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ABSTRACT. It is well-known that the Ceva and Menelaus theorems are deducible from each other in the Euclidean case. In this paper we show that Ceva’s theorem holds whereas Menelaus’ theorem fails on Matsumoto’s mountain slope geometry.Mathematics Subject Classification (2010): 58B20, 53A35, 53C22.

Keywords: Non-Euclidean geometry, Finsler surface, geodesics.