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Pasch's Theorem

A theorem stated in 1882 which cannot be derived from Euclid's Postulates. Given points $a$, $b$, $c$, and $d$ on a Line, if it is known that the points are ordered as $(a,b,c)$ and $(b,c,d)$, it is also true that $(a,b,d)$.

See also Euclid's Postulates, Line, Pasch's Axiom

© 1996-9 Eric W. Weisstein