## Geometry IVolume I of this 2-volume textbook provides a lively and readable presentation of large parts of classical geometry. For each topic the author presents an esthetically pleasing and easily stated theorem - although the proof may be difficult and concealed. The mathematical text is illustrated with figures, open problems and references to modern literature, providing a unified reference to geometry in the full breadth of its subfields and ramifications. |

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affine frame affine geometry affine plane affine space affine subspace algebraic apply arbitrary assume barycenter basis bijection bisectors called chapter circle collinear points compact set complex complexification consider construction containing convex function convex set coordinates COROLLARY cross-ratio crystallographic groups curve defined definition denoted differential dimension elements equal equivalent Euclidean affine space Euclidean plane Euclidean space Euclidean structure Euclidean vector space example exists a unique fact Figure finite finite-dimensional fixed point formula function GA(X geometry given GL(E half-lines homeomorphic homogeneous homography homothety inequality intersection invariant inverse isometry isomorphism Lebesgue measure lemma linear map f Math metric space morphism non-empty notation O+(E obtained orbit oriented angles orthogonal orthonormal path-connected projective line projective space Proof PROPOSITION quotient real number resp result rotation satisfying scalar Show simplex sphere Springer-Verlag subgroup tangent theorem tilings triangle vector subspace