  We improve upon Huntington's affine geometry by showing that his independence
proofs can be, in some cases, simplified. We carry out a systematic
investigation of the strict notion of betweenness that Huntington employs (the
three arguments are supposed to be distinct) by comparing it to McPhee's three
axiom systems for the same intended class of structures, which employs weak
betweenness (the arguments are permitted to be equal). Upon closely inspecting
the proof that McPhee's axiom systems are equivalent to Huntington's (subject
of course to the definition of weak betweenness in terms of strict and vice
versa), one finds surprisingly that McPhee's axiom systems have quite different
relations to strict betweenness.
