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Pappus' law
Show plain example
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<iframe 
    src="http://jsxgraph.uni-bayreuth.de/share/iframe/pappus-hexagon-theorem" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Pappus' law" 
    allowfullscreen
></iframe>
This code has to
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    JXG.Options.label.autoPosition = true;
    JXG.Options.text.fontSize = 24;
    
    var board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-5, 5, 5, -5],
        keepaspectratio: true,
        showCopyright: false,
        showNavigation: false
    }, );
    
    var q = board.create('point', [-4, -2], { name: 'q' });
    var q1 = board.create('point', [-1.5, -2], { name: '', color: 'blue' });
    var q2 = board.create('point', [-1.5, -1], { name: '', color: 'blue' });
    var l1 = board.create('line', [q, q1], { straightFirst: false });
    var l2 = board.create('line', [q, q2], { straightFirst: false });
    
    var p1 = board.create('glider', [-1, -2, l1], { name: 'p_1' });
    var p3 = board.create('glider', [3, -2, l1], { name: 'p_3' });
    
    var p3s = board.create('glider', [-1.5, 1, l2], { name: "p_3'" });
    var p2s = board.create('glider', [0, 1, l2], { name: "p_2'" });
    
    // Lines p_1p_3' and p_1'p_3
    var s3 = board.create('segment', [p1, p3s], { color: 'black' });
    var par1 = board.create('parallel', [s3, p3], { visible: false });
    var p1s = board.create('intersection', [par1, l2], { name: "p_1'", color: 'black' });
    var s1 = board.create('segment', [p1s, p3], { color: 'black' });
    
    // Lines p_1p_2' and p_1'p_2
    var s2 = board.create('segment', [p1, p2s], { color: JXG.palette.red });
    var par2 = board.create('parallel', [s2, p1s], { visible: false });
    var p2 = board.create('intersection', [par2, l1], { name: "p_2", color: 'black' });
    var s4 = board.create('segment', [p1s, p2], { color: JXG.palette.red });
    
    // Lines p_2p_3' and p_2'p_3
    var s5 = board.create('segment', [p2, p3s], { color: JXG.palette.blue, dash: 3 });
    var s6 = board.create('segment', [p2s, p3], { color: JXG.palette.blue, dash: 3 });
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 24;

var board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    keepaspectratio: true,
    showCopyright: false,
    showNavigation: false
}, );

var q = board.create('point', [-4, -2], { name: 'q' });
var q1 = board.create('point', [-1.5, -2], { name: '', color: 'blue' });
var q2 = board.create('point', [-1.5, -1], { name: '', color: 'blue' });
var l1 = board.create('line', [q, q1], { straightFirst: false });
var l2 = board.create('line', [q, q2], { straightFirst: false });

var p1 = board.create('glider', [-1, -2, l1], { name: 'p_1' });
var p3 = board.create('glider', [3, -2, l1], { name: 'p_3' });

var p3s = board.create('glider', [-1.5, 1, l2], { name: "p_3'" });
var p2s = board.create('glider', [0, 1, l2], { name: "p_2'" });

// Lines p_1p_3' and p_1'p_3
var s3 = board.create('segment', [p1, p3s], { color: 'black' });
var par1 = board.create('parallel', [s3, p3], { visible: false });
var p1s = board.create('intersection', [par1, l2], { name: "p_1'", color: 'black' });
var s1 = board.create('segment', [p1s, p3], { color: 'black' });

// Lines p_1p_2' and p_1'p_2
var s2 = board.create('segment', [p1, p2s], { color: JXG.palette.red });
var par2 = board.create('parallel', [s2, p1s], { visible: false });
var p2 = board.create('intersection', [par2, l1], { name: "p_2", color: 'black' });
var s4 = board.create('segment', [p1s, p2], { color: JXG.palette.red });

// Lines p_2p_3' and p_2'p_3
var s5 = board.create('segment', [p2, p3s], { color: JXG.palette.blue, dash: 3 });
var s6 = board.create('segment', [p2s, p3], { color: JXG.palette.blue, dash: 3 });
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Pappus' law" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   JXG.Options.label.autoPosition = true;
   JXG.Options.text.fontSize = 24;
   
   var board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-5, 5, 5, -5],
       keepaspectratio: true,
       showCopyright: false,
       showNavigation: false
   }, );
   
   var q = board.create('point', [-4, -2], { name: 'q' });
   var q1 = board.create('point', [-1.5, -2], { name: '', color: 'blue' });
   var q2 = board.create('point', [-1.5, -1], { name: '', color: 'blue' });
   var l1 = board.create('line', [q, q1], { straightFirst: false });
   var l2 = board.create('line', [q, q2], { straightFirst: false });
   
   var p1 = board.create('glider', [-1, -2, l1], { name: 'p_1' });
   var p3 = board.create('glider', [3, -2, l1], { name: 'p_3' });
   
   var p3s = board.create('glider', [-1.5, 1, l2], { name: "p_3'" });
   var p2s = board.create('glider', [0, 1, l2], { name: "p_2'" });
   
   // Lines p_1p_3' and p_1'p_3
   var s3 = board.create('segment', [p1, p3s], { color: 'black' });
   var par1 = board.create('parallel', [s3, p3], { visible: false });
   var p1s = board.create('intersection', [par1, l2], { name: "p_1'", color: 'black' });
   var s1 = board.create('segment', [p1s, p3], { color: 'black' });
   
   // Lines p_1p_2' and p_1'p_2
   var s2 = board.create('segment', [p1, p2s], { color: JXG.palette.red });
   var par2 = board.create('parallel', [s2, p1s], { visible: false });
   var p2 = board.create('intersection', [par2, l1], { name: "p_2", color: 'black' });
   var s4 = board.create('segment', [p1s, p2], { color: JXG.palette.red });
   
   // Lines p_2p_3' and p_2'p_3
   var s5 = board.create('segment', [p2, p3s], { color: JXG.palette.blue, dash: 3 });
   var s6 = board.create('segment', [p2s, p3], { color: JXG.palette.blue, dash: 3 });
</jsxgraph>

Pappus' law

Euclidean
Famous theorems
Geometry
Suppose $p_1$, $p_2$, $p_3$ are on one line and $p_1'$, $p_2'$, $p_3'$ on another. If the (black) lines $p_1p_3'$ and $p_1'p_3$ are parallel and the (red) lines $p_1p_2'$ and $p_1'p_2$ are parallel, then the (dashed blue) lines $p_2p_3'$ and $p_2'p_3$ are parallel. The theorem is also known as *Pappus-Pascal theorem* and it is the affine version of *Pappus's hexagon theorem.*
Web references
  • Pappus' law - Wikipedia
// Define the id of your board in BOARDID

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 24;

var board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    keepaspectratio: true,
    showCopyright: false,
    showNavigation: false
}, );

var q = board.create('point', [-4, -2], { name: 'q' });
var q1 = board.create('point', [-1.5, -2], { name: '', color: 'blue' });
var q2 = board.create('point', [-1.5, -1], { name: '', color: 'blue' });
var l1 = board.create('line', [q, q1], { straightFirst: false });
var l2 = board.create('line', [q, q2], { straightFirst: false });

var p1 = board.create('glider', [-1, -2, l1], { name: 'p_1' });
var p3 = board.create('glider', [3, -2, l1], { name: 'p_3' });

var p3s = board.create('glider', [-1.5, 1, l2], { name: "p_3'" });
var p2s = board.create('glider', [0, 1, l2], { name: "p_2'" });

// Lines p_1p_3' and p_1'p_3
var s3 = board.create('segment', [p1, p3s], { color: 'black' });
var par1 = board.create('parallel', [s3, p3], { visible: false });
var p1s = board.create('intersection', [par1, l2], { name: "p_1'", color: 'black' });
var s1 = board.create('segment', [p1s, p3], { color: 'black' });

// Lines p_1p_2' and p_1'p_2
var s2 = board.create('segment', [p1, p2s], { color: JXG.palette.red });
var par2 = board.create('parallel', [s2, p1s], { visible: false });
var p2 = board.create('intersection', [par2, l1], { name: "p_2", color: 'black' });
var s4 = board.create('segment', [p1s, p2], { color: JXG.palette.red });

// Lines p_2p_3' and p_2'p_3
var s5 = board.create('segment', [p2, p3s], { color: JXG.palette.blue, dash: 3 });
var s6 = board.create('segment', [p2s, p3], { color: JXG.palette.blue, dash: 3 });

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.