In this little treatise
on the Geometry of the Triangle are presented some of the more important
researches on the subject which have been undertaken during the last thirty
years. The author ventures to express not merely his hope, but his confident
expectation, that these novel and interesting theorems some British, but the
greater part derived from French and German sources will widen the outlook of
our mathematical instructors and lend new vigour to their teaching.
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
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.