Bamberg, J.Penttila, T.2023-04-112023-04-112023Forum Mathematicum, 2023; 35(5):1301-13250933-77411435-5337https://hdl.handle.net/2440/137875Published Online: 2023-03-03H. L. Skala (1992) gave the first elegant first-order axiom system for hyperbolic geometry by replacing Menger’s axiom involving projectivities with the theorems of Pappus and Desargues for the hyperbolic plane. In so doing, Skala showed that hyperbolic geometry is incidence geometry. We improve upon Skala’s formulation by doing away with Pappus and Desargues altogether, by substituting for them two simpler axioms.en© 2023 Walter de Gruyter GmbH, Berlin/BostonHyperbolic plane; metric plane; first-order axiomatisation; abstract ovalJournal article10.1515/forum-2022-02682023-04-11622138