## 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 space algebraic algebraic topology angles apply arbitrary associated assume bases basis called canonical chapter circle closed compact complex condition consider construction containing continuous converse convex set coordinates COROLLARY corresponding curve defined definition denoted determined dimension direction discuss distance distinct elements equal equivalent Euclidean exactly example exists fact field Figure finite formula four frame function geometry given gives hyperplane implies intersection introduce invariant inverse linear measure metric natural necessary NOTE Observe obtained oriented orthogonal parallel particular plane points polygon positive problem projective space Proof properties PROPOSITION prove reader references reflection relation remark resp respect result rotation satisfying Show sides similarity sphere structure subgroup subset subspace tangent theorem tilings topology translation triangle unique vector space volume write