4. Amer. Math. Soc., Trans., 2, 1901, 86-99 = Ges. Abh., 2, 437-48. The proof and further historical details can be found in Appendix V of David Hubert’s Grundlagen der Geometrie, 7th ed., B. G. Teubner, 1930. The theorem presupposes that the lines of hyperbolic geometry would be the geodesies of the surface and the lengths and angles would be the Euclidean lengths and angles on the surface.