<?xml version="1.0" encoding="UTF-8"?>

<record version="2" id="2328">
 <title>Pappus's theorem</title>
 <name>PappussTheorem</name>
 <created>2002-02-20 23:06:38</created>
 <modified>2003-08-19 15:52:05</modified>
 <type>Theorem</type>
 <creator id="3" name="drini"/>
 <author id="3" name="drini"/>
 <classification>
	<category scheme="msc" code="51A05"/>
 </classification>
 <related>
	<object name="PascalsMysticHexagram"/>
	<object name="Collinear"/>
	<object name="Concurrent"/>
 </related>
 <preamble>\usepackage{graphicx}
%\usepackage{xypic} 
\usepackage{bbm}
\newcommand{\Z}{\mathbbmss{Z}}
\newcommand{\C}{\mathbbmss{C}}
\newcommand{\R}{\mathbbmss{R}}
\newcommand{\Q}{\mathbbmss{Q}}
\newcommand{\mathbb}[1]{\mathbbmss{#1}}</preamble>
 <content>\PMlinkescapeword{order}
Let $A,B,C$ be points on a line (not necessarily in that order) and let $D,E,F$ points on another line (not necessarily in that order). Then the intersection points of $AD$ with $FC$, $DB$with $CE$ and $BF$ with $EA$ are collinear.

This is a special case of Pascal's mystic hexagram.
\begin{center}
\includegraphics[scale=2.0]{pappus}
\end{center}</content>
</record>
