http://geometrie.idea-sketch.com/index.php?action=history&feed=atom&title=Strahlens%C3%A4tze_%282011%2F12%29 2026-08-06T00:20:00Z Versionsgeschichte dieser Seite in Geometrie-Wiki MediaWiki 1.43.9 http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10845&oldid=prev 2012-01-25T16:25:43Z

<p><span class="autocomment">Satz II.03: Inkommensurabilität von Quadratseite und Quadratdiagonale</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 25. Januar 2012, 16:25 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l21">Zeile 21:</td> <td colspan="2" class="diff-lineno">Zeile 21:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Definition II.06===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Definition II.06===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::Zwei Strecken &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt; heißen genau dann kommensurabel, wenn es eine Strecke &lt;math&gt;m&lt;/math&gt; und ganze Zahlen &lt;math&gt;p&lt;/math&gt; und &lt;math&gt;q&lt;/math&gt; derart gibt, dass &lt;math&gt;p|m|=|a|&lt;/math&gt; und &lt;math&gt;q|m|=|b|&lt;/math&gt; gilt.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::Zwei Strecken &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt; heißen genau dann kommensurabel, wenn es eine Strecke &lt;math&gt;m&lt;/math&gt; und ganze Zahlen &lt;math&gt;p&lt;/math&gt; und &lt;math&gt;q&lt;/math&gt; derart gibt, dass &lt;math&gt;p|m|=|a|&lt;/math&gt; und &lt;math&gt;q|m|=|b|&lt;/math&gt; gilt.</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===Satz II.<del style="font-weight: bold; text-decoration: none;">03</del>: Inkommensurabilität von Quadratseite und Quadratdiagonale===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===Satz II.<ins style="font-weight: bold; text-decoration: none;">07</ins>: Inkommensurabilität von Quadratseite und Quadratdiagonale===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: Die Seite &lt;math&gt;a&lt;/math&gt; und die Diagonale &lt;math&gt;d&lt;/math&gt; ein und desselben Quadrates sind nicht kommensurabel zueinander.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: Die Seite &lt;math&gt;a&lt;/math&gt; und die Diagonale &lt;math&gt;d&lt;/math&gt; ein und desselben Quadrates sind nicht kommensurabel zueinander.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <!-- diff cache key geometrie:diff:1.41:old-10844:rev-10845:php=table --> </table>

*m.g.* http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10844&oldid=prev 2012-01-25T16:25:24Z

<p><span class="autocomment">3. Strahlensatz (STS 3)</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 25. Januar 2012, 16:25 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16">Zeile 16:</td> <td colspan="2" class="diff-lineno">Zeile 16:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Satz II.05: 2. Strahlensatz (STS 2)===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Satz II.05: 2. Strahlensatz (STS 2)===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===3. Strahlensatz (STS 3)===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===<ins style="font-weight: bold; text-decoration: none;">Satz II.06: </ins>3. Strahlensatz (STS 3)===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Kommensurabilität==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Kommensurabilität==</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-10843:rev-10844:php=table --> </table>

*m.g.* http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10843&oldid=prev 2012-01-25T16:24:58Z

<p><span class="autocomment">2. Strahlensatz (STS 2)</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 25. Januar 2012, 16:24 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l14">Zeile 14:</td> <td colspan="2" class="diff-lineno">Zeile 14:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt; --[[Benutzer:HecklF|Flo60]] 13:03, 18. Jan. 2012 (CET)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt; --[[Benutzer:HecklF|Flo60]] 13:03, 18. Jan. 2012 (CET)</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===2. Strahlensatz (STS 2)===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===<ins style="font-weight: bold; text-decoration: none;">Satz II.05: </ins>2. Strahlensatz (STS 2)===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===3. Strahlensatz (STS 3)===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===3. Strahlensatz (STS 3)===</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-10842:rev-10843:php=table --> </table>

*m.g.* http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10842&oldid=prev 2012-01-25T16:24:20Z

<p><span class="autocomment">Strahlensätze</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 25. Januar 2012, 16:24 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Strahlensätze==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Strahlensätze==</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===1. Strahlensatz (STS I)===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===<ins style="font-weight: bold; text-decoration: none;">Satz II.04: </ins>1. Strahlensatz (STS I)===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Seien a und b zwei Strahlen aus einem Büschel mit dem gemeinsamen Punkt A. Ferner seien g und h zwei parallele Gerade, die mit a und b jeweils genau einen gemeinsamen Punkt haben.&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Seien a und b zwei Strahlen aus einem Büschel mit dem gemeinsamen Punkt A. Ferner seien g und h zwei parallele Gerade, die mit a und b jeweils genau einen gemeinsamen Punkt haben.&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das Verhältnis zweier Strahlenabschnitte des Strahls a ist identisch dem Verhältnis der zwei gleichliegenden Strahlenabschnitte des Strahls b. Gleichliegende Strahlenabschnitte sind dabei Abschnitte von verschiedenen Strahlen, die jeweils zwischen dem Scheitelpunkt A und derselben Parallele oder zwischen den gleichen Parallelen liegen.&lt;br /&gt; --[[Benutzer:HecklF|Flo60]] 13:03, 18. Jan. 2012 (CET)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das Verhältnis zweier Strahlenabschnitte des Strahls a ist identisch dem Verhältnis der zwei gleichliegenden Strahlenabschnitte des Strahls b. Gleichliegende Strahlenabschnitte sind dabei Abschnitte von verschiedenen Strahlen, die jeweils zwischen dem Scheitelpunkt A und derselben Parallele oder zwischen den gleichen Parallelen liegen.&lt;br /&gt; --[[Benutzer:HecklF|Flo60]] 13:03, 18. Jan. 2012 (CET)</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===Beweis: AB <del style="font-weight: bold; text-decoration: none;">: </del>BC = AB' <del style="font-weight: bold; text-decoration: none;">: B'C</del>'===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===Beweis : <ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;\frac{|</ins>AB<ins style="font-weight: bold; text-decoration: none;">|}{|</ins>BC<ins style="font-weight: bold; text-decoration: none;">|}</ins>=<ins style="font-weight: bold; text-decoration: none;">\frac{|</ins>AB'<ins style="font-weight: bold; text-decoration: none;">|}{|BC</ins>'<ins style="font-weight: bold; text-decoration: none;">|}&lt;/math&gt;</ins>===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Bei allen Beweisen wird hier das Problem der Kommensurabilität auftauchen. Dieses lagern wir jedoch aus!&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Bei allen Beweisen wird hier das Problem der Kommensurabilität auftauchen. Dieses lagern wir jedoch aus!&lt;br /&gt;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width=&quot;1366&quot; height=&quot;607&quot;  version=&quot;4.0&quot; 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*m.g.* http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10657&oldid=prev 2012-01-18T13:21:23Z

<p><span class="autocomment">Beweis der Inkommensurabilität von Quadratseite und -diagonale</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 18. Januar 2012, 13:21 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l26">Zeile 26:</td> <td colspan="2" class="diff-lineno">Zeile 26:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Beweis der Inkommensurabilität von Quadratseite und -diagonale===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Beweis der Inkommensurabilität von Quadratseite und -diagonale===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; 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vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Kategorie: Elementargeometrie]]</ins></div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-10656:rev-10657:php=table --> </table>

HecklF http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10656&oldid=prev 2012-01-18T12:03:15Z

<p><span class="autocomment">1. Strahlensatz (STS I)</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 18. Januar 2012, 12:03 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Zeile 2:</td> <td colspan="2" class="diff-lineno">Zeile 2:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===1. Strahlensatz (STS I)===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===1. Strahlensatz (STS I)===</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Seien a und b zwei Strahlen aus einem Büschel mit dem gemeinsamen Punkt A. Ferner seien g und h zwei parallele Gerade, die mit a und b jeweils genau einen gemeinsamen Punkt haben.&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Das Verhältnis zweier Strahlenabschnitte des Strahls a ist identisch dem Verhältnis der zwei gleichliegenden Strahlenabschnitte des Strahls b. Gleichliegende Strahlenabschnitte sind dabei Abschnitte von verschiedenen Strahlen, die jeweils zwischen dem Scheitelpunkt A und derselben Parallele oder zwischen den gleichen Parallelen liegen.&lt;br /&gt; --[[Benutzer:HecklF|Flo60]] 13:03, 18. Jan. 2012 (CET)</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===Beweis: AB : BC = AB' : B'C'===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Bei allen Beweisen wird hier das Problem der Kommensurabilität auftauchen. Dieses lagern wir jedoch aus!&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;ggb_applet width="1366" height="607"  version="4.0" 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showResetIcon = "true" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt;--[[Benutzer:HecklF|Flo60]] 13:03, 18. Jan. 2012 (CET)</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===Beweis: AC : AB = AC' : AB'===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;ggb_applet width="1350" height="591"  version="4.0" ggbBase64="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" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt; --[[Benutzer:HecklF|Flo60]] 13:03, 18. Jan. 2012 (CET)</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===2. Strahlensatz (STS 2)===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===2. Strahlensatz (STS 2)===</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-10654:rev-10656:php=table --> </table>

HecklF http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10654&oldid=prev 2012-01-18T11:48:09Z

<p><span class="autocomment">Strahlenstätze</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 18. Januar 2012, 11:48 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>==<del style="font-weight: bold; text-decoration: none;">Strahlenstätze</del>==</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>==<ins style="font-weight: bold; text-decoration: none;">Strahlensätze</ins>==</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===1. Strahlensatz (STS I)===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===1. Strahlensatz (STS I)===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <!-- diff cache key geometrie:diff:1.41:old-10653:rev-10654:php=table --> </table>

HecklF http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10653&oldid=prev 2012-01-18T11:47:20Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 18. Januar 2012, 11:47 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Strahlenstätze==</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===1. Strahlensatz (STS I)===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===2. Strahlensatz (STS 2)===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===3. Strahlensatz (STS 3)===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Kommensurabilität==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Kommensurabilität==</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Definition II.06===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Definition II.06===</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-10607:rev-10653:php=table --> </table>

HecklF http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10607&oldid=prev 2012-01-16T17:01:57Z

<p><span class="autocomment">Satz II.04: Inkommensurabilität von Quadratseite und Quadratdiagonale</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Januar 2012, 17:01 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Zeile 2:</td> <td colspan="2" class="diff-lineno">Zeile 2:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Definition II.06===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Definition II.06===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::Zwei Strecken &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt; heißen genau dann kommensurabel, wenn es eine Strecke &lt;math&gt;m&lt;/math&gt; und ganze Zahlen &lt;math&gt;p&lt;/math&gt; und &lt;math&gt;q&lt;/math&gt; derart gibt, dass &lt;math&gt;p|m|=|a|&lt;/math&gt; und &lt;math&gt;q|m|=|b|&lt;/math&gt; gilt.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::Zwei Strecken &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt; heißen genau dann kommensurabel, wenn es eine Strecke &lt;math&gt;m&lt;/math&gt; und ganze Zahlen &lt;math&gt;p&lt;/math&gt; und &lt;math&gt;q&lt;/math&gt; derart gibt, dass &lt;math&gt;p|m|=|a|&lt;/math&gt; und &lt;math&gt;q|m|=|b|&lt;/math&gt; gilt.</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===Satz II.<del style="font-weight: bold; text-decoration: none;">04</del>: Inkommensurabilität von Quadratseite und Quadratdiagonale===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===Satz II.<ins style="font-weight: bold; text-decoration: none;">03</ins>: Inkommensurabilität von Quadratseite und Quadratdiagonale===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: Die Seite &lt;math&gt;a&lt;/math&gt; und die Diagonale &lt;math&gt;d&lt;/math&gt; ein und desselben Quadrates sind nicht kommensurabel zueinander.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: Die Seite &lt;math&gt;a&lt;/math&gt; und die Diagonale &lt;math&gt;d&lt;/math&gt; ein und desselben Quadrates sind nicht kommensurabel zueinander.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Beweis der Inkommensurabilität von Quadratseite und -diagonale===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Beweis der Inkommensurabilität von Quadratseite und -diagonale===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width=&quot;364&quot; height=&quot;447&quot;  version=&quot;4.0&quot; ggbBase64=&quot;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&quot; 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*m.g.* http://geometrie.idea-sketch.com/index.php?title=Strahlens%C3%A4tze_(2011/12)&diff=10606&oldid=prev 2012-01-16T16:59:58Z

<p><span class="autocomment">Definition II.03</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. Januar 2012, 16:59 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Kommensurabilität==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Kommensurabilität==</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===Definition II.<del style="font-weight: bold; text-decoration: none;">03</del>===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===Definition II.<ins style="font-weight: bold; text-decoration: none;">06</ins>===</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::Zwei Strecken &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt; heißen genau dann kommensurabel, wenn es eine Strecke &lt;math&gt;m&lt;/math&gt; und ganze Zahlen &lt;math&gt;p&lt;/math&gt; und &lt;math&gt;q&lt;/math&gt; derart gibt, dass &lt;math&gt;p|m|=|a|&lt;/math&gt; und &lt;math&gt;q|m|=|b|&lt;/math&gt; gilt.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::Zwei Strecken &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt; heißen genau dann kommensurabel, wenn es eine Strecke &lt;math&gt;m&lt;/math&gt; und ganze Zahlen &lt;math&gt;p&lt;/math&gt; und &lt;math&gt;q&lt;/math&gt; derart gibt, dass &lt;math&gt;p|m|=|a|&lt;/math&gt; und &lt;math&gt;q|m|=|b|&lt;/math&gt; gilt.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===Satz II.04: Inkommensurabilität von Quadratseite und Quadratdiagonale===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:: Die Seite &lt;math&gt;a&lt;/math&gt; und die Diagonale &lt;math&gt;d&lt;/math&gt; ein und desselben Quadrates sind nicht kommensurabel zueinander.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===Beweis der Inkommensurabilität von Quadratseite und -diagonale===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;ggb_applet width="364" height="447"  version="4.0" ggbBase64="UEsDBBQACAAIALmNMEAAAAAAAAAAAAAAAAAWAAAAZ2VvZ2VicmFfamF2YXNjcmlwdC5qc0srzUsuyczPU0hPT/LP88zLLNHQVKiuBQBQSwcI1je9uRkAAAAXAAAAUEsDBBQACAAIALmNMEAAAAAAAAAAAAAAAAAMAAAAZ2VvZ2VicmEueG1s7VtZb9vGFn5Of8VA6GMkzcolkFM4bpw4SJsCzr24uC8FRY4kxhSpkpQtBf3xPTNDUuJiW1LiWDYaJBmSczjL+c42n6TRL6t5hK5lmoVJfNIjA9xDMvaTIIynJ71lPuk7vV9e/zSaymQqx6mHJkk69/KTHleSYXDSG3PqM+z7fcvCTp9Tm/THAZ70Xekyb8wcPGEgiVZZ+CpOfvfmMlt4vrz0Z3LufUx8L9cTz/J88Wo4vLm5GZRTDZJ0OpxOx4NVFvQQLDPOTnrFxSsYrvbSDdPiFGMy/N9vH83w/TDOci/2ZQ+pLSzD1z+9GN2EcZDcoJswyGcnPVhfD81kOJ3BniwMN0MltACFLKSfh9cyg1e3bvWe8/mip8W8WPW/MFcoqrbTQ0F4HQYyPenhAbUYEbbjcptZDqekh5I0lHFeyJJizmE52ug6lDdmWHWlZ+Q9lCdJNPbUiOjvvxHFFKOXqiGmodBYlunC5hlmpqGm4aYRRoab17kR5UaGGxnOeug6zMJxJE96Ey/KQINhPEkBveo+y9eR1OspHmx2T17CnrLwKwgzpVKjcniO8Uv1D/T8kpe63tok2Zo1T5d7TlpNafHdp6TftFFWzkm6tknFLdu07pjU7HuXfRKxNSdMpf/qf60Z2V3bbM5o7r9tQgXBD9jiaFi6yqjwDpTNlGxhPbmcZ8pfmIuEq8yeIAG+Ydlg5QIRFxqbIvAGRATiAm6JgyzV2ojZ0MERQw5ScoQh7RzCgf+4rQezkIDB1FMbfBIRmIgjwRDRPsUReBLSfgk+ShlICIEEvKSmJ1QNwSzELbhjDuKwRuWSNgFBBi/CPUxPESOIqZeJjaiFLDUe4crVLUctHYakyMLIImpA8GrwaOPNIO8gpnZjFeoK48Uyr6nInwflZZ4sKixAGuLRJuqZ+FQLii9GkTeWEeSJS4UkQtdepDxCTzRJ4hwVIFJsnk1TbzEL/exS5jm8laEv3rX30cvl6hyks3JuLesncfZHmuRnSbScxxlCfhLhas1JRLauabVquGFbHXy7Q2x1WFvXdue8CfSgZSZh/iTNSnEvCC6UxCY0gCY/xdH6TSq9q0US1rcxGuqUM5JLPwqD0Iv/C8aqZlF6QVUGUr5SZiBO3HIhSRpcrjOwYLT6v0wT6BMDvP0HvGRteghh9S4YMfM95XsC13sgEKxv6SLcTC2vK4S8ldxsdpqGla2o64vsTRIFVbfe/pm3yJeprh0gNqZqU6fxNJLaRHS0hcTsX42T1aVxcGbG+rxewF1hKOOpVjuC0ECFAIGiHZtWy6iVVVJYy2AtURlbGFT9xKVaQrdj02opsF6ztGKnpNwlweU0YaYDGu4VblMGK2X7Ks8v4zD/WN7koX9VbJWYF35fzseysqD6mOR7jTkaNkxsdCXTWEaFRQOWy2SZGQfdMvZA+uEcbk1HoRJPwfUfWIB5GshpKsuFR7ouMwrTvXjbWFuP9VDnaTK/iK8/gy00FjAalqscZX4aLpTJoTFkgSu5saogzDxIIsH2e8oFYeu+ShagnlypBpxzmc+SVJdeEFOgVZ4XyTkUWijX5qUttFLzqa7glD5RMv4CYa3KfKZ/S1HQ32lr2iq9aDHzVJlX7Dry1jKt6UEP+FsSNLUDytdbACdfqAEUvAspjWWYJcPFAgbUDlULU6DwDK3MtGh90uvrevyrqeBNCat2q7ysFpjN0wZUYD9GUfeo7M2RqewQhYnvrTA/mc+9OECxrm3+SKL1NIl7m2zrYWVryCNKf8ijqpY3KlrmZT94bQRhkRgxz4iNoYF05kMDmQyOQB7ksDNoIH39alZRzN0Bm1lFCUw1fj3o5ZCOr+DMkenInBcxWF+8D4NA6lJseBDmRDCNuiBFVN6ATvYB/XbTzORU3VUL8Q4zzjsWuqd1tp1SFCZGN2MdoHv5V2xeyUwWCOeLKPTDvLKiSJn7RZxDTpA6KLZD/ZWUC5VjP8WfUy/O1CHeyGylkB31PL5Hz5tEt63mMpHjPbX8aTLJZK6U2idGqXB66gKBNUEAB3drfxz9Oi4xaXazOxCyjwAh2BsUVyr46cc/e3/in/dDzj8eD+mTAWOUWrZFXQFHMsd23vaJKCNzHRlXA9Z++lw8KjgeXKrs6Awch9gOnEdsOBlQQQEeS+PQZwMhqE2YZTsOxgCeRu6pglGvcM4Og0Id4aamGZvm4BJnuQqj0EvXLedvYYSb8c1+8ALw1yegnlssd12Q29+94rssvLmz4jtrlXry7sqtGRvkQdlWhYSDSu6tdMtcEwlEJx67ptsdS6BjTLBBR4KtQ38Wpn4kG8iflbV+E/nJ3cjDqTb0N57Uxr3OEuxw1vqGjHBQIA+nMr6GpSZphtAKFw63xmXRVT5ZgXr6pkYmpVeSLbeEM14artBpKX9aSp1SfVEjrcC2T1kxwylX9qqvhJ6iFSA7rUmRmuEElH8n2JV1NfCeGLxlC++3puO+k9p2fH372PF1489kwC3OLQu7HFs2tZiJBnQgmBCMuVi4jNrMdh4gpBq/Ok39btd6a87HbQ+b7uBhCy/d6Hv67YTGgzmZsuzn5GUPXtftQsQUPnl6DxFDC5/+kxhBT1+AAmaGjAkNGXNuyJh3B5Ex9DmTMUpzR3OoaYYySk0s6whxX7VpO8J2LM7gcGpBnGt9VvBkzjYtiuxQVA5lb/YHpfmYmPzSwITbR15L7o7J7LHoNEO2kF3L+xYwvBMvWhxCIbJwmzgWFTaIUvfYAWuza2RPdi08GtdqBzbSHfBKRocMhOUITrnLXcrsKoUfLVq78hXnj11P78BXdEU8fe5uetaDszvvnoC26MClDpw8iOMQxgXlFWeM6xXrD2N63t123v+yH9Pz5Xjix+0UGh1gm4A5OgRiu+C2mvyr4tyoo775SbnNLeJi6wnFj10wPi8Pnk2Mr/bD+Orx2DwTVUinBbSz/S1uRgaEYEoZphwyOxGWMJ/a6I9nai/cWTUfgwm02b52wt+B7SsOlO9alrHYh+1b/Mv2dfMQvBFYeJOH6DjDKVaig6Z6AOpvYcC/aoH/fn/q7/1jJ9/7z8t8YGF4SmxiQ41ICfuB1F/hZ+8NH9N2t7/2pf7++pf6283l6Hd2uaPgAc9r5nQrD8iM2KTkAWclDxgZHnBueMALwwN+OIgHZM+ZB5wcEw8ILlFnkcwnnHzAOXZcil1HYAw91VcdyIAKODwzCqdiwYnDn893TmbHBEz1JdYOgMw3TlxBHOYK7DLhOC5/NjBER3Po6/YNOAhQ9aswCx5QgcEXNt8DwgNBMXPUD8uoA++0v1R/ZCX/7rDMH4uU5VbB1O1Iy5ae00TPcYpDmeXYto1t1+YMQ+eRI9RmYek9LGy9iL547CJ6BwYLN6to9pDV9V3a+vAUtfWQ5OguVNCHsnJslozxflRQ/GhUEN3ze9TdmaH1lBYf1FHsEEEdBRnD5SHgyUScoCPiDLd/cKR/1lf8Qv31P1BLBwjCLbuHJwoAAD4/AABQSwECFAAUAAgACAC5jTBA1je9uRkAAAAXAAAAFgAAAAAAAAAAAAAAAAAAAAAAZ2VvZ2VicmFfamF2YXNjcmlwdC5qc1BLAQIUABQACAAIALmNMEDCLbuHJwoAAD4/AAAMAAAAAAAAAAAAAAAAAF0AAABnZW9nZWJyYS54bWxQSwUGAAAAAAIAAgB+AAAAvgoAAAAA" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" /&gt;</ins></div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-10605:rev-10606:php=table --> </table>

*m.g.*