Geodesic
Order in Affine and Projective Geometry
Canadian mathematical bulletin, Tome 6 (1963) no. 1, pp. 37-43

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In this note we give a characterisation of ordered skew fields by certain properties of the negative elements.Properties of negative elements of a skew field K are then interpreted as statements about "betweenness" in any affine geometry over K, or as statements about "separation" in any projective geometry over K.In this way, our axioms for ordered fields permit of immediate translation into postulates of order for affine or projective geometry (over a field). The postulates so obtained seem simple enough to be of interest, (cf. [4], p. 22) 
Lipman, Joe. Order in Affine and Projective Geometry. Canadian mathematical bulletin, Tome 6 (1963) no. 1, pp. 37-43. doi: 10.4153/CMB-1963-006-1
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     title = {Order in {Affine} and {Projective} {Geometry}},
     journal = {Canadian mathematical bulletin},
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