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class="vector-pinnable-header-label">Περιεχόμενα</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">μετακίνηση στην πλαϊνή μπάρα</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">απόκρυψη</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Αρχή</div> </a> </li> <li id="toc-Απόδειξη" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Απόδειξη"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Απόδειξη</span> </div> </a> <ul id="toc-Απόδειξη-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Δείτε_επίσης" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Δείτε_επίσης"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Δείτε επίσης</span> </div> </a> <ul id="toc-Δείτε_επίσης-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Παραπομπές" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Παραπομπές"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Παραπομπές</span> </div> </a> <ul id="toc-Παραπομπές-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Περιεχόμενα" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Εναλλαγή του πίνακα περιεχομένων" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Εναλλαγή του πίνακα περιεχομένων</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Σημείο Gergonne</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Μεταβείτε σε ένα λήμμα σε άλλη γλώσσα. Διαθέσιμο σε 12 γλώσσες" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-12" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">12 γλώσσες</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Gergonne-Punkt" title="Gergonne-Punkt – Γερμανικά" lang="de" hreflang="de" data-title="Gergonne-Punkt" data-language-autonym="Deutsch" data-language-local-name="Γερμανικά" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Gergonnen_piste" title="Gergonnen piste – Φινλανδικά" lang="fi" hreflang="fi" data-title="Gergonnen piste" data-language-autonym="Suomi" data-language-local-name="Φινλανδικά" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Punto_di_Gergonne" title="Punto di Gergonne – Ιταλικά" lang="it" hreflang="it" data-title="Punto di Gergonne" data-language-autonym="Italiano" data-language-local-name="Ιταλικά" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B8%E3%82%A7%E3%83%AB%E3%82%B4%E3%83%B3%E3%83%8C%E7%82%B9" title="ジェルゴンヌ点 – Ιαπωνικά" lang="ja" hreflang="ja" data-title="ジェルゴンヌ点" data-language-autonym="日本語" data-language-local-name="Ιαπωνικά" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D0%B5%D1%80%D0%B3%D0%BE%D0%BD%D0%BD_%D0%BD%D2%AF%D0%BA%D1%82%D0%B5%D1%81%D1%96" title="Жергонн нүктесі – Καζακικά" lang="kk" hreflang="kk" data-title="Жергонн нүктесі" data-language-autonym="Қазақша" data-language-local-name="Καζακικά" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Punt_van_Gergonne" title="Punt van Gergonne – Ολλανδικά" lang="nl" hreflang="nl" data-title="Punt van Gergonne" data-language-autonym="Nederlands" data-language-local-name="Ολλανδικά" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Pont_%C3%ABd_Gergonne" title="Pont ëd Gergonne – Piedmontese" lang="pms" hreflang="pms" data-title="Pont ëd Gergonne" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ponto_de_Gergonne" title="Ponto de Gergonne – Πορτογαλικά" lang="pt" hreflang="pt" data-title="Ponto de Gergonne" data-language-autonym="Português" data-language-local-name="Πορτογαλικά" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Punctul_lui_Gergonne" title="Punctul lui Gergonne – Ρουμανικά" lang="ro" hreflang="ro" data-title="Punctul lui Gergonne" data-language-autonym="Română" data-language-local-name="Ρουμανικά" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%BE%D1%87%D0%BA%D0%B0_%D0%96%D0%B5%D1%80%D0%B3%D0%BE%D0%BD%D0%BD%D0%B0" title="Точка Жергонна – Ρωσικά" lang="ru" hreflang="ru" data-title="Точка Жергонна" data-language-autonym="Русский" data-language-local-name="Ρωσικά" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Gergonne_noktas%C4%B1" title="Gergonne noktası – Τουρκικά" lang="tr" hreflang="tr" data-title="Gergonne noktası" data-language-autonym="Türkçe" data-language-local-name="Τουρκικά" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%BE%D1%87%D0%BA%D0%B0_%D0%96%D0%B5%D1%80%D0%B3%D0%BE%D0%BD%D0%BD%D0%B0" title="Точка Жергонна – Ουκρανικά" lang="uk" hreflang="uk" data-title="Точка Жергонна" data-language-autonym="Українська" data-language-local-name="Ουκρανικά" class="interlanguage-link-target"><span>Українська</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1751577#sitelinks-wikipedia" title="Επεξεργασία διαγλωσσικών συνδέσεων" class="wbc-editpage">Επεξεργασία συνδέσμων</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Ονοματοχώροι"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF_Gergonne" title="Προβολή της σελίδας περιεχομένου [c]" accesskey="c"><span>Λήμμα</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a 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class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Εμφάνιση</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">μετακίνηση στην πλαϊνή μπάρα</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">απόκρυψη</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Από τη Βικιπαίδεια, την ελεύθερη εγκυκλοπαίδεια</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="el" dir="ltr"><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%CE%91%CF%81%CF%87%CE%B5%CE%AF%CE%BF:Gergonne_point_el.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Gergonne_point_el.svg/220px-Gergonne_point_el.svg.png" decoding="async" width="220" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Gergonne_point_el.svg/330px-Gergonne_point_el.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Gergonne_point_el.svg/440px-Gergonne_point_el.svg.png 2x" data-file-width="178" data-file-height="132" /></a><figcaption>Το σημείο Gergonne του τριγώνου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {AB\Gamma } }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">Γ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {AB\Gamma } }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/612e145b375b84f995485f37d1bbfe01e1f81700" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.841ex; height:2.176ex;" alt="{\displaystyle \mathrm {AB\Gamma } }"></span>, όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I_{A}} ,\mathrm {I_{B}} ,\mathrm {I_{\Gamma }} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I_{A}} ,\mathrm {I_{B}} ,\mathrm {I_{\Gamma }} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc313196fb256574aaffffaf6f9250fdd86303a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.707ex; height:2.509ex;" alt="{\displaystyle \mathrm {I_{A}} ,\mathrm {I_{B}} ,\mathrm {I_{\Gamma }} }"></span> τα σημεία επαφης του εγγεγραμμένου κύκλου.</figcaption></figure> <p>Στην <a href="/wiki/%CE%93%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1" title="Γεωμετρία">γεωμετρία</a>, σε ένα <a href="/wiki/%CE%A4%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Τρίγωνο">τρίγωνο</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {AB\Gamma } }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">Γ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {AB\Gamma } }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/612e145b375b84f995485f37d1bbfe01e1f81700" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.841ex; height:2.176ex;" alt="{\displaystyle \mathrm {AB\Gamma } }"></span> το <b>σημείο Gergonne</b> είναι το σημείο τομής των <a href="/wiki/%CE%95%CF%85%CE%B8%CF%8D%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%BF_%CF%84%CE%BC%CE%AE%CE%BC%CE%B1" title="Ευθύγραμμο τμήμα">ευθυγράμμων τμημάτων</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I_{A}I} ,\mathrm {I_{B}I} ,\mathrm {I_{\Gamma }I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> <mi mathvariant="normal">I</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> <mi mathvariant="normal">I</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </msub> <mi mathvariant="normal">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I_{A}I} ,\mathrm {I_{B}I} ,\mathrm {I_{\Gamma }I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfb93534103ac6687744eddbcbc9429bbaf76f26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.226ex; height:2.509ex;" alt="{\displaystyle \mathrm {I_{A}I} ,\mathrm {I_{B}I} ,\mathrm {I_{\Gamma }I} }"></span>, όπου <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe7a69180f25bbb4c73e091f97c7c5f9941ed17b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.176ex;" alt="{\displaystyle \mathrm {I} }"></span> είναι το <a href="/wiki/%CE%88%CE%B3%CE%BA%CE%B5%CE%BD%CF%84%CF%81%CE%BF_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Έγκεντρο τριγώνου">έγκεντρο</a> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I_{A}} ,\mathrm {I_{B}} ,\mathrm {I_{\Gamma }} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I_{A}} ,\mathrm {I_{B}} ,\mathrm {I_{\Gamma }} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc313196fb256574aaffffaf6f9250fdd86303a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.707ex; height:2.509ex;" alt="{\displaystyle \mathrm {I_{A}} ,\mathrm {I_{B}} ,\mathrm {I_{\Gamma }} }"></span> είναι τα σημεία που εφάπτεται ο <a href="/wiki/%CE%95%CE%B3%CE%B3%CE%B5%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%AD%CE%BD%CE%BF%CF%82_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CF%82_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Εγγεγραμμένος κύκλος τριγώνου">εγγεγραμμένος κύκλος</a> με τις πλευρές του τριγώνου.<sup id="cite_ref-P74_1-0" class="reference"><a href="#cite_note-P74-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:36</sup><sup id="cite_ref-Tav_2-0" class="reference"><a href="#cite_note-Tav-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:187</sup> </p><p>Το σημείο παίρνει το όνομά του από τον μαθηματικό <a href="/w/index.php?title=Joseph_Diez_Gergonne&action=edit&redlink=1" class="new" title="Joseph Diez Gergonne (δεν έχει γραφτεί ακόμα)">Joseph Diez Gergonne</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Απόδειξη"><span id=".CE.91.CF.80.CF.8C.CE.B4.CE.B5.CE.B9.CE.BE.CE.B7"></span>Απόδειξη</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF_Gergonne&veaction=edit&section=1" title="Επεξεργασία ενότητας: Απόδειξη" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF_Gergonne&action=edit&section=1" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Απόδειξη"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%CE%91%CF%81%CF%87%CE%B5%CE%AF%CE%BF:Gergonne_point_proof.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Gergonne_point_proof.svg/220px-Gergonne_point_proof.svg.png" decoding="async" width="220" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Gergonne_point_proof.svg/330px-Gergonne_point_proof.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Gergonne_point_proof.svg/440px-Gergonne_point_proof.svg.png 2x" data-file-width="178" data-file-height="132" /></a><figcaption>Σχήμα απόδειξης.</figcaption></figure> <p>Τα <a href="/wiki/%CE%9F%CF%81%CE%B8%CE%BF%CE%B3%CF%8E%CE%BD%CE%B9%CE%BF_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Ορθογώνιο τρίγωνο">ορθογώνια τρίγωνα</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I\Gamma I_{B}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">Γ</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I\Gamma I_{B}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afbcdd461fb1fbaa3819e8abf652bd73ed5c5bf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.528ex; height:2.509ex;" alt="{\displaystyle \mathrm {I\Gamma I_{B}} }"></span> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I\Gamma I_{A}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">Γ</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I\Gamma I_{A}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da968e706b6c1767243d9d106b66bcb91e9bb065" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.597ex; height:2.509ex;" alt="{\displaystyle \mathrm {I\Gamma I_{A}} }"></span> είναι <a href="/wiki/%CE%8A%CF%83%CE%B1_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%B1#Κριτήρια_ισότητας_ορθογωνίων_τριγώνων" title="Ίσα τρίγωνα">ίσα</a> καθώς η <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {\Gamma I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> <mi mathvariant="normal">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {\Gamma I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71ecf0153689b1b65db10d8e999902d3a89f7965" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.292ex; height:2.176ex;" alt="{\displaystyle \mathrm {\Gamma I} }"></span> είναι κοινή και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \angle \mathrm {\Gamma I~I_{A}} =\angle \mathrm {\Gamma I~I_{B}} ={\tfrac {\hat {\mathrm {\Gamma } }}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∠</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> <mi mathvariant="normal">I</mi> <mtext> </mtext> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> </mrow> <mo>=</mo> <mi mathvariant="normal">∠</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> <mi mathvariant="normal">I</mi> <mtext> </mtext> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle \mathrm {\Gamma I~I_{A}} =\angle \mathrm {\Gamma I~I_{B}} ={\tfrac {\hat {\mathrm {\Gamma } }}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a7fdc042b5c905abe2f6bba44b057454ece2744" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:21.702ex; height:4.176ex;" alt="{\displaystyle \angle \mathrm {\Gamma I~I_{A}} =\angle \mathrm {\Gamma I~I_{B}} ={\tfrac {\hat {\mathrm {\Gamma } }}{2}}}"></span> (καθώς <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {\Gamma I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> <mi mathvariant="normal">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {\Gamma I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71ecf0153689b1b65db10d8e999902d3a89f7965" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.292ex; height:2.176ex;" alt="{\displaystyle \mathrm {\Gamma I} }"></span> είναι <a href="/wiki/%CE%94%CE%B9%CF%87%CE%BF%CF%84%CF%8C%CE%BC%CE%BF%CF%82_%CE%B3%CF%89%CE%BD%CE%AF%CE%B1%CF%82" title="Διχοτόμος γωνίας">διχοτόμος</a>). Επομένως, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {\Gamma I_{A}} =\mathrm {\Gamma I_{B}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {\Gamma I_{A}} =\mathrm {\Gamma I_{B}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81034a6f631470a5d5d2ae50822a4b78d5a4ba84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.544ex; height:2.509ex;" alt="{\displaystyle \mathrm {\Gamma I_{A}} =\mathrm {\Gamma I_{B}} }"></span>. </p><p>Αντίστοιχα, έχουμε ότι <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {AI_{B}} =\mathrm {AI_{\Gamma }} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {AI_{B}} =\mathrm {AI_{\Gamma }} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/867c33b0abc8ae0914a1844ae493969ba1345a32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.919ex; height:2.509ex;" alt="{\displaystyle \mathrm {AI_{B}} =\mathrm {AI_{\Gamma }} }"></span> και <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {BI_{A}} =\mathrm {BI_{\Gamma }} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {BI_{A}} =\mathrm {BI_{\Gamma }} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1a1a439f6319834dd18359142bbfd33542956fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.793ex; height:2.509ex;" alt="{\displaystyle \mathrm {BI_{A}} =\mathrm {BI_{\Gamma }} }"></span>. </p><p>Συνεπώς, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\mathrm {BI_{A}} }{\mathrm {\Gamma I_{A}} }}\cdot {\frac {\mathrm {\Gamma I_{B}} }{\mathrm {AI_{B}} }}\cdot {\frac {\mathrm {AI_{\Gamma }} }{\mathrm {BI_{\Gamma }} }}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {BI_{A}} }{\mathrm {\Gamma I_{A}} }}\cdot {\frac {\mathrm {\Gamma I_{B}} }{\mathrm {AI_{B}} }}\cdot {\frac {\mathrm {AI_{\Gamma }} }{\mathrm {BI_{\Gamma }} }}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c75652f31b1fd3eb480dd10893784f9c2a91468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.898ex; height:5.843ex;" alt="{\displaystyle {\frac {\mathrm {BI_{A}} }{\mathrm {\Gamma I_{A}} }}\cdot {\frac {\mathrm {\Gamma I_{B}} }{\mathrm {AI_{B}} }}\cdot {\frac {\mathrm {AI_{\Gamma }} }{\mathrm {BI_{\Gamma }} }}=1}"></span>,</dd></dl> <p>και από το <a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CF%84%CE%BF%CF%85_%CE%A4%CF%83%CE%AD%CE%B2%CE%B1" class="mw-redirect" title="Θεώρημα του Τσέβα">αντίστροφο του θεωρήματος του Τσέβα</a> έχουμε ότι τα <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I_{A}I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> <mi mathvariant="normal">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I_{A}I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae12dcbb4f1dfaf7e156a093c91adfc979d5edd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.144ex; height:2.509ex;" alt="{\displaystyle \mathrm {I_{A}I} }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I_{B}I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> <mi mathvariant="normal">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I_{B}I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1be58b2b40595259f241e34a826b725d242efe8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.075ex; height:2.509ex;" alt="{\displaystyle \mathrm {I_{B}I} }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I_{\Gamma }I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Γ</mi> </mrow> </msub> <mi mathvariant="normal">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I_{\Gamma }I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d01e5c59799d57b47ea76e1cc40ca66a77c33532" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.939ex; height:2.509ex;" alt="{\displaystyle \mathrm {I_{\Gamma }I} }"></span> συντρέχουν. </p> <div class="mw-heading mw-heading2"><h2 id="Δείτε_επίσης"><span id=".CE.94.CE.B5.CE.AF.CF.84.CE.B5_.CE.B5.CF.80.CE.AF.CF.83.CE.B7.CF.82"></span>Δείτε επίσης</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF_Gergonne&veaction=edit&section=2" title="Επεξεργασία ενότητας: Δείτε επίσης" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF_Gergonne&action=edit&section=2" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Δείτε επίσης"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%CE%A4%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF_Gergonne" title="Τρίγωνο Gergonne">Τρίγωνο Gergonne</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CF%84%CE%BF%CF%85_%CE%A4%CF%83%CE%AD%CE%B2%CE%B1" class="mw-redirect" title="Θεώρημα του Τσέβα">Θεώρημα του Τσέβα</a></li> <li><a href="/wiki/%CE%88%CE%B3%CE%BA%CE%B5%CE%BD%CF%84%CF%81%CE%BF_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Έγκεντρο τριγώνου">Έγκεντρο τριγώνου</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Παραπομπές"><span id=".CE.A0.CE.B1.CF.81.CE.B1.CF.80.CE.BF.CE.BC.CF.80.CE.AD.CF.82"></span>Παραπομπές</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF_Gergonne&veaction=edit&section=3" title="Επεξεργασία ενότητας: Παραπομπές" class="mw-editsection-visualeditor"><span>Επεξεργασία</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF_Gergonne&action=edit&section=3" title="Επεξεργαστείτε τον πηγαίο κώδικα της ενότητας: Παραπομπές"><span>επεξεργασία κώδικα</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-P74-1"><span class="mw-cite-backlink"><a href="#cite_ref-P74_1-0">↑</a></span> <span class="reference-text"><cite class="citation book">Πανάκης, Ιωάννης (1974). <i>Μαθηματικά Δ',Ε',ΣΤ' Γυμνασίου Τόμος Δεύτερος</i>. Αθήνα: Οργανισμός Εκδόσεως Διδακτικών Βιβλίων.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%CE%9C%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC+%CE%94%27%2C%CE%95%27%2C%CE%A3%CE%A4%27+%CE%93%CF%85%CE%BC%CE%BD%CE%B1%CF%83%CE%AF%CE%BF%CF%85+%CE%A4%CF%8C%CE%BC%CE%BF%CF%82+%CE%94%CE%B5%CF%8D%CF%84%CE%B5%CF%81%CE%BF%CF%82&rft.place=%CE%91%CE%B8%CE%AE%CE%BD%CE%B1&rft.pub=%CE%9F%CF%81%CE%B3%CE%B1%CE%BD%CE%B9%CF%83%CE%BC%CF%8C%CF%82+%CE%95%CE%BA%CE%B4%CF%8C%CF%83%CE%B5%CF%89%CF%82+%CE%94%CE%B9%CE%B4%CE%B1%CE%BA%CF%84%CE%B9%CE%BA%CF%8E%CE%BD+%CE%92%CE%B9%CE%B2%CE%BB%CE%AF%CF%89%CE%BD&rft.date=1974&rft.aulast=%CE%A0%CE%B1%CE%BD%CE%AC%CE%BA%CE%B7%CF%82&rft.aufirst=%CE%99%CF%89%CE%AC%CE%BD%CE%BD%CE%B7%CF%82&rfr_id=info%3Asid%2Fel.wikipedia.org%3A%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF+Gergonne" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Tav-2"><span class="mw-cite-backlink"><a href="#cite_ref-Tav_2-0">↑</a></span> <span class="reference-text"><cite class="citation book">Ταβανλης, Χ. <i>Επίπεδος Γεωμετρία</i>. Αθήνα: Ι. Χιωτελη.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%CE%95%CF%80%CE%AF%CF%80%CE%B5%CE%B4%CE%BF%CF%82+%CE%93%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1&rft.place=%CE%91%CE%B8%CE%AE%CE%BD%CE%B1&rft.pub=%CE%99.+%CE%A7%CE%B9%CF%89%CF%84%CE%B5%CE%BB%CE%B7&rft.aulast=%CE%A4%CE%B1%CE%B2%CE%B1%CE%BD%CE%BB%CE%B7%CF%82&rft.aufirst=%CE%A7.&rfr_id=info%3Asid%2Fel.wikipedia.org%3A%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF+Gergonne" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r10387572">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline 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style="width:1%">Είδη τριγώνου</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Βάσει μεγαλύτερης γωνίας</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%9F%CE%BE%CF%85%CE%B3%CF%8E%CE%BD%CE%B9%CE%BF_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Οξυγώνιο τρίγωνο">οξυγώνιο</a></li> <li><a href="/wiki/%CE%91%CE%BC%CE%B2%CE%BB%CF%85%CE%B3%CF%8E%CE%BD%CE%B9%CE%BF_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Αμβλυγώνιο τρίγωνο">αμβλυγώνιο</a></li> <li><a href="/wiki/%CE%9F%CF%81%CE%B8%CE%BF%CE%B3%CF%8E%CE%BD%CE%B9%CE%BF_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Ορθογώνιο τρίγωνο">ορθογώνιο</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Βάσει πλευρών</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%A3%CE%BA%CE%B1%CE%BB%CE%B7%CE%BD%CF%8C_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Σκαληνό τρίγωνο">σκαληνό</a></li> <li><a href="/wiki/%CE%99%CF%83%CE%BF%CF%83%CE%BA%CE%B5%CE%BB%CE%AD%CF%82_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Ισοσκελές τρίγωνο">ισοσκελές</a></li> <li><a href="/wiki/%CE%99%CF%83%CF%8C%CF%80%CE%BB%CE%B5%CF%85%CF%81%CE%BF_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Ισόπλευρο τρίγωνο">ισόπλευρο</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Άλλα</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%A8%CE%B5%CF%85%CE%B4%CE%BF%CF%81%CE%B8%CE%BF%CE%B3%CF%8E%CE%BD%CE%B9%CE%BF_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Ψευδορθογώνιο τρίγωνο">ψευδορθογώνιο</a></li> <li><a href="/wiki/%CE%A4%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF_%CF%84%CE%BF%CF%85_%CE%89%CF%81%CF%89%CE%BD%CE%B1" title="Τρίγωνο του Ήρωνα">τρίγωνο Ήρωνα</a></li> <li><a href="/wiki/%CE%A4%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF_%CF%84%CE%BF%CF%85_%CE%9A%CE%AD%CF%80%CE%BB%CE%B5%CF%81" title="Τρίγωνο του Κέπλερ">τρίγωνο Κέπλερ</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Σημεία τριγώνου</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Βασικά</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%92%CE%B1%CF%81%CF%8D%CE%BA%CE%B5%CE%BD%CF%84%CF%81%CE%BF_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" title="Βαρύκεντρο τριγώνου">βαρύκεντρο</a></li> <li><a href="/wiki/%CE%A0%CE%B5%CF%81%CE%AF%CE%BA%CE%B5%CE%BD%CF%84%CF%81%CE%BF_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Περίκεντρο τριγώνου">περίκεντρο</a></li> <li><a href="/wiki/%CE%9F%CF%81%CE%B8%CF%8C%CE%BA%CE%B5%CE%BD%CF%84%CF%81%CE%BF_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" title="Ορθόκεντρο τριγώνου">ορθόκεντρο</a></li> <li><a href="/wiki/%CE%88%CE%B3%CE%BA%CE%B5%CE%BD%CF%84%CF%81%CE%BF_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Έγκεντρο τριγώνου">έγκεντρο</a></li> <li><a href="/wiki/%CE%A0%CE%B1%CF%81%CE%AC%CE%BA%CE%B5%CE%BD%CF%84%CF%81%CE%B1_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Παράκεντρα τριγώνου">παράκεντρα</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Άλλα</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">σημείο Gergonne</a></li> <li><a href="/wiki/%CE%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF_%CE%9D%CE%AC%CE%B3%CE%BA%CE%B5%CE%BB" title="Σημείο Νάγκελ">σημείο Νάγκελ</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Ευθείες τριγώνου</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%CE%A3%CE%B5%CE%B2%CE%B9%CE%B1%CE%BD%CE%AE" title="Σεβιανή">Σεβιανές</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%94%CE%B9%CF%87%CE%BF%CF%84%CF%8C%CE%BC%CE%BF%CF%82_%CE%B3%CF%89%CE%BD%CE%AF%CE%B1%CF%82#Εσωτερικές_διχοτόμοι_τριγώνου" title="Διχοτόμος γωνίας">εσωτερική διχοτόμος</a></li> <li><a href="/wiki/%CE%95%CE%BE%CF%89%CF%84%CE%B5%CF%81%CE%B9%CE%BA%CE%AE_%CE%B4%CE%B9%CF%87%CE%BF%CF%84%CF%8C%CE%BC%CE%BF%CF%82" class="mw-redirect" title="Εξωτερική διχοτόμος">εξωτερική διχοτόμος</a></li> <li><a href="/wiki/%CE%8E%CF%88%CE%BF%CF%82_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" title="Ύψος τριγώνου">ύψος</a></li> <li><a href="/wiki/%CE%94%CE%B9%CE%AC%CE%BC%CE%B5%CF%83%CE%BF%CF%82_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Διάμεσος (γεωμετρία)">διάμεσος</a></li> <li><a href="/wiki/%CE%A3%CF%85%CE%BC%CE%BC%CE%B5%CF%84%CF%81%CE%BF%CE%B4%CE%B9%CE%AC%CE%BC%CE%B5%CF%83%CE%BF%CF%82_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" title="Συμμετροδιάμεσος τριγώνου">συμμετροδιάμεσος</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Άλλες</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%9C%CE%B5%CF%83%CE%BF%CE%BA%CE%AC%CE%B8%CE%B5%CF%84%CE%B7_%CE%B5%CF%85%CE%B8%CF%8D%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%BF%CF%85_%CF%84%CE%BC%CE%AE%CE%BC%CE%B1%CF%84%CE%BF%CF%82#Μεσοκάθετοι_τριγώνου" title="Μεσοκάθετη ευθύγραμμου τμήματος">μεσοκάθετοι</a></li> <li><a href="/wiki/%CE%95%CF%85%CE%B8%CE%B5%CE%AF%CE%B1_%CE%A3%CE%AF%CE%BC%CF%83%CE%BF%CE%BD-%CE%93%CE%BF%CF%85%CE%AC%CE%BB%CE%B1%CF%82" class="mw-redirect" title="Ευθεία Σίμσον-Γουάλας">ευθεία Σίμσον-Γουάλας</a></li> <li><a href="/wiki/%CE%95%CF%85%CE%B8%CE%B5%CE%AF%CE%B1_%CE%8C%CE%B9%CE%BB%CE%B5%CF%81" title="Ευθεία Όιλερ">ευθεία Όιλερ</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Κύκλοι τριγώνου</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Βασικοί</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%A0%CE%B5%CF%81%CE%B9%CE%B3%CE%B5%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%AD%CE%BD%CE%BF%CF%82_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CF%82_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" title="Περιγεγραμμένος κύκλος τριγώνου">περιγεγραμμένος</a></li> <li><a href="/wiki/%CE%95%CE%B3%CE%B3%CE%B5%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%AD%CE%BD%CE%BF%CF%82_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CF%82_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Εγγεγραμμένος κύκλος τριγώνου">εγγεγραμμένος</a></li> <li><a href="/wiki/%CE%A0%CE%B1%CF%81%CE%B5%CE%B3%CE%B3%CE%B5%CE%B3%CF%81%CE%B1%CE%BC%CE%BC%CE%AD%CE%BD%CE%BF%CE%B9_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CE%B9_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" class="mw-redirect" title="Παρεγγεγραμμένοι κύκλοι τριγώνου">παρεγγεγραμμένοι</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Άλλοι</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%9A%CF%8D%CE%BA%CE%BB%CE%BF%CF%82_%CF%84%CE%BF%CF%85_%CE%8C%CE%B9%CE%BB%CE%B5%CF%81" title="Κύκλος του Όιλερ">κύκλος του Όιλερ</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Μετρικές σχέσεις</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Αναλογίες</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%98%CE%B1%CE%BB%CE%AE" class="mw-redirect" title="Θεώρημα Θαλή">θεώρημα Θαλή</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%B4%CE%B9%CF%87%CE%BF%CF%84%CF%8C%CE%BC%CE%BF%CF%85" title="Θεώρημα διχοτόμου">θεώρημα εσωτερικής και εξωτερικής διχοτόμου</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%9C%CE%B5%CE%BD%CE%B5%CE%BB%CE%AC%CE%BF%CF%85" title="Θεώρημα Μενελάου">θεώρημα Μενελάου</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%A4%CF%83%CE%AD%CE%B2%CE%B1" title="Θεώρημα Τσέβα">θεώρημα Τσέβα</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Εμβαδόν</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%A4%CF%8D%CF%80%CE%BF%CF%82_%CF%84%CE%BF%CF%85_%CE%89%CF%81%CF%89%CE%BD%CE%B1" title="Τύπος του Ήρωνα">τύπος του Ήρωνα</a></li> <li><a href="/wiki/%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD_%CF%84%CF%81%CE%B9%CE%B3%CF%8E%CE%BD%CE%BF%CF%85" title="Εμβαδόν τριγώνου">εμβαδόν τριγώνου</a></li> <li><a href="/wiki/%CE%95%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD#Τρίγωνο" title="Εμβαδόν">λίστα τύπων για το εμβαδόν</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Μήκη σεβιανών</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%A0%CF%85%CE%B8%CE%B1%CE%B3%CF%8C%CF%81%CE%B5%CE%B9%CE%BF_%CE%B8%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1" title="Πυθαγόρειο θεώρημα">Πυθαγόρειο θεώρημα</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%A3%CF%84%CE%B9%CE%BF%CF%8D%CE%B1%CF%81%CF%84" title="Θεώρημα Στιούαρτ">θεώρημα Στιούαρτ</a></li> <li><a href="/wiki/%CE%A0%CF%81%CF%8E%CF%84%CE%BF_%CE%B8%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%B4%CE%B9%CE%B1%CE%BC%CE%AD%CF%83%CF%89%CE%BD" title="Πρώτο θεώρημα διαμέσων">1ο</a> και <a href="/wiki/%CE%94%CE%B5%CF%8D%CF%84%CE%B5%CF%81%CE%BF_%CE%B8%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%B4%CE%B9%CE%B1%CE%BC%CE%AD%CF%83%CF%89%CE%BD" class="mw-redirect" title="Δεύτερο θεώρημα διαμέσων">2ο</a> θεώρημα διαμέσων</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Τριγωνομετρικές<br /> σχέσεις</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%9D%CF%8C%CE%BC%CE%BF%CF%82_%CF%84%CF%89%CE%BD_%CE%B7%CE%BC%CE%B9%CF%84%CF%8C%CE%BD%CF%89%CE%BD" title="Νόμος των ημιτόνων">νόμος των ημιτόνων</a></li> <li><a href="/wiki/%CE%9D%CF%8C%CE%BC%CE%BF%CF%82_%CF%84%CF%89%CE%BD_%CF%83%CF%85%CE%BD%CE%B7%CE%BC%CE%B9%CF%84%CF%8C%CE%BD%CF%89%CE%BD" title="Νόμος των συνημιτόνων">νόμος των συνημιτόνων</a></li> <li><a href="/wiki/%CE%9D%CF%8C%CE%BC%CE%BF%CF%82_%CF%84%CF%89%CE%BD_%CE%B5%CF%86%CE%B1%CF%80%CF%84%CE%BF%CE%BC%CE%AD%CE%BD%CF%89%CE%BD" title="Νόμος των εφαπτομένων">νόμος των εφαπτομένων</a></li> <li><a href="/wiki/%CE%A4%CF%8D%CF%80%CE%BF%CE%B9_Mollweide" title="Τύποι Mollweide">τύποι Mollweide</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Άλλες</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%9A%CE%B1%CF%81%CE%BD%CF%8C_(%CE%B1%CE%BA%CF%84%CE%AF%CE%BD%CE%B5%CF%82)" title="Θεώρημα Καρνό (ακτίνες)">θεώρημα Καρνό (ακτίνες)</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%9A%CE%B1%CF%81%CE%BD%CF%8C_(%CE%BA%CE%AC%CE%B8%CE%B5%CF%84%CE%BF%CE%B9)" title="Θεώρημα Καρνό (κάθετοι)">θεώρημα Καρνό (κάθετοι)</a></li> <li><a href="/wiki/%CE%A3%CF%87%CE%AD%CF%83%CE%B7_%CF%84%CE%BF%CF%85_%CE%9B%CE%AC%CE%B9%CE%BC%CF%80%CE%BD%CE%B9%CF%84%CF%82" title="Σχέση του Λάιμπνιτς">σχέση του Λάιμπνιτς</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CF%84%CE%BF%CF%85_%CE%8C%CE%B9%CE%BB%CE%B5%CF%81_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Θεώρημα του Όιλερ (γεωμετρία)">θεώρημα Όιλερ</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Σχετικά θεωρήματα</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CF%84%CF%81%CE%B9%CF%87%CE%BF%CF%84%CF%8C%CE%BC%CF%89%CE%BD_%CF%84%CE%BF%CF%85_%CE%9C%CF%8C%CF%81%CE%BB%CE%B5%CF%8A" title="Θεώρημα τριχοτόμων του Μόρλεϊ">θεώρημα τριχοτόμων του Μόρλεϊ</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%9D%CE%B1%CF%80%CE%BF%CE%BB%CE%AD%CE%BF%CE%BD%CF%84%CE%B1" title="Θεώρημα Ναπολέοντα">θεώρημα Ναπολέοντα</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%A0%CE%AC%CF%80%CF%80%CE%BF%CF%85_%CE%B3%CE%B9%CE%B1_%CF%84%CE%BF_%CE%B5%CE%BC%CE%B2%CE%B1%CE%B4%CF%8C%CE%BD" title="Θεώρημα Πάππου για το εμβαδόν">θεώρημα Πάππου</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_Steiner-Lehmus" title="Θεώρημα Steiner-Lehmus">θεώρημα Steiner-Lehmus</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%9D%CE%AC%CE%B3%CE%BA%CE%B5%CE%BB" title="Θεώρημα Νάγκελ">θεώρημα Νάγκελ</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%92%CE%B9%CE%B2%CE%B9%CE%AC%CE%BD%CE%B9" title="Θεώρημα Βιβιάνι">θεώρημα Βιβιάνι</a></li> <li><a href="/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_van_Schooten" title="Θεώρημα van Schooten">θεώρημα van Schooten</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Παράγωγα τρίγωνα</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%CE%A3%CF%85%CE%BC%CF%80%CE%BB%CE%B7%CF%81%CF%89%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CF%8C_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Συμπληρωματικό τρίγωνο">συμπληρωματικό</a></li> <li><a href="/wiki/%CE%A3%CF%85%CE%BC%CF%80%CE%BB%CE%B7%CF%81%CF%89%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CF%8C_%CF%84%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Συμπληρωματικό τρίγωνο">αντισυμπληρωματικό</a></li> <li><a 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title="Κατηγορία:Τρίγωνα">Κατηγορία</a></b></li> <li><span typeof="mw:File"><span title="Commons page"><img alt="Commons page" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Triangle" class="extiw" title="commons:Category:Triangle">Commons</a></b></li></ul> </div></td></tr></tbody></table></div> <table class="metadata plainlinks stub" style="background: transparent;" role="presentation"><tbody><tr> <td><span typeof="mw:File"><a href="/wiki/%CE%91%CF%81%CF%87%CE%B5%CE%AF%CE%BF:Anglaucentrepolaire.svg" class="mw-file-description"><img alt="Stub icon" 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