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Lösung von Aufg. 7 - Versionsgeschichte
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Schnirch am 22. Dezember 2010 um 13:48 Uhr
2010-12-22T13:48:54Z
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<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 22. Dezember 2010, 13:48 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"></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>Gegeben seien drei paarweise verschiedene und '''kollineare''' Punkte ''A'', ''B'' und ''C'' in einer Ebene ''E''. Ferner sei eine Gerade ''g'' Teilmenge der Ebene ''E'', wobei keiner der Punkte ''A'', ''B'' und ''C'' auf ''g'' liegen möge. Beweisen Sie folgenden Zusammenhang:<br /><br /></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>Gegeben seien drei paarweise verschiedene und '''kollineare''' Punkte ''A'', ''B'' und ''C'' in einer Ebene ''E''. Ferner sei eine Gerade ''g'' Teilmenge der Ebene ''E'', wobei keiner der Punkte ''A'', ''B'' und ''C'' auf ''g'' liegen möge. Beweisen Sie folgenden Zusammenhang:<br /><br /></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><math>\overline{AB} \cap g \neq \lbrace \rbrace \wedge \overline{BC} \cap g = \lbrace \rbrace \Rightarrow \overline{AC} \cap g \neq \lbrace \rbrace </math> <br /> </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><math>\overline{AB} \cap g \neq \lbrace \rbrace \wedge \overline{BC} \cap g = \lbrace \rbrace \Rightarrow \overline{AC} \cap g \neq \lbrace \rbrace </math> <br /> </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><del style="font-weight: bold; text-decoration: none;"><ggb_applet width="892" height="512" version="3.2" ggbBase64="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" framePossible = "true" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" /></del></div></td><td colspan="2" class="diff-side-added"></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 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;">==Lösung--[[Benutzer:Schnirch|Schnirch]] 12:33, 22. Dez. 2010 (UTC)==</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;">Vor.:<br /></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;">*drei paarweise verschiedene und '''kollineare''' Punkte ''A'', ''B'' und ''C'' in einer Ebene ''E''</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;">*<math>\ g \subset E</math></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;">*<math>\ A,B,C \notin g</math></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;">*<math>\overline{AB} \cap g \neq \lbrace \rbrace \wedge \overline{BC} \cap g = \lbrace \rbrace </math><br /></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;">Beh.: <math>\overline{AC} \cap g \neq \lbrace \rbrace </math><br /><br /></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;">Der folgende Beweis ist nur einer von vielen möglichen. Fühlen Sie sich frei Ihre Version auch mit hier einzustellen!<br /></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 Idee des folgenden Beweises liegt darin, sich einen weiteren Punkt ''P'' in der Halbebene <math>\ gA^{+}</math> zu erzeugen, der nichtkollinear zu ''A,B,C'' ist und dann das Axiom von Pasch mehrfach anzuwenden:<br /> </ins></div></td></tr>
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<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;">{| class="wikitable "</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 </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;">! Nr.</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;">! Beweisschritt</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;">! Begründung</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;">! style="background: #FFDDDD;"|(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;">| <math>\exists S: \overline{AB} \cap g = \lbrace S \rbrace </math> </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;">| Vor.</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;">! style="background: #FFDDDD;"|(II)</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;">| <math>\exists T \in g \wedge T \not= S</math></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;">| Axiom I/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;">! style="background: #FFDDDD;"|(III)</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;">| <math>\exists P \in \overline{AT} \wedge P \notin g \wedge P \not=A</math></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;">| Axiom vom Lineal </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;">! style="background: #FFDDDD;"|(IV)</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;">| <math>\ P \in gA^{+}</math></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;">| (II), (III) </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;">! style="background: #FFDDDD;"|(V)</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;">| <math>\overline{PA} \cap g = \lbrace \rbrace</math></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;">| (IV), Def. Halbebene</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;">! style="background: #FFDDDD;"|(VI)</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;">| <math>\overline{AB} \cap g \not= \lbrace \rbrace</math></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;">| Vor. </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;">! style="background: #FFDDDD;"|(VII)</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;">| <math>\overline{PB} \cap g \not= \lbrace \rbrace</math></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;">| (V), (VI), Axiom von Pasch</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;">! style="background: #FFDDDD;"|(VIII)</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;">| <math>\overline{BC} \cap g = \lbrace \rbrace</math></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;">| Vor.</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;">! style="background: #FFDDDD;"|(IX)</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;">| <math>\overline{PC} \cap g \not= \lbrace \rbrace</math></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;">| (VII), (VIII), Axiom von Pasch</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;">! style="background: #FFDDDD;"|(X)</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;">| <math>\overline{AC} \cap g \not= \lbrace \rbrace</math></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;">| (V), (IX), Axiom von Pasch</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;">|}</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;"><ggb_applet width="400" height="400" version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" /></ins></div></td></tr>
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Schnirch
http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufg._7&diff=5845&oldid=prev
Schnirch am 21. Dezember 2010 um 15:02 Uhr
2010-12-21T15:02:43Z
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<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 21. Dezember 2010, 15:02 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><math>\overline{AB} \cap g \neq \lbrace \rbrace \wedge \overline{BC} \cap g = \lbrace \rbrace \Rightarrow \overline{AC} \cap g \neq \lbrace \rbrace </math> <br /> </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><math>\overline{AB} \cap g \neq \lbrace \rbrace \wedge \overline{BC} \cap g = \lbrace \rbrace \Rightarrow \overline{AC} \cap g \neq \lbrace \rbrace </math> <br /> </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><ggb_applet width="892" height="512" version="3.2" ggbBase64="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" framePossible = "true" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" /></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><ggb_applet width="892" height="512" version="3.2" ggbBase64="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" framePossible = "true" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" /></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;"></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;">[[Category:Einführung_Geometrie]]</ins></div></td></tr>
</table>
Schnirch
http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufg._7&diff=5829&oldid=prev
Schnirch am 21. Dezember 2010 um 14:57 Uhr
2010-12-21T14:57:45Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<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 21. Dezember 2010, 14:57 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> </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;">Gegeben seien drei paarweise verschiedene und '''kollineare''' Punkte ''A'', ''B'' und ''C'' in einer Ebene ''E''. Ferner sei eine Gerade ''g'' Teilmenge der Ebene ''E'', wobei keiner der Punkte ''A'', ''B'' und ''C'' auf ''g'' liegen möge. Beweisen Sie folgenden Zusammenhang:<br /><br /></ins></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> </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;"><math>\overline{AB} \cap g \neq \lbrace \rbrace \wedge \overline{BC} \cap g = \lbrace \rbrace \Rightarrow \overline{AC} \cap g \neq \lbrace \rbrace </math> <br /> </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><ggb_applet width="892" height="512" version="3.2" ggbBase64="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" framePossible = "true" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" /></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><ggb_applet width="892" height="512" version="3.2" ggbBase64="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" framePossible = "true" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" /></div></td></tr>
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Schnirch
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2010-12-21T14:57:15Z
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