Geodesic
On Ordered Geometries
Canadian mathematical bulletin, Tome 6 (1963) no. 1, pp. 27-36

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In Theorem 2.20 of his Geometric Algebra, Artin shows that any ordering of a plane geometry is equivalent to a weak ordering of its skew field. Referring to his Theorem 1. 16 that every weakly ordered field with more than two elements is ordered, he deduces his Theorem 2.21 that any ordering of a Desarguian plane with more than four points is (canonically) equivalent to an ordering of its field. We should like to present another proof of this theorem stimulated by Lipman's paper [this Bulletin, vol.4, 3, pp. 265-278]. Our proof seems to bypass Artin's Theorem 1. 16; cf. the postscript. 
On Ordered Geometries. Canadian mathematical bulletin, Tome 6 (1963) no. 1, pp. 27-36. doi: 10.4153/CMB-1963-005-5
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