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I have a friend that believes that the Pasch's axiom can be proven via Menelaus theorem (!?). However, I believe that it's required in the Menelaus proof. Can you provide me a Menelaus proof and the exact point in proof where it's required?

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    $\begingroup$ In en.wikipedia.org/wiki/Menelaus%27_theorem#Proof it is implicit when saying either all three ratios are negative or that one is negative and the other two are positive. In reverse, since the product of the three ratios is negative, then when one of the ratios is positive another ratio must also be positive. $\endgroup$ – Henry Apr 25 '17 at 10:41
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    $\begingroup$ This answer might provide some interesting context to your question: math.stackexchange.com/a/81151/58629 $\endgroup$ – HSN Apr 25 '17 at 14:30

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