Eugenio Beltrami
In 1868, (in Essay on an interpretation of non-Euclidean geometry) Beltrami gave the first model of hyperbolic geometry.  In Beltrami's model, lines of hyperbolic geometry are represented by geodesics on the pseudosphere.  Thus, Beltrami provided the first proof that Euclid's parallel postulate could not be derived from the other axioms of Euclidean geometry.