This note covers the following
topics: The classical theorem of Ceva, Ceva, Menelaus and Selftransversality,
The general transversality theorem, The theorems of Hoehn and Pratt-Kasapi,
Circular products of ratios involving circles, Circle transversality theorems, A
basic lemma and some applications, Affinely Regular Polygons, Linear
transformations; smoothing vectors, Affine-Regular Components, The general
Napoleon's Theorem, The iteration of smoothing operations.

This note covers the following
topics: The classical theorem of Ceva, Ceva, Menelaus and Selftransversality,
The general transversality theorem, The theorems of Hoehn and Pratt-Kasapi,
Circular products of ratios involving circles, Circle transversality theorems, A
basic lemma and some applications, Affinely Regular Polygons, Linear
transformations; smoothing vectors, Affine-Regular Components, The general
Napoleon's Theorem, The iteration of smoothing operations.

This is a course note on Euclidean and
non-Euclidean geometries with emphasis on (i) the contrast between the
traditional and modern approaches to geometry, and (ii) the history and role of
the parallel postulate. This course will be useful to students who want to teach
and use Euclidean geometry, to students who want to learn more about the history
of geometry, and to students who want an introduction to non-Euclidean
geometry.

The
objective of this book is to lay down and illustrate the more elementary principles
of those Geometrical Methods which, in recent times, have been so successfully
employed to investigate the properties of figured space.