Is there some book, or systematic theory, that proves theorems of euclidean geometry by viewing them as invariable properties of certain geometric configurations ?

So that from an easy special case, because of invariance, we conclude the validity of the more difficult general case.

(Like, for example, in http://www.alainconnes.org/docs/morley.pdf where Morley's theorem is proved with fixed points and group theory.)

  • $\begingroup$ The standard works are the four volumes by I M Yaglom, Geometric Transformations. Sounds great, but unfortunately many of the standard Euclidean geometry results are hard to prove that way (or maybe we have just got used to the more traditional style of proof because it is in all the textbooks and so insufficient effort has been put into this kind of proof). $\endgroup$ – almagest Jun 17 '16 at 10:11

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