of elements

Abstract

We now know that geometric systems can be very numerous and varied, since very diverse geometric images can be taken as elements of systems. To establish any such system, it is necessary to determine the complete set of its elements and provide proof that from two elements arbitrarily taken from it it is possible to unambiguously compose an infinite set of them such that, by replacing the two taken in it with two arbitrary other elements included in its composition, we from them they would also unambiguously deduce the same set, which would constitute the linear principle of the system.