ABSTRACT
A deeper study of elliptic and hyperbolic geometry will be undertaken here to explore a theory largely unattainable by synthetic methods. The emphasis, with the exception of the very last section, will be on exploring further identities in uniŠed trigonometry and their use in establishing theorems analogous to classical Euclidean geometry. For example, analogies to the theorems of Menelaus and Ceva are established for the two nonEuclidean geometries, which, in turn, provide proofs of the concurrency of the medians and altitudes of a triangle, as well as Desargues’ theorem, and other results that are synthetically inaccessible.
