2 Affine Geometry
In Chapter 1 we studied conics in Euclidean geometry. In the rest of the book we prove a whole range of results about figures such as lines and conics, in geometries other than Euclidean geometry. In the process of doing this, we meet two particular features of our approach to geometry which may be new to you.
The first feature is the use of transformations in geometry to simplify problems and bring out their essential character. You may have met some of these transformations previously in courses on Group Theory or on Linear Algebra.1
The second feature arises from the fact that the transformations we introduce form groups. Generally, we restrict our attention to geometry in the plane, 2, but even in this familiar setting ...