  This paper introduces advances in the geometry of the transforms for cross
ratio of four points in a line in the Desargues affine plane. The results given
here have a clean, based Desargues affine plan axiomatic's and definitions of
addition and multiplication of points on a line in this plane, and for skew
field properties. In this paper are studied, properties and results related to
the some transforms for cross ratio for 4-points, in a line, which we divide
into two categories, \emph{Invariant} and \emph{Preserving} transforms for
cross ratio. The results in this paper are (1) the cross-ratio of four points
is \emph{Invariant} under transforms: Inversion, Natural Translation, Natural
Dilation, Mobi\"us Transform, in a line of Desargues affine plane. (2) the
cross-ratio of four points is \emph{Preserved} under transforms: parallel
projection, translations and dilation's in the Desargues affine plane.
