In the previous chapter we discussed properties possessed by hyperbolic geometries. Now we turn our attention to Euclidean geometries. In this first section we will present several equivalent formulations of the Euclidean Parallel Property. In many of the theorems we shall contrast the Euclidean and the hyperbolic results. In the second section we will be concerned with the theory of similar triangles and proportion. The third section will cover certain classical results of Euclidean geometry, including the Euler Line, the Nine Point Circle, and Morley’s Theorem.
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