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.
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