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November 10th 2013 | Paperback | PDF, EPUB, FB2, DjVu, AUDIO, mp3, ZIP | 222 pages | ISBN: 9781461392835 | 7.31 Mb

Along with many small improvements, this revised edition contains van Yzerens new proof of Pascals theorem ( 1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity,MoreAlong with many small improvements, this revised edition contains van Yzerens new proof of Pascals theorem ( 1.7) and, in Chapter 2, an improved treatment of order and sense.

The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation ( 3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane?

To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility.

Moreover, real geometry is exactly what is needed for the projective approach to non-Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of points at infinity to be a conic, or replace the absolute involution by an absolute polarity.

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