Cross Ratio Geometry Advances for Four Co-Linear Points in the Desargues Affine Plane-Skew Field

Abstract

This paper introduces advances in the geometry of the cross ratio of four co-linear points in in the Desargues affine plane. The cross-ratio of co-linear points of a skew field in the Desargues affine plane. The results given here have a clean rendition, based on Desargues affine plane axiomatics, skew field properties and the addition and multiplication of planar co-linear points. Contents 1. Introduction and Preliminaries 1 1.1. Desargues Affine Plane 2 1.2. Addition and Multiplication of points in a line of Desargues affine plane 3 1.3. Some algebraic properties of Skew Fields 3 1.4. Ratio of two and three points 4 2. Cross-Ratio for Fuor points in a line of Desargues affine plane 6 References 15