Fragmente der ebenen hyperbolischen Geometrie

We provide quantifier-free axiomatizations for two fragments of hyperbolic geometry: the hyperbolic geometry of restricted ruler (which can be used to draw the line joining two distinct points, but not to construct the intersection point of two lines), segment-transporter, and set square constructions, and the geometry of BACHMANN's Treffgeradenebenen, and show that both are, in a precise sense, naturally occuring fragments of standard hyperbolic geometry.