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David A. Brannan, Matthew F. Esplen, and Jeremy J. Grey
Publisher: Cambridge University Press (2012)
Details: 587 pages, Paperback
Topics: Non-Euclidean Geometry, Geometry, Euclidean Geometry
MAA Review[Reviewed by Fernando Q. Gouvêa, on 05/28/2012]
See J. I. Hall's review of the first edition (1999). In addition to many small changes and improvements, the authors have added some new material on conics as envelopes, barycentric coordinates, Poncelet's Porism, planar maps, and Ptolemy's Theorem. They have also changed their approach to projective transformations, hyperbolic distance, and asymptotic d-triangles. Probably under pressure from American users, they have switched from "gradient" to "slope" and from ]0,1[ to (0,1) for open intervals.
This remains one of the best textbooks on elementary geometry.