The Use of Coordinates

H. S. M. Coxeter and George Beck
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H. S. M. Coxeter: University of Toronto, Department of Mathematics

Chapter Chapter 12 in The Real Projective Plane, 1993, pp 169-199 from Springer

Abstract: Abstract In Chapter 11 we saw how a system of coordinates is inherent in synthetic geometry. In the present chapter we shall reverse the process, building up the analytic geometry from first principles, and deriving the theorems (including the axioms) from properties of numbers. We shall find that the analytic method enables us to solve some problems more easily. On the other hand, it would be a grave mistake to abandon the synthetic method, which is far more stimulating to one’s geometrical ingenuity.

Keywords: Conjugate Point; Analytic Geometry; Analytic Proof; Affine Plane; Primitive Concept (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2734-2_12

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DOI: 10.1007/978-1-4612-2734-2_12

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