Archimedisierung absoluter Ebenen

In a nonarchimedean absolute plane let an origin o and a unit of distance o, e] be given. By omitting those points which are infinitely distant to o relative to o, e] and by identifying those of the resting points which are infinitely close together relative to o, e], we get an archimedean absolute plane if certain two conditions are fulfilled. In the euclidean and in the hyperbolic case this geometric procedure corresponds to the well-known algebraic one in the underlying coordinate field.