From: "Thomas H. Foregger" <foregger@lucent.com>
Subject: Re: Four Points in the Plane
Date: 14 Sep 2000 10:30:03 -0500
Newsgroups: sci.math.research
Summary: Compound between-ness properties for planar geometries

If you need an explicit reference where this is proved,
see Forder, Foundations of Euclidean Geometry
page 49, paragraph 6
Thomas H. Foregger


Rainer Rosenthal wrote:

> Hello to the friends of Geometry,
>
> the following finding seems to me non-trivial and I
> would like to know more about related Theorems.
>
> I use the following useful [ ]-notation of mine:
>
> Definition:
> [ X Y Z ]   holds iff Z lies strictly between X and Z
>
> Lemma P4
>
> Given 4 distinct points in the plane A, B, C, D. If there
> exists a point  P  satisfying
>
>              [ A B P ]  and  [ C P D ]
>
> then there exist points  Q and  R  satisfying
>
>              [ C B Q ]  and  [ D Q A ]
> and
>              [ D B R ]  and  [ A R C ]


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