An Axiomatic Approach to Geometry by Francis Borceux

Author:Francis Borceux
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

6.2 Projective Versus Euclidean

The projective plane has thus been defined as the Euclidean plane, to which intersection points of parallel lines are added “at infinity” (see Definition 6.1.1). In this spirit, it sounds a priori natural to handle a projective problem via Euclidean methods, as long as it concerns Euclidean points, and via Euclidean parallel lines, as soon as points at infinity must be considered. In this way, every projective problem can be fully treated via Euclidean methods. This is what was done at the beginning of projective geometry and essentially, up to the nineteenth century. Let us comment on this method for the example of Pappus’ theorem 4.14.5. In the projective plane, consider: two distinct lines d and d′;

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.