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Advanced Plane Geometry
This book begins at the point where Professor Barry's text 'Geometry with Trigonometry' leaves off, and develops advanced elements of plane geometry. It culminates in an account of the geometry of conics in the complex projective plane. Along the way it considers invariants of affine, projective, and complex-affine plane geometry under the various appropriate group actions. The ideas and progressive generalisations are introduced in a gradual way, and thoroughly explored at each stage. Some of these ideas go back to difficult and little-read works from the nineteenth century, and are here rescued and made more accessible. Included are many gems of plane geometry that originated with masters such as Newton, Pascal, Carnot, Simson, and Desargues, and unexpected variations on classical Greek results such as Pythagoras' Theorem. The material is almost all accessible to anyone who understands elementary plane geometry.
Geometry with Trigonometry
Geometry with Trigonometry Second Edition is a second course in plane Euclidean geometry, second in the sense that many of its basic concepts will have been dealt with at school, less precisely. It gets underway with a large section of pure geometry in Chapters 2 to 5 inclusive, in which many familiar results are efficiently proved, although the logical frame work is not traditional. In Chapter 6 there is a convenient introduction of coordinate geometry in which the only use of angles is to handle the perpendicularity or parallelism of lines. Cartesian equations and parametric equations of a line are developed and there are several applications. In Chapter 7 basic properties of circles are d...
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