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Tilgjengelig på 66 språk" > <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-66" 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">66 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Apollonios_fr%C3%A5_Perga" title="Apollonios frå Perga – norsk nynorsk" lang="nn" hreflang="nn" data-title="Apollonios frå Perga" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Apollonius" title="Apollonius – dansk" lang="da" hreflang="da" data-title="Apollonius" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Apollonios_fr%C3%A5n_Perga" title="Apollonios från Perga – svensk" lang="sv" hreflang="sv" data-title="Apollonios från Perga" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Apollon%C3%ADos_fr%C3%A1_Perga" title="Apolloníos frá Perga – islandsk" lang="is" hreflang="is" data-title="Apolloníos frá Perga" data-language-autonym="Íslenska" data-language-local-name="islandsk" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A3%D8%A8%D9%84%D9%88%D9%86%D9%8A%D9%88%D8%B3_%D8%A7%D9%84%D8%A8%D8%B1%D8%BA%D8%A7%D9%88%D9%8A" title="أبلونيوس البرغاوي – arabisk" lang="ar" hreflang="ar" data-title="أبلونيوس البرغاوي" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Apolonio_de_Perge" title="Apolonio de Perge – asturisk" lang="ast" hreflang="ast" data-title="Apolonio de Perge" data-language-autonym="Asturianu" data-language-local-name="asturisk" 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/Perqal%C4%B1_Apolloni" title="Perqalı Apolloni – aserbajdsjansk" lang="az" hreflang="az" data-title="Perqalı Apolloni" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%87%E0%A6%B0%E0%A6%97%E0%A6%BE-%E0%A6%B0_%E0%A6%86%E0%A6%AA%E0%A7%8B%E0%A6%B2%E0%A7%8D%E0%A6%B2%E0%A7%8B%E0%A6%A8%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A7%81%E0%A6%B8" title="পেরগা-র আপোল্লোনিয়ুস – bengali" lang="bn" hreflang="bn" data-title="পেরগা-র আপোল্লোনিয়ুস" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%BF%D0%B0%D0%BB%D0%BE%D0%BD%D1%96%D0%B9_%D0%9F%D0%B5%D1%80%D0%B3%D1%81%D0%BA%D1%96" title="Апалоній Пергскі – belarusisk" lang="be" hreflang="be" data-title="Апалоній Пергскі" data-language-autonym="Беларуская" data-language-local-name="belarusisk" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%BF%D0%BE%D0%BB%D0%BE%D0%BD%D0%B8%D0%B9_%D0%9F%D0%B5%D1%80%D0%B3%D1%81%D0%BA%D0%B8" title="Аполоний Пергски – bulgarsk" lang="bg" hreflang="bg" data-title="Аполоний Пергски" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Apol%C2%B7loni_de_Perge" title="Apol·loni de Perge – katalansk" lang="ca" hreflang="ca" data-title="Apol·loni de Perge" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Apoll%C3%B3nios_z_Pergy" title="Apollónios z Pergy – tsjekkisk" lang="cs" hreflang="cs" data-title="Apollónios z Pergy" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Apollonios_von_Perge" title="Apollonios von Perge – tysk" lang="de" hreflang="de" data-title="Apollonios von Perge" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Apollonios_Pergest" title="Apollonios Pergest – estisk" lang="et" hreflang="et" data-title="Apollonios Pergest" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%80%CE%BF%CE%BB%CE%BB%CF%8E%CE%BD%CE%B9%CE%BF%CF%82_%CE%BF_%CE%A0%CE%B5%CF%81%CE%B3%CE%B1%CE%AF%CE%BF%CF%82" title="Απολλώνιος ο Περγαίος – gresk" lang="el" hreflang="el" data-title="Απολλώνιος ο Περγαίος" data-language-autonym="Ελληνικά" data-language-local-name="gresk" 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/Apollonius_of_Perga" title="Apollonius of Perga – engelsk" lang="en" hreflang="en" data-title="Apollonius of Perga" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Apolonio_de_Perge" title="Apolonio de Perge – spansk" lang="es" hreflang="es" data-title="Apolonio de Perge" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Apolonio_de_Pergo" title="Apolonio de Pergo – esperanto" lang="eo" hreflang="eo" data-title="Apolonio de Pergo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Apolonio_Pergakoa" title="Apolonio Pergakoa – baskisk" lang="eu" hreflang="eu" data-title="Apolonio Pergakoa" data-language-autonym="Euskara" data-language-local-name="baskisk" 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%A2%D9%BE%D9%88%D9%84%D9%88%D9%86%DB%8C%D9%88%D8%B3" title="آپولونیوس – persisk" lang="fa" hreflang="fa" data-title="آپولونیوس" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Apollonios_de_Perga" title="Apollonios de Perga – fransk" lang="fr" hreflang="fr" data-title="Apollonios de Perga" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Apolonio_de_Perge" title="Apolonio de Perge – galisisk" lang="gl" hreflang="gl" data-title="Apolonio de Perge" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8E%98%EB%A5%B4%EA%B2%8C%EC%9D%98_%EC%95%84%ED%8F%B4%EB%A1%9C%EB%8B%88%EC%98%A4%EC%8A%A4" title="페르게의 아폴로니오스 – koreansk" lang="ko" hreflang="ko" data-title="페르게의 아폴로니오스" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Apollonius_na_Perga" title="Apollonius na Perga – hausa" lang="ha" hreflang="ha" data-title="Apollonius na Perga" data-language-autonym="Hausa" data-language-local-name="hausa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%BA%D5%B8%D5%AC%D5%AC%D5%B8%D5%B6%D5%AB%D5%B8%D5%BD_%D5%8A%D5%A5%D6%80%D5%A3%D5%A1%D6%81%D5%AB" title="Ապոլլոնիոս Պերգացի – armensk" lang="hy" hreflang="hy" data-title="Ապոլլոնիոս Պերգացի" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%8F%E0%A4%AA%E0%A5%8B%E0%A4%B2%E0%A5%8B%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%B8" title="एपोलोनियस – hindi" lang="hi" hreflang="hi" data-title="एपोलोनियस" data-language-autonym="हिन्दी" data-language-local-name="hindi" 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/Apolonije_iz_Perge" title="Apolonije iz Perge – kroatisk" lang="hr" hreflang="hr" data-title="Apolonije iz Perge" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Apollonius_dari_Perga" title="Apollonius dari Perga – indonesisk" lang="id" hreflang="id" data-title="Apollonius dari Perga" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Apollonio_di_Perga" title="Apollonio di Perga – italiensk" lang="it" hreflang="it" data-title="Apollonio di Perga" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A4%D7%95%D7%9C%D7%95%D7%A0%D7%99%D7%95%D7%A1_%D7%9E%D7%A4%D7%A8%D7%92%D7%94" title="אפולוניוס מפרגה – hebraisk" lang="he" hreflang="he" data-title="אפולוניוס מפרגה" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%BF%D0%BE%D0%BB%D0%BB%D0%BE%D0%BD%D0%B8%D1%83%D1%81" title="Аполлониус – kasakhisk" lang="kk" hreflang="kk" data-title="Аполлониус" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Apolonios" title="Apolonios – kurdisk" lang="ku" hreflang="ku" data-title="Apolonios" data-language-autonym="Kurdî" data-language-local-name="kurdisk" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Apollonius_Pergaeus" title="Apollonius Pergaeus – latin" lang="la" hreflang="la" data-title="Apollonius Pergaeus" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Apolonijas_Pergietis" title="Apolonijas Pergietis – litauisk" lang="lt" hreflang="lt" data-title="Apolonijas Pergietis" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Pergai_Apoll%C3%B3niosz" title="Pergai Apollóniosz – ungarsk" lang="hu" hreflang="hu" data-title="Pergai Apollóniosz" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Apollonios_de_Perga" title="Apollonios de Perga – gassisk" lang="mg" hreflang="mg" data-title="Apollonios de Perga" data-language-autonym="Malagasy" data-language-local-name="gassisk" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B5%8B%E0%B4%B3%E0%B5%8B%E0%B4%A3%E0%B4%BF%E0%B4%AF%E0%B4%B8%E0%B5%8D" title="അപ്പോളോണിയസ് – malayalam" lang="ml" hreflang="ml" data-title="അപ്പോളോണിയസ്" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%AA%E0%A5%8B%E0%A4%B2%E0%A5%8B%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%B8_(%E0%A4%AA%E0%A5%87%E0%A4%B0%E0%A5%8D%E0%A4%97%E0%A4%BE)" title="अपोलोनियस (पेर्गा) – marathi" lang="mr" hreflang="mr" data-title="अपोलोनियस (पेर्गा)" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D8%A8%D9%88%D9%84%D9%88%D9%86%D9%8A%D9%88%D8%B3" title="ابولونيوس – egyptisk arabisk" lang="arz" hreflang="arz" data-title="ابولونيوس" data-language-autonym="مصرى" data-language-local-name="egyptisk arabisk" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Apollonius_van_Perga" title="Apollonius van Perga – nederlandsk" lang="nl" hreflang="nl" data-title="Apollonius van Perga" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9A%E3%83%AB%E3%82%AC%E3%81%AE%E3%82%A2%E3%83%9D%E3%83%AD%E3%83%8B%E3%82%A6%E3%82%B9" title="ペルガのアポロニウス – japansk" lang="ja" hreflang="ja" data-title="ペルガのアポロニウス" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Apolloniy_pergayos" title="Apolloniy pergayos – usbekisk" lang="uz" hreflang="uz" data-title="Apolloniy pergayos" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%AA%E0%A9%8B%E0%A8%B2%E0%A9%8B%E0%A8%A8%E0%A9%80%E0%A8%85%E0%A8%B8" title="ਅਪੋਲੋਨੀਅਸ – panjabi" lang="pa" hreflang="pa" data-title="ਅਪੋਲੋਨੀਅਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Apol%C3%B2ni" title="Apolòni – piemontesisk" lang="pms" hreflang="pms" data-title="Apolòni" data-language-autonym="Piemontèis" data-language-local-name="piemontesisk" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Apoloniusz_z_Pergi" title="Apoloniusz z Pergi – polsk" lang="pl" hreflang="pl" data-title="Apoloniusz z Pergi" data-language-autonym="Polski" data-language-local-name="polsk" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Apol%C3%B4nio_de_Perga" title="Apolônio de Perga – portugisisk" lang="pt" hreflang="pt" data-title="Apolônio de Perga" data-language-autonym="Português" data-language-local-name="portugisisk" 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/Apoloniu_din_Perga" title="Apoloniu din Perga – rumensk" lang="ro" hreflang="ro" data-title="Apoloniu din Perga" data-language-autonym="Română" data-language-local-name="rumensk" 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%90%D0%BF%D0%BE%D0%BB%D0%BB%D0%BE%D0%BD%D0%B8%D0%B9_%D0%9F%D0%B5%D1%80%D0%B3%D1%81%D0%BA%D0%B8%D0%B9" title="Аполлоний Пергский – russisk" lang="ru" hreflang="ru" data-title="Аполлоний Пергский" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Apollonius_o_Perga" title="Apollonius o Perga – skotsk" lang="sco" hreflang="sco" data-title="Apollonius o Perga" data-language-autonym="Scots" data-language-local-name="skotsk" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Apolloni_i_Perg%C3%ABs" title="Apolloni i Pergës – albansk" lang="sq" hreflang="sq" data-title="Apolloni i Pergës" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Apollonius_of_Perga" title="Apollonius of Perga – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Apollonius of Perga" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Apolonij" title="Apolonij – slovensk" lang="sl" hreflang="sl" data-title="Apolonij" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%D8%A7%D9%BE%DB%86%D9%84%DB%86%D9%86%DB%8C%D9%88%D8%B3" title="ئاپۆلۆنیوس – sentralkurdisk" lang="ckb" hreflang="ckb" data-title="ئاپۆلۆنیوس" data-language-autonym="کوردی" data-language-local-name="sentralkurdisk" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BF%D0%BE%D0%BB%D0%BE%D0%BD%D0%B8%D1%98%D0%B5" title="Аполоније – serbisk" lang="sr" hreflang="sr" data-title="Аполоније" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Apolonije_iz_Pergama" title="Apolonije iz Pergama – serbokroatisk" lang="sh" hreflang="sh" data-title="Apolonije iz Pergama" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Apollonius_ti_Perga" title="Apollonius ti Perga – sundanesisk" lang="su" hreflang="su" data-title="Apollonius ti Perga" data-language-autonym="Sunda" data-language-local-name="sundanesisk" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Apollonios_Pergel%C3%A4inen" title="Apollonios Pergeläinen – finsk" lang="fi" hreflang="fi" data-title="Apollonios Pergeläinen" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%8B%E0%AE%B2%E0%AF%8B%E0%AE%A9%E0%AE%BF%E0%AE%AF%E0%AE%B8%E0%AF%8D" title="அப்போலோனியஸ் – tamil" lang="ta" hreflang="ta" data-title="அப்போலோனியஸ்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%BF%D0%BE%D0%BB%D0%BB%D0%BE%D0%BD%D0%B8_%D0%9F%D0%B5%D1%80%D0%B3%D3%A3" title="Аполлони Пергӣ – tadsjikisk" lang="tg" hreflang="tg" data-title="Аполлони Пергӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="tadsjikisk" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Apollonios_(Pergeli_matematik%C3%A7i)" title="Apollonios (Pergeli matematikçi) – tyrkisk" lang="tr" hreflang="tr" data-title="Apollonios (Pergeli matematikçi)" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" 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%90%D0%BF%D0%BE%D0%BB%D0%BB%D0%BE%D0%BD%D1%96%D0%B9_%D0%9F%D0%B5%D1%80%D0%B7%D1%8C%D0%BA%D0%B8%D0%B9" title="Аполлоній Перзький – ukrainsk" lang="uk" hreflang="uk" data-title="Аполлоній Перзький" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Apollonius_x%E1%BB%A9_Perga" title="Apollonius xứ Perga – vietnamesisk" lang="vi" hreflang="vi" data-title="Apollonius xứ Perga" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" 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/Apolonio_han_Perga" title="Apolonio han Perga – waray-waray" lang="war" hreflang="war" data-title="Apolonio han Perga" data-language-autonym="Winaray" data-language-local-name="waray-waray" 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/%E9%98%BF%E6%B3%A2%E7%BD%97%E5%B0%BC%E5%A5%A5%E6%96%AF" title="阿波罗尼奥斯 – wu" lang="wuu" hreflang="wuu" data-title="阿波罗尼奥斯" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%98%BF%E6%B3%A2%E7%BE%85%E5%B0%BC%E6%96%AF" title="阿波羅尼斯 – kantonesisk" lang="yue" hreflang="yue" data-title="阿波羅尼斯" data-language-autonym="粵語" data-language-local-name="kantonesisk" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%98%BF%E6%B3%A2%E7%BD%97%E5%B0%BC%E5%A5%A5%E6%96%AF" title="阿波罗尼奥斯 – kinesisk" lang="zh" hreflang="zh" data-title="阿波罗尼奥斯" data-language-autonym="中文" data-language-local-name="kinesisk" class="interlanguage-link-target"><span>中文</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/Q180109#sitelinks-wikipedia" title="Rediger lenker til artikkelen på andre språk" class="wbc-editpage">Rediger lenker</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="Navnerom"> <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" 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th{padding-left:0px;padding-right:0px;padding-top:0.2em;padding-bottom:0.1em}.mw-parser-output table.infoboks tr.bilde td{text-align:center;font-weight:normal;border:none;padding-left:3px;padding-right:3px;padding-top:0;padding-bottom:0;background-color:#f9f9f9}.mw-parser-output table.infoboks tr.overskrift td{text-align:center;font-weight:bold;background-color:#eee;border:none;padding-left:0px;padding-right:0px;padding-top:0.2em;padding-bottom:0.1em}.mw-parser-output .infoboks.geografi tr.overskrift th{background-color:#f9f9f9;color:black}.mw-parser-output .infoboks.biografi tr.overskrift th{background-color:#f9f9f9;color:black}.mw-parser-output .infoboks.transport tr.overskrift th{background-color:#f9f9f9;color:black}.mw-parser-output .infoboks.bygning tr.overskrift th{background-color:#f9f9f9;color:black}.mw-parser-output .infoboks.infrastruktur tr.overskrift th{background-color:#f9f9f9;color:black}.mw-parser-output .infoboks.bred tr.overskrift td{font-size:larger}.mw-parser-output .infoboks.ekstrabred tr.overskrift td{font-size:larger}.mw-parser-output .infoboks.bordered tr.rad th{border-bottom:1px solid #ccc}.mw-parser-output .infoboks.bordered tr.rad td{border-bottom:1px solid #ccc}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r24829246"><table class="infobox infoboks biografi fastbredde"><tbody><tr class="hode overskrift"><th colspan="4">Apollonios fra Perge</th></tr> <tr class="bilde" valign="top"><td colspan="4" class="sentrert"><figure class="mw-default-size mw-halign-center" typeof="mw:File/Frameless"><a href="/wiki/Fil:Apollonii_Pergei_Opera_1537_detail.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/63/Apollonii_Pergei_Opera_1537_detail.jpg" decoding="async" width="248" height="257" class="mw-file-element" data-file-width="248" data-file-height="257" /></a><figcaption></figcaption></figure></td></tr> <tr class="rad"><th colspan="2"><span class="edit-props-marker edit-props-P1477 edit-props-P569 edit-props-P19">Født</span></th><td colspan="2"><span><span><span lang="grc">Ἀπολλώνιος</span></span></span><br />ca. <span><a href="/wiki/262_f.Kr." title="262 f.Kr.">262 f.Kr.</a></span><sup id="cite_ref-hash-297a4b7281d16c4630cf70f1a4e5e763c0407ebb_1-0" class="reference"><a href="#cite_note-hash-297a4b7281d16c4630cf70f1a4e5e763c0407ebb-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-hash-6d50b37d03a719ce55a3c7b733bfb1efaf269587_2-0" class="reference"><a href="#cite_note-hash-6d50b37d03a719ce55a3c7b733bfb1efaf269587-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-hash-5cc0249f5351e4b1e523b5fb3d0386f4dd578010_3-0" class="reference"><a href="#cite_note-hash-5cc0249f5351e4b1e523b5fb3d0386f4dd578010-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-hash-8571a3397df273e65ed25f212d0af78a4998cd9d_4-0" class="reference"><a href="#cite_note-hash-8571a3397df273e65ed25f212d0af78a4998cd9d-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="wb-edithandle" data-bridge-edit-flow="single-best-value"><span class="mw-valign-text-top" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q180109?uselang=nb#P569" title="Rediger på Wikidata"><img alt="Rediger på Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span><br />Perge<sup id="cite_ref-hash-6d50b37d03a719ce55a3c7b733bfb1efaf269587_2-1" class="reference"><a href="#cite_note-hash-6d50b37d03a719ce55a3c7b733bfb1efaf269587-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-hash-5cc0249f5351e4b1e523b5fb3d0386f4dd578010_3-1" class="reference"><a href="#cite_note-hash-5cc0249f5351e4b1e523b5fb3d0386f4dd578010-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-hash-3bb296aa84e71c0b536642c34ff48c4f814f7b1b_5-0" class="reference"><a href="#cite_note-hash-3bb296aa84e71c0b536642c34ff48c4f814f7b1b-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></td></tr><tr class="rad"><th colspan="2"><span class="edit-props-marker edit-props-P570 edit-props-P20 edit-props-P509">Død</span></th><td colspan="2">ca. <span><a href="/wiki/190_f.Kr." title="190 f.Kr.">190 f.Kr.</a></span><sup id="cite_ref-hash-303da2d322612c127ee1aaf100ee8bdf6713b177_6-0" class="reference"><a href="#cite_note-hash-303da2d322612c127ee1aaf100ee8bdf6713b177-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-hash-297a4b7281d16c4630cf70f1a4e5e763c0407ebb_1-1" class="reference"><a href="#cite_note-hash-297a4b7281d16c4630cf70f1a4e5e763c0407ebb-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-hash-8571a3397df273e65ed25f212d0af78a4998cd9d_4-1" class="reference"><a href="#cite_note-hash-8571a3397df273e65ed25f212d0af78a4998cd9d-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><span class="wb-edithandle" data-bridge-edit-flow="single-best-value"><span class="mw-valign-text-top" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q180109?uselang=nb#P570" title="Rediger på Wikidata"><img alt="Rediger på Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span> <br /><a href="/wiki/Alexandria" title="Alexandria">Alexandria</a></td></tr><tr class="rad"><th colspan="2">Beskjeftigelse</th><td colspan="2"><a href="/wiki/Matematiker" title="Matematiker">Matematiker</a>, <a href="/wiki/Astronom" title="Astronom">astronom</a> <span class="penicon autoconfirmed-show"><span class="mw-valign-text-top" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q180109?uselang=nb#P106" title="Rediger på Wikidata"><img alt="Rediger på Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span></td></tr><tr class="rad"><td colspan="4"><hr /><div class="sentrert"><a href="https://commons.wikimedia.org/wiki/Category:Apollonius_of_Perga" class="extiw" title="commons:Category:Apollonius of Perga">Apollonios fra Perge på Commons</a></div></td></tr> </tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Apollonius_-_Conica,_1654_-_845996.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Apollonius_-_Conica%2C_1654_-_845996.jpg/250px-Apollonius_-_Conica%2C_1654_-_845996.jpg" decoding="async" width="250" height="405" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Apollonius_-_Conica%2C_1654_-_845996.jpg/375px-Apollonius_-_Conica%2C_1654_-_845996.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/5/52/Apollonius_-_Conica%2C_1654_-_845996.jpg 2x" data-file-width="444" data-file-height="719" /></a><figcaption>Forsiden til Apollonios' verk om <a href="/wiki/Kjeglesnitt" title="Kjeglesnitt">kjeglesnitt</a>, utgitt <a href="/wiki/1654" title="1654">1654</a> på <a href="/wiki/Latin" title="Latin">latin</a>.</figcaption></figure> <p><b>Apollonios</b> (<a href="/wiki/Gresk" title="Gresk">gresk</a>: Απολλώνιος, født 262, død 190 f.Kr.) var en <a href="/wiki/Gresk" title="Gresk">gresk</a> <a href="/wiki/Matematikk" title="Matematikk">matematiker</a> som er ansett for å være en av <a href="/wiki/Antikkens_Hellas" title="Antikkens Hellas">antikkens</a> aller største på dette feltet. Han kom fra byen Perge som lå like øst for <a href="/wiki/Antalya" title="Antalya">Antalya</a> i dagens Tyrkia. Apollonios er forfatteren til et stort verk om <a href="/wiki/Kjeglesnitt" title="Kjeglesnitt">kjeglesnitt</a>, hvor han samlet datidens vitenskap om disse geometriske <a href="/wiki/Kurve" title="Kurve">kurvene</a> og bidro selv med mange nye resultat. Hans arbeider ble senere studert og videreført av mange andre. Da interessen for matematikk tok seg opp igjen i Europa etter <a href="/wiki/Renessansen" title="Renessansen">renessansen</a>, fikk de også stor betydning. De nye teoriene til <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a>, <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Fermat</a>, <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes</a> og <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> bygget i stor grad på Apollonios' matematiske resultater. </p><p>Lite er kjent om hans liv. Han studerte og arbeidet i <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a> på den tiden faraoene <a href="/wiki/Ptolemaios_III_Euergetes" title="Ptolemaios III Euergetes">Ptolemaios III</a> og <a href="/wiki/Ptolemaios_IV_Filopator" title="Ptolemaios IV Filopator">Ptolemaios IV</a> regjerte. Der hadde <a href="/wiki/Evklid" class="mw-redirect" title="Evklid">Euklid</a> grunnlagt en matematiske skole som fikk stor betydning. Fra bøkene til Apollonios går det frem at han besøkte <a href="/wiki/Pergamon" title="Pergamon">Pergamon</a>, hvor det tilsvarende som i Alexandria også fantes et stort bibliotek. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Vitenskapelige_bidrag">Vitenskapelige bidrag</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Apollonios_fra_Perge&veaction=edit&section=1" title="Rediger avsnitt: Vitenskapelige bidrag" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Apollonios_fra_Perge&action=edit&section=1" title="Rediger kildekoden til seksjonen Vitenskapelige bidrag"><span>rediger kilde</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/Fil:Conica_of_Apollonius_of_Perga_fol._162b_and_164a.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Conica_of_Apollonius_of_Perga_fol._162b_and_164a.jpg/250px-Conica_of_Apollonius_of_Perga_fol._162b_and_164a.jpg" decoding="async" width="250" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Conica_of_Apollonius_of_Perga_fol._162b_and_164a.jpg/375px-Conica_of_Apollonius_of_Perga_fol._162b_and_164a.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Conica_of_Apollonius_of_Perga_fol._162b_and_164a.jpg/500px-Conica_of_Apollonius_of_Perga_fol._162b_and_164a.jpg 2x" data-file-width="886" data-file-height="642" /></a><figcaption>To sider i en arabisk oversettelse fra 800-tallet av Apollonios' verk om kjeglesnitt.</figcaption></figure> <p>Apollonios' verk om kjeglesnitt (κωνικά) fantes opprinnelig i åtte bøker. De fire første av disse har overlevd som utgaver på gresk, mens de fire andre ble lenge antatt å ikke eksistere lenger. Men på 1600-tallet ble de tre neste bøkene i arabisk oversettelse funnet i <a href="/wiki/Biblioteca_Medicea_Laurenziana" title="Biblioteca Medicea Laurenziana">Biblioteca Medicea Laurenziana</a> i Firenze og publisert på latin i 1661. Den åttende boken er nå antatt å være tapt for godt. </p><p>De tre første bøkene ser ut til å gi en oppsummering om det som på den tiden var allerede kjent om kjeglesnitt. I tredje bok ble for første gang klarlagt sammenhengene mellom <a href="/wiki/Pol_og_polare" title="Pol og polare">pol og polare</a> samt betydningen av <a href="/wiki/Harmonisk_deling" title="Harmonisk deling">harmonisk konjugerte</a> punkt. Fra og med fjerde bok presenteres egne bidrag. Han ga her en ny og bedre definisjon av disse kurvene, som snittet mellom en vilkårlig <a href="/wiki/Kjegle" title="Kjegle">kjegle</a> og et <a href="/wiki/Plan_(matematikk)" title="Plan (matematikk)">plan</a>. Avhengig av orienteringen av planet i forhold til kjeglen, kan det oppstå tre typer kjeglesnitt, som han ga navnene <a href="/wiki/Ellipse" title="Ellipse">ellipse</a>, <a href="/wiki/Hyperbel" title="Hyperbel">hyperbel</a> og <a href="/wiki/Parabel" title="Parabel">parabel</a>. I de følgende bøkene kunne han så utlede nye egenskaper ved disse, som bl.a. har med <a href="/wiki/Tangent_(matematikk)" title="Tangent (matematikk)">tangenter</a> og <a href="/wiki/Normal_(geometri)" title="Normal (geometri)">normaler</a> til slike geometriske kurver. </p><p>Andre, geometriske problem som han studerte, var å finne det <a href="/wiki/Geometrisk_sted" title="Geometrisk sted">geometriske sted</a> for de punkt hvis avstand til to gitte punkt har et konstant forhold. Løsningen av dette problemet som han fant, kalles ofte for <a href="/wiki/Apollonios%27_sirkel" class="mw-redirect" title="Apollonios' sirkel">Apollonios' sirkel</a>. Tilsvarende problem med geometrisk sted for punkt med avstander til tre eller fire linjer i bestemte forhold, løste han også ved å vise at det var kjeglesnitt. Dette problemet ble senere generalisert av <a href="/wiki/Pappos_fra_Alexandria" title="Pappos fra Alexandria">Pappos</a> til å involvere mer enn fire linjer og er derfor blitt kalt <a href="/w/index.php?title=Pappos%27_problem&action=edit&redlink=1" class="new" title="Pappos' problem (ikke skrevet ennå)">Pappos' problem</a>. Det spilte en viktig rolle da Descartes innførte den moderne bruken av <a href="/wiki/Kartesisk_koordinatsystem" title="Kartesisk koordinatsystem">koordinater</a> som la grunnlaget for <a href="/wiki/Analytisk_geometri" title="Analytisk geometri">analytisk geometri</a>. </p><p>Han viste også hvordan man kunne konstruere en sirkel som berørte tre andre geometriske objekt som kunne være et eller flere punkt, linjer eller sirkler. For det siste tilfellet med bare sirkler fant en meget elegant og vakker løsning som senere fått navnet <a href="/w/index.php?title=Apollonios%27_sirkler&action=edit&redlink=1" class="new" title="Apollonios' sirkler (ikke skrevet ennå)">Apollonios' sirkler</a>. </p><p>Apollonios var også opptatt av <a href="/wiki/Astronomi" title="Astronomi">astronomi</a> og spesielt månen og planetenes bevegelser. Han utviklet teorien om <a href="/wiki/Episyklus" title="Episyklus">episykler</a> og viste at det var ekvivalent med <a href="/wiki/Geosentrisme" title="Geosentrisme">eksentrisk</a> bevegelse i en sirkel. Omtrent samtidig ble dette teoretiske grunnlaget benyttet av <a href="/wiki/Hipparkhos_(astronom)" title="Hipparkhos (astronom)">Hipparkhos</a> i hans analyse av astronomiske observasjoner. </p> <div class="mw-heading mw-heading2"><h2 id="Referanser">Referanser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Apollonios_fra_Perge&veaction=edit&section=2" title="Rediger avsnitt: Referanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Apollonios_fra_Perge&action=edit&section=2" title="Rediger kildekoden til seksjonen Referanser"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-hash-297a4b7281d16c4630cf70f1a4e5e763c0407ebb-1"><b>^</b> <a href="#cite_ref-hash-297a4b7281d16c4630cf70f1a4e5e763c0407ebb_1-0"><sup>a</sup></a> <a href="#cite_ref-hash-297a4b7281d16c4630cf70f1a4e5e763c0407ebb_1-1"><sup>b</sup></a> <span class="reference-text"> <span><span><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">Gemeinsame Normdatei</a></span></span>, GND-ID <span><span><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/11864548X">11864548X</a></span></span>, besøkt 24. april 2022<sup><small>[Hentet fra Wikidata]</small></sup></span> </li> <li id="cite_note-hash-6d50b37d03a719ce55a3c7b733bfb1efaf269587-2"><b>^</b> <a href="#cite_ref-hash-6d50b37d03a719ce55a3c7b733bfb1efaf269587_2-0"><sup>a</sup></a> <a href="#cite_ref-hash-6d50b37d03a719ce55a3c7b733bfb1efaf269587_2-1"><sup>b</sup></a> <span class="reference-text"> <span><span>Enciclopedia della Matematica</span></span>, oppført som <span><span>Apollonio di Perge</span></span>, Treccani's Enciclopedia della Matematica ID <span><span><a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/apollonio-di-perge_(Enciclopedia-della-Matematica)">apollonio-di-perge</a></span></span>, utgitt 2013, besøkt 24. april 2022<sup><small>[Hentet fra Wikidata]</small></sup></span> </li> <li id="cite_note-hash-5cc0249f5351e4b1e523b5fb3d0386f4dd578010-3"><b>^</b> <a href="#cite_ref-hash-5cc0249f5351e4b1e523b5fb3d0386f4dd578010_3-0"><sup>a</sup></a> <a href="#cite_ref-hash-5cc0249f5351e4b1e523b5fb3d0386f4dd578010_3-1"><sup>b</sup></a> <span class="reference-text"> <span><span><a href="/wiki/Treccani-leksikonet" title="Treccani-leksikonet">Treccani-leksikonet</a></span></span>, oppført som <span><span>APOLLONIO Pergeo</span></span>, Enciclopedia Italiana-ID <span><span><a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/apollonio-pergeo_(Enciclopedia-Italiana)">apollonio-pergeo</a></span></span>, utgitt 1929, besøkt 24. april 2022<sup><small>[Hentet fra Wikidata]</small></sup></span> </li> <li id="cite_note-hash-8571a3397df273e65ed25f212d0af78a4998cd9d-4"><b>^</b> <a href="#cite_ref-hash-8571a3397df273e65ed25f212d0af78a4998cd9d_4-0"><sup>a</sup></a> <a href="#cite_ref-hash-8571a3397df273e65ed25f212d0af78a4998cd9d_4-1"><sup>b</sup></a> <span class="reference-text"> <span><span>Apollonios 112 (Pauly-Wissowa)</span></span>, besøkt 24. april 2022<sup><small>[Hentet fra Wikidata]</small></sup></span> </li> <li id="cite_note-hash-3bb296aa84e71c0b536642c34ff48c4f814f7b1b-5"><b><a href="#cite_ref-hash-3bb296aa84e71c0b536642c34ff48c4f814f7b1b_5-0">^</a></b> <span class="reference-text"> <span><span>EL / Apollonij</span></span><sup><small>[Hentet fra Wikidata]</small></sup></span> </li> <li id="cite_note-hash-303da2d322612c127ee1aaf100ee8bdf6713b177-6"><b><a href="#cite_ref-hash-303da2d322612c127ee1aaf100ee8bdf6713b177_6-0">^</a></b> <span class="reference-text"> <span><span>Encyclopædia Britannica Online</span></span>, Encyclopædia Britannica Online-ID <span><span><a rel="nofollow" class="external text" href="https://www.britannica.com/biography/Apollonius-of-Perga">biography/Apollonius-of-Perga</a></span></span>, besøkt 24. april 2022<sup><small>[Hentet fra Wikidata]</small></sup></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Litteratur">Litteratur</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Apollonios_fra_Perge&veaction=edit&section=3" title="Rediger avsnitt: Litteratur" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Apollonios_fra_Perge&action=edit&section=3" title="Rediger kildekoden til seksjonen Litteratur"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>M. Kline, <i> Mathematical Thought from Ancient to Modern Times,</i> Vol. I, Oxford University Press, Oxford (1972). <a href="/wiki/Spesial:Bokkilder/9780195061352" class="internal mw-magiclink-isbn">ISBN 978-0-19-506135-2</a>.</li> <li>C.B. Boyer, <i>A History of Mathematics</i>, Princeton University Press, New Jersey (1985). <a href="/wiki/Spesial:Bokkilder/0691023913" class="internal mw-magiclink-isbn">ISBN 0-691-02391-3</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Eksterne_lenker">Eksterne lenker</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Apollonios_fra_Perge&veaction=edit&section=4" title="Rediger avsnitt: Eksterne lenker" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Apollonios_fra_Perge&action=edit&section=4" title="Rediger kildekoden til seksjonen Eksterne lenker"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Encyclopedia.com, <a rel="nofollow" class="external text" href="http://www.encyclopedia.com/topic/Apollonius_of_Perga.aspx">Apollonius biography</a>.</li> <li>University of St. Andrews, <a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Apollonius.html">Apollonius biography</a>.</li></ul> <p><br /> </p> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r23230704">.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 ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": 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