Some Neutral Theorems of Plane Geometry
We discuss some of those theorems of Euclidean plane geometry that are independent of the parallel axiom. They will be needed in the development of hyperbolic geometry. We assume they are more or less known, so that our treatment is not as complete as a full treatment of Euclidean geometry would be. Some of the theorems are weaker than the corresponding Euclidean ones, because the more complete form would require the parallel axiom. Some of them go a little beyond Euclid in that they use the notion of continuity as it appears in calculus. Results in the last two sections go beyond Euclid in that the ideas in them are more recent, as in the Jordan Curve Theorem or the study of isometries.
KeywordsPlane Geometry Hyperbolic Plane Isosceles Triangle Hyperbolic Geometry Polygonal Path
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