ABSTRACT
In order to advance our knowledge of the two non-Euclidean geometries, it is necessary to develop a non-Euclidean “trigonometry.” This necessitates the development of a few inequalities for midlines in right triangles and Lambert quadrilaterals. That will be the goal of the Šrst part of this chapter. The development of uniŠed trigonometry will then occupy the second half-material that includes a special “Pythagorean theorem” for the two non-Euclidean geometries.
