Abstract
We have seen a point defined as an ordered number pair (x, y), and a line defined as the solution set of an equation such as lx + my + 1 = 0. The pair (l, m) defines a unique line, and two distinct lines have an intersection, a point, except when lm′ = l′m; this is a relation between two lines which is familiar as the equivalence relation defining a set of ‘parallel’ lines.
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© 1964 A. J. Moakes
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Moakes, A.J. (1964). The Structure of a Pure Geometry. In: The Core of Mathematics. Introductory Monographs in Mathematics. Palgrave, London. https://doi.org/10.1007/978-1-349-00327-3_8
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DOI: https://doi.org/10.1007/978-1-349-00327-3_8
Publisher Name: Palgrave, London
Print ISBN: 978-0-333-04818-4
Online ISBN: 978-1-349-00327-3
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