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vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Pratélaning isi</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">lih menyang wilah sisih</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">dhelikaké</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">Wiwitan</div> </a> </li> <li id="toc-Jagad_Ptolemaic" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Jagad_Ptolemaic"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Jagad Ptolemaic</span> </div> </a> <ul id="toc-Jagad_Ptolemaic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Teorema_Ptolemaic" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Teorema_Ptolemaic"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Teorema Ptolemaic</span> </div> </a> <ul id="toc-Teorema_Ptolemaic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sitiran" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sitiran"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Sitiran</span> </div> </a> <ul id="toc-Sitiran-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="Pratélaning isi" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Pratélan Isi" > <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="Gulingkan daftar isi" > <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">Gulingkan daftar isi</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">Claudius Ptolemaeus</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="Ngalih menyang artikel jroning basa liya. Ana 117 basa" > <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-117" 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">117 basa</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af badge-Q17437796 badge-featuredarticle mw-list-item" title="artikel pethingan"><a href="https://af.wikipedia.org/wiki/Ptolemeus" title="Ptolemeus – Afrika" lang="af" hreflang="af" data-title="Ptolemeus" data-language-autonym="Afrikaans" data-language-local-name="Afrika" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Claudius_Ptolem%C3%A4us" title="Claudius Ptolemäus – Jerman Swiss" lang="gsw" hreflang="gsw" data-title="Claudius Ptolemäus" data-language-autonym="Alemannisch" data-language-local-name="Jerman Swiss" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%89%B6%E1%88%88%E1%88%9A" title="ቶለሚ – Amharik" lang="am" hreflang="am" data-title="ቶለሚ" data-language-autonym="አማርኛ" data-language-local-name="Amharik" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Claudio_Ptolomeu" title="Claudio Ptolomeu – Aragonese" lang="an" hreflang="an" data-title="Claudio Ptolomeu" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%B7%D9%84%D9%8A%D9%85%D9%88%D8%B3" title="بطليموس – Arab" lang="ar" hreflang="ar" data-title="بطليموس" data-language-autonym="العربية" data-language-local-name="Arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%83%D9%84%D8%A7%D9%88%D8%AF%D9%8A%D9%88%D8%B3_%D9%BE%D8%B7%D9%88%D9%84%D9%8A%D9%85%D8%A7%D9%8A%D9%88%D8%B3" title="كلاوديوس پطوليمايوس – Arab Maroko" lang="ary" hreflang="ary" data-title="كلاوديوس پطوليمايوس" data-language-autonym="الدارجة" data-language-local-name="Arab Maroko" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%83%D9%84%D8%A7%D9%88%D8%AF%D9%8A%D9%88%D8%B3_%D8%A8%D8%B7%D9%84%D9%8A%D9%85%D9%88%D8%B3" title="كلاوديوس بطليموس – Arab Mesir" lang="arz" hreflang="arz" data-title="كلاوديوس بطليموس" data-language-autonym="مصرى" data-language-local-name="Arab Mesir" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Tolom%C3%A9u" title="Toloméu – Asturia" lang="ast" hreflang="ast" data-title="Toloméu" data-language-autonym="Asturianu" data-language-local-name="Asturia" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Ptolemey" title="Ptolemey – Azerbaijan" lang="az" hreflang="az" data-title="Ptolemey" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijan" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8%D0%B9_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавдий Птолемей – Bashkir" lang="ba" hreflang="ba" data-title="Клавдий Птолемей" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Ptolemy" title="Ptolemy – Central Bikol" lang="bcl" hreflang="bcl" data-title="Ptolemy" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D1%9E%D0%B4%D0%B7%D1%96%D0%B9_%D0%9F%D1%82%D0%B0%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клаўдзій Пталемей – Belarus" lang="be" hreflang="be" data-title="Клаўдзій Пталемей" data-language-autonym="Беларуская" data-language-local-name="Belarus" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D0%BB%D1%8F%D1%9E%D0%B4%D1%8B%D1%8E%D1%81_%D0%9F%D1%82%D0%B0%D0%BB%D0%B5%D0%BC%D1%8D%D0%B9" title="Кляўдыюс Пталемэй – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Кляўдыюс Пталемэй" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8%D0%B9_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавдий Птолемей – Bulgaria" lang="bg" hreflang="bg" data-title="Клавдий Птолемей" data-language-autonym="Български" data-language-local-name="Bulgaria" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9F%E0%A6%B2%E0%A7%87%E0%A6%AE%E0%A6%BF" title="টলেমি – Bengali" lang="bn" hreflang="bn" data-title="টলেমি" data-language-autonym="বাংলা" data-language-local-name="Bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Klaudios_Ptolemaios" title="Klaudios Ptolemaios – Breton" lang="br" hreflang="br" data-title="Klaudios Ptolemaios" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Ptolemej" title="Ptolemej – Bosnia lan Hercegovina" lang="bs" hreflang="bs" data-title="Ptolemej" data-language-autonym="Bosanski" data-language-local-name="Bosnia lan Hercegovina" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Claudi_Ptolemeu" title="Claudi Ptolemeu – Katala" lang="ca" hreflang="ca" data-title="Claudi Ptolemeu" data-language-autonym="Català" data-language-local-name="Katala" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cbk-zam mw-list-item"><a href="https://cbk-zam.wikipedia.org/wiki/Claudio_Ptolomeo" title="Claudio Ptolomeo – Chavacano" lang="cbk" hreflang="cbk" data-title="Claudio Ptolomeo" data-language-autonym="Chavacano de Zamboanga" data-language-local-name="Chavacano" class="interlanguage-link-target"><span>Chavacano de Zamboanga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%95%D8%AA%DA%B5%DB%8C%D9%85%DB%86%D8%B3" title="بەتڵیمۆس – Kurdi Tengah" lang="ckb" hreflang="ckb" data-title="بەتڵیمۆس" data-language-autonym="کوردی" data-language-local-name="Kurdi Tengah" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Klaudios_Ptolemaios" title="Klaudios Ptolemaios – Ceska" lang="cs" hreflang="cs" data-title="Klaudios Ptolemaios" data-language-autonym="Čeština" data-language-local-name="Ceska" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ptolemi" title="Ptolemi – Welsh" lang="cy" hreflang="cy" data-title="Ptolemi" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Ptolem%C3%A6us" title="Ptolemæus – Dansk" lang="da" hreflang="da" data-title="Ptolemæus" data-language-autonym="Dansk" data-language-local-name="Dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Claudius_Ptolem%C3%A4us" title="Claudius Ptolemäus – Jérman" lang="de" hreflang="de" data-title="Claudius Ptolemäus" data-language-autonym="Deutsch" data-language-local-name="Jérman" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Batlamyus" title="Batlamyus – Dimli" lang="diq" hreflang="diq" data-title="Batlamyus" data-language-autonym="Zazaki" data-language-local-name="Dimli" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%BB%CE%B1%CF%8D%CE%B4%CE%B9%CE%BF%CF%82_%CE%A0%CF%84%CE%BF%CE%BB%CE%B5%CE%BC%CE%B1%CE%AF%CE%BF%CF%82" title="Κλαύδιος Πτολεμαίος – Yunani" lang="el" hreflang="el" data-title="Κλαύδιος Πτολεμαίος" data-language-autonym="Ελληνικά" data-language-local-name="Yunani" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Ptolemy" title="Ptolemy – Inggris" lang="en" hreflang="en" data-title="Ptolemy" data-language-autonym="English" data-language-local-name="Inggris" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ptolemeo" title="Ptolemeo – Esperanto" lang="eo" hreflang="eo" data-title="Ptolemeo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Claudio_Ptolomeo" title="Claudio Ptolomeo – Spanyol" lang="es" hreflang="es" data-title="Claudio Ptolomeo" data-language-autonym="Español" data-language-local-name="Spanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Ptolemaios" title="Ptolemaios – Estonia" lang="et" hreflang="et" data-title="Ptolemaios" data-language-autonym="Eesti" data-language-local-name="Estonia" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Klaudio_Ptolomeo" title="Klaudio Ptolomeo – Basque" lang="eu" hreflang="eu" data-title="Klaudio Ptolomeo" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D8%B7%D9%84%D9%85%DB%8C%D9%88%D8%B3" title="بطلمیوس – Persia" lang="fa" hreflang="fa" data-title="بطلمیوس" data-language-autonym="فارسی" data-language-local-name="Persia" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Klaudios_Ptolemaios" title="Klaudios Ptolemaios – Suomi" lang="fi" hreflang="fi" data-title="Klaudios Ptolemaios" data-language-autonym="Suomi" data-language-local-name="Suomi" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Ptolemaios%C3%B5_Klaudios" title="Ptolemaiosõ Klaudios – Võro" lang="vro" hreflang="vro" data-title="Ptolemaiosõ Klaudios" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Claude_Ptol%C3%A9m%C3%A9e" title="Claude Ptolémée – Prancis" lang="fr" hreflang="fr" data-title="Claude Ptolémée" data-language-autonym="Français" data-language-local-name="Prancis" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Claudius_Ptolem%C3%A4us" title="Claudius Ptolemäus – Frisian Lor Segara" lang="frr" hreflang="frr" data-title="Claudius Ptolemäus" data-language-autonym="Nordfriisk" data-language-local-name="Frisian Lor Segara" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Ptolem%C3%A9us" title="Ptoleméus – Frisia Sisih Kulon" lang="fy" hreflang="fy" data-title="Ptoleméus" data-language-autonym="Frysk" data-language-local-name="Frisia Sisih Kulon" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Tolamaes" title="Tolamaes – Irlandia" lang="ga" hreflang="ga" data-title="Tolamaes" data-language-autonym="Gaeilge" data-language-local-name="Irlandia" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Ptolomaidh" title="Ptolomaidh – Gaulia" lang="gd" hreflang="gd" data-title="Ptolomaidh" data-language-autonym="Gàidhlig" data-language-local-name="Gaulia" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Claudio_Tolomeo" title="Claudio Tolomeo – Galisia" lang="gl" hreflang="gl" data-title="Claudio Tolomeo" data-language-autonym="Galego" data-language-local-name="Galisia" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%9C%D7%9E%D7%99_(%D7%90%D7%A1%D7%98%D7%A8%D7%95%D7%A0%D7%95%D7%9D)" title="תלמי (אסטרונום) – Ibrani" lang="he" hreflang="he" data-title="תלמי (אסטרונום)" data-language-autonym="עברית" data-language-local-name="Ibrani" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%BE%E0%A4%A1%E0%A4%BF%E0%A4%AF%E0%A4%B8_%E0%A4%9F%E0%A5%89%E0%A4%B2%E0%A4%AE%E0%A5%80" title="क्लाडियस टॉलमी – India" lang="hi" hreflang="hi" data-title="क्लाडियस टॉलमी" data-language-autonym="हिन्दी" data-language-local-name="India" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Klaudije_Ptolemej" title="Klaudije Ptolemej – Kroasia" lang="hr" hreflang="hr" data-title="Klaudije Ptolemej" data-language-autonym="Hrvatski" data-language-local-name="Kroasia" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Toleme" title="Toleme – Kreol Haiti" lang="ht" hreflang="ht" data-title="Toleme" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Kreol Haiti" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Klaudiosz_Ptolemaiosz" title="Klaudiosz Ptolemaiosz – Hungaria" lang="hu" hreflang="hu" data-title="Klaudiosz Ptolemaiosz" data-language-autonym="Magyar" data-language-local-name="Hungaria" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%AC%D5%A1%D5%BE%D5%A4%D5%AB%D5%B8%D5%BD_%D5%8A%D5%BF%D5%B2%D5%B8%D5%B4%D5%A5%D5%B8%D5%BD" title="Կլավդիոս Պտղոմեոս – Armenia" lang="hy" hreflang="hy" data-title="Կլավդիոս Պտղոմեոս" data-language-autonym="Հայերեն" data-language-local-name="Armenia" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Ptolemeo" title="Ptolemeo – Interlingua" lang="ia" hreflang="ia" data-title="Ptolemeo" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Klaudius_Ptolemaeus" title="Klaudius Ptolemaeus – Indonesia" lang="id" hreflang="id" data-title="Klaudius Ptolemaeus" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Claudius_Ptolemaeus" title="Claudius Ptolemaeus – Ido" lang="io" hreflang="io" data-title="Claudius Ptolemaeus" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Kl%C3%A1d%C3%ADus_Pt%C3%B3lm%C3%A6os" title="Kládíus Ptólmæos – Islandia" lang="is" hreflang="is" data-title="Kládíus Ptólmæos" data-language-autonym="Íslenska" data-language-local-name="Islandia" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Claudio_Tolomeo" title="Claudio Tolomeo – Italia" lang="it" hreflang="it" data-title="Claudio Tolomeo" data-language-autonym="Italiano" data-language-local-name="Italia" 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%AF%E3%83%A9%E3%82%A6%E3%83%87%E3%82%A3%E3%82%AA%E3%82%B9%E3%83%BB%E3%83%97%E3%83%88%E3%83%AC%E3%83%9E%E3%82%A4%E3%82%AA%E3%82%B9" title="クラウディオス・プトレマイオス – Jepang" lang="ja" hreflang="ja" data-title="クラウディオス・プトレマイオス" data-language-autonym="日本語" data-language-local-name="Jepang" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9E%E1%83%A2%E1%83%9D%E1%83%9A%E1%83%94%E1%83%9B%E1%83%94" title="პტოლემე – Georgia" lang="ka" hreflang="ka" data-title="პტოლემე" data-language-autonym="ქართული" data-language-local-name="Georgia" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Claude_Ptol%C3%A9m%C3%A9e" title="Claude Ptolémée – Kabiye" lang="kbp" hreflang="kbp" data-title="Claude Ptolémée" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8%D0%B9_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавдий Птолемей – Kazakh" lang="kk" hreflang="kk" data-title="Клавдий Птолемей" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%95%E0%B3%8D%E0%B2%B2%E0%B2%BE%E0%B2%A1%E0%B2%BF%E0%B2%AF%E0%B2%B8%E0%B3%8D_%E0%B2%9F%E0%B2%BE%E0%B2%B2%E0%B3%86%E0%B2%AE%E0%B2%BF" title="ಕ್ಲಾಡಿಯಸ್ ಟಾಲೆಮಿ – Kannada" lang="kn" hreflang="kn" data-title="ಕ್ಲಾಡಿಯಸ್ ಟಾಲೆಮಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%81%B4%EB%9D%BC%EC%9A%B0%EB%94%94%EC%98%A4%EC%8A%A4_%ED%94%84%ED%86%A8%EB%A0%88%EB%A7%88%EC%9D%B4%EC%98%A4%EC%8A%A4" title="클라우디오스 프톨레마이오스 – Korea" lang="ko" hreflang="ko" data-title="클라우디오스 프톨레마이오스" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Ptolema%C3%AEos" title="Ptolemaîos – Kurdis" lang="ku" hreflang="ku" data-title="Ptolemaîos" data-language-autonym="Kurdî" data-language-local-name="Kurdis" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Птолемей – Kirgis" lang="ky" hreflang="ky" data-title="Птолемей" data-language-autonym="Кыргызча" data-language-local-name="Kirgis" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Claudius_Ptolemaeus" title="Claudius Ptolemaeus – Latin" lang="la" hreflang="la" data-title="Claudius Ptolemaeus" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Ptolem%C3%A4us" title="Ptolemäus – Luksemburg" lang="lb" hreflang="lb" data-title="Ptolemäus" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luksemburg" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Ptolemeo" title="Ptolemeo – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Ptolemeo" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Klaudijus_Ptolem%C4%97jus" title="Klaudijus Ptolemėjus – Lithuania" lang="lt" hreflang="lt" data-title="Klaudijus Ptolemėjus" data-language-autonym="Lietuvių" data-language-local-name="Lithuania" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Ptolemajs" title="Ptolemajs – Latvia" lang="lv" hreflang="lv" data-title="Ptolemajs" data-language-autonym="Latviešu" data-language-local-name="Latvia" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавди Птолемей – Moksha" lang="mdf" hreflang="mdf" data-title="Клавди Птолемей" data-language-autonym="Мокшень" data-language-local-name="Moksha" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Klaodio_Pt%C3%B4lemeo" title="Klaodio Ptôlemeo – Malagasi" lang="mg" hreflang="mg" data-title="Klaodio Ptôlemeo" data-language-autonym="Malagasy" data-language-local-name="Malagasi" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8%D1%98_%D0%9F%D1%82%D0%BE%D0%BB%D0%BE%D0%BC%D0%B5%D1%98" title="Клавдиј Птоломеј – Makedonia" lang="mk" hreflang="mk" data-title="Клавдиј Птоломеј" data-language-autonym="Македонски" data-language-local-name="Makedonia" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%9F%E0%B5%8B%E0%B4%B3%E0%B4%AE%E0%B4%BF" title="ടോളമി – Malayalam" lang="ml" hreflang="ml" data-title="ടോളമി" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8%D0%B9_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавдий Птолемей – Mongolia" lang="mn" hreflang="mn" data-title="Клавдий Птолемей" data-language-autonym="Монгол" data-language-local-name="Mongolia" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%9F%E0%A5%89%E0%A4%B2%E0%A5%87%E0%A4%AE%E0%A5%80" title="टॉलेमी – Marathi" lang="mr" hreflang="mr" data-title="टॉलेमी" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ptolemy" title="Ptolemy – Melayu" lang="ms" hreflang="ms" data-title="Ptolemy" data-language-autonym="Bahasa Melayu" data-language-local-name="Melayu" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%90%E1%80%B1%E1%80%AC%E1%80%BA%E1%80%9C%E1%80%99%E1%80%AE" title="တော်လမီ – Myanmar" lang="my" hreflang="my" data-title="တော်လမီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Myanmar" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds-nl mw-list-item"><a href="https://nds-nl.wikipedia.org/wiki/Ptolemaeus" title="Ptolemaeus – Low Saxon" lang="nds-NL" hreflang="nds-NL" data-title="Ptolemaeus" data-language-autonym="Nedersaksies" data-language-local-name="Low Saxon" class="interlanguage-link-target"><span>Nedersaksies</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Claudius_Ptolemaeus" title="Claudius Ptolemaeus – Walanda" lang="nl" hreflang="nl" data-title="Claudius Ptolemaeus" data-language-autonym="Nederlands" data-language-local-name="Walanda" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Klaudios_Ptolemaios" title="Klaudios Ptolemaios – Nynorsk Norwegia" lang="nn" hreflang="nn" data-title="Klaudios Ptolemaios" data-language-autonym="Norsk nynorsk" data-language-local-name="Nynorsk Norwegia" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Klaudios_Ptolemaios" title="Klaudios Ptolemaios – Bokmål Norwegia" lang="nb" hreflang="nb" data-title="Klaudios Ptolemaios" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmål Norwegia" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Claudi_Ptolem%C3%A8u" title="Claudi Ptolemèu – Ossitan" lang="oc" hreflang="oc" data-title="Claudi Ptolemèu" data-language-autonym="Occitan" data-language-local-name="Ossitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%95%E0%AD%8D%E0%AC%B2%E0%AC%BE%E0%AC%A1%E0%AC%BF%E0%AD%9F%E0%AC%B8_%E0%AC%9F%E0%AC%B2%E0%AD%87%E0%AC%AE%E0%AD%80" title="କ୍ଲାଡିୟସ ଟଲେମୀ – Odia" lang="or" hreflang="or" data-title="କ୍ଲାଡିୟସ ଟଲେମୀ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A8%B2%E0%A9%8C%E0%A8%A1%E0%A9%80%E0%A8%85%E0%A8%B8_%E0%A8%9F%E0%A9%8B%E0%A8%B2%E0%A9%87%E0%A8%AE%E0%A9%80" title="ਕਲੌਡੀਅਸ ਟੋਲੇਮੀ – Punjab" lang="pa" hreflang="pa" data-title="ਕਲੌਡੀਅਸ ਟੋਲੇਮੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjab" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pam badge-Q17437798 badge-goodarticle mw-list-item" title="artikel bagus"><a href="https://pam.wikipedia.org/wiki/Claudio_Ptolomeo" title="Claudio Ptolomeo – Pampanga" lang="pam" hreflang="pam" data-title="Claudio Ptolomeo" data-language-autonym="Kapampangan" data-language-local-name="Pampanga" class="interlanguage-link-target"><span>Kapampangan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Klaudiusz_Ptolemeusz" title="Klaudiusz Ptolemeusz – Polandia" lang="pl" hreflang="pl" data-title="Klaudiusz Ptolemeusz" data-language-autonym="Polski" data-language-local-name="Polandia" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Cl%C3%A0udi_Tolom%C3%A9" title="Clàudi Tolomé – Piedmontese" lang="pms" hreflang="pms" data-title="Clàudi Tolomé" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A8%D8%B7%D9%84%DB%8C%D9%85%D9%88%D8%B3" title="بطلیموس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="بطلیموس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A8%D8%B7%D9%84%D9%85%DB%8C%D9%88%D8%B3" title="بطلمیوس – Pashto" lang="ps" hreflang="ps" data-title="بطلمیوس" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ptolemeu" title="Ptolemeu – Portugis" lang="pt" hreflang="pt" data-title="Ptolemeu" data-language-autonym="Português" data-language-local-name="Portugis" 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/Ptolemeu" title="Ptolemeu – Rumania" lang="ro" hreflang="ro" data-title="Ptolemeu" data-language-autonym="Română" data-language-local-name="Rumania" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-roa-rup mw-list-item"><a href="https://roa-rup.wikipedia.org/wiki/Claudius_Ptolemeu" title="Claudius Ptolemeu – Aromanian" lang="rup" hreflang="rup" data-title="Claudius Ptolemeu" data-language-autonym="Armãneashti" data-language-local-name="Aromanian" class="interlanguage-link-target"><span>Armãneashti</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8%D0%B9_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавдий Птолемей – Rusia" lang="ru" hreflang="ru" data-title="Клавдий Птолемей" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8%D0%B9_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавдий Птолемей – Rusyn" lang="rue" hreflang="rue" data-title="Клавдий Птолемей" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8%D0%B9_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавдий Птолемей – Yakut" lang="sah" hreflang="sah" data-title="Клавдий Птолемей" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Tulumeu" title="Tulumeu – Sisilia" lang="scn" hreflang="scn" data-title="Tulumeu" data-language-autonym="Sicilianu" data-language-local-name="Sisilia" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Ptolemy" title="Ptolemy – Skots" lang="sco" hreflang="sco" data-title="Ptolemy" data-language-autonym="Scots" data-language-local-name="Skots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A8%D8%B7%D9%84%D9%8A%D9%85%D9%88%D8%B3" title="بطليموس – Sindhi" lang="sd" hreflang="sd" data-title="بطليموس" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Klaudije_Ptolomej" title="Klaudije Ptolomej – Serbo-Kroasia" lang="sh" hreflang="sh" data-title="Klaudije Ptolomej" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Kroasia" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Ptolemy" title="Ptolemy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Ptolemy" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Klaudios_Ptolemaios" title="Klaudios Ptolemaios – Slowakia" lang="sk" hreflang="sk" data-title="Klaudios Ptolemaios" data-language-autonym="Slovenčina" data-language-local-name="Slowakia" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Ptolemaj" title="Ptolemaj – Slovenia" lang="sl" hreflang="sl" data-title="Ptolemaj" data-language-autonym="Slovenščina" data-language-local-name="Slovenia" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Ptolemeu" title="Ptolemeu – Albania" lang="sq" hreflang="sq" data-title="Ptolemeu" data-language-autonym="Shqip" data-language-local-name="Albania" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D1%83%D0%B4%D0%B8%D1%98%D0%B5_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D1%98" title="Клаудије Птолемеј – Serbia" lang="sr" hreflang="sr" data-title="Клаудије Птолемеј" data-language-autonym="Српски / srpski" data-language-local-name="Serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Klaudios_Ptolemaios" title="Klaudios Ptolemaios – Swedia" lang="sv" hreflang="sv" data-title="Klaudios Ptolemaios" data-language-autonym="Svenska" data-language-local-name="Swedia" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Klaudio_Ptolemaio" title="Klaudio Ptolemaio – Swahili" lang="sw" hreflang="sw" data-title="Klaudio Ptolemaio" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%8A%E0%AE%B2%E0%AF%86%E0%AE%AE%E0%AE%BF" title="தொலெமி – Tamil" lang="ta" hreflang="ta" data-title="தொலெமி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%9F%E0%B1%8B%E0%B0%B2%E0%B1%86%E0%B0%AE%E0%B1%80" title="టోలెమీ – Telugu" lang="te" hreflang="te" data-title="టోలెమీ" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%91%D0%B0%D1%82%D0%BB%D0%B0%D0%BC%D0%B8%D1%8E%D1%81" title="Батламиюс – Tajik" lang="tg" hreflang="tg" data-title="Батламиюс" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%81%E0%B8%A5%E0%B8%B2%E0%B8%94%E0%B8%B5%E0%B9%82%E0%B8%AD%E0%B8%AA_%E0%B8%9B%E0%B9%82%E0%B8%95%E0%B9%80%E0%B8%A5%E0%B9%84%E0%B8%A1%E0%B9%82%E0%B8%AD%E0%B8%AA" title="เกลาดีโอส ปโตเลไมโอส – Thailand" lang="th" hreflang="th" data-title="เกลาดีโอส ปโตเลไมโอส" data-language-autonym="ไทย" data-language-local-name="Thailand" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Ptolomeo" title="Ptolomeo – Tagalog" lang="tl" hreflang="tl" data-title="Ptolomeo" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Batlamyus" title="Batlamyus – Turki" lang="tr" hreflang="tr" data-title="Batlamyus" data-language-autonym="Türkçe" data-language-local-name="Turki" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D0%B8%D0%B9_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавдий Птолемей – Tatar" lang="tt" hreflang="tt" data-title="Клавдий Птолемей" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D0%B2%D0%B4%D1%96%D0%B9_%D0%9F%D1%82%D0%BE%D0%BB%D0%B5%D0%BC%D0%B5%D0%B9" title="Клавдій Птолемей – Ukraina" lang="uk" hreflang="uk" data-title="Клавдій Птолемей" data-language-autonym="Українська" data-language-local-name="Ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%D8%B7%D9%84%DB%8C%D9%85%D9%88%D8%B3" title="بطلیموس – Urdu" lang="ur" hreflang="ur" data-title="بطلیموس" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ptolemey_Klavdiy" title="Ptolemey Klavdiy – Uzbek" lang="uz" hreflang="uz" data-title="Ptolemey Klavdiy" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Claudius_Ptolemaeus" title="Claudius Ptolemaeus – Vietnam" lang="vi" hreflang="vi" data-title="Claudius Ptolemaeus" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnam" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Ptolemy" title="Ptolemy – Warai" lang="war" hreflang="war" data-title="Ptolemy" data-language-autonym="Winaray" data-language-local-name="Warai" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%85%8B%E5%8A%B3%E7%8B%84%E4%B9%8C%E6%96%AF%C2%B7%E6%89%98%E5%8B%92%E5%AF%86" title="克劳狄乌斯·托勒密 – Tyonghwa Wu" lang="wuu" hreflang="wuu" data-title="克劳狄乌斯·托勒密" data-language-autonym="吴语" data-language-local-name="Tyonghwa Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%9E%E1%83%A2%E1%83%9D%E1%83%9A%E1%83%94%E1%83%9B%E1%83%94" title="პტოლემე – Mingrelian" lang="xmf" hreflang="xmf" data-title="პტოლემე" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%85%8B%E5%8A%B3%E7%8B%84%E4%B9%8C%E6%96%AF%C2%B7%E6%89%98%E5%8B%92%E5%AF%86" title="克劳狄乌斯·托勒密 – Tyonghwa" lang="zh" hreflang="zh" data-title="克劳狄乌斯·托勒密" data-language-autonym="中文" data-language-local-name="Tyonghwa" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%89%98%E5%8B%92%E5%AF%86" title="托勒密 – Kanton" lang="yue" hreflang="yue" data-title="托勒密" data-language-autonym="粵語" data-language-local-name="Kanton" class="interlanguage-link-target"><span>粵語</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/Q34943#sitelinks-wikipedia" title="Besut pranala antarabasa" class="wbc-editpage">Besut pranala</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="Mandhala aran"> <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/Claudius_Ptolemaeus" title="Deleng kaca 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Wikipédia Jawa, bauwarna mardika basa Jawa</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="jv" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r1616449">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}body.skin-minerva .mw-parser-output .infobox-header,body.skin-minerva .mw-parser-output .infobox-subheader,body.skin-minerva .mw-parser-output .infobox-above,body.skin-minerva .mw-parser-output .infobox-title,body.skin-minerva .mw-parser-output .infobox-image,body.skin-minerva .mw-parser-output .infobox-full-data,body.skin-minerva .mw-parser-output .infobox-below{text-align:center}.mw-parser-output .infobox{border:1px solid 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.infobox-header,.mw-parser-output .infobox .infobox-subheader,.mw-parser-output .infobox .infobox-image,.mw-parser-output .infobox .infobox-full-data,.mw-parser-output .infobox .infobox-below{text-align:center}.mw-parser-output .infobox .infobox-navbar{text-align:right}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above"><span class="fn">Ptolemeus</span></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/Barkas:Ptolemy_1476_with_armillary_sphere_model.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Ptolemy_1476_with_armillary_sphere_model.jpg/220px-Ptolemy_1476_with_armillary_sphere_model.jpg" decoding="async" width="220" height="324" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Ptolemy_1476_with_armillary_sphere_model.jpg/330px-Ptolemy_1476_with_armillary_sphere_model.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Ptolemy_1476_with_armillary_sphere_model.jpg/440px-Ptolemy_1476_with_armillary_sphere_model.jpg 2x" data-file-width="1020" data-file-height="1500" /></a></span><div class="infobox-caption">Potret Ptolemeus déning <a href="/w/index.php?title=Justus_van_Gent&action=edit&redlink=1" class="new" title="Justus van Gent (kaca ora ana)">Justus van Gent</a> lan <a href="/w/index.php?title=Pedro_Berruguete&action=edit&redlink=1" class="new" title="Pedro Berruguete (kaca ora ana)">Pedro Berruguete</a> (taun 1476)</div></td></tr><tr><th scope="row" class="infobox-label">Jeneng lair</th><td class="infobox-data"><span class="nickname">Κλαύδιος Πτολεμαῖος</span></td></tr><tr><th scope="row" class="infobox-label">Lair</th><td class="infobox-data"><abbr title="udakara">u.</abbr> 100 Masehi<sup id="cite_ref-britannica.com_1-0" class="reference"><a href="#cite_note-britannica.com-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><br /><span class="birthplace"><a href="/w/index.php?title=Egypt_(Roman_province)&action=edit&redlink=1" class="new" title="Egypt (Roman province) (kaca ora ana)">Mesir</a>, Kekaisaran Romawi</span></td></tr><tr><th scope="row" class="infobox-label">Pati</th><td class="infobox-data"><abbr title="udakara">u.</abbr><span style="white-space:nowrap;"> 170 (yuswa 69–70) Masehi</span><sup id="cite_ref-britannica.com_1-1" class="reference"><a href="#cite_note-britannica.com-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><br /><span class="deathplace"><a href="/wiki/Alexandria" title="Alexandria">Alexandria</a>, Mesir, Kekaisaran Romawi</span></td></tr><tr><th scope="row" class="infobox-label">Warga nagara</th><td class="infobox-data category"><a href="/wiki/Romawi" class="mw-disambig" title="Romawi">Romawi</a>; etnik: Greko-Mesir</td></tr><tr><th scope="row" class="infobox-label">Kondhang ing</th><td class="infobox-data"><a href="/w/index.php?title=Ptolemaic_universe&action=edit&redlink=1" class="new" title="Ptolemaic universe (kaca ora ana)">Ptolemaic universe</a><br /><a href="/w/index.php?title=Ptolemeus%27s_world_map&action=edit&redlink=1" class="new" title="Ptolemeus's world map (kaca ora ana)">Ptolemeus's world map</a><br /><a href="/w/index.php?title=Ptolemeus%27s_intense_diatonic_scale&action=edit&redlink=1" class="new" title="Ptolemeus's intense diatonic scale (kaca ora ana)">Ptolemeus's intense diatonic scale</a><br /><a href="/w/index.php?title=Ptolemeus%27s_table_of_chords&action=edit&redlink=1" class="new" title="Ptolemeus's table of chords (kaca ora ana)">Ptolemeus's table of chords</a><br /><a href="/w/index.php?title=Ptolemeus%27s_inequality&action=edit&redlink=1" class="new" title="Ptolemeus's inequality (kaca ora ana)">Ptolemeus's inequality</a><br /><a href="/w/index.php?title=Ptolemic%27s_theorem&action=edit&redlink=1" class="new" title="Ptolemic's theorem (kaca ora ana)">Ptolemic's theorem</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1616449" /><b>Karièr ngèlmiah</b></td></tr><tr><th scope="row" class="infobox-label">Babagan</th><td class="infobox-data category"><a href="/wiki/Astronomi" title="Astronomi">Astronomi</a>, <a href="/wiki/Geografi" class="mw-redirect" title="Geografi">Geografi</a>, <a href="/wiki/Astrologi" title="Astrologi">Astrologi</a>, <a href="/wiki/Optika" title="Optika">Optika</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Claudius Ptolemeus</b> (<span class="nowrap"><span class="IPA nopopups"><a href="https://en.wikipedia.org/wiki/Help:IPA_for_English" class="extiw" title="en:Help:IPA for English">/<span style="border-bottom:1px dotted"><span title="/ˈ/ strès kapisan">ˈ</span><span title="'t' ing 'tie'">t</span><span title="/ɒ/ 'o' cendhek ing 'body'">ɒ</span><span title="'l' ing 'lie'">l</span><span title="/ə/ 'a' ing 'about'">ə</span><span title="'m' ing 'my'">m</span><span title="/i/ 'y' ing 'happy'">i</span></span>/</a></span></span>; <a href="/wiki/Basa_Yunani" class="mw-redirect" title="Basa Yunani">Yunani</a>: <span lang="grc"><a href="https://jv.wiktionary.org/wiki/%CE%A0%CF%84%CE%BF%CE%BB%CE%B5%CE%BC%CE%B1%E1%BF%96%CE%BF%CF%82" class="extiw" title="wikt:Πτολεμαῖος">Πτολεμαῖος</a></span>, <a href="/w/index.php?title=Cithakan:Transliteration&action=edit&redlink=1" class="new" title="Cithakan:Transliteration (kaca ora ana)">Cithakan:Transliteration</a>; <a href="/wiki/Basa_Latin" title="Basa Latin">Latin</a>: <span lang="la"><i>Claudius Ptolemaeus</i></span>; <abbr title="udakara">u.</abbr><span style="white-space:nowrap;"> 100</span> – c.<span style="white-space:nowrap;"> 170</span> AD)<sup id="cite_ref-britannica.com_1-2" class="reference"><a href="#cite_note-britannica.com-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> punika salah satunggaling ahli matematika, ahli astronomi, ahli astrologi, ahli geografi, miwah teoritisi musik<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> ingkang asalipun saking Alexandria. Ptolemeus nyerataken sepisanan buku-buku ilmiah ingkang saget ngudi kawruh. Telung saking buku-buku punika gadhah kautaman kanggé ilmu pengetahuan ing peradaban Roma <a href="/w/index.php?title=Byzantine&action=edit&redlink=1" class="new" title="Byzantine (kaca ora ana)">Byzantine</a>, <a href="/w/index.php?title=Peradaban_Islam&action=edit&redlink=1" class="new" title="Peradaban Islam (kaca ora ana)">Islam</a>, lan <a href="/wiki/%C3%89ropa_Kulon" title="Éropa Kulon">Eropa Kulon</a>. Serat ingkang pisanan penting punika aslinipun kaserat kanthi irah-irahan <i>Mathēmatikē Syntaxis utawi</i> "Serat Matematika", nanging sapunika dipunsebat <i>Almagest</i> utawi "Serat Ageng". Punika serat astronomi. Serat ingkang kaping kalih ingkang wigati punika <i>Geography</i>, serat ingkang ngrembakan babagan peta lan kawruh geografi ing jagad Greco-Roman. Serat ingkang kaping tiga wigati nyobi nyocogaken astrologi horoskopik kaliyan filsafat alam <a href="/wiki/Aristoteles" class="mw-redirect" title="Aristoteles">Aristoteles</a>. Asring dipunsebat <i>Apotelesmatika</i> ("Babagan Efek") nanging luwih kondhang kanthi nama <i>Tetrábiblos</i> ("Papat Buku") utawi ing basa Latin Quadripartite. </p> <div class="mw-heading mw-heading2"><h2 id="Jagad_Ptolemaic">Jagad Ptolemaic</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Claudius_Ptolemaeus&veaction=edit&section=1" title="Besut pérangan: Jagad Ptolemaic" class="mw-editsection-visualeditor"><span>besut</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Claudius_Ptolemaeus&action=edit&section=1" title="Sunting kode sumber bagian: Jagad Ptolemaic"><span>besut sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sistem Jagad Ptolemaic inggih punika model geosentris, ingkang ngandharaken <a href="/wiki/Bumi" title="Bumi">bumi</a> wonten ing tengah-tengahing <a href="/wiki/Jagat" class="mw-redirect" title="Jagat">jagad raya</a>. Sistem punika ngginakaken sepasang balungbung (<a href="/wiki/Lingkaran" class="mw-redirect" title="Lingkaran">lingkaran</a>) kangge saben planet kangge nerangaken gerakanipun. Balungbung ingkang langkung jangkep dipunwastani <a href="/w/index.php?title=Deferent&action=edit&redlink=1" class="new" title="Deferent (kaca ora ana)">deferent</a>. Tengahing deferent, ingkang dipunwastani eksentrik (dipuntandhani minangka X), wonten ing panggenan ingkang adoh saking bumi. Tujuanipun eksentrik menika kangge maringi penjelasan dhateng panjangipun <a href="/w/index.php?title=Musim&action=edit&redlink=1" class="new" title="Musim (kaca ora ana)">musim</a> ingkang boten rata kanthi nggeser bumi saking tengah. Balungbung ingkang langkung alit, ingkang dipunwastani <a href="/w/index.php?title=Episiklus&action=edit&redlink=1" class="new" title="Episiklus (kaca ora ana)">episiklus</a>, lebet ing deferent. Planet-planet bergerak sabudeureun episiklus, lan episiklus punika ugi bergerak ngelilingi deferent. Gerakan gabungan punika nggawe planet katingal maju cepet, alon, mandeg, mbaleni arah, lan nerusaken arah normal saking pandangan bumi. Punika nerangaken fenomena <a href="/w/index.php?title=Gerakan_retrograde&action=edit&redlink=1" class="new" title="Gerakan retrograde (kaca ora ana)">gerakan retrograde</a> saking planet ingkang katingal. </p> <div class="mw-heading mw-heading2"><h2 id="Teorema_Ptolemaic">Teorema Ptolemaic</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Claudius_Ptolemaeus&veaction=edit&section=2" title="Besut pérangan: Teorema Ptolemaic" class="mw-editsection-visualeditor"><span>besut</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Claudius_Ptolemaeus&action=edit&section=2" title="Sunting kode sumber bagian: Teorema Ptolemaic"><span>besut sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ing <a href="/w/index.php?title=Geometri_Euclidean&action=edit&redlink=1" class="new" title="Geometri Euclidean (kaca ora ana)">Geometri Euclidean</a>, <b>Teorema Ptolemeus</b> punika sesambetan antawisipun sakawan sisih lan kalih diagonal ing <a href="/w/index.php?title=Kuadrilateral_siklik&action=edit&redlink=1" class="new" title="Kuadrilateral siklik (kaca ora ana)">kuadrilateral siklik</a> (kuadrilateral ingkang <a href="/w/index.php?title=Titik_(geometri)&action=edit&redlink=1" class="new" title="Titik (geometri) (kaca ora ana)">titik-titikipun</a> wonten ing lingkaran ingkang sami). Teorema punika asesirahaken adhedhasar <a href="/wiki/Yunani" class="mw-redirect" title="Yunani">Yunani</a> <a href="/wiki/Astronom" title="Astronom">astronom</a> lan <a href="/w/index.php?title=Matematikawan&action=edit&redlink=1" class="new" title="Matematikawan (kaca ora ana)">matematikawan</a> <a href="/wiki/Ptolemeus" class="mw-redirect" title="Ptolemeus">Ptolemeus</a> (Claudius Ptolemeus).<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Ptolemeus ngginakaken teorema punika minangka pirantos kanggé nyipta <a href="/w/index.php?title=Tabel_tali_busur_Ptolemeus&action=edit&redlink=1" class="new" title="Tabel tali busur Ptolemeus (kaca ora ana)">tabel tali busurnipun</a>, tabel trigonometri ingkang dipunlampahi dhateng astronomi. </p><p>Manawi titik-titik kuadrilateral siklik punika 'A', 'B', 'C', lan 'D' sacara urut, lalu teorema punika nyebataken: </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 AC\cdot BD=AB\cdot CD+BC\cdot AD}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>C</mi> <mo>⋅</mo> <mi>B</mi> <mi>D</mi> <mo>=</mo> <mi>A</mi> <mi>B</mi> <mo>⋅</mo> <mi>C</mi> <mi>D</mi> <mo>+</mo> <mi>B</mi> <mi>C</mi> <mo>⋅</mo> <mi>A</mi> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle AC\cdot BD=AB\cdot CD+BC\cdot AD}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1a3355d706c67c614eed4dc8362f492cb1c6923" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:32.569ex; height:2.343ex;" alt="{\displaystyle AC\cdot BD=AB\cdot CD+BC\cdot AD}" /></span></dd></dl> <p>Hubungan punika saged dipunwastani kanthi lisan kados punika: </p> <dl><dd><i>Menawi kuadrilateral punika <a href="/w/index.php?title=Kuadrilateral_Siklik&action=edit&redlink=1" class="new" title="Kuadrilateral Siklik (kaca ora ana)">siklik</a> lalu peparabipun dawa diagonalipun sami kali kaliyan jumlah peparabipun dawa pasangan sisih ingkang sabalik-balik.</i></dd></dl> <p>Langkung malih, <a href="/w/index.php?title=Konvers&action=edit&redlink=1" class="new" title="Konvers (kaca ora ana)">konvers</a> saking Teorema Ptolemeus ugi leres: </p> <dl><dd><i>Ing kuadrilateral, menawi jumlah peparabipun dawa rong pasangan sisih ingkang sabalik-balik sami kali kaliyan peparabipun dawa diagonalipun, mila kuadrilateral wau saged dipunsketsa wonten ing lingkaran, tegesipun kuadrilateral punika siklik.</i></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Sitiran">Sitiran</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Claudius_Ptolemaeus&veaction=edit&section=3" title="Besut pérangan: Sitiran" class="mw-editsection-visualeditor"><span>besut</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Claudius_Ptolemaeus&action=edit&section=3" title="Sunting kode sumber bagian: Sitiran"><span>besut sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-britannica.com-1"><span class="mw-cite-backlink">↑ <a href="#cite_ref-britannica.com_1-0"><sup>a</sup></a> <a href="#cite_ref-britannica.com_1-1"><sup>b</sup></a> <a href="#cite_ref-britannica.com_1-2"><sup>c</sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.britannica.com/EBchecked/topic/482098">Ptolemeus</a> ing <i><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Encyclopædia Britannica</a></i></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1706644">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFRichter2001" class="citation encyclopaedia cs1">Richter, Lukas (2001). <span class="cs1-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.oxfordmusiconline.com/grovemusic/view/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e-0000022510">"Ptolemeus"</a></span>. <i><a href="/w/index.php?title=Grove_Music_Online&action=edit&redlink=1" class="new" title="Grove Music Online (kaca ora ana)">Grove Music Online</a></i>. Oxford: <a href="/w/index.php?title=Oxford_University_Press&action=edit&redlink=1" class="new" title="Oxford University Press (kaca ora ana)">Oxford University Press</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgmo%2F9781561592630.article.22510">10.1093/gmo/9781561592630.article.22510</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Mirunggan:Sumber_buku/978-1-56159-263-0" title="Mirunggan:Sumber buku/978-1-56159-263-0"><bdi>978-1-56159-263-0</bdi></a><span class="reference-accessdate">. Dibukak ing <span class="nowrap">25 September</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Ptolemeus&rft.btitle=Grove+Music+Online&rft.place=Oxford&rft.pub=Oxford+University+Press&rft.date=2001&rft_id=info%3Adoi%2F10.1093%2Fgmo%2F9781561592630.article.22510&rft.isbn=978-1-56159-263-0&rft.aulast=Richter&rft.aufirst=Lukas&rft_id=https%3A%2F%2Fwww.oxfordmusiconline.com%2Fgrovemusic%2Fview%2F10.1093%2Fgmo%2F9781561592630.001.0001%2Fomo-9781561592630-e-0000022510&rfr_id=info%3Asid%2Fjv.wikipedia.org%3AClaudius+Ptolemaeus" class="Z3988"></span> <a href="/w/index.php?title=Cithakan:Grove_Music_subscription&action=edit&redlink=1" class="new" title="Cithakan:Grove Music subscription (kaca ora ana)">Cithakan:Grove Music subscription</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">C. Ptolemeus, <a href="/w/index.php?title=Almagest&action=edit&redlink=1" class="new" title="Almagest (kaca ora ana)">Almagest</a>, Kitab 1, Bab 10.</span> </li> </ol>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Dijupuk saka "<a dir="ltr" href="https://jv.wikipedia.org/w/index.php?title=Claudius_Ptolemaeus&oldid=1668279">https://jv.wikipedia.org/w/index.php?title=Claudius_Ptolemaeus&oldid=1668279</a>"</div></div> <div id="catlinks" class="catlinks catlinks-allhidden" data-mw="interface"><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Kategori ndhelik: <ul><li><a href="/wiki/Kategori:Artikel_mawa_hCards" title="Kategori:Artikel mawa hCards">Artikel mawa hCards</a></li><li><a href="/wiki/Kategori:Artikel_ngandhut_cithakan_basa_ISO_639_sing_ora_kaweruhan" title="Kategori:Artikel ngandhut cithakan basa ISO 639 sing ora kaweruhan">Artikel ngandhut cithakan basa ISO 639 sing ora kaweruhan</a></li><li><a href="/wiki/Kategori:Artikel_ngandhut_tulisan_abasa_Latin" title="Kategori:Artikel ngandhut tulisan abasa Latin">Artikel ngandhut tulisan abasa Latin</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Kaca iki pungkasan diowah nalika 18.59, 20 Januari 2024.</li> <li id="footer-info-copyright">Tèks iki cumepak kanthi <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Lisènsi Atribusi-DumSaèmper Creative Commons</a>; paugeran tambahan bokmanawa uga lumaku. 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