  This paper introduces ordered skew fields that result from the construction
of a skew field over an ordered line in a Desargues affine plane. A special
case of a finite ordered skew field in the construction of a skew field over an
ordered line in a Desargues affine plane in Euclidean space, is also
considered. Two main results are given in this paper: (1) every skew field
constructed over a skew field over an ordered line in a Desargues affine plane
is an ordered skew field and (2) every finite skew field constructed over a
skew field over an ordered line in a Desargues affine plane in $\mathbb{R}^2$
is a finite ordered skew field.
