Abstract
The subject of this chapter, the euclidean plane, can be approached in many ways. One can take the view that plane geometry is about points, lines, and circles, and proceed from “self-evident” properties of these figures (axioms) to deduce the less obvious properties as theorems. This was the classical approach to geometry, also known as synthetic. It was based on the conviction that geometry describes actual space and, in particular, that the theory of lines and circles describes what one can do with ruler and compass. To develop this theory systematically, Euclid (c. 300 BC) stated certain plausible properties of lines and circles as axioms and derived theorems from them by pure logic. Actually he occasionally made use of unstated axioms; nevertheless his approach is feasible and it was eventually made rigorous by Hubert [1899].
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© 1992 Springer Science+Business Media New York
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Stillwell, J. (1992). The Euclidean Plane. In: Geometry of Surfaces. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0929-4_1
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DOI: https://doi.org/10.1007/978-1-4612-0929-4_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97743-0
Online ISBN: 978-1-4612-0929-4
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