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id="toc-Contents" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Contents"> <div class="vector-toc-text"> 2.1.1 Contents </div> </a> <ul id="toc-Contents-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Other_works" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_works"> <div class="vector-toc-text"> 2.2 Other works </div> </a> <ul id="toc-Other_works-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lost_works" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lost_works"> <div class="vector-toc-text"> 2.3 Lost works </div> </a> <ul id="toc-Lost_works-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Legacy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legacy"> <div class="vector-toc-text"> 3 Legacy </div> </a> <ul id="toc-Legacy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 4 References </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle References subsection </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> 4.1 Notes </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> 4.2 Citations </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> 4.3 Sources </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 5 External links </div> </a> <ul id="toc-External_links-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="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <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="Toggle the table of contents" > <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" > Toggle the table of contents </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">Euclid</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="Go to an article in another language. Available in 163 languages" > <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-163" aria-hidden="true" > 163 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Euklides" title="Euklides – Afrikaans" lang="af" hreflang="af" data-title="Euklides" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Euklid" title="Euklid – Alemannic" lang="gsw" hreflang="gsw" data-title="Euklid" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target">Alemannisch</a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A9%E1%8A%AD%E1%88%8A%E1%8B%B5" title="ዩክሊድ – Amharic" lang="am" hreflang="am" data-title="ዩክሊድ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target">አማርኛ</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D9%82%D9%84%D9%8A%D8%AF%D8%B3" title="إقليدس – Arabic" lang="ar" hreflang="ar" data-title="إقليدس" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Euclides" title="Euclides – Aragonese" lang="an" hreflang="an" data-title="Euclides" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%87%E0%A6%89%E0%A6%95%E0%A7%8D%E0%A6%B2%E0%A6%BF%E0%A6%A1" title="ইউক্লিড – Assamese" lang="as" hreflang="as" data-title="ইউক্লিড" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target">অসমীয়া</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Euclides" title="Euclides – Asturian" lang="ast" hreflang="ast" data-title="Euclides" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Euclides" title="Euclides – Guarani" lang="gn" hreflang="gn" data-title="Euclides" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" class="interlanguage-link-target">Avañe'ẽ</a></li><li class="interlanguage-link interwiki-av mw-list-item"><a href="https://av.wikipedia.org/wiki/%D0%AD%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Эвклид – Avaric" lang="av" hreflang="av" data-title="Эвклид" data-language-autonym="Авар" data-language-local-name="Avaric" class="interlanguage-link-target">Авар</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Evklid" title="Evklid – Azerbaijani" lang="az" hreflang="az" data-title="Evklid" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D9%88%D9%82%D9%84%DB%8C%D8%AF%D8%B3" title="اوقلیدس – South Azerbaijani" lang="azb" hreflang="azb" data-title="اوقلیدس" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target">تۆرکجه</a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/%C3%89uclid" title="Éuclid – Balinese" lang="ban" hreflang="ban" data-title="Éuclid" data-language-autonym="Basa Bali" data-language-local-name="Balinese" class="interlanguage-link-target">Basa Bali</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%87%E0%A6%89%E0%A6%95%E0%A7%8D%E0%A6%B2%E0%A6%BF%E0%A6%A1" title="ইউক্লিড – Bangla" lang="bn" hreflang="bn" data-title="ইউক্লিড" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Eukleides" title="Eukleides – Minnan" lang="nan" hreflang="nan" data-title="Eukleides" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Bashkir" lang="ba" hreflang="ba" data-title="Евклид" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target">Башҡортса</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D1%9E%D0%BA%D0%BB%D1%96%D0%B4" title="Эўклід – Belarusian" lang="be" hreflang="be" data-title="Эўклід" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%AD%D1%9E%D0%BA%D0%BB%D1%96%D0%B4" title="Эўклід – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Эўклід" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target">Беларуская (тарашкевіца)</a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AF%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%BF%E0%A4%A1" title="यूक्लिड – Bhojpuri" lang="bh" hreflang="bh" data-title="यूक्लिड" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target">भोजपुरी</a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Euclid" title="Euclid – Central Bikol" lang="bcl" hreflang="bcl" data-title="Euclid" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target">Bikol Central</a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Euclid" title="Euclid – Bislama" lang="bi" hreflang="bi" data-title="Euclid" data-language-autonym="Bislama" data-language-local-name="Bislama" class="interlanguage-link-target">Bislama</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Bulgarian" lang="bg" hreflang="bg" data-title="Евклид" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A1%E0%BD%BC%E0%BD%A0%E0%BD%B4%E0%BC%8B%E0%BD%81%E0%BD%BA%E0%BC%8B%E0%BD%A3%E0%BD%BA%E0%BC%8B%E0%BD%8F%E0%BD%BA%E0%BC%8D" title="ཡོའུ་ཁེ་ལེ་ཏེ། – Tibetan" lang="bo" hreflang="bo" data-title="ཡོའུ་ཁེ་ལེ་ཏེ།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target">བོད་ཡིག</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Euklid" title="Euklid – Bosnian" lang="bs" hreflang="bs" data-title="Euklid" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Euklides" title="Euklides – Breton" lang="br" hreflang="br" data-title="Euklides" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target">Brezhoneg</a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Евклид" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target">Буряад</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Euclides" title="Euclides – Catalan" lang="ca" hreflang="ca" data-title="Euclides" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Chuvash" lang="cv" hreflang="cv" data-title="Евклид" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Eukleid%C3%A9s" title="Eukleidés – Czech" lang="cs" hreflang="cs" data-title="Eukleidés" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-tum mw-list-item"><a href="https://tum.wikipedia.org/wiki/Euclid" title="Euclid – Tumbuka" lang="tum" hreflang="tum" data-title="Euclid" data-language-autonym="ChiTumbuka" data-language-local-name="Tumbuka" class="interlanguage-link-target">ChiTumbuka</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Euclid" title="Euclid – Welsh" lang="cy" hreflang="cy" data-title="Euclid" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Euklid" title="Euklid – Danish" lang="da" hreflang="da" data-title="Euklid" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Euklid" title="Euklid – German" lang="de" hreflang="de" data-title="Euklid" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Eukleides" title="Eukleides – Estonian" lang="et" hreflang="et" data-title="Eukleides" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B7%CF%82" title="Ευκλείδης – Greek" lang="el" hreflang="el" data-title="Ευκλείδης" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Euclides" title="Euclides – Spanish" lang="es" hreflang="es" data-title="Euclides" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/E%C5%ADklido" title="Eŭklido – Esperanto" lang="eo" hreflang="eo" data-title="Eŭklido" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Uclidi" title="Uclidi – Extremaduran" lang="ext" hreflang="ext" data-title="Uclidi" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target">Estremeñu</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Euklides" title="Euklides – Basque" lang="eu" hreflang="eu" data-title="Euklides" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3" title="اقلیدس – Persian" lang="fa" hreflang="fa" data-title="اقلیدس" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Euclid" title="Euclid – Fiji Hindi" lang="hif" hreflang="hif" data-title="Euclid" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target">Fiji Hindi</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Euclide" title="Euclide – French" lang="fr" hreflang="fr" data-title="Euclide" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Euklides" title="Euklides – Western Frisian" lang="fy" hreflang="fy" data-title="Euklides" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target">Frysk</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Eoicl%C3%ADd%C3%A9as" title="Eoiclídéas – Irish" lang="ga" hreflang="ga" data-title="Eoiclídéas" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Euclides" title="Euclides – Galician" lang="gl" hreflang="gl" data-title="Euclides" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E6%AD%90%E5%87%A0%E9%87%8C%E5%BE%97" title="歐几里得 – Gan" lang="gan" hreflang="gan" data-title="歐几里得" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target">贛語</a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AF%E0%AB%81%E0%AA%95%E0%AB%8D%E0%AA%B2%E0%AA%BF%E0%AA%A1" title="યુક્લિડ – Gujarati" lang="gu" hreflang="gu" data-title="યુક્લિડ" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target">ગુજરાતી</a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Euclid" title="Euclid – Hakka Chinese" lang="hak" hreflang="hak" data-title="Euclid" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target">客家語 / Hak-kâ-ngî</a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%AD%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Эвклид – Kalmyk" lang="xal" hreflang="xal" data-title="Эвклид" data-language-autonym="Хальмг" data-language-local-name="Kalmyk" class="interlanguage-link-target">Хальмг</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%90%EC%9A%B0%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8D%B0%EC%8A%A4" title="에우클레이데스 – Korean" lang="ko" hreflang="ko" data-title="에우클레이데스" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Euclid" title="Euclid – Hausa" lang="ha" hreflang="ha" data-title="Euclid" data-language-autonym="Hausa" data-language-local-name="Hausa" class="interlanguage-link-target">Hausa</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B7%D5%BE%D5%AF%D5%AC%D5%AB%D5%A4%D5%A5%D5%BD" title="Էվկլիդես – Armenian" lang="hy" hreflang="hy" data-title="Էվկլիդես" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AF%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%BF%E0%A4%A1" title="यूक्लिड – Hindi" lang="hi" hreflang="hi" data-title="यूक्लिड" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Euklid" title="Euklid – Croatian" lang="hr" hreflang="hr" data-title="Euklid" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Euklid" title="Euklid – Ido" lang="io" hreflang="io" data-title="Euklid" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target">Ido</a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Euklides" title="Euklides – Iloko" lang="ilo" hreflang="ilo" data-title="Euklides" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target">Ilokano</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Euklides" title="Euklides – Indonesian" lang="id" hreflang="id" data-title="Euklides" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Euclide" title="Euclide – Interlingua" lang="ia" hreflang="ia" data-title="Euclide" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target">Interlingua</a></li><li class="interlanguage-link interwiki-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Euclid" title="Euclid – Interlingue" lang="ie" hreflang="ie" data-title="Euclid" data-language-autonym="Interlingue" data-language-local-name="Interlingue" class="interlanguage-link-target">Interlingue</a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/U-Euclid" title="U-Euclid – Xhosa" lang="xh" hreflang="xh" data-title="U-Euclid" data-language-autonym="IsiXhosa" data-language-local-name="Xhosa" class="interlanguage-link-target">IsiXhosa</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Evkl%C3%AD%C3%B0" title="Evklíð – Icelandic" lang="is" hreflang="is" data-title="Evklíð" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Euclide" title="Euclide – Italian" lang="it" hreflang="it" data-title="Euclide" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%95%D7%A7%D7%9C%D7%99%D7%93%D7%A1" title="אוקלידס – Hebrew" lang="he" hreflang="he" data-title="אוקלידס" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Euklides" title="Euklides – Javanese" lang="jv" hreflang="jv" data-title="Euklides" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target">Jawa</a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Euclid" title="Euclid – Kabiye" lang="kbp" hreflang="kbp" data-title="Euclid" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target">Kabɩyɛ</a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AF%E0%B3%82%E0%B2%95%E0%B3%8D%E0%B2%B2%E0%B2%BF%E0%B2%A1%E0%B3%8D" title="ಯೂಕ್ಲಿಡ್ – Kannada" lang="kn" hreflang="kn" data-title="ಯೂಕ್ಲಿಡ್" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%94%E1%83%95%E1%83%99%E1%83%9A%E1%83%98%E1%83%93%E1%83%94" title="ევკლიდე – Georgian" lang="ka" hreflang="ka" data-title="ევკლიდე" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Kazakh" lang="kk" hreflang="kk" data-title="Евклид" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Euclid" title="Euclid – Cornish" lang="kw" hreflang="kw" data-title="Euclid" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target">Kernowek</a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Euklides" title="Euklides – Swahili" lang="sw" hreflang="sw" data-title="Euklides" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target">Kiswahili</a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/%C3%89klid" title="Éklid – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Éklid" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target">Kriyòl gwiyannen</a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Iql%C3%AEdes" title="Iqlîdes – Kurdish" lang="ku" hreflang="ku" data-title="Iqlîdes" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target">Kurdî</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Kyrgyz" lang="ky" hreflang="ky" data-title="Евклид" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Euclides" title="Euclides – Latin" lang="la" hreflang="la" data-title="Euclides" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Eikl%C4%ABds" title="Eiklīds – Latvian" lang="lv" hreflang="lv" data-title="Eiklīds" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-lez mw-list-item"><a href="https://lez.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Lezghian" lang="lez" hreflang="lez" data-title="Евклид" data-language-autonym="Лезги" data-language-local-name="Lezghian" class="interlanguage-link-target">Лезги</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Euklidas_Aleksandrietis" title="Euklidas Aleksandrietis – Lithuanian" lang="lt" hreflang="lt" data-title="Euklidas Aleksandrietis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Euclide" title="Euclide – Ligurian" lang="lij" hreflang="lij" data-title="Euclide" data-language-autonym="Ligure" data-language-local-name="Ligurian" class="interlanguage-link-target">Ligure</a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Euclides" title="Euclides – Limburgish" lang="li" hreflang="li" data-title="Euclides" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target">Limburgs</a></li><li class="interlanguage-link interwiki-olo mw-list-item"><a href="https://olo.wikipedia.org/wiki/Eukleides" title="Eukleides – Livvi-Karelian" lang="olo" hreflang="olo" data-title="Eukleides" data-language-autonym="Livvinkarjala" data-language-local-name="Livvi-Karelian" class="interlanguage-link-target">Livvinkarjala</a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/euklides" title="euklides – Lojban" lang="jbo" hreflang="jbo" data-title="euklides" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target">La .lojban.</a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Euclid" title="Euclid – Lombard" lang="lmo" hreflang="lmo" data-title="Euclid" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target">Lombard</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Eukleid%C3%A9sz_(matematikus)" title="Eukleidész (matematikus) – Hungarian" lang="hu" hreflang="hu" data-title="Eukleidész (matematikus)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Macedonian" lang="mk" hreflang="mk" data-title="Евклид" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Eoklida" title="Eoklida – Malagasy" lang="mg" hreflang="mg" data-title="Eoklida" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target">Malagasy</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AF%E0%B5%82%E0%B4%95%E0%B5%8D%E0%B4%B2%E0%B4%BF%E0%B4%A1%E0%B5%8D" title="യൂക്ലിഡ് – Malayalam" lang="ml" hreflang="ml" data-title="യൂക്ലിഡ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Ewklide" title="Ewklide – Maltese" lang="mt" hreflang="mt" data-title="Ewklide" data-language-autonym="Malti" data-language-local-name="Maltese" class="interlanguage-link-target">Malti</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AF%E0%A5%81%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%BF%E0%A4%A1" title="युक्लिड – Marathi" lang="mr" hreflang="mr" data-title="युक्लिड" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%94%E1%83%95%E1%83%99%E1%83%9A%E1%83%98%E1%83%93%E1%83%94" title="ევკლიდე – Mingrelian" lang="xmf" hreflang="xmf" data-title="ევკლიდე" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target">მარგალური</a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%8A%D9%83%D9%84%D9%8A%D8%AF%D9%8A%D8%B3" title="ايكليديس – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ايكليديس" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target">مصرى</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Euclid" title="Euclid – Malay" lang="ms" hreflang="ms" data-title="Euclid" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Ouclides" title="Ouclides – Mirandese" lang="mwl" hreflang="mwl" data-title="Ouclides" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target">Mirandés</a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Mongolian" lang="mn" hreflang="mn" data-title="Евклид" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target">Монгол</a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9A%E1%80%B0%E1%80%80%E1%80%9C%E1%80%85%E1%80%BA" title="ယူကလစ် – Burmese" lang="my" hreflang="my" data-title="ယူကလစ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Euclides_van_Alexandri%C3%AB" title="Euclides van Alexandrië – Dutch" lang="nl" hreflang="nl" data-title="Euclides van Alexandrië" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%AF%E0%A5%81%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%BF%E0%A4%A6" title="युक्लिद – Newari" lang="new" hreflang="new" data-title="युक्लिद" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target">नेपाल भाषा</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A8%E3%82%A6%E3%82%AF%E3%83%AC%E3%82%A4%E3%83%87%E3%82%B9" title="エウクレイデス – Japanese" lang="ja" hreflang="ja" data-title="エウクレイデス" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Chechen" lang="ce" hreflang="ce" data-title="Евклид" data-language-autonym="Нохчийн" data-language-local-name="Chechen" class="interlanguage-link-target">Нохчийн</a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Euklid" title="Euklid – Northern Frisian" lang="frr" hreflang="frr" data-title="Euklid" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target">Nordfriisk</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Euklid" title="Euklid – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Euklid" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Evklid" title="Evklid – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Evklid" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Euclides" title="Euclides – Occitan" lang="oc" hreflang="oc" data-title="Euclides" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AD%9F%E0%AD%81%E0%AC%95%E0%AD%8D%E0%AC%B2%E0%AC%BF%E0%AC%A1%E0%AD%8D" title="ୟୁକ୍ଲିଡ୍ – Odia" lang="or" hreflang="or" data-title="ୟୁକ୍ଲିଡ୍" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target">ଓଡ଼ିଆ</a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Yuukiliid" title="Yuukiliid – Oromo" lang="om" hreflang="om" data-title="Yuukiliid" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target">Oromoo</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Yevklid" title="Yevklid – Uzbek" lang="uz" hreflang="uz" data-title="Yevklid" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AF%E0%A9%82%E0%A8%95%E0%A8%B2%E0%A8%BF%E0%A8%A1" title="ਯੂਕਲਿਡ – Punjabi" lang="pa" hreflang="pa" data-title="ਯੂਕਲਿਡ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3" title="اقلیدس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="اقلیدس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A7%D9%82%D9%84%D9%8A%D8%AF%D8%B3" title="اقليدس – Pashto" lang="ps" hreflang="ps" data-title="اقليدس" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Euclid" title="Euclid – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Euclid" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target">Patois</a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Euclid" title="Euclid – Piedmontese" lang="pms" hreflang="pms" data-title="Euclid" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target">Piemontèis</a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Euklid" title="Euklid – Low German" lang="nds" hreflang="nds" data-title="Euklid" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target">Plattdüütsch</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Euklides" title="Euklides – Polish" lang="pl" hreflang="pl" data-title="Euklides" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Euclides" title="Euclides – Portuguese" lang="pt" hreflang="pt" data-title="Euclides" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Evklid" title="Evklid – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Evklid" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target">Qaraqalpaqsha</a></li><li class="interlanguage-link interwiki-ksh mw-list-item"><a href="https://ksh.wikipedia.org/wiki/Euklid_va_Alexandria" title="Euklid va Alexandria – Colognian" lang="ksh" hreflang="ksh" data-title="Euklid va Alexandria" data-language-autonym="Ripoarisch" data-language-local-name="Colognian" class="interlanguage-link-target">Ripoarisch</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Euclid" title="Euclid – Romanian" lang="ro" hreflang="ro" data-title="Euclid" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D1%96%D0%B4" title="Евклід – Rusyn" lang="rue" hreflang="rue" data-title="Евклід" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target">Русиньскый</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид – Russian" lang="ru" hreflang="ru" data-title="Евклид" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%AD%D0%BA%D0%BB%D0%B8%D0%B4" title="Эклид – Yakut" lang="sah" hreflang="sah" data-title="Эклид" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target">Саха тыла</a></li><li class="interlanguage-link interwiki-szy mw-list-item"><a href="https://szy.wikipedia.org/wiki/U-ci-li-te" title="U-ci-li-te – Sakizaya" lang="szy" hreflang="szy" data-title="U-ci-li-te" data-language-autonym="Sakizaya" data-language-local-name="Sakizaya" class="interlanguage-link-target">Sakizaya</a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%A4%E1%B1%A3%E1%B1%A0%E1%B1%9E%E1%B1%A4%E1%B1%B0" title="ᱤᱣᱠᱞᱤᱰ – Santali" lang="sat" hreflang="sat" data-title="ᱤᱣᱠᱞᱤᱰ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="Santali" class="interlanguage-link-target">ᱥᱟᱱᱛᱟᱲᱤ</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Euclid" title="Euclid – Scots" lang="sco" hreflang="sco" data-title="Euclid" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Euklidi" title="Euklidi – Albanian" lang="sq" hreflang="sq" data-title="Euklidi" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Euclidi" title="Euclidi – Sicilian" lang="scn" hreflang="scn" data-title="Euclidi" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target">Sicilianu</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Euclid" title="Euclid – Simple English" lang="en-simple" hreflang="en-simple" data-title="Euclid" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A7%D9%82%D9%84%D9%8A%D8%AF%D8%B3" title="اقليدس – Sindhi" lang="sd" hreflang="sd" data-title="اقليدس" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target">سنڌي</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Eukleides_z_Alexandrie" title="Eukleides z Alexandrie – Slovak" lang="sk" hreflang="sk" data-title="Eukleides z Alexandrie" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Evklid" title="Evklid – Slovenian" lang="sl" hreflang="sl" data-title="Evklid" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Euklides" title="Euklides – Silesian" lang="szl" hreflang="szl" data-title="Euklides" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target">Ślůnski</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%DB%8C%D9%82%D9%84%DB%8C%D8%AF%D8%B3" title="ئیقلیدس – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ئیقلیدس" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%95%D1%83%D0%BA%D0%BB%D0%B8%D0%B4" title="Еуклид – Serbian" lang="sr" hreflang="sr" data-title="Еуклид" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Euklid" title="Euklid – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Euklid" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Eukleides" title="Eukleides – Finnish" lang="fi" hreflang="fi" data-title="Eukleides" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Euklides" title="Euklides – Swedish" lang="sv" hreflang="sv" data-title="Euklides" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Euclides" title="Euclides – Tagalog" lang="tl" hreflang="tl" data-title="Euclides" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AF%E0%AF%82%E0%AE%95%E0%AF%8D%E0%AE%B3%E0%AE%BF%E0%AE%9F%E0%AF%81" title="யூக்ளிடு – Tamil" lang="ta" hreflang="ta" data-title="யூக்ளிடு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Uklid_(Euclide)" title="Uklid (Euclide) – Tachelhit" lang="shi" hreflang="shi" data-title="Uklid (Euclide)" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target">Taclḥit</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%AD%D1%83%D0%BA%D0%BB%D0%B8%D0%B4" title="Эуклид – Tatar" lang="tt" hreflang="tt" data-title="Эуклид" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AF%E0%B1%82%E0%B0%95%E0%B1%8D%E0%B0%B2%E0%B0%BF%E0%B0%A1%E0%B1%8D" title="యూక్లిడ్ – Telugu" lang="te" hreflang="te" data-title="యూక్లిడ్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A2%E0%B8%B8%E0%B8%84%E0%B8%A5%E0%B8%B4%E0%B8%94" title="ยุคลิด – Thai" lang="th" hreflang="th" data-title="ยุคลิด" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A3%D2%9B%D0%BB%D0%B8%D0%B4%D1%83%D1%81" title="Уқлидус – Tajik" lang="tg" hreflang="tg" data-title="Уқлидус" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target">Тоҷикӣ</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%96klid" title="Öklid – Turkish" lang="tr" hreflang="tr" data-title="Öklid" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D1%96%D0%B4" title="Евклід – Ukrainian" lang="uk" hreflang="uk" data-title="Евклід" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3" title="اقلیدس – Urdu" lang="ur" hreflang="ur" data-title="اقلیدس" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-za mw-list-item"><a href="https://za.wikipedia.org/wiki/Euclid" title="Euclid – Zhuang" lang="za" hreflang="za" data-title="Euclid" data-language-autonym="Vahcuengh" data-language-local-name="Zhuang" class="interlanguage-link-target">Vahcuengh</a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Euclide" title="Euclide – Venetian" lang="vec" hreflang="vec" data-title="Euclide" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target">Vèneto</a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Evklid" title="Evklid – Veps" lang="vep" hreflang="vep" data-title="Evklid" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target">Vepsän kel’</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Euclid" title="Euclid – Vietnamese" lang="vi" hreflang="vi" data-title="Euclid" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-vo mw-list-item"><a href="https://vo.wikipedia.org/wiki/Eukleides" title="Eukleides – Volapük" lang="vo" hreflang="vo" data-title="Eukleides" data-language-autonym="Volapük" data-language-local-name="Volapük" class="interlanguage-link-target">Volapük</a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Eukleides" title="Eukleides – Võro" lang="vro" hreflang="vro" data-title="Eukleides" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target">Võro</a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%AD%90%E5%B9%BE%E9%87%8C%E5%BE%97" title="歐幾里得 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="歐幾里得" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target">文言</a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Eukleides" title="Eukleides – Waray" lang="war" hreflang="war" data-title="Eukleides" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target">Winaray</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97" title="欧几里得 – Wu" lang="wuu" hreflang="wuu" data-title="欧几里得" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%95%D7%A7%D7%9C%D7%99%D7%93%D7%95%D7%A1" title="אוקלידוס – Yiddish" lang="yi" hreflang="yi" data-title="אוקלידוס" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target">ייִדיש</a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Euclid" title="Euclid – Yoruba" lang="yo" hreflang="yo" data-title="Euclid" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target">Yorùbá</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%AD%90%E5%B9%BE%E9%87%8C%E5%BE%97" title="歐幾里得 – Cantonese" lang="yue" hreflang="yue" data-title="歐幾里得" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/%C3%96klid" title="Öklid – Dimli" lang="diq" hreflang="diq" data-title="Öklid" data-language-autonym="Zazaki" data-language-local-name="Dimli" class="interlanguage-link-target">Zazaki</a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Eukl%C4%97ds" title="Euklėds – Samogitian" lang="sgs" hreflang="sgs" data-title="Euklėds" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target">Žemaitėška</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97" title="欧几里得 – Chinese" lang="zh" hreflang="zh" data-title="欧几里得" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li><li class="interlanguage-link interwiki-ann mw-list-item"><a href="https://ann.wikipedia.org/wiki/Yukilidi" title="Yukilidi – Obolo" lang="ann" hreflang="ann" data-title="Yukilidi" data-language-autonym="Obolo" data-language-local-name="Obolo" class="interlanguage-link-target">Obolo</a></li><li class="interlanguage-link interwiki-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/Iklid%C3%A8s" title="Iklidès – Betawi" lang="bew" hreflang="bew" data-title="Iklidès" data-language-autonym="Betawi" data-language-local-name="Betawi" class="interlanguage-link-target">Betawi</a></li><li class="interlanguage-link interwiki-btm 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.hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the philosopher, see <a href="/wiki/Euclid_of_Megara" title="Euclid of Megara">Euclid of Megara</a>. For other uses, see <a href="/wiki/Euclid_(disambiguation)" class="mw-disambig" title="Euclid (disambiguation)">Euclid (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.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%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Euclid</div></th></tr><tr><td colspan="2" class="infobox-subheader" style="font-size:125%;">Εὐκλείδης</td></tr><tr><td colspan="2" class="infobox-image"><a href="/wiki/File:Jusepe_de_Ribera_-_Euclid_-_2001.26_-_J._Paul_Getty_Museum.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Jusepe_de_Ribera_-_Euclid_-_2001.26_-_J._Paul_Getty_Museum.jpg/220px-Jusepe_de_Ribera_-_Euclid_-_2001.26_-_J._Paul_Getty_Museum.jpg" decoding="async" width="220" height="298" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Jusepe_de_Ribera_-_Euclid_-_2001.26_-_J._Paul_Getty_Museum.jpg/330px-Jusepe_de_Ribera_-_Euclid_-_2001.26_-_J._Paul_Getty_Museum.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Jusepe_de_Ribera_-_Euclid_-_2001.26_-_J._Paul_Getty_Museum.jpg/440px-Jusepe_de_Ribera_-_Euclid_-_2001.26_-_J._Paul_Getty_Museum.jpg 2x" data-file-width="3174" data-file-height="4306" /></a><div class="infobox-caption">Euclid by <a href="/wiki/Jusepe_de_Ribera" title="Jusepe de Ribera">Jusepe de Ribera</a>, <abbr title="circa">c.</abbr> 1630–1635<a href="#cite_note-FOOTNOTEGetty-1">[1]</a></div></td></tr><tr><th scope="row" class="infobox-label">Years active</th><td class="infobox-data"><abbr title="floruit ('flourished' – known to have been active at a particular time or during a particular period)">fl.</abbr> 300 BC</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1129693374">.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:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"><ul><li>The <a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Elements</a></li><li><a href="/wiki/Euclid%27s_Optics" title="Euclid's Optics">Optics</a></li><li><a href="/wiki/Euclid%27s_Data" title="Euclid's Data">Data</a></li></ul></div> <div class="collapsible-list mw-collapsible mw-collapsed" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold;"><div><style data-mw-deduplicate="TemplateStyles:r886047488">.mw-parser-output .nobold{font-weight:normal}</style>Various concepts</div></div> <ul class="mw-collapsible-content" style="margin-top: 0; margin-bottom: 0; line-height: inherit; list-style: none; margin-left: 0;"><li style="line-height: inherit; margin: 0"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"> <ul><li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a></li> <li><a href="/wiki/Euclidean_algorithm" title="Euclidean algorithm">Euclidean algorithm</a></li> <li><a href="/wiki/Euclid%27s_theorem" title="Euclid's theorem">Euclid's theorem</a></li> <li><a href="/wiki/Euclidean_relation" title="Euclidean relation">Euclidean relation</a></li> <li><a href="/wiki/Pythagorean_triple#Generating_a_triple" title="Pythagorean triple">Euclid's formula</a></li> <li><a href="/wiki/List_of_things_named_after_Euclid" title="List of things named after Euclid">Numerous other namesakes</a></li></ul> </div></li></ul> </div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546" />Scientific career</td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a> (<a href="/wiki/Geometry" title="Geometry">Geometry</a>)</td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> Euclid (<a href="/wiki/Help:IPA/English" title="Help:IPA/English">/ˈjuːklɪd/</a>; <a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: Εὐκλείδης; <abbr title="floruit ('flourished' – known to have been active at a particular time or during a particular period)">fl.</abbr> 300 BC) was an <a href="/wiki/Ancient_Greece" title="Ancient Greece">ancient Greek</a> <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> active as a <a href="/wiki/Geometer" class="mw-redirect" title="Geometer">geometer</a> and <a href="/wiki/Logician" class="mw-redirect" title="Logician">logician</a>.<a href="#cite_note-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage125_125]-2">[2]</a> Considered the "father of geometry",<a href="#cite_note-FOOTNOTESialaros2021§_"Summary"-3">[3]</a> he is chiefly known for the <a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Elements</a> treatise, which established the foundations of <a href="/wiki/Geometry" title="Geometry">geometry</a> that largely dominated the field until the early 19th century. His system, now referred to as <a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a>, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including <a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus of Cnidus</a>, <a href="/wiki/Hippocrates_of_Chios" title="Hippocrates of Chios">Hippocrates of Chios</a>, <a href="/wiki/Thales" class="mw-redirect" title="Thales">Thales</a> and <a href="/wiki/Theaetetus_(mathematician)" title="Theaetetus (mathematician)">Theaetetus</a>. With <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> and <a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius of Perga</a>, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the <a href="/wiki/History_of_mathematics" title="History of mathematics">history of mathematics</a>. Very little is known of Euclid's life, and most information comes from the scholars <a href="/wiki/Proclus" title="Proclus">Proclus</a> and <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus of Alexandria</a> many centuries later. <a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Medieval Islamic mathematicians</a> invented a fanciful biography, and medieval <a href="/wiki/Byzantine_Empire" title="Byzantine Empire">Byzantine</a> and early <a href="/wiki/Renaissance" title="Renaissance">Renaissance</a> scholars mistook him for the earlier philosopher <a href="/wiki/Euclid_of_Megara" title="Euclid of Megara">Euclid of Megara</a>. It is now generally accepted that he spent his career in <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a> and lived around 300 BC, after <a href="/wiki/Plato" title="Plato">Plato</a>'s students and before Archimedes. There is some speculation that Euclid studied at the <a href="/wiki/Platonic_Academy" title="Platonic Academy">Platonic Academy</a> and later taught at the <a href="/wiki/Musaeum" class="mw-redirect" title="Musaeum">Musaeum</a>; he is regarded as bridging the earlier Platonic tradition in <a href="/wiki/Athens" title="Athens">Athens</a> with the later tradition of Alexandria. In the Elements, Euclid deduced the <a href="/wiki/Theorem" title="Theorem">theorems</a> from a small set of <a href="/wiki/Axiom" title="Axiom">axioms</a>. He also wrote works on <a href="/wiki/Perspective_(visual)" class="mw-redirect" title="Perspective (visual)">perspective</a>, <a href="/wiki/Conic_section" title="Conic section">conic sections</a>, <a href="/wiki/Spherical_geometry" title="Spherical geometry">spherical geometry</a>, <a href="/wiki/Number_theory" title="Number theory">number theory</a>, and <a href="/wiki/Rigour#Mathematical_proof" title="Rigour">mathematical rigour</a>. In addition to the Elements, Euclid wrote a central early text in the <a href="/wiki/Optics" title="Optics">optics</a> field, <a href="/wiki/Euclid%27s_Optics" title="Euclid's Optics">Optics</a>, and lesser-known works including <a href="/wiki/Euclid%27s_Data" title="Euclid's Data">Data</a> and Phaenomena. Euclid's authorship of On Divisions of Figures and Catoptrics has been questioned. He is thought to have written many <a href="#Lost_works">lost works</a>. <style data-mw-deduplicate="TemplateStyles:r886046785">.mw-parser-output .toclimit-2 .toclevel-1 ul,.mw-parser-output .toclimit-3 .toclevel-2 ul,.mw-parser-output .toclimit-4 .toclevel-3 ul,.mw-parser-output .toclimit-5 .toclevel-4 ul,.mw-parser-output .toclimit-6 .toclevel-5 ul,.mw-parser-output .toclimit-7 .toclevel-6 ul{display:none}</style><div class="toclimit-3"><meta property="mw:PageProp/toc" /></div> <div class="mw-heading mw-heading2"><h2 id="Life">Life</h2></div> <div class="mw-heading mw-heading3"><h3 id="Traditional_narrative">Traditional narrative</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:0_Chambre_de_Rapha%C3%ABl_-_%C3%89cole_d%27Ath%C3%A8nes_-_Mus%C3%A9es_du_Vatican.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/0_Chambre_de_Rapha%C3%ABl_-_%C3%89cole_d%27Ath%C3%A8nes_-_Mus%C3%A9es_du_Vatican.JPG/330px-0_Chambre_de_Rapha%C3%ABl_-_%C3%89cole_d%27Ath%C3%A8nes_-_Mus%C3%A9es_du_Vatican.JPG" decoding="async" width="310" height="268" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/0_Chambre_de_Rapha%C3%ABl_-_%C3%89cole_d%27Ath%C3%A8nes_-_Mus%C3%A9es_du_Vatican.JPG/500px-0_Chambre_de_Rapha%C3%ABl_-_%C3%89cole_d%27Ath%C3%A8nes_-_Mus%C3%A9es_du_Vatican.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/0_Chambre_de_Rapha%C3%ABl_-_%C3%89cole_d%27Ath%C3%A8nes_-_Mus%C3%A9es_du_Vatican.JPG/960px-0_Chambre_de_Rapha%C3%ABl_-_%C3%89cole_d%27Ath%C3%A8nes_-_Mus%C3%A9es_du_Vatican.JPG 2x" data-file-width="3000" data-file-height="2592" /></a><figcaption>Detail of <a href="/wiki/Raphael" title="Raphael">Raphael</a>'s impression of Euclid, teaching students in <a href="/wiki/The_School_of_Athens" title="The School of Athens">The School of Athens</a> (1509–1511)</figcaption></figure> The English name 'Euclid' is the anglicized version of the <a href="/wiki/Ancient_Greek" title="Ancient Greek">Ancient Greek</a> name Eukleídes (Εὐκλείδης).<a href="#cite_note-FOOTNOTESialaros2021§_"Life"-4">[4]</a><a href="#cite_note-6">[a]</a> It is derived from '<a href="https://en.wiktionary.org/wiki/eu-#English" class="extiw" title="wikt:eu-">eu-</a>' (<a href="https://en.wiktionary.org/wiki/%CE%B5%E1%BD%96#Ancient_Greek" class="extiw" title="wikt:εὖ">εὖ</a>; 'well') and 'klês' (<a href="https://en.wiktionary.org/wiki/#-κλῆς" class="extiw" title="wikt:">-κλῆς</a>; 'fame'), meaning "renowned, glorious".<a href="#cite_note-FOOTNOTE''OED''b-7">[6]</a> In English, by <a href="/wiki/Metonymy" title="Metonymy">metonymy</a>, 'Euclid' can mean his most well-known work, <a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Euclid's Elements</a>, or a copy thereof,<a href="#cite_note-FOOTNOTE''OED''a-5">[5]</a> and is sometimes synonymous with 'geometry'.<a href="#cite_note-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage125_125]-2">[2]</a> As with many <a href="/wiki/Ancient_Greek_mathematicians" class="mw-redirect" title="Ancient Greek mathematicians">ancient Greek mathematicians</a>, the details of Euclid's life are mostly unknown.<a href="#cite_note-FOOTNOTEHeath1981354-8">[7]</a> He is accepted as the author of four mostly extant treatises—the Elements, <a href="/wiki/Euclid%27s_Optics" title="Euclid's Optics">Optics</a>, <a href="/wiki/Euclid%27s_Data" title="Euclid's Data">Data</a>, <a href="/wiki/Euclid%27s_Phaenomena" title="Euclid's Phaenomena">Phaenomena</a>—but besides this, there is nothing known for certain of him.<a href="#cite_note-FOOTNOTEAsper2010§_para._1-9">[8]</a><a href="#cite_note-11">[b]</a> The traditional narrative mainly follows the 5th century AD account by <a href="/wiki/Proclus" title="Proclus">Proclus</a> in his Commentary on the First Book of Euclid's Elements, as well as a few anecdotes from <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus of Alexandria</a> in the early 4th century.<a href="#cite_note-FOOTNOTESialaros2021§_"Life"-4">[4]</a><a href="#cite_note-13">[c]</a> According to Proclus, Euclid lived shortly after several of <a href="/wiki/Plato" title="Plato">Plato</a>'s (<abbr title="died">d.</abbr> 347 BC) followers and before the mathematician <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> (<abbr title="circa">c.</abbr> 287 – c. 212 BC);<a href="#cite_note-14">[d]</a> specifically, Proclus placed Euclid during the rule of <a href="/wiki/Ptolemy_I_Soter" title="Ptolemy I Soter">Ptolemy I</a> (<abbr title="reigned">r.</abbr> 305/304–282 BC).<a href="#cite_note-FOOTNOTEHeath1981354-8">[7]</a><a href="#cite_note-FOOTNOTEAsper2010§_para._1-9">[8]</a><a href="#cite_note-15">[e]</a> Euclid's birthdate is unknown; some scholars estimate around 330<a href="#cite_note-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52]-16">[11]</a><a href="#cite_note-FOOTNOTESialaros2020141-17">[12]</a> or 325 BC,<a href="#cite_note-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage125_125]-2">[2]</a><a href="#cite_note-FOOTNOTEGoulding2010125-18">[13]</a> but others refrain from speculating.<a href="#cite_note-FOOTNOTESmorynski20082-19">[14]</a> It is presumed that he was of Greek descent,<a href="#cite_note-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52]-16">[11]</a> but his birthplace is unknown.<a href="#cite_note-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_100]-20">[15]</a><a href="#cite_note-22">[f]</a> Proclus held that Euclid followed the <a href="/wiki/Platonism" title="Platonism">Platonic tradition</a>, but there is no definitive confirmation for this.<a href="#cite_note-FOOTNOTEHeath1981355-23">[17]</a> It is unlikely he was a contemporary of Plato, so it is often presumed that he was educated by Plato's disciples at the <a href="/wiki/Platonic_Academy" title="Platonic Academy">Platonic Academy</a> in Athens.<a href="#cite_note-FOOTNOTEGoulding2010126-24">[18]</a> Historian <a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Thomas Heath</a> supported this theory, noting that most capable geometers lived in Athens, including many of those whose work Euclid built on;<a href="#cite_note-FOOTNOTEHeath1908[httpsarchiveorgdetailsbub_gb_UhgPAAAAIAAJpagen13mode2up_2]-25">[19]</a> historian Michalis Sialaros considers this a mere conjecture.<a href="#cite_note-FOOTNOTESialaros2021§_"Life"-4">[4]</a><a href="#cite_note-FOOTNOTESialaros2020147–148-26">[20]</a> In any event, the contents of Euclid's work demonstrate familiarity with the Platonic geometry tradition.<a href="#cite_note-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52]-16">[11]</a> In his Collection, Pappus mentions that <a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius</a> studied with Euclid's students in <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a>, and this has been taken to imply that Euclid worked and founded a <a href="/wiki/School_of_thought" title="School of thought">mathematical tradition</a> there.<a href="#cite_note-FOOTNOTEAsper2010§_para._1-9">[8]</a><a href="#cite_note-FOOTNOTESialaros2020142-27">[21]</a><a href="#cite_note-FOOTNOTEHeath1908[httpsarchiveorgdetailsbub_gb_UhgPAAAAIAAJpagen13mode2up_2]-25">[19]</a> The city was founded by <a href="/wiki/Alexander_the_Great" title="Alexander the Great">Alexander the Great</a> in 331 BC,<a href="#cite_note-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage126_126]-28">[22]</a> and the rule of Ptolemy I from 306 BC onwards gave it a stability which was relatively unique amid the chaotic <a href="/wiki/Wars_of_the_Diadochi" title="Wars of the Diadochi">wars over dividing Alexander's empire</a>.<a href="#cite_note-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage50mode2up_51]-29">[23]</a> Ptolemy began a process of <a href="/wiki/Hellenization" title="Hellenization">hellenization</a> and commissioned numerous constructions, building the massive <a href="/wiki/Musaeum" class="mw-redirect" title="Musaeum">Musaeum</a> institution, which was a leading center of education.<a href="#cite_note-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_100]-20">[15]</a><a href="#cite_note-31">[g]</a> Euclid is speculated to have been among the Musaeum's first scholars.<a href="#cite_note-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage126_126]-28">[22]</a> Euclid's date of death is unknown; it has been speculated that he died <abbr title="circa">c.</abbr> 270 BC.<a href="#cite_note-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage126_126]-28">[22]</a> <div class="mw-heading mw-heading3"><h3 id="Identity_and_historicity">Identity and historicity</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Domenico_Marol%C3%AC_-_Euclid_of_Megara.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Domenico_Marol%C3%AC_-_Euclid_of_Megara.jpg/330px-Domenico_Marol%C3%AC_-_Euclid_of_Megara.jpg" decoding="async" width="330" height="207" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Domenico_Marol%C3%AC_-_Euclid_of_Megara.jpg/500px-Domenico_Marol%C3%AC_-_Euclid_of_Megara.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Domenico_Marol%C3%AC_-_Euclid_of_Megara.jpg/960px-Domenico_Marol%C3%AC_-_Euclid_of_Megara.jpg 2x" data-file-width="1326" data-file-height="830" /></a><figcaption><a href="/wiki/Domenico_Maroli" title="Domenico Maroli">Domenico Maroli</a>'s 1650s painting Euclide di Megara si traveste da donna per recarsi ad Atene a seguire le lezioni di Socrate [Euclid of Megara Dressing as a Woman to Hear Socrates Teach in Athens]. At the time, Euclid the philosopher and Euclid the mathematician were wrongly considered the same person, so this painting includes mathematical objects on the table.<a href="#cite_note-FOOTNOTESialaros2021§_"Life"_and_Note_5-32">[25]</a></figcaption></figure> Euclid is often referred to as 'Euclid of Alexandria' to differentiate him from the earlier philosopher <a href="/wiki/Euclid_of_Megara" title="Euclid of Megara">Euclid of Megara</a>, a pupil of <a href="/wiki/Socrates" title="Socrates">Socrates</a> included in <a href="/wiki/List_of_speakers_in_Plato%27s_dialogues" title="List of speakers in Plato's dialogues">dialogues of Plato</a> with whom he was historically conflated.<a href="#cite_note-FOOTNOTESialaros2021§_"Life"-4">[4]</a><a href="#cite_note-FOOTNOTESmorynski20082-19">[14]</a> <a href="/wiki/Valerius_Maximus" title="Valerius Maximus">Valerius Maximus</a>, the 1st century AD Roman compiler of anecdotes, mistakenly substituted Euclid's name for <a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus</a> (4th century BC) as the mathematician to whom Plato sent those asking how to <a href="/wiki/Doubling_the_cube" title="Doubling the cube">double the cube</a>.<a href="#cite_note-FOOTNOTEJones2005-33">[26]</a> Perhaps on the basis of this mention of a mathematical Euclid roughly a century early, Euclid became mixed up with Euclid of Megara in medieval <a href="/wiki/Byzantine_Empire" title="Byzantine Empire">Byzantine</a> sources (now lost),<a href="#cite_note-FOOTNOTEGoulding2010120-34">[27]</a> eventually leading Euclid the mathematician to be ascribed details of both men's biographies and described as Megarensis (<abbr style="font-size:85%" title="literal translation">lit.</abbr> 'of Megara').<a href="#cite_note-FOOTNOTESialaros2021§_"Life"-4">[4]</a><a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Life"-35">[28]</a> The Byzantine scholar <a href="/wiki/Theodore_Metochites" title="Theodore Metochites">Theodore Metochites</a> (<abbr title="circa">c.</abbr> 1300) explicitly conflated the two Euclids, as did printer <a href="/wiki/Erhard_Ratdolt" title="Erhard Ratdolt">Erhard Ratdolt</a>'s 1482 <a href="/wiki/Editio_princeps" title="Editio princeps">editio princeps</a> of <a href="/wiki/Campanus_of_Novara" title="Campanus of Novara">Campanus of Novara</a>'s Latin translation of the Elements.<a href="#cite_note-FOOTNOTEGoulding2010120-34">[27]</a> After the mathematician <a href="/w/index.php?title=Bartolomeo_Zamberti&action=edit&redlink=1" class="new" title="Bartolomeo Zamberti (page does not exist)">Bartolomeo Zamberti</a> [<a href="https://fr.wikipedia.org/wiki/Bartolomeo_Zamberti" class="extiw" title="fr:Bartolomeo Zamberti">fr</a>; <a href="https://de.wikipedia.org/wiki/Bartolomeo_Zamberti" class="extiw" title="de:Bartolomeo Zamberti">de</a>] appended most of the extant biographical fragments about either Euclid to the preface of his 1505 translation of the Elements, subsequent publications passed on this identification.<a href="#cite_note-FOOTNOTEGoulding2010120-34">[27]</a> Later Renaissance scholars, particularly <a href="/wiki/Peter_Ramus" class="mw-redirect" title="Peter Ramus">Peter Ramus</a>, reevaluated this claim, proving it false via issues in chronology and contradiction in early sources.<a href="#cite_note-FOOTNOTEGoulding2010120-34">[27]</a> <a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Medieval Arabic sources</a> give vast amounts of information concerning Euclid's life, but are completely unverifiable.<a href="#cite_note-FOOTNOTESialaros2021§_"Life"-4">[4]</a> Most scholars consider them of dubious authenticity;<a href="#cite_note-FOOTNOTEAsper2010§_para._1-9">[8]</a> Heath in particular contends that the fictionalization was done to strengthen the connection between a revered mathematician and the Arab world.<a href="#cite_note-FOOTNOTEHeath1981355-23">[17]</a> There are also numerous anecdotal stories concerning to Euclid, all of uncertain historicity, which "picture him as a kindly and gentle old man".<a href="#cite_note-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_101]-36">[29]</a> The best known of these is Proclus' story about Ptolemy asking Euclid if there was a quicker path to learning geometry than reading his Elements, which Euclid replied with "there is no royal road to geometry".<a href="#cite_note-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_101]-36">[29]</a> This anecdote is questionable since a very similar interaction between <a href="/wiki/Menaechmus" title="Menaechmus">Menaechmus</a> and Alexander the Great is recorded from <a href="/wiki/Stobaeus" title="Stobaeus">Stobaeus</a>.<a href="#cite_note-FOOTNOTEBoyer199196-37">[30]</a> Both accounts were written in the 5th century AD, neither indicates its source, and neither appears in ancient Greek literature.<a href="#cite_note-FOOTNOTESialaros201890-38">[31]</a> Any firm dating of Euclid's activity <abbr title="circa">c.</abbr> 300 BC is called into question by a lack of contemporary references.<a href="#cite_note-FOOTNOTESialaros2021§_"Life"-4">[4]</a> The earliest original reference to Euclid is in Apollonius' <a href="/wiki/Prefatory" class="mw-redirect" title="Prefatory">prefatory</a> letter to the <a href="/wiki/Conics" class="mw-redirect" title="Conics">Conics</a> (early 2nd century BC): "The third book of the Conics contains many astonishing theorems that are useful for both the syntheses and the determinations of number of solutions of solid <a href="/wiki/Locus_(mathematics)" title="Locus (mathematics)">loci</a>. Most of these, and the finest of them, are novel. And when we discovered them we realized that Euclid had not made the synthesis of the locus on three and four lines but only an accidental fragment of it, and even that was not felicitously done."<a href="#cite_note-FOOTNOTEJones2005-33">[26]</a> The Elements is speculated to have been at least partly in circulation by the 3rd century BC, as Archimedes and Apollonius take several of its propositions for granted;<a href="#cite_note-FOOTNOTESialaros2021§_"Life"-4">[4]</a> however, Archimedes employs an older variant of the <a href="/w/index.php?title=Theory_of_proportions&action=edit&redlink=1" class="new" title="Theory of proportions (page does not exist)">theory of proportions</a> than the one found in the Elements.<a href="#cite_note-FOOTNOTEAsper2010§_para._1-9">[8]</a> The oldest physical copies of material included in the Elements, dating from roughly 100 AD, can be found on <a href="/wiki/Oxyrhynchus_Papyri" title="Oxyrhynchus Papyri">papyrus fragments unearthed</a> in an ancient rubbish heap from <a href="/wiki/Oxyrhynchus" title="Oxyrhynchus">Oxyrhynchus</a>, <a href="/wiki/Roman_Egypt" title="Roman Egypt">Roman Egypt</a>. The oldest extant direct citations to the Elements in works whose dates are firmly known are not until the 2nd century AD, by <a href="/wiki/Galen" title="Galen">Galen</a> and <a href="/wiki/Alexander_of_Aphrodisias" title="Alexander of Aphrodisias">Alexander of Aphrodisias</a>; by this time it was a standard school text.<a href="#cite_note-FOOTNOTEJones2005-33">[26]</a> Some ancient Greek mathematicians mention Euclid by name, but he is usually referred to as "ὁ στοιχειώτης" ("the author of Elements").<a href="#cite_note-FOOTNOTEHeath1981357-39">[32]</a> In the Middle Ages, some scholars contended Euclid was not a historical personage and that his name arose from a <a href="/wiki/Language_change" title="Language change">corruption</a> of Greek mathematical terms.<a href="#cite_note-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52–53]-40">[33]</a> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2></div> <div class="mw-heading mw-heading3"><h3 id="Elements">Elements</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Euclid's Elements</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:P._Oxy._I_29.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/P._Oxy._I_29.jpg/350px-P._Oxy._I_29.jpg" decoding="async" width="350" height="213" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/P._Oxy._I_29.jpg/525px-P._Oxy._I_29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/P._Oxy._I_29.jpg/700px-P._Oxy._I_29.jpg 2x" data-file-width="1694" data-file-height="1032" /></a><figcaption>A <a href="/wiki/Papyrus_Oxyrhynchus_29" title="Papyrus Oxyrhynchus 29">papyrus fragment</a> of Euclid's Elements dated to <abbr title="circa">c.</abbr> 75–125 AD. Found at <a href="/wiki/Oxyrhynchus" title="Oxyrhynchus">Oxyrhynchus</a>, the diagram accompanies Book II, Proposition 5.<a href="#cite_note-FOOTNOTEFowler1999210–211-41">[34]</a></figcaption></figure> Euclid is best known for his thirteen-book treatise, the Elements (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: <a href="https://en.wiktionary.org/wiki/%CF%83%CF%84%CE%BF%CE%B9%CF%87%CE%B5%CE%AF%CE%B1" class="extiw" title="wikt:στοιχεία">Στοιχεῖα</a>; Stoicheia), considered his <a href="/wiki/Magnum_opus" class="mw-redirect" title="Magnum opus">magnum opus</a>.<a href="#cite_note-FOOTNOTESialaros2021§_"Summary"-3">[3]</a><a href="#cite_note-FOOTNOTEAsper2010§_para._2-42">[35]</a> Much of its content originates from earlier mathematicians, including <a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus</a>, <a href="/wiki/Hippocrates_of_Chios" title="Hippocrates of Chios">Hippocrates of Chios</a>, <a href="/wiki/Thales" class="mw-redirect" title="Thales">Thales</a> and <a href="/wiki/Theaetetus_(mathematician)" title="Theaetetus (mathematician)">Theaetetus</a>, while other theorems are mentioned by Plato and Aristotle.<a href="#cite_note-FOOTNOTEAsper2010§_para._6-43">[36]</a> It is difficult to differentiate the work of Euclid from that of his predecessors, especially because the Elements essentially superseded much earlier and now-lost Greek mathematics.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">[37]</a><a href="#cite_note-45">[h]</a> The classicist Markus Asper concludes that "apparently Euclid's achievement consists of assembling accepted mathematical knowledge into a cogent order and adding new proofs to fill in the gaps" and the historian <a href="/wiki/Serafina_Cuomo" title="Serafina Cuomo">Serafina Cuomo</a> described it as a "reservoir of results".<a href="#cite_note-FOOTNOTECuomo2005131-46">[38]</a><a href="#cite_note-FOOTNOTEAsper2010§_para._6-43">[36]</a> Despite this, Sialaros furthers that "the remarkably tight structure of the Elements reveals authorial control beyond the limits of a mere editor".<a href="#cite_note-FOOTNOTESialaros2021§_"Works"-10">[9]</a> The Elements does not exclusively discuss geometry as is sometimes believed.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">[37]</a> It is traditionally divided into three topics: <a href="/wiki/Plane_geometry" class="mw-redirect" title="Plane geometry">plane geometry</a> (books 1–6), basic <a href="/wiki/Number_theory" title="Number theory">number theory</a> (books 7–10) and <a href="/wiki/Solid_geometry" title="Solid geometry">solid geometry</a> (books 11–13)—though book 5 (on proportions) and 10 (on <a href="/wiki/Irrational_number" title="Irrational number">irrational</a> lines) do not exactly fit this scheme.<a href="#cite_note-FOOTNOTEArtmann20123-47">[39]</a><a href="#cite_note-FOOTNOTEAsper2010§_para._4-48">[40]</a> The heart of the text is the <a href="/wiki/Theorem" title="Theorem">theorems</a> scattered throughout.<a href="#cite_note-FOOTNOTEAsper2010§_para._2-42">[35]</a> Using Aristotle's terminology, these may be generally separated into two categories: "first principles" and "second principles".<a href="#cite_note-FOOTNOTESialaros2021§_"The_''Elements''"-49">[41]</a> The first group includes statements labeled as a "definition" (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: ὅρος or ὁρισμός), "postulate" (αἴτημα), or a "common notion" (κοινὴ ἔννοια);<a href="#cite_note-FOOTNOTESialaros2021§_"The_''Elements''"-49">[41]</a><a href="#cite_note-FOOTNOTEJahnke201018-50">[42]</a> only the first book includes postulates—later known as <a href="/wiki/Axiom" title="Axiom">axioms</a>—and common notions.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">[37]</a><a href="#cite_note-51">[i]</a> The second group consists of propositions, presented alongside <a href="/wiki/Mathematical_proof" title="Mathematical proof">mathematical proofs</a> and diagrams.<a href="#cite_note-FOOTNOTESialaros2021§_"The_''Elements''"-49">[41]</a> It is unknown if Euclid intended the Elements as a textbook, but its method of presentation makes it a natural fit.<a href="#cite_note-FOOTNOTESialaros2021§_"Works"-10">[9]</a> As a whole, the <a href="/wiki/Authorial_voice" class="mw-redirect" title="Authorial voice">authorial voice</a> remains general and impersonal.<a href="#cite_note-FOOTNOTEAsper2010§_para._6-43">[36]</a> <div class="mw-heading mw-heading4"><h4 id="Contents">Contents</h4></div> <table class="wikitable plainrowheaders floatright" style="font-size:90%"> <caption>Euclid's postulates and common notions<a href="#cite_note-FOOTNOTEHeath1908154–155-52">[43]</a> </caption> <tbody><tr> <th scope="col"><abbr title="Number">No.</abbr> </th> <th scope="col">Postulates </th></tr> <tr> <td colspan="2">Let the following be postulated: </td></tr> <tr> <td>1 </td> <td>To draw a straight line from any point to any point<a href="#cite_note-53">[j]</a> </td></tr> <tr> <td>2 </td> <td>To produce a finite straight line continuously in a straight line </td></tr> <tr> <td>3 </td> <td>To describe a circle with any centre and distance </td></tr> <tr> <td>4 </td> <td>That all right angles are equal to one another </td></tr> <tr> <td>5 </td> <td>That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles </td></tr> <tr> <th scope="col"><abbr title="Number">No.</abbr> </th> <th scope="col">Common notions </th></tr> <tr> <td>1 </td> <td>Things which are equal to the same thing are also equal to one another </td></tr> <tr> <td>2 </td> <td>If equals be added to equals, the wholes are equal </td></tr> <tr> <td>3 </td> <td>If equals be subtracted from equals, the remainders are equal </td></tr> <tr> <td>4 </td> <td>Things which coincide with one another are equal to one another </td></tr> <tr> <td>5 </td> <td>The whole is greater than the part </td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Foundations_of_geometry" title="Foundations of geometry">Foundations of geometry</a></div> Book 1 of the Elements is foundational for the entire text.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">[37]</a> It begins with a series of 20 definitions for basic geometric concepts such as <a href="/wiki/Line_(geometry)" title="Line (geometry)">lines</a>, <a href="/wiki/Angle" title="Angle">angles</a> and various <a href="/wiki/Regular_polygon" title="Regular polygon">regular polygons</a>.<a href="#cite_note-FOOTNOTEArtmann20123–4-54">[44]</a> Euclid then presents 10 assumptions (see table, right), grouped into five postulates (axioms) and five common notions.<a href="#cite_note-FOOTNOTEWolfe19454-55">[45]</a><a href="#cite_note-56">[k]</a> These assumptions are intended to provide the logical basis for every subsequent theorem, i.e. serve as an <a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatic system</a>.<a href="#cite_note-FOOTNOTEPickover200956-57">[46]</a><a href="#cite_note-59">[l]</a> The common notions exclusively concern the comparison of <a href="/wiki/Magnitude_(mathematics)" title="Magnitude (mathematics)">magnitudes</a>.<a href="#cite_note-FOOTNOTEArtmann20124-60">[48]</a> While postulates 1 through 4 are relatively straightforward,<a href="#cite_note-61">[m]</a> the 5th is known as the <a href="/wiki/Parallel_postulate" title="Parallel postulate">parallel postulate</a> and particularly famous.<a href="#cite_note-FOOTNOTEArtmann20124-60">[48]</a><a href="#cite_note-63">[n]</a> Book 1 also includes 48 propositions, which can be loosely divided into those concerning basic theorems and constructions of plane geometry and <a href="/wiki/Triangle_congruence" class="mw-redirect" title="Triangle congruence">triangle congruence</a> (1–26); <a href="/wiki/Parallel_line" class="mw-redirect" title="Parallel line">parallel lines</a> (27–34); the <a href="/wiki/Area" title="Area">area</a> of <a href="/wiki/Triangle" title="Triangle">triangles</a> and <a href="/wiki/Parallelogram" title="Parallelogram">parallelograms</a> (35–45); and the <a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a> (46–48).<a href="#cite_note-FOOTNOTEArtmann20124-60">[48]</a> The last of these includes the earliest surviving proof of the Pythagorean theorem, described by Sialaros as "remarkably delicate".<a href="#cite_note-FOOTNOTESialaros2021§_"The_''Elements''"-49">[41]</a> Book 2 is traditionally understood as concerning "<a href="/wiki/Greek_geometric_algebra" class="mw-redirect" title="Greek geometric algebra">geometric algebra</a>", though this interpretation has been heavily debated since the 1970s; critics describe the characterization as anachronistic, since the foundations of even nascent algebra occurred many centuries later.<a href="#cite_note-FOOTNOTESialaros2021§_"The_''Elements''"-49">[41]</a> The second book has a more focused scope and mostly provides algebraic theorems to accompany various geometric shapes.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">[37]</a><a href="#cite_note-FOOTNOTEArtmann20124-60">[48]</a> It focuses on the area of <a href="/wiki/Rectangle" title="Rectangle">rectangles</a> and <a href="/wiki/Square" title="Square">squares</a> (see <a href="/wiki/Quadrature_(geometry)" title="Quadrature (geometry)">Quadrature</a>), and leads up to a geometric precursor of the <a href="/wiki/Law_of_cosines" title="Law of cosines">law of cosines</a>.<a href="#cite_note-FOOTNOTEKatzMichalowicz202059-64">[50]</a> Book 3 focuses on circles, while the 4th discusses <a href="/wiki/Regular_polygons" class="mw-redirect" title="Regular polygons">regular polygons</a>, especially the <a href="/wiki/Pentagon" title="Pentagon">pentagon</a>.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">[37]</a><a href="#cite_note-FOOTNOTEArtmann20125-65">[51]</a> Book 5 is among the work's most important sections and presents what is usually termed as the "general theory of proportion".<a href="#cite_note-FOOTNOTEArtmann20125–6-66">[52]</a><a href="#cite_note-67">[o]</a> Book 6 utilizes the "theory of <a href="/wiki/Ratio" title="Ratio">ratios</a>" in the context of plane geometry.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">[37]</a> It is built almost entirely of its first proposition:<a href="#cite_note-FOOTNOTEArtmann20126-68">[53]</a> "Triangles and parallelograms which are under the same height are to one another as their bases".<a href="#cite_note-FOOTNOTEHeath1908b191-69">[54]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Platonic_Solids_Transparent.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Platonic_Solids_Transparent.svg/220px-Platonic_Solids_Transparent.svg.png" decoding="async" width="220" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Platonic_Solids_Transparent.svg/330px-Platonic_Solids_Transparent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Platonic_Solids_Transparent.svg/440px-Platonic_Solids_Transparent.svg.png 2x" data-file-width="496" data-file-height="404" /></a><figcaption>The five <a href="/wiki/Platonic_solids" class="mw-redirect" title="Platonic solids">Platonic solids</a>, foundational components of <a href="/wiki/Solid_geometry" title="Solid geometry">solid geometry</a> which feature in Books 11–13</figcaption></figure> From Book 7 onwards, the mathematician <a href="/w/index.php?title=Benno_Artmann&action=edit&redlink=1" class="new" title="Benno Artmann (page does not exist)">Benno Artmann</a> [<a href="https://de.wikipedia.org/wiki/Benno_Artmann" class="extiw" title="de:Benno Artmann">de</a>] notes that "Euclid starts afresh. Nothing from the preceding books is used".<a href="#cite_note-FOOTNOTEArtmann20127-70">[55]</a> <a href="/wiki/Number_theory" title="Number theory">Number theory</a> is covered by books 7 to 10, the former beginning with a set of 22 definitions for <a href="/wiki/Parity_(mathematics)" title="Parity (mathematics)">parity</a>, <a href="/wiki/Prime_number" title="Prime number">prime numbers</a> and other arithmetic-related concepts.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">[37]</a> Book 7 includes the <a href="/wiki/Euclidean_algorithm" title="Euclidean algorithm">Euclidean algorithm</a>, a method for finding the <a href="/wiki/Greatest_common_divisor" title="Greatest common divisor">greatest common divisor</a> of two numbers.<a href="#cite_note-FOOTNOTEArtmann20127-70">[55]</a> The 8th book discusses <a href="/wiki/Geometric_progression" title="Geometric progression">geometric progressions</a>, while book 9 includes the proposition, now called <a href="/wiki/Euclid%27s_theorem" title="Euclid's theorem">Euclid's theorem</a>, that there are infinitely many <a href="/wiki/Prime_number" title="Prime number">prime numbers</a>.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">[37]</a> Of the Elements, book 10 is by far the largest and most complex, dealing with irrational numbers in the context of magnitudes.<a href="#cite_note-FOOTNOTESialaros2021§_"The_''Elements''"-49">[41]</a> The final three books (11–13) primarily discuss <a href="/wiki/Solid_geometry" title="Solid geometry">solid geometry</a>.<a href="#cite_note-FOOTNOTEArtmann20123-47">[39]</a> By introducing a list of 37 definitions, Book 11 contextualizes the next two.<a href="#cite_note-FOOTNOTEArtmann20129-71">[56]</a> Although its foundational character resembles Book 1, unlike the latter it features no axiomatic system or postulates.<a href="#cite_note-FOOTNOTEArtmann20129-71">[56]</a> The three sections of Book 11 include content on solid geometry (1–19), solid angles (20–23) and <a href="/wiki/Parallelepiped" title="Parallelepiped">parallelepipedal</a> solids (24–37).<a href="#cite_note-FOOTNOTEArtmann20129-71">[56]</a> <div class="mw-heading mw-heading3"><h3 id="Other_works">Other works</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Euclid_Dodecahedron_1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Euclid_Dodecahedron_1.svg/250px-Euclid_Dodecahedron_1.svg.png" decoding="async" width="220" height="249" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Euclid_Dodecahedron_1.svg/330px-Euclid_Dodecahedron_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Euclid_Dodecahedron_1.svg/500px-Euclid_Dodecahedron_1.svg.png 2x" data-file-width="750" data-file-height="850" /></a><figcaption>Euclid's construction of a regular <a href="/wiki/Dodecahedron" title="Dodecahedron">dodecahedron</a></figcaption></figure> In addition to the Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure as Elements, with definitions and proved propositions. <ul><li>Catoptrics concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors, though the attribution is sometimes questioned.<a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a></li> <li>The <a href="/wiki/Euclid%27s_Data" title="Euclid's Data">Data</a> (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: Δεδομένα), is a somewhat short text which deals with the nature and implications of "given" information in geometrical problems.<a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a></li> <li>On Divisions (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: Περὶ Διαιρέσεων) survives only partially in <a href="/wiki/Arabic_language" class="mw-redirect" title="Arabic language">Arabic</a> translation, and concerns the division of geometrical figures into two or more equal parts or into parts in given <a href="/wiki/Ratio" title="Ratio">ratios</a>. It includes thirty-six propositions and is similar to Apollonius' Conics.<a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a></li> <li>The <a href="/wiki/Euclid%27s_Optics" title="Euclid's Optics">Optics</a> (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: Ὀπτικά) is the earliest surviving Greek treatise on perspective. It includes an introductory discussion of <a href="/wiki/Geometrical_optics" title="Geometrical optics">geometrical optics</a> and basic rules of <a href="/wiki/Perspective_(graphical)" title="Perspective (graphical)">perspective</a>.<a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a></li> <li>The <a href="/wiki/Euclid%27s_Phaenomena" title="Euclid's Phaenomena">Phaenomena</a> (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: Φαινόμενα) is a treatise on <a href="/wiki/Spherical_astronomy" title="Spherical astronomy">spherical astronomy</a>, survives in Greek; it is similar to On the Moving Sphere by <a href="/wiki/Autolycus_of_Pitane" title="Autolycus of Pitane">Autolycus of Pitane</a>, who flourished around 310 BC.<a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Lost_works">Lost works</h3></div> Four other works are credibly attributed to Euclid, but have been lost.<a href="#cite_note-FOOTNOTESialaros2021§_"Works"-10">[9]</a> <ul><li>The Conics (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: Κωνικά) was a four-book survey on <a href="/wiki/Conic_section" title="Conic section">conic sections</a>, which was later superseded by Apollonius' more comprehensive treatment of the same name.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"-73">[58]</a><a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a> The work's existence is known primarily from Pappus, who asserts that the first four books of Apollonius' Conics are largely based on Euclid's earlier work.<a href="#cite_note-FOOTNOTEJones1986399–400-74">[59]</a> Doubt has been cast on this assertion by the historian <a href="/w/index.php?title=Alexander_Jones_(classicist)&action=edit&redlink=1" class="new" title="Alexander Jones (classicist) (page does not exist)">Alexander Jones</a> [<a href="https://de.wikipedia.org/wiki/Alexander_Jones_(Wissenschaftshistoriker)" class="extiw" title="de:Alexander Jones (Wissenschaftshistoriker)">de</a>], owing to sparse evidence and no other corroboration of Pappus' account.<a href="#cite_note-FOOTNOTEJones1986399–400-74">[59]</a></li> <li>The Pseudaria (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: Ψευδάρια; <abbr style="font-size:85%" title="literal translation">lit.</abbr> 'Fallacies'), was—according to Proclus in (70.1–18)—a text in geometrical <a href="/wiki/Reasoning" class="mw-redirect" title="Reasoning">reasoning</a>, written to advise beginners in avoiding common fallacies.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"-73">[58]</a><a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a> Very little is known of its specific contents aside from its scope and a few extant lines.<a href="#cite_note-FOOTNOTEAcerbi2008511-75">[60]</a></li> <li>The Porisms (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: Πορίσματα; <abbr style="font-size:85%" title="literal translation">lit.</abbr> 'Corollaries') was, based on accounts from Pappus and Proclus, probably a three-book treatise with approximately 200 propositions.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"-73">[58]</a><a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a> The term '<a href="/wiki/Porism" title="Porism">porism</a>' in this context does not refer to a <a href="/wiki/Corollary" title="Corollary">corollary</a>, but to "a third type of proposition—an intermediate between a theorem and a problem—the aim of which is to discover a feature of an existing geometrical entity, for example, to find the centre of a circle".<a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a> The mathematician <a href="/wiki/Michel_Chasles" title="Michel Chasles">Michel Chasles</a> speculated that these now-lost propositions included content related to the modern theories of <a href="/wiki/Transversal_(geometry)" title="Transversal (geometry)">transversals</a> and <a href="/wiki/Projective_geometry" title="Projective geometry">projective geometry</a>.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"-73">[58]</a><a href="#cite_note-76">[p]</a></li> <li>The Surface Loci (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: Τόποι πρὸς ἐπιφανείᾳ) is of virtually unknown contents, aside from speculation based on the work's title.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"-73">[58]</a> Conjecture based on later accounts has suggested it discussed cones and cylinders, among other subjects.<a href="#cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">[57]</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Legacy">Legacy</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/List_of_things_named_after_Euclid" title="List of things named after Euclid">List of things named after Euclid</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Byrne1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Byrne1.png/170px-Byrne1.png" decoding="async" width="170" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Byrne1.png/255px-Byrne1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Byrne1.png/340px-Byrne1.png 2x" data-file-width="543" data-file-height="688" /></a><figcaption>The cover page of <a href="/wiki/Oliver_Byrne_(mathematician)" title="Oliver Byrne (mathematician)">Oliver Byrne</a>'s 1847 colored edition of the Elements</figcaption></figure> Euclid is generally considered with Archimedes and Apollonius of Perga as among the greatest mathematicians of antiquity.<a href="#cite_note-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52]-16">[11]</a> Many commentators cite him as one of the most influential figures in the <a href="/wiki/History_of_mathematics" title="History of mathematics">history of mathematics</a>.<a href="#cite_note-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage125_125]-2">[2]</a> The geometrical system established by the Elements long dominated the field; however, today that system is often referred to as '<a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a>' to distinguish it from other <a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean geometries</a> discovered in the early 19th century.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Legacy"-77">[61]</a> Among Euclid's <a href="/wiki/List_of_things_named_after_Euclid" title="List of things named after Euclid">many namesakes</a> are the <a href="/wiki/European_Space_Agency" title="European Space Agency">European Space Agency</a>'s (ESA) <a href="/wiki/Euclid_(spacecraft)" title="Euclid (spacecraft)">Euclid</a> spacecraft,<a href="#cite_note-78">[62]</a> the lunar crater <a href="/wiki/Euclides_(crater)" title="Euclides (crater)">Euclides</a>,<a href="#cite_note-79">[63]</a> and the minor planet <a href="/wiki/4354_Euclides" title="4354 Euclides">4354 Euclides</a>.<a href="#cite_note-80">[64]</a> The Elements is often considered after the <a href="/wiki/Bible" title="Bible">Bible</a> as the most frequently translated, published, and studied book in the <a href="/wiki/Western_World" class="mw-redirect" title="Western World">Western World</a>'s history.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Legacy"-77">[61]</a> With Aristotle's <a href="/wiki/Metaphysics_(Aristotle)" title="Metaphysics (Aristotle)">Metaphysics</a>, the Elements is perhaps the most successful ancient Greek text, and was the dominant mathematical textbook in the Medieval Arab and Latin worlds.<a href="#cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Legacy"-77">[61]</a> The first English edition of the Elements was published in 1570 by <a href="/wiki/Henry_Billingsley" title="Henry Billingsley">Henry Billingsley</a> and <a href="/wiki/John_Dee" title="John Dee">John Dee</a>.<a href="#cite_note-FOOTNOTEGoulding2010120-34">[27]</a> The mathematician <a href="/wiki/Oliver_Byrne_(mathematician)" title="Oliver Byrne (mathematician)">Oliver Byrne</a> published a well-known version of the Elements in 1847 entitled The First Six Books of the Elements of Euclid in Which Coloured Diagrams and Symbols Are Used Instead of Letters for the Greater Ease of Learners, which included colored diagrams intended to increase its pedagogical effect.<a href="#cite_note-FOOTNOTEHawesKolpas2015-81">[65]</a> <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a> authored a <a href="/wiki/Hilbert%27s_axioms" title="Hilbert's axioms">modern axiomatization</a> of the Elements.<a href="#cite_note-FOOTNOTEHählPeters2022§_para._1-82">[66]</a> <a href="/wiki/Edna_St._Vincent_Millay" title="Edna St. Vincent Millay">Edna St. Vincent Millay</a> wrote that "Euclid alone has looked on Beauty bare."<a href="#cite_note-83">[67]</a> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-lower-alpha" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-6"><a href="#cite_ref-6">^</a> In modern English, 'Euclid' is pronounced as <a href="/wiki/Help:IPA/English" title="Help:IPA/English">/ˈjuːklɪd/</a>.<a href="#cite_note-FOOTNOTE''OED''a-5">[5]</a> </li> <li id="cite_note-11"><a href="#cite_ref-11">^</a> Euclid's oeuvre also includes the treatise On Divisions, which survives fragmented in a later Arabic source.<a href="#cite_note-FOOTNOTESialaros2021§_"Works"-10">[9]</a> He authored numerous <a href="#Lost_works">lost works</a> as well.<a href="#cite_note-FOOTNOTESialaros2021§_"Works"-10">[9]</a> </li> <li id="cite_note-13"><a href="#cite_ref-13">^</a> Some of the information from <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus of Alexandria</a> on Euclid is now lost and was preserved in <a href="/wiki/Proclus" title="Proclus">Proclus</a>'s Commentary on the First Book of Euclid's Elements.<a href="#cite_note-FOOTNOTEHeath1911741-12">[10]</a> </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> Proclus was likely working from (now-lost) 4th-century BC histories of mathematics written by <a href="/wiki/Theophrastus" title="Theophrastus">Theophrastus</a> and <a href="/wiki/Eudemus_of_Rhodes" title="Eudemus of Rhodes">Eudemus of Rhodes</a>. <a href="/wiki/Proclus#Commentary_on_Euclid's_Elements" title="Proclus">Proclus explicitly mentions</a> Amyclas of Heracleia, <a href="/wiki/Menaechmus" title="Menaechmus">Menaechmus</a> and his brother <a href="/wiki/Dinostratus" title="Dinostratus">Dinostratus</a>, <a href="/wiki/Theudius" title="Theudius">Theudius of Magnesia</a>, <a href="/wiki/Athenaeus_of_Cyzicus" title="Athenaeus of Cyzicus">Athenaeus of Cyzicus</a>, <a href="/w/index.php?title=Hermotimus_of_Colophon&action=edit&redlink=1" class="new" title="Hermotimus of Colophon (page does not exist)">Hermotimus of Colophon</a>, and <a href="/wiki/Philip_of_Opus" title="Philip of Opus">Philippus of Mende</a>, and says that Euclid came "not long after" these men. </li> <li id="cite_note-15"><a href="#cite_ref-15">^</a> See <a href="#CITEREFHeath1981">Heath 1981</a>, p. 354 for an English translation on Proclus's account of Euclid's life. </li> <li id="cite_note-22"><a href="#cite_ref-22">^</a> Later Arab sources state he was a Greek born in modern-day <a href="/wiki/Tyre,_Lebanon" title="Tyre, Lebanon">Tyre, Lebanon</a>, though these accounts are considered dubious and speculative.<a href="#cite_note-FOOTNOTEAsper2010§_para._1-9">[8]</a><a href="#cite_note-FOOTNOTESialaros2021§_"Life"-4">[4]</a> See <a href="#CITEREFHeath1981">Heath 1981</a>, p. 355 for an English translation of the Arab account. He was long held to have been born in Megara, but by the <a href="/wiki/Renaissance" title="Renaissance">Renaissance</a> it was concluded that he had been confused with the philosopher <a href="/wiki/Euclid_of_Megara" title="Euclid of Megara">Euclid of Megara</a>,<a href="#cite_note-FOOTNOTEGoulding2010118-21">[16]</a> see <a href="#Identity_and_historicity">§Identity and historicity</a> </li> <li id="cite_note-31"><a href="#cite_ref-31">^</a> The <a href="/wiki/Musaeum" class="mw-redirect" title="Musaeum">Musaeum</a> would later include the famous <a href="/wiki/Library_of_Alexandria" title="Library of Alexandria">Library of Alexandria</a>, but it was likely founded later, during the reign of <a href="/wiki/Ptolemy_II_Philadelphus" title="Ptolemy II Philadelphus">Ptolemy II Philadelphus</a> (285–246 BC).<a href="#cite_note-FOOTNOTETracy2000343–344-30">[24]</a> </li> <li id="cite_note-45"><a href="#cite_ref-45">^</a> The Elements version available today also includes "post-Euclidean" mathematics, probably added later by later editors such as the mathematician <a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a> in the 4th century.<a href="#cite_note-FOOTNOTEAsper2010§_para._6-43">[36]</a> </li> <li id="cite_note-51"><a href="#cite_ref-51">^</a> The use of the term "axiom" instead of "postulate" derives from the choice of <a href="/wiki/Proclus" title="Proclus">Proclus</a> to do so in his highly influential commentary on the Elements. Proclus also substituted the term "hypothesis" instead of "common notion", though preserved "postulate".<a href="#cite_note-FOOTNOTEJahnke201018-50">[42]</a> </li> <li id="cite_note-53"><a href="#cite_ref-53">^</a> See also: <a href="/wiki/Euclidean_relation" title="Euclidean relation">Euclidean relation</a> </li> <li id="cite_note-56"><a href="#cite_ref-56">^</a> The distinction between these categories is not immediately clear; postulates may simply refer to geometry specifically, while common notions are more general in scope.<a href="#cite_note-FOOTNOTEWolfe19454-55">[45]</a> </li> <li id="cite_note-59"><a href="#cite_ref-59">^</a> The mathematician Gerard Venema notes that this <a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatic system</a> is not complete: "Euclid assumed more than just what he stated in the postulates".<a href="#cite_note-FOOTNOTEVenema200610-58">[47]</a> </li> <li id="cite_note-61"><a href="#cite_ref-61">^</a> See <a href="#CITEREFHeath1908">Heath 1908</a>, pp. 195–201 for a detailed overview of postulates 1 through 4 </li> <li id="cite_note-63"><a href="#cite_ref-63">^</a> Since antiquity, enormous amounts of scholarship have been written about the 5th postulate, usually from mathematicians attempting to <a href="/wiki/Proving_(math)" class="mw-redirect" title="Proving (math)">prove</a> the postulate—which would make it different from the other, unprovable, four postulates.<a href="#cite_note-FOOTNOTEHeath1908202-62">[49]</a> </li> <li id="cite_note-67"><a href="#cite_ref-67">^</a> Much of Book 5 was probably ascertained from earlier mathematicians, perhaps Eudoxus.<a href="#cite_note-FOOTNOTESialaros2021§_"The_''Elements''"-49">[41]</a> </li> <li id="cite_note-76"><a href="#cite_ref-76">^</a> See <a href="#CITEREFJones1986">Jones 1986</a>, pp. 547–572 for further information on the Porisms </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626" /><div class="reflist reflist-columns references-column-width" style="column-width: 20em;"> <ol class="references"> <li id="cite_note-FOOTNOTEGetty-1"><a href="#cite_ref-FOOTNOTEGetty_1-0">^</a> <a href="#CITEREFGetty">Getty</a>. </li> <li id="cite_note-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage125_125]-2">^ <a href="#cite_ref-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage125_125]_2-0">a</a> <a href="#cite_ref-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage125_125]_2-1">b</a> <a href="#cite_ref-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage125_125]_2-2">c</a> <a href="#cite_ref-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage125_125]_2-3">d</a> <a href="#CITEREFBruno2003">Bruno 2003</a>, p. <a rel="nofollow" class="external text" href="https://archive.org/details/mathmathematicia00brun/page/125">125</a>. </li> <li id="cite_note-FOOTNOTESialaros2021§_"Summary"-3">^ <a href="#cite_ref-FOOTNOTESialaros2021§_"Summary"_3-0">a</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Summary"_3-1">b</a> <a href="#CITEREFSialaros2021">Sialaros 2021</a>, § "Summary". </li> <li id="cite_note-FOOTNOTESialaros2021§_"Life"-4">^ <a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_4-0">a</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_4-1">b</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_4-2">c</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_4-3">d</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_4-4">e</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_4-5">f</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_4-6">g</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_4-7">h</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_4-8">i</a> <a href="#CITEREFSialaros2021">Sialaros 2021</a>, § "Life". </li> <li id="cite_note-FOOTNOTE''OED''a-5">^ <a href="#cite_ref-FOOTNOTE''OED''a_5-0">a</a> <a href="#cite_ref-FOOTNOTE''OED''a_5-1">b</a> <a href="#CITEREFOEDa">OEDa</a>. </li> <li id="cite_note-FOOTNOTE''OED''b-7"><a href="#cite_ref-FOOTNOTE''OED''b_7-0">^</a> <a href="#CITEREFOEDb">OEDb</a>. </li> <li id="cite_note-FOOTNOTEHeath1981354-8">^ <a href="#cite_ref-FOOTNOTEHeath1981354_8-0">a</a> <a href="#cite_ref-FOOTNOTEHeath1981354_8-1">b</a> <a href="#CITEREFHeath1981">Heath 1981</a>, p. 354. </li> <li id="cite_note-FOOTNOTEAsper2010§_para._1-9">^ <a href="#cite_ref-FOOTNOTEAsper2010§_para._1_9-0">a</a> <a href="#cite_ref-FOOTNOTEAsper2010§_para._1_9-1">b</a> <a href="#cite_ref-FOOTNOTEAsper2010§_para._1_9-2">c</a> <a href="#cite_ref-FOOTNOTEAsper2010§_para._1_9-3">d</a> <a href="#cite_ref-FOOTNOTEAsper2010§_para._1_9-4">e</a> <a href="#cite_ref-FOOTNOTEAsper2010§_para._1_9-5">f</a> <a href="#CITEREFAsper2010">Asper 2010</a>, § para. 1. </li> <li id="cite_note-FOOTNOTESialaros2021§_"Works"-10">^ <a href="#cite_ref-FOOTNOTESialaros2021§_"Works"_10-0">a</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Works"_10-1">b</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Works"_10-2">c</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Works"_10-3">d</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Works"_10-4">e</a> <a href="#CITEREFSialaros2021">Sialaros 2021</a>, § "Works". </li> <li id="cite_note-FOOTNOTEHeath1911741-12"><a href="#cite_ref-FOOTNOTEHeath1911741_12-0">^</a> <a href="#CITEREFHeath1911">Heath 1911</a>, p. 741. </li> <li id="cite_note-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52]-16">^ <a href="#cite_ref-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52]_16-0">a</a> <a href="#cite_ref-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52]_16-1">b</a> <a href="#cite_ref-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52]_16-2">c</a> <a href="#cite_ref-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52]_16-3">d</a> <a href="#CITEREFBall1960">Ball 1960</a>, p. <a rel="nofollow" class="external text" href="https://archive.org/details/shortaccountofhi0000ball/page/52/mode/2up">52</a>. </li> <li id="cite_note-FOOTNOTESialaros2020141-17"><a href="#cite_ref-FOOTNOTESialaros2020141_17-0">^</a> <a href="#CITEREFSialaros2020">Sialaros 2020</a>, p. 141. </li> <li id="cite_note-FOOTNOTEGoulding2010125-18"><a href="#cite_ref-FOOTNOTEGoulding2010125_18-0">^</a> <a href="#CITEREFGoulding2010">Goulding 2010</a>, p. 125. </li> <li id="cite_note-FOOTNOTESmorynski20082-19">^ <a href="#cite_ref-FOOTNOTESmorynski20082_19-0">a</a> <a href="#cite_ref-FOOTNOTESmorynski20082_19-1">b</a> <a href="#CITEREFSmorynski2008">Smorynski 2008</a>, p. 2. </li> <li id="cite_note-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_100]-20">^ <a href="#cite_ref-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_100]_20-0">a</a> <a href="#cite_ref-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_100]_20-1">b</a> <a href="#CITEREFBoyer1991">Boyer 1991</a>, p. <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema00boye/page/100/mode/2up?view=theater">100</a>. </li> <li id="cite_note-FOOTNOTEGoulding2010118-21"><a href="#cite_ref-FOOTNOTEGoulding2010118_21-0">^</a> <a href="#CITEREFGoulding2010">Goulding 2010</a>, p. 118. </li> <li id="cite_note-FOOTNOTEHeath1981355-23">^ <a href="#cite_ref-FOOTNOTEHeath1981355_23-0">a</a> <a href="#cite_ref-FOOTNOTEHeath1981355_23-1">b</a> <a href="#CITEREFHeath1981">Heath 1981</a>, p. 355. </li> <li id="cite_note-FOOTNOTEGoulding2010126-24"><a href="#cite_ref-FOOTNOTEGoulding2010126_24-0">^</a> <a href="#CITEREFGoulding2010">Goulding 2010</a>, p. 126. </li> <li id="cite_note-FOOTNOTEHeath1908[httpsarchiveorgdetailsbub_gb_UhgPAAAAIAAJpagen13mode2up_2]-25">^ <a href="#cite_ref-FOOTNOTEHeath1908[httpsarchiveorgdetailsbub_gb_UhgPAAAAIAAJpagen13mode2up_2]_25-0">a</a> <a href="#cite_ref-FOOTNOTEHeath1908[httpsarchiveorgdetailsbub_gb_UhgPAAAAIAAJpagen13mode2up_2]_25-1">b</a> <a href="#CITEREFHeath1908">Heath 1908</a>, p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_UhgPAAAAIAAJ/page/n13/mode/2up">2</a>. </li> <li id="cite_note-FOOTNOTESialaros2020147–148-26"><a href="#cite_ref-FOOTNOTESialaros2020147–148_26-0">^</a> <a href="#CITEREFSialaros2020">Sialaros 2020</a>, pp. 147–148. </li> <li id="cite_note-FOOTNOTESialaros2020142-27"><a href="#cite_ref-FOOTNOTESialaros2020142_27-0">^</a> <a href="#CITEREFSialaros2020">Sialaros 2020</a>, p. 142. </li> <li id="cite_note-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage126_126]-28">^ <a href="#cite_ref-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage126_126]_28-0">a</a> <a href="#cite_ref-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage126_126]_28-1">b</a> <a href="#cite_ref-FOOTNOTEBruno2003[httpsarchiveorgdetailsmathmathematicia00brunpage126_126]_28-2">c</a> <a href="#CITEREFBruno2003">Bruno 2003</a>, p. <a rel="nofollow" class="external text" href="https://archive.org/details/mathmathematicia00brun/page/126">126</a>. </li> <li id="cite_note-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage50mode2up_51]-29"><a href="#cite_ref-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage50mode2up_51]_29-0">^</a> <a href="#CITEREFBall1960">Ball 1960</a>, p. <a rel="nofollow" class="external text" href="https://archive.org/details/shortaccountofhi0000ball/page/50/mode/2up">51</a>. </li> <li id="cite_note-FOOTNOTETracy2000343–344-30"><a href="#cite_ref-FOOTNOTETracy2000343–344_30-0">^</a> <a href="#CITEREFTracy2000">Tracy 2000</a>, pp. 343–344. </li> <li id="cite_note-FOOTNOTESialaros2021§_"Life"_and_Note_5-32"><a href="#cite_ref-FOOTNOTESialaros2021§_"Life"_and_Note_5_32-0">^</a> <a href="#CITEREFSialaros2021">Sialaros 2021</a>, § "Life" and Note 5. </li> <li id="cite_note-FOOTNOTEJones2005-33">^ <a href="#cite_ref-FOOTNOTEJones2005_33-0">a</a> <a href="#cite_ref-FOOTNOTEJones2005_33-1">b</a> <a href="#cite_ref-FOOTNOTEJones2005_33-2">c</a> <a href="#CITEREFJones2005">Jones 2005</a>. </li> <li id="cite_note-FOOTNOTEGoulding2010120-34">^ <a href="#cite_ref-FOOTNOTEGoulding2010120_34-0">a</a> <a href="#cite_ref-FOOTNOTEGoulding2010120_34-1">b</a> <a href="#cite_ref-FOOTNOTEGoulding2010120_34-2">c</a> <a href="#cite_ref-FOOTNOTEGoulding2010120_34-3">d</a> <a href="#cite_ref-FOOTNOTEGoulding2010120_34-4">e</a> <a href="#CITEREFGoulding2010">Goulding 2010</a>, p. 120. </li> <li id="cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Life"-35"><a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Life"_35-0">^</a> <a href="#CITEREFTaisbakVan_der_Waerden2021">Taisbak & Van der Waerden 2021</a>, § "Life". </li> <li id="cite_note-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_101]-36">^ <a href="#cite_ref-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_101]_36-0">a</a> <a href="#cite_ref-FOOTNOTEBoyer1991[httpsarchiveorgdetailshistoryofmathema00boyepage100mode2upviewtheater_101]_36-1">b</a> <a href="#CITEREFBoyer1991">Boyer 1991</a>, p. <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema00boye/page/100/mode/2up?view=theater">101</a>. </li> <li id="cite_note-FOOTNOTEBoyer199196-37"><a href="#cite_ref-FOOTNOTEBoyer199196_37-0">^</a> <a href="#CITEREFBoyer1991">Boyer 1991</a>, p. 96. </li> <li id="cite_note-FOOTNOTESialaros201890-38"><a href="#cite_ref-FOOTNOTESialaros201890_38-0">^</a> <a href="#CITEREFSialaros2018">Sialaros 2018</a>, p. 90. </li> <li id="cite_note-FOOTNOTEHeath1981357-39"><a href="#cite_ref-FOOTNOTEHeath1981357_39-0">^</a> <a href="#CITEREFHeath1981">Heath 1981</a>, p. 357. </li> <li id="cite_note-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52–53]-40"><a href="#cite_ref-FOOTNOTEBall1960[httpsarchiveorgdetailsshortaccountofhi0000ballpage52mode2up_52–53]_40-0">^</a> <a href="#CITEREFBall1960">Ball 1960</a>, pp. <a rel="nofollow" class="external text" href="https://archive.org/details/shortaccountofhi0000ball/page/52/mode/2up">52–53</a>. </li> <li id="cite_note-FOOTNOTEFowler1999210–211-41"><a href="#cite_ref-FOOTNOTEFowler1999210–211_41-0">^</a> <a href="#CITEREFFowler1999">Fowler 1999</a>, pp. 210–211. </li> <li id="cite_note-FOOTNOTEAsper2010§_para._2-42">^ <a href="#cite_ref-FOOTNOTEAsper2010§_para._2_42-0">a</a> <a href="#cite_ref-FOOTNOTEAsper2010§_para._2_42-1">b</a> <a href="#CITEREFAsper2010">Asper 2010</a>, § para. 2. </li> <li id="cite_note-FOOTNOTEAsper2010§_para._6-43">^ <a href="#cite_ref-FOOTNOTEAsper2010§_para._6_43-0">a</a> <a href="#cite_ref-FOOTNOTEAsper2010§_para._6_43-1">b</a> <a href="#cite_ref-FOOTNOTEAsper2010§_para._6_43-2">c</a> <a href="#cite_ref-FOOTNOTEAsper2010§_para._6_43-3">d</a> <a href="#CITEREFAsper2010">Asper 2010</a>, § para. 6. </li> <li id="cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"-44">^ <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"_44-0">a</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"_44-1">b</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"_44-2">c</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"_44-3">d</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"_44-4">e</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"_44-5">f</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"_44-6">g</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"_44-7">h</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Sources_and_contents_of_the_''Elements''"_44-8">i</a> <a href="#CITEREFTaisbakVan_der_Waerden2021">Taisbak & Van der Waerden 2021</a>, § "Sources and contents of the Elements". </li> <li id="cite_note-FOOTNOTECuomo2005131-46"><a href="#cite_ref-FOOTNOTECuomo2005131_46-0">^</a> <a href="#CITEREFCuomo2005">Cuomo 2005</a>, p. 131. </li> <li id="cite_note-FOOTNOTEArtmann20123-47">^ <a href="#cite_ref-FOOTNOTEArtmann20123_47-0">a</a> <a href="#cite_ref-FOOTNOTEArtmann20123_47-1">b</a> <a href="#CITEREFArtmann2012">Artmann 2012</a>, p. 3. </li> <li id="cite_note-FOOTNOTEAsper2010§_para._4-48"><a href="#cite_ref-FOOTNOTEAsper2010§_para._4_48-0">^</a> <a href="#CITEREFAsper2010">Asper 2010</a>, § para. 4. </li> <li id="cite_note-FOOTNOTESialaros2021§_"The_''Elements''"-49">^ <a href="#cite_ref-FOOTNOTESialaros2021§_"The_''Elements''"_49-0">a</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"The_''Elements''"_49-1">b</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"The_''Elements''"_49-2">c</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"The_''Elements''"_49-3">d</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"The_''Elements''"_49-4">e</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"The_''Elements''"_49-5">f</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"The_''Elements''"_49-6">g</a> <a href="#CITEREFSialaros2021">Sialaros 2021</a>, § "The Elements". </li> <li id="cite_note-FOOTNOTEJahnke201018-50">^ <a href="#cite_ref-FOOTNOTEJahnke201018_50-0">a</a> <a href="#cite_ref-FOOTNOTEJahnke201018_50-1">b</a> <a href="#CITEREFJahnke2010">Jahnke 2010</a>, p. 18. </li> <li id="cite_note-FOOTNOTEHeath1908154–155-52"><a href="#cite_ref-FOOTNOTEHeath1908154–155_52-0">^</a> <a href="#CITEREFHeath1908">Heath 1908</a>, pp. 154–155. </li> <li id="cite_note-FOOTNOTEArtmann20123–4-54"><a href="#cite_ref-FOOTNOTEArtmann20123–4_54-0">^</a> <a href="#CITEREFArtmann2012">Artmann 2012</a>, p. 3–4. </li> <li id="cite_note-FOOTNOTEWolfe19454-55">^ <a href="#cite_ref-FOOTNOTEWolfe19454_55-0">a</a> <a href="#cite_ref-FOOTNOTEWolfe19454_55-1">b</a> <a href="#CITEREFWolfe1945">Wolfe 1945</a>, p. 4. </li> <li id="cite_note-FOOTNOTEPickover200956-57"><a href="#cite_ref-FOOTNOTEPickover200956_57-0">^</a> <a href="#CITEREFPickover2009">Pickover 2009</a>, p. 56. </li> <li id="cite_note-FOOTNOTEVenema200610-58"><a href="#cite_ref-FOOTNOTEVenema200610_58-0">^</a> <a href="#CITEREFVenema2006">Venema 2006</a>, p. 10. </li> <li id="cite_note-FOOTNOTEArtmann20124-60">^ <a href="#cite_ref-FOOTNOTEArtmann20124_60-0">a</a> <a href="#cite_ref-FOOTNOTEArtmann20124_60-1">b</a> <a href="#cite_ref-FOOTNOTEArtmann20124_60-2">c</a> <a href="#cite_ref-FOOTNOTEArtmann20124_60-3">d</a> <a href="#CITEREFArtmann2012">Artmann 2012</a>, p. 4. </li> <li id="cite_note-FOOTNOTEHeath1908202-62"><a href="#cite_ref-FOOTNOTEHeath1908202_62-0">^</a> <a href="#CITEREFHeath1908">Heath 1908</a>, p. 202. </li> <li id="cite_note-FOOTNOTEKatzMichalowicz202059-64"><a href="#cite_ref-FOOTNOTEKatzMichalowicz202059_64-0">^</a> <a href="#CITEREFKatzMichalowicz2020">Katz & Michalowicz 2020</a>, p. 59. </li> <li id="cite_note-FOOTNOTEArtmann20125-65"><a href="#cite_ref-FOOTNOTEArtmann20125_65-0">^</a> <a href="#CITEREFArtmann2012">Artmann 2012</a>, p. 5. </li> <li id="cite_note-FOOTNOTEArtmann20125–6-66"><a href="#cite_ref-FOOTNOTEArtmann20125–6_66-0">^</a> <a href="#CITEREFArtmann2012">Artmann 2012</a>, pp. 5–6. </li> <li id="cite_note-FOOTNOTEArtmann20126-68"><a href="#cite_ref-FOOTNOTEArtmann20126_68-0">^</a> <a href="#CITEREFArtmann2012">Artmann 2012</a>, p. 6. </li> <li id="cite_note-FOOTNOTEHeath1908b191-69"><a href="#cite_ref-FOOTNOTEHeath1908b191_69-0">^</a> <a href="#CITEREFHeath1908b">Heath 1908b</a>, p. 191. </li> <li id="cite_note-FOOTNOTEArtmann20127-70">^ <a href="#cite_ref-FOOTNOTEArtmann20127_70-0">a</a> <a href="#cite_ref-FOOTNOTEArtmann20127_70-1">b</a> <a href="#CITEREFArtmann2012">Artmann 2012</a>, p. 7. </li> <li id="cite_note-FOOTNOTEArtmann20129-71">^ <a href="#cite_ref-FOOTNOTEArtmann20129_71-0">a</a> <a href="#cite_ref-FOOTNOTEArtmann20129_71-1">b</a> <a href="#cite_ref-FOOTNOTEArtmann20129_71-2">c</a> <a href="#CITEREFArtmann2012">Artmann 2012</a>, p. 9. </li> <li id="cite_note-FOOTNOTESialaros2021§_"Other_Works"-72">^ <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-0">a</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-1">b</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-2">c</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-3">d</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-4">e</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-5">f</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-6">g</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-7">h</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-8">i</a> <a href="#cite_ref-FOOTNOTESialaros2021§_"Other_Works"_72-9">j</a> <a href="#CITEREFSialaros2021">Sialaros 2021</a>, § "Other Works". </li> <li id="cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"-73">^ <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"_73-0">a</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"_73-1">b</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"_73-2">c</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"_73-3">d</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Other_writings"_73-4">e</a> <a href="#CITEREFTaisbakVan_der_Waerden2021">Taisbak & Van der Waerden 2021</a>, § "Other writings". </li> <li id="cite_note-FOOTNOTEJones1986399–400-74">^ <a href="#cite_ref-FOOTNOTEJones1986399–400_74-0">a</a> <a href="#cite_ref-FOOTNOTEJones1986399–400_74-1">b</a> <a href="#CITEREFJones1986">Jones 1986</a>, pp. 399–400. </li> <li id="cite_note-FOOTNOTEAcerbi2008511-75"><a href="#cite_ref-FOOTNOTEAcerbi2008511_75-0">^</a> <a href="#CITEREFAcerbi2008">Acerbi 2008</a>, p. 511. </li> <li id="cite_note-FOOTNOTETaisbakVan_der_Waerden2021§_"Legacy"-77">^ <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Legacy"_77-0">a</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Legacy"_77-1">b</a> <a href="#cite_ref-FOOTNOTETaisbakVan_der_Waerden2021§_"Legacy"_77-2">c</a> <a href="#CITEREFTaisbakVan_der_Waerden2021">Taisbak & Van der Waerden 2021</a>, § "Legacy". </li> <li id="cite_note-78"><a href="#cite_ref-78">^</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.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.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background: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.id-lock-subscription a{background: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:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.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:#085;margin-left:0.3em}.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}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.jpl.nasa.gov/news/news.php?feature=6840">"NASA Delivers Detectors for ESA's Euclid Spacecraft"</a>. <a href="/wiki/Jet_Propulsion_Laboratory" title="Jet Propulsion Laboratory">Jet Propulsion Laboratory</a>. 9 May 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=NASA+Delivers+Detectors+for+ESA%27s+Euclid+Spacecraft&rft.date=2017-05-09&rft_id=https%3A%2F%2Fwww.jpl.nasa.gov%2Fnews%2Fnews.php%3Ffeature%3D6840&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"> </li> <li id="cite_note-79"><a href="#cite_ref-79">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://planetarynames.wr.usgs.gov/Feature/1860">"Gazetteer of Planetary Nomenclature | Euclides"</a>. usgs.gov. <a href="/wiki/International_Astronomical_Union" title="International Astronomical Union">International Astronomical Union</a>. Retrieved 3 September 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=usgs.gov&rft.atitle=Gazetteer+of+Planetary+Nomenclature+%7C+Euclides&rft_id=http%3A%2F%2Fplanetarynames.wr.usgs.gov%2FFeature%2F1860&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"> </li> <li id="cite_note-80"><a href="#cite_ref-80">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.minorplanetcenter.net/db_search/show_object?object_id=4354">"4354 Euclides (2142 P-L)"</a>. Minor Planet Center. Retrieved 27 May 2018.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=4354+Euclides+%282142+P-L%29&rft.pub=Minor+Planet+Center&rft_id=https%3A%2F%2Fwww.minorplanetcenter.net%2Fdb_search%2Fshow_object%3Fobject_id%3D4354&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"> </li> <li id="cite_note-FOOTNOTEHawesKolpas2015-81"><a href="#cite_ref-FOOTNOTEHawesKolpas2015_81-0">^</a> <a href="#CITEREFHawesKolpas2015">Hawes & Kolpas 2015</a>. </li> <li id="cite_note-FOOTNOTEHählPeters2022§_para._1-82"><a href="#cite_ref-FOOTNOTEHählPeters2022§_para._1_82-0">^</a> <a href="#CITEREFHählPeters2022">Hähl & Peters 2022</a>, § para. 1. </li> <li id="cite_note-83"><a href="#cite_ref-83">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMillay" class="citation book cs1"><a href="/wiki/Edna_St._Vincent_Millay" title="Edna St. Vincent Millay">Millay, Edna St. Vincent</a>. <a rel="nofollow" class="external text" href="https://www.poetryfoundation.org/poems/148566/euclid-alone-has-looked-on-beauty-bare">Euclid alone has looked on Beauty bare</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Euclid+alone+has+looked+on+Beauty+bare&rft.aulast=Millay&rft.aufirst=Edna+St.+Vincent&rft_id=https%3A%2F%2Fwww.poetryfoundation.org%2Fpoems%2F148566%2Feuclid-alone-has-looked-on-beauty-bare&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3></div> <dl><dd>Books</dd></dl> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFArtmann2012" class="citation book cs1">Artmann, Benno (2012) [1999]. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=F8XgBwAAQBAJ">Euclid: The Creation of Mathematics</a>. New York: <a href="/wiki/Springer_Publishing" title="Springer Publishing">Springer Publishing</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4612-1412-0" title="Special:BookSources/978-1-4612-1412-0"><bdi>978-1-4612-1412-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Euclid%3A+The+Creation+of+Mathematics&rft.place=New+York&rft.pub=Springer+Publishing&rft.date=2012&rft.isbn=978-1-4612-1412-0&rft.aulast=Artmann&rft.aufirst=Benno&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DF8XgBwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBall1960" class="citation book cs1"><a href="/wiki/W._W._Rouse_Ball" title="W. W. Rouse Ball">Ball, W.W. Rouse</a> (1960) [1908]. <a rel="nofollow" class="external text" href="https://archive.org/details/shortaccountofhi0000ball">A Short Account of the History of Mathematics</a> (4th ed.). Mineola: <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-20630-1" title="Special:BookSources/978-0-486-20630-1"><bdi>978-0-486-20630-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Short+Account+of+the+History+of+Mathematics&rft.place=Mineola&rft.edition=4th&rft.pub=Dover+Publications&rft.date=1960&rft.isbn=978-0-486-20630-1&rft.aulast=Ball&rft.aufirst=W.W.+Rouse&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fshortaccountofhi0000ball&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBruno2003" class="citation book cs1">Bruno, Leonard C. (2003) [1999]. <a rel="nofollow" class="external text" href="https://archive.org/details/mathmathematicia00brun">Math and Mathematicians: The History of Math Discoveries Around the World</a>. Baker, Lawrence W. Detroit: U X L. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7876-3813-9" title="Special:BookSources/978-0-7876-3813-9"><bdi>978-0-7876-3813-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/41497065">41497065</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Math+and+Mathematicians%3A+The+History+of+Math+Discoveries+Around+the+World&rft.place=Detroit&rft.pub=U+X+L&rft.date=2003&rft_id=info%3Aoclcnum%2F41497065&rft.isbn=978-0-7876-3813-9&rft.aulast=Bruno&rft.aufirst=Leonard+C.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmathmathematicia00brun&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBoyer1991" class="citation book cs1"><a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer">Boyer, Carl B.</a> (1991) [1968]. <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema00boye">A History of Mathematics</a> (2nd ed.). John Wiley & Sons, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-54397-8" title="Special:BookSources/978-0-471-54397-8"><bdi>978-0-471-54397-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Mathematics&rft.edition=2nd&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=1991&rft.isbn=978-0-471-54397-8&rft.aulast=Boyer&rft.aufirst=Carl+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryofmathema00boye&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCuomo2005" class="citation book cs1"><a href="/wiki/Serafina_Cuomo" title="Serafina Cuomo">Cuomo, Serafina</a> (2005) [2001]. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=KXuFAgAAQBAJ">Ancient Mathematics</a>. London and New York: <a href="/wiki/Routledge" title="Routledge">Routledge</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-134-71019-5" title="Special:BookSources/978-1-134-71019-5"><bdi>978-1-134-71019-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ancient+Mathematics&rft.place=London+and+New+York&rft.pub=Routledge&rft.date=2005&rft.isbn=978-1-134-71019-5&rft.aulast=Cuomo&rft.aufirst=Serafina&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DKXuFAgAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFowler1999" class="citation book cs1"><a href="/wiki/David_Fowler_(mathematician)" title="David Fowler (mathematician)">Fowler, David</a> (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HuwwIdk-xL8C">The Mathematics of Plato's Academy</a> (2nd ed.). Oxford: <a href="/wiki/Clarendon_Press" class="mw-redirect" title="Clarendon Press">Clarendon Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-850258-6" title="Special:BookSources/978-0-19-850258-6"><bdi>978-0-19-850258-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematics+of+Plato%27s+Academy&rft.place=Oxford&rft.edition=2nd&rft.pub=Clarendon+Press&rft.date=1999&rft.isbn=978-0-19-850258-6&rft.aulast=Fowler&rft.aufirst=David&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHuwwIdk-xL8C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGoulding2010" class="citation book cs1">Goulding, Robert (2010). Defending Hypatia: Ramus, Savile, and the Renaissance Rediscovery of Mathematical History. Dordrecht: Springer Netherlands. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-481-3542-4" title="Special:BookSources/978-90-481-3542-4"><bdi>978-90-481-3542-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Defending+Hypatia%3A+Ramus%2C+Savile%2C+and+the+Renaissance+Rediscovery+of+Mathematical+History&rft.place=Dordrecht&rft.pub=Springer+Netherlands&rft.date=2010&rft.isbn=978-90-481-3542-4&rft.aulast=Goulding&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHeath1908" class="citation book cs1">Heath, Thomas, ed. (1908). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_UhgPAAAAIAAJ/mode/2up">The Thirteen Books of Euclid's Elements</a>. Vol. 1. New York: <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-60088-8" title="Special:BookSources/978-0-486-60088-8"><bdi>978-0-486-60088-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Thirteen+Books+of+Euclid%27s+Elements&rft.place=New+York&rft.pub=Dover+Publications&rft.date=1908&rft.isbn=978-0-486-60088-8&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_UhgPAAAAIAAJ%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHeath1908b" class="citation book cs1"><a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Heath, Thomas</a>, ed. (1908b). The Thirteen Books of Euclid's Elements. Vol. 2. New York: <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Thirteen+Books+of+Euclid%27s+Elements&rft.place=New+York&rft.pub=Dover+Publications&rft.date=1908&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHeath1981" class="citation book cs1"><a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Heath, Thomas L.</a> (1981) [1921]. <a href="/wiki/A_History_of_Greek_Mathematics" title="A History of Greek Mathematics">A History of Greek Mathematics</a>. Vol. 2. New York: <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Greek+Mathematics&rft.place=New+York&rft.pub=Dover+Publications&rft.date=1981&rft.aulast=Heath&rft.aufirst=Thomas+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-24073-8" title="Special:BookSources/0-486-24073-8">0-486-24073-8</a>, <a href="/wiki/Special:BookSources/0-486-24074-6" title="Special:BookSources/0-486-24074-6">0-486-24074-6</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJahnke2010" class="citation book cs1">Jahnke, Hans Niels (2010). "The Conjoint Origin of Proof and Theoretical Physics". In <a href="/wiki/Gila_Hanna" title="Gila Hanna">Hanna, Gila</a>; Jahnke, Hans Niels; Pulte, Helmut (eds.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3bLHye8kSAwC">Explanation and Proof in Mathematics: Philosophical and Educational Perspectives</a>. Berlin: <a href="/wiki/Springer_US" class="mw-redirect" title="Springer US">Springer US</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4419-0576-5" title="Special:BookSources/978-1-4419-0576-5"><bdi>978-1-4419-0576-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Conjoint+Origin+of+Proof+and+Theoretical+Physics&rft.btitle=Explanation+and+Proof+in+Mathematics%3A+Philosophical+and+Educational+Perspectives&rft.place=Berlin&rft.pub=Springer+US&rft.date=2010&rft.isbn=978-1-4419-0576-5&rft.aulast=Jahnke&rft.aufirst=Hans+Niels&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D3bLHye8kSAwC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJones1986" class="citation book cs1 cs1-prop-long-vol">Jones, Alexander, ed. (1986). <a rel="nofollow" class="external text" href="https://archive.org/details/book7ofcollectio0000papp/mode/2up">Pappus of Alexandria: Book 7 of the Collection</a>. Vol. Part 2: Commentary, Index, and Figures. New York: <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer Science+Business Media</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-96257-1" title="Special:BookSources/978-3-540-96257-1"><bdi>978-3-540-96257-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Pappus+of+Alexandria%3A+Book+7+of+the+Collection&rft.place=New+York&rft.pub=Springer+Science%2BBusiness+Media&rft.date=1986&rft.isbn=978-3-540-96257-1&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbook7ofcollectio0000papp%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKatzMichalowicz2020" class="citation book cs1"><a href="/wiki/Victor_J._Katz" title="Victor J. Katz">Katz, Victor J.</a>; Michalowicz, Karen Dee (2020) [2005]. Historical Modules for the Teaching and Learning of Mathematics. Washington D.C.: <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4704-5711-2" title="Special:BookSources/978-1-4704-5711-2"><bdi>978-1-4704-5711-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Historical+Modules+for+the+Teaching+and+Learning+of+Mathematics&rft.place=Washington+D.C.&rft.pub=Mathematical+Association+of+America&rft.date=2020&rft.isbn=978-1-4704-5711-2&rft.aulast=Katz&rft.aufirst=Victor+J.&rft.au=Michalowicz%2C+Karen+Dee&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPickover2009" class="citation book cs1"><a href="/wiki/Clifford_A._Pickover" title="Clifford A. Pickover">Pickover, Clifford A.</a> (2009). The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics. New York: <a href="/wiki/Sterling_Publishing" title="Sterling Publishing">Sterling Publishing</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4027-5796-9" title="Special:BookSources/978-1-4027-5796-9"><bdi>978-1-4027-5796-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Math+Book%3A+From+Pythagoras+to+the+57th+Dimension%2C+250+Milestones+in+the+History+of+Mathematics&rft.place=New+York&rft.pub=Sterling+Publishing&rft.date=2009&rft.isbn=978-1-4027-5796-9&rft.aulast=Pickover&rft.aufirst=Clifford+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSialaros2018" class="citation book cs1">Sialaros, Michalis (2018). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DZRdDwAAQBAJ">"How Much Does a Theorem Cost?"</a>. In Sialaros, Michalis (ed.). Revolutions and Continuity in Greek Mathematics. Berlin: <a href="/wiki/De_Gruyter" title="De Gruyter">De Gruyter</a>. pp. 89–106. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-11-056595-9" title="Special:BookSources/978-3-11-056595-9"><bdi>978-3-11-056595-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=How+Much+Does+a+Theorem+Cost%3F&rft.btitle=Revolutions+and+Continuity+in+Greek+Mathematics&rft.place=Berlin&rft.pages=%3Cspan+class%3D%22nowrap%22%3E89-%3C%2Fspan%3E106&rft.pub=De+Gruyter&rft.date=2018&rft.isbn=978-3-11-056595-9&rft.aulast=Sialaros&rft.aufirst=Michalis&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DDZRdDwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSialaros2020" class="citation book cs1">Sialaros, Michalis (2020). 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Cambridge: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. pp. 141–152. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-108-42644-2" title="Special:BookSources/978-1-108-42644-2"><bdi>978-1-108-42644-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euclid+of+Alexandria%3A+A+Child+of+the+Academy%3F&rft.btitle=Plato%27s+Academy&rft.place=Cambridge&rft.pages=%3Cspan+class%3D%22nowrap%22%3E141-%3C%2Fspan%3E152&rft.pub=Cambridge+University+Press&rft.date=2020&rft.isbn=978-1-108-42644-2&rft.aulast=Sialaros&rft.aufirst=Michalis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSmorynski2008" class="citation book cs1">Smorynski, Craig (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=_zliInaOM8UC">History of Mathematics: A Supplement</a>. 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In Fortenbaugh, William W.; Schütrumpf, Eckhart (eds.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=IvdKDwAAQBAJ">Demetrius of Phalerum: Text, Translation and Discussion</a>. Rutgers University Studies in Classical Humanities. Vol. IX. New Brunswick and London: <a href="/wiki/Transaction_Publishers" title="Transaction Publishers">Transaction Publishers</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-3513-2690-2" title="Special:BookSources/978-1-3513-2690-2"><bdi>978-1-3513-2690-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Demetrius+of+Phalerum%3A+Who+was+He+and+Who+was+He+Not%3F&rft.btitle=Demetrius+of+Phalerum%3A+Text%2C+Translation+and+Discussion&rft.place=New+Brunswick+and+London&rft.series=Rutgers+University+Studies+in+Classical+Humanities&rft.pub=Transaction+Publishers&rft.date=2000&rft.isbn=978-1-3513-2690-2&rft.aulast=Tracy&rft.aufirst=Stephen+V&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DIvdKDwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFVenema2006" class="citation book cs1">Venema, Gerard (2006). 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New York: <a href="/wiki/Dryden_Press" class="mw-redirect" title="Dryden Press">Dryden Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+To+Non-Euclidean+Geometry&rft.place=New+York&rft.pub=Dryden+Press&rft.date=1945&rft.aulast=Wolfe&rft.aufirst=Harold+E.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontono031680mbp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li></ul> </div> <dl><dd>Articles</dd></dl> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239549316" /><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAcerbi2008" class="citation journal cs1">Acerbi, Fabio (September 2008). "Euclid's Pseudaria". Archive for History of Exact Sciences. 62 (5): 511–551. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00407-007-0017-3">10.1007/s00407-007-0017-3</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41134289">41134289</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120860272">120860272</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=Euclid%27s+Pseudaria&rft.volume=62&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E511-%3C%2Fspan%3E551&rft.date=2008-09&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120860272%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F41134289%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1007%2Fs00407-007-0017-3&rft.aulast=Acerbi&rft.aufirst=Fabio&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJones2005" class="citation conference cs1">Jones, Alexander (2005). <a rel="nofollow" class="external text" href="https://archive.nyu.edu/bitstream/2451/63988/2/Jones%202005%20Euclid%20the%20Elusive%20Geometer%20Oxford.pdf">"Euclid, the Elusive Geometer"</a> (PDF). 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Mathematische Semesterberichte. 69 (2): 253–258. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00591-022-00320-3">10.1007/s00591-022-00320-3</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:249581871">249581871</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Semesterberichte&rft.atitle=A+Variation+of+Hilbert%27s+Axioms+for+Euclidean+Geometry&rft.volume=69&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E253-%3C%2Fspan%3E258&rft.date=2022-06-10&rft_id=info%3Adoi%2F10.1007%2Fs00591-022-00320-3&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A249581871%23id-name%3DS2CID&rft.aulast=H%C3%A4hl&rft.aufirst=Hermann&rft.au=Peters%2C+Hanna&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%252Fs00591-022-00320-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHawesKolpas2015" class="citation web cs1">Hawes, Susan M.; Kolpas, Sid (August 2015). <a rel="nofollow" class="external text" href="https://www.maa.org/press/periodicals/convergence/oliver-byrne-the-matisse-of-mathematics-biography-1810-1829">"Oliver Byrne: The Matisse of Mathematics – Biography 1810–1829"</a>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. 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In <a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm, Hugh</a> (ed.). <a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a>. Vol. 20 (11th ed.). Cambridge University Press. pp. 470–471.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Pappus+of+Alexandria&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=%3Cspan+class%3D%22nowrap%22%3E470-%3C%2Fspan%3E471&rft.edition=11th&rft.pub=Cambridge+University+Press&rft.date=1911&rft.aulast=Heath&rft.aufirst=Thomas+Little&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSialaros2021" class="citation encyclopaedia cs1">Sialaros, Michalis (2021) [2015]. <a rel="nofollow" class="external text" href="https://oxfordre.com/classics/view/10.1093/acrefore/9780199381135.001.0001/acrefore-9780199381135-e-2521">"Euclid"</a>. <a href="/wiki/Oxford_Classical_Dictionary" title="Oxford Classical Dictionary">Oxford Classical Dictionary</a>. 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Chicago: <a href="/wiki/Encyclop%C3%A6dia_Britannica,_Inc." title="Encyclopædia Britannica, Inc.">Encyclopædia Britannica, Inc.</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euclid&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.place=Chicago&rft.pub=Encyclop%C3%A6dia+Britannica%2C+Inc.&rft.date=2021-01-05&rft.aulast=Taisbak&rft.aufirst=Christian+Marinus&rft.au=Van+der+Waerden%2C+Bartel+Leendert&rft_id=https%3A%2F%2Fwww.britannica.com%2FEBchecked%2Ftopic%2F194880%2FEuclid&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li></ul> </div> <dl><dd>Online</dd></dl> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239549316" /><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGetty" class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.getty.edu/art/collection/object/108GV4">"Euclid"</a>. <a href="/wiki/J._Paul_Getty_Museum" title="J. Paul Getty Museum">J. Paul Getty Museum</a>. Retrieved 11 August 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Euclid&rft.pub=J.+Paul+Getty+Museum&rft_id=https%3A%2F%2Fwww.getty.edu%2Fart%2Fcollection%2Fobject%2F108GV4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFOEDa" class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://www.oed.com/view/Entry/64929">"Euclid, n"</a>. <a href="/wiki/OED_Online" class="mw-redirect" title="OED Online">OED Online</a>. Oxford: <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. Retrieved 10 August 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euclid%2C+n&rft.btitle=OED+Online&rft.place=Oxford&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Fwww.oed.com%2Fview%2FEntry%2F64929&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"> (subscription required)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFOEDb" class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="http://www.etymonline.com/index.php?term=Euclidean">"Euclidean (adj.)"</a>. <a href="/wiki/Online_Etymology_Dictionary" class="mw-redirect" title="Online Etymology Dictionary">Online Etymology Dictionary</a>. Retrieved 18 March 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euclidean+%28adj.%29&rft.btitle=Online+Etymology+Dictionary&rft_id=http%3A%2F%2Fwww.etymonline.com%2Findex.php%3Fterm%3DEuclidean&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEuclid" class="Z3988"></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div> <style data-mw-deduplicate="TemplateStyles:r1235611614">.mw-parser-output .spoken-wikipedia{border:1px solid #a2a9b1;background-color:var(--background-color-interactive-subtle,#f8f9fa);margin:0.5em 0;padding:0.2em;line-height:1.5em;font-size:90%}.mw-parser-output .spoken-wikipedia-header{text-align:center}.mw-parser-output .spoken-wikipedia-listen-to{font-weight:bold}.mw-parser-output .spoken-wikipedia-files{text-align:center;margin-top:10px;margin-bottom:0.4em}.mw-parser-output .spoken-wikipedia-icon{float:left;margin-left:5px;margin-top:10px}.mw-parser-output .spoken-wikipedia-disclaimer{margin-left:60px;margin-top:10px;font-size:95%;line-height:1.4em}.mw-parser-output .spoken-wikipedia-footer{margin-top:10px;text-align:center}@media(min-width:720px){.mw-parser-output .spoken-wikipedia{width:20em;float:right;clear:right;margin-left:1em}}</style><div class="spoken-wikipedia noprint haudio"><div class="spoken-wikipedia-header">Listen to this article (13 minutes)</div><div class="spoken-wikipedia-files"><figure class="mw-halign-center" typeof="mw:File"><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="200" style="width:200px;" data-durationhint="763" data-mwtitle="En-Euclid-article.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/ff/En-Euclid-article.ogg/En-Euclid-article.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/f/ff/En-Euclid-article.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /></audio><figcaption></figcaption></figure> </div><div class="spoken-wikipedia-icon"><img alt="Spoken Wikipedia icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/45px-Sound-icon.svg.png" decoding="async" width="45" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/68px-Sound-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/90px-Sound-icon.svg.png 2x" data-file-width="128" data-file-height="96" /></div><div class="spoken-wikipedia-disclaimer"><a href="/wiki/File:En-Euclid-article.ogg" title="File:En-Euclid-article.ogg">This audio file</a> was created from a revision of this article dated 29 September 2020 (2020-9-29), and does not reflect subsequent edits.</div><div class="spoken-wikipedia-footer">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help">Audio help</a> · <a href="/wiki/Wikipedia:Spoken_articles" title="Wikipedia:Spoken articles">More spoken articles</a>)</div></div> <dl><dt>Works</dt></dl> <ul><li><a rel="nofollow" class="external text" href="https://www.gutenberg.org/ebooks/author/9719">Works by Euclid</a> at <a href="/wiki/Project_Gutenberg" title="Project Gutenberg">Project Gutenberg</a></li> <li><a rel="nofollow" class="external text" href="https://archive.org/search.php?query=%28%28subject%3A%22Euclid%22%20OR%20creator%3A%22Euclid%22%20OR%20description%3A%22Euclid%22%20OR%20title%3A%22Euclid%22%29%29%20AND%20%28-mediatype:software%29">Works by or about Euclid</a> at the <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a></li> <li><a rel="nofollow" class="external text" href="https://librivox.org/author/2304">Works by Euclid</a> at <a href="/wiki/LibriVox" title="LibriVox">LibriVox</a> (public domain audiobooks) <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/15px-Speaker_Icon.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/23px-Speaker_Icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/30px-Speaker_Icon.svg.png 2x" data-file-width="500" data-file-height="500" /></li> <li><a rel="nofollow" class="external text" href="https://www.ucl.ac.uk/library/special-collections/a-z/euclid">Euclid Collection</a> at <a href="/wiki/University_College_London" title="University College London">University College London</a> (c.500 editions of works by Euclid), available online through the <a rel="nofollow" class="external text" href="https://ucl.primo.exlibrisgroup.com/discovery/collectionDiscovery?vid=44UCL_INST:UCL_VU2&collectionId=81354471580004761">Stavros Niarchos Foundation Digital Library</a>.</li> <li>Scans of <a href="/wiki/Johan_Ludvig_Heiberg_(historian)" title="Johan Ludvig Heiberg (historian)">Johan Heiberg</a>'s <a rel="nofollow" class="external text" href="https://wilbourhall.org/index.html#euclid">edition of Euclid</a> at wilbourhall.org</li></ul> <dl><dt>The Elements</dt></dl> <ul><li><a rel="nofollow" class="external text" href="https://farside.ph.utexas.edu/books/Euclid/Euclid.html">PDF copy</a>, with the original Greek and an English translation on facing pages, <a href="/wiki/University_of_Texas" class="mw-redirect" title="University of Texas">University of Texas</a>.</li> <li><a rel="nofollow" class="external text" href="https://euclides.org">All thirteen books</a>, in several languages as Spanish, Catalan, English, German, Portuguese, Arabic, Italian, Russian and Chinese.</li></ul> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output 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alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/21px-Parthenon_from_west.jpg" decoding="async" width="21" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/32px-Parthenon_from_west.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/42px-Parthenon_from_west.jpg 2x" data-file-width="2048" data-file-height="1536" /> <a href="/wiki/Portal:Ancient_Greece" title="Portal:Ancient Greece">Ancient Greece</a></li><li class="portal-bar-item"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/19px-P_vip.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/28px-P_vip.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/37px-P_vip.svg.png 2x" data-file-width="1911" data-file-height="1944" /> <a href="/wiki/Portal:Biography" 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decoding="async" width="18" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/40px-Wikisource-logo.svg.png 1.5x" data-file-width="410" data-file-height="430" /><a href="https://en.wikisource.org/wiki/Author:Euclid" class="extiw" title="s:Author:Euclid">Texts</a> from Wikisource</li><li class="sister-bar-item"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/19px-Wikibooks-logo.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/29px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/38px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /><a href="https://en.wikibooks.org/wiki/Mathematical_Proof_and_the_Principles_of_Mathematics/History/Euclid" class="extiw" title="b:Mathematical Proof and the Principles of Mathematics/History/Euclid">Textbooks</a> from Wikibooks</li><li class="sister-bar-item"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/21px-Wikiversity_logo_2017.svg.png" decoding="async" width="21" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/32px-Wikiversity_logo_2017.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/42px-Wikiversity_logo_2017.svg.png 2x" data-file-width="626" data-file-height="512" /><a href="https://en.wikiversity.org/wiki/Euclidean_geometry" class="extiw" title="v:Euclidean geometry">Resources</a> from Wikiversity</li></ul></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid 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title="Special:EditPage/Template:Euclid"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Euclid145" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Euclid</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Works</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Euclid%27s_Data" title="Euclid's Data">Data</a></li> <li><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Elements</a></li> <li><a href="/wiki/Euclid%27s_Optics" title="Euclid's Optics">Optics</a></li> <li><a href="/wiki/Euclid%27s_Phaenomena" title="Euclid's Phaenomena">Phaenomena</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_things_named_after_Euclid" title="List of things named after Euclid">Namesakes</a></li> <li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a></li> <li><a href="/wiki/Euclidean_algorithm" title="Euclidean algorithm">Euclidean algorithm</a></li> <li><a href="/wiki/Euclid%27s_theorem" title="Euclid's theorem">Euclid's theorem</a></li> <li><a href="/wiki/Euclidean_relation" title="Euclidean relation">Euclidean relation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Scholars</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Thomas Heath</a></li> <li><a href="/wiki/Johan_Ludvig_Heiberg_(historian)" title="Johan Ludvig Heiberg (historian)">Johan Ludvig Heiberg</a></li> <li><a href="/wiki/Robert_Simson" title="Robert Simson">Robert Simson</a></li> <li><a href="/wiki/Isaac_Todhunter" title="Isaac Todhunter">Isaac Todhunter</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Papyrus_Oxyrhynchus_29" title="Papyrus Oxyrhynchus 29">Papyrus Oxyrhynchus 29</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:Euclid" title="Category:Euclid">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Ancient_Greek_mathematics550" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Ancient_Greek_mathematics" title="Template:Ancient Greek mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Ancient_Greek_mathematics" title="Template talk:Ancient Greek mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Ancient_Greek_mathematics" title="Special:EditPage/Template:Ancient Greek mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Ancient_Greek_mathematics550" style="font-size:114%;margin:0 4em"><a href="/wiki/Greek_mathematics" title="Greek mathematics">Ancient Greek mathematics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_Greek_mathematicians" title="List of Greek mathematicians">Mathematicians</a> <a href="/wiki/Timeline_of_ancient_Greek_mathematicians" title="Timeline of ancient Greek mathematicians">(timeline)</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anaxagoras" title="Anaxagoras">Anaxagoras</a></li> <li><a href="/wiki/Anthemius_of_Tralles" title="Anthemius of Tralles">Anthemius</a></li> <li><a href="/wiki/Archytas" title="Archytas">Archytas</a></li> <li><a href="/wiki/Aristaeus_the_Elder" title="Aristaeus the Elder">Aristaeus the Elder</a></li> <li><a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus</a></li> <li><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a></li> <li><a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius</a></li> <li><a href="/wiki/Archimedes" title="Archimedes">Archimedes</a></li> <li><a href="/wiki/Autolycus_of_Pitane" title="Autolycus of Pitane">Autolycus</a></li> <li><a href="/wiki/Bion_of_Abdera" title="Bion of Abdera">Bion</a></li> <li><a href="/wiki/Bryson_of_Heraclea" title="Bryson of Heraclea">Bryson</a></li> <li><a href="/wiki/Callippus" title="Callippus">Callippus</a></li> <li><a href="/wiki/Carpus_of_Antioch" title="Carpus of Antioch">Carpus</a></li> <li><a href="/wiki/Chrysippus" title="Chrysippus">Chrysippus</a></li> <li><a href="/wiki/Cleomedes" title="Cleomedes">Cleomedes</a></li> <li><a href="/wiki/Conon_of_Samos" title="Conon of Samos">Conon</a></li> <li><a href="/wiki/Ctesibius" title="Ctesibius">Ctesibius</a></li> <li><a href="/wiki/Democritus" title="Democritus">Democritus</a></li> <li><a href="/wiki/Dicaearchus" title="Dicaearchus">Dicaearchus</a></li> <li><a href="/wiki/Diocles_(mathematician)" title="Diocles (mathematician)">Diocles</a></li> <li><a href="/wiki/Diophantus" title="Diophantus">Diophantus</a></li> <li><a href="/wiki/Dinostratus" title="Dinostratus">Dinostratus</a></li> <li><a href="/wiki/Dionysodorus" title="Dionysodorus">Dionysodorus</a></li> <li><a href="/wiki/Domninus_of_Larissa" title="Domninus of Larissa">Domninus</a></li> <li><a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a></li> <li><a href="/wiki/Eudemus_of_Rhodes" title="Eudemus of Rhodes">Eudemus</a></li> <li><a class="mw-selflink selflink">Euclid</a></li> <li><a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus</a></li> <li><a href="/wiki/Eutocius_of_Ascalon" title="Eutocius of Ascalon">Eutocius</a></li> <li><a href="/wiki/Geminus" title="Geminus">Geminus</a></li> <li><a href="/wiki/Heliodorus_of_Larissa" title="Heliodorus of Larissa">Heliodorus</a></li> <li><a href="/wiki/Hero_of_Alexandria" title="Hero of Alexandria">Heron</a></li> <li><a href="/wiki/Hipparchus" title="Hipparchus">Hipparchus</a></li> <li><a href="/wiki/Hippasus" title="Hippasus">Hippasus</a></li> <li><a href="/wiki/Hippias" title="Hippias">Hippias</a></li> <li><a href="/wiki/Hippocrates_of_Chios" title="Hippocrates of Chios">Hippocrates</a></li> <li><a href="/wiki/Hypatia" title="Hypatia">Hypatia</a></li> <li><a href="/wiki/Hypsicles" title="Hypsicles">Hypsicles</a></li> <li><a href="/wiki/Isidore_of_Miletus" title="Isidore of Miletus">Isidore of Miletus</a></li> <li><a href="/wiki/Leon_(mathematician)" title="Leon (mathematician)">Leon</a></li> <li><a href="/wiki/Marinus_of_Neapolis" title="Marinus of Neapolis">Marinus</a></li> <li><a href="/wiki/Menaechmus" title="Menaechmus">Menaechmus</a></li> <li><a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria">Menelaus</a></li> <li><a href="/wiki/Metrodorus_(grammarian)" title="Metrodorus (grammarian)">Metrodorus</a></li> <li><a href="/wiki/Nicomachus" title="Nicomachus">Nicomachus</a></li> <li><a href="/wiki/Nicomedes_(mathematician)" title="Nicomedes (mathematician)">Nicomedes</a></li> <li><a href="/wiki/Nicoteles_of_Cyrene" title="Nicoteles of Cyrene">Nicoteles</a></li> <li><a href="/wiki/Oenopides" title="Oenopides">Oenopides</a></li> <li><a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus</a></li> <li><a href="/wiki/Perseus_(geometer)" title="Perseus (geometer)">Perseus</a></li> <li><a href="/wiki/Philolaus" title="Philolaus">Philolaus</a></li> <li><a href="/wiki/Philon" title="Philon">Philon</a></li> <li><a href="/wiki/Philonides_of_Laodicea" title="Philonides of Laodicea">Philonides</a></li> <li><a href="/wiki/Plato" title="Plato">Plato</a></li> <li><a href="/wiki/Porphyry_of_Tyre" title="Porphyry of Tyre">Porphyry of Tyre</a></li> <li><a href="/wiki/Posidonius" title="Posidonius">Posidonius</a></li> <li><a href="/wiki/Proclus" title="Proclus">Proclus</a></li> <li><a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a></li> <li><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li> <li><a href="/wiki/Serenus_of_Antino%C3%B6polis" title="Serenus of Antinoöpolis">Serenus </a></li> <li><a href="/wiki/Simplicius_of_Cilicia" title="Simplicius of Cilicia">Simplicius</a></li> <li><a href="/wiki/Sosigenes_of_Alexandria" class="mw-redirect" title="Sosigenes of Alexandria">Sosigenes</a></li> <li><a href="/wiki/Sporus_of_Nicaea" title="Sporus of Nicaea">Sporus</a></li> <li><a href="/wiki/Thales_of_Miletus" title="Thales of Miletus">Thales</a></li> <li><a href="/wiki/Theaetetus_(mathematician)" title="Theaetetus (mathematician)">Theaetetus</a></li> <li><a href="/wiki/Theano_(philosopher)" title="Theano (philosopher)">Theano</a></li> <li><a href="/wiki/Theodorus_of_Cyrene" title="Theodorus of Cyrene">Theodorus</a></li> <li><a href="/wiki/Theodosius_of_Bithynia" title="Theodosius of Bithynia">Theodosius</a></li> <li><a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a></li> <li><a href="/wiki/Theon_of_Smyrna" title="Theon of Smyrna">Theon of Smyrna</a></li> <li><a href="/wiki/Thymaridas" title="Thymaridas">Thymaridas</a></li> <li><a href="/wiki/Xenocrates" title="Xenocrates">Xenocrates</a></li> <li><a href="/wiki/Zeno_of_Elea" title="Zeno of Elea">Zeno of Elea</a></li> <li><a href="/wiki/Zeno_of_Sidon" title="Zeno of Sidon">Zeno of Sidon</a></li> <li><a href="/wiki/Zenodorus_(mathematician)" title="Zenodorus (mathematician)">Zenodorus</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Treatises</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Almagest" title="Almagest">Almagest</a></li> <li><a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a></li> <li><a href="/wiki/Arithmetica" title="Arithmetica">Arithmetica</a></li> <li><a href="/wiki/Apollonius_of_Perga#Conics" title="Apollonius of Perga">Conics (Apollonius)</a></li> <li><a href="/wiki/Catoptrics" title="Catoptrics">Catoptrics</a></li> <li><a href="/wiki/Data_(Euclid)" class="mw-redirect" title="Data (Euclid)">Data (Euclid)</a></li> <li><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Elements (Euclid)</a></li> <li><a href="/wiki/Measurement_of_a_Circle" title="Measurement of a Circle">Measurement of a Circle</a></li> <li><a href="/wiki/On_Conoids_and_Spheroids" title="On Conoids and Spheroids">On Conoids and Spheroids</a></li> <li><a href="/wiki/On_the_Sizes_and_Distances_(Aristarchus)" title="On the Sizes and Distances (Aristarchus)">On the Sizes and Distances (Aristarchus)</a></li> <li><a href="/wiki/On_Sizes_and_Distances_(Hipparchus)" title="On Sizes and Distances (Hipparchus)">On Sizes and Distances (Hipparchus)</a></li> <li><a href="/wiki/Autolycus_of_Pitane" title="Autolycus of Pitane">On the Moving Sphere (Autolycus)</a></li> <li><a href="/wiki/Euclid%27s_Optics" title="Euclid's Optics">Optics (Euclid)</a></li> <li><a href="/wiki/On_Spirals" title="On Spirals">On Spirals</a></li> <li><a href="/wiki/On_the_Sphere_and_Cylinder" title="On the Sphere and Cylinder">On the Sphere and Cylinder</a></li> <li><a href="/wiki/Ostomachion" title="Ostomachion">Ostomachion</a></li> <li><a href="/wiki/Planisphaerium" title="Planisphaerium">Planisphaerium</a></li> <li><a href="/wiki/Theodosius%27_Spherics" title="Theodosius' Spherics">Spherics (Theodosius)</a></li> <li><a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria">Spherics (Menelaus)</a></li> <li><a href="/wiki/The_Quadrature_of_the_Parabola" class="mw-redirect" title="The Quadrature of the Parabola">The Quadrature of the Parabola</a></li> <li><a href="/wiki/The_Sand_Reckoner" title="The Sand Reckoner">The Sand Reckoner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Problems</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Constructible_number" title="Constructible number">Constructible numbers</a> <ul><li><a href="/wiki/Angle_trisection" title="Angle trisection">Angle trisection</a></li> <li><a href="/wiki/Doubling_the_cube" title="Doubling the cube">Doubling the cube</a></li> <li><a href="/wiki/Squaring_the_circle" title="Squaring the circle">Squaring the circle</a></li></ul></li> <li><a href="/wiki/Problem_of_Apollonius" title="Problem of Apollonius">Problem of Apollonius</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts and definitions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Angle" title="Angle">Angle</a> <ul><li><a href="/wiki/Central_angle" title="Central angle">Central</a></li> <li><a href="/wiki/Inscribed_angle" title="Inscribed angle">Inscribed</a></li></ul></li> <li><a href="/wiki/Axiomatic_system" title="Axiomatic system">Axiomatic system</a> <ul><li><a href="/wiki/Axiom" title="Axiom">Axiom</a></li></ul></li> <li><a href="/wiki/Chord_(geometry)" title="Chord (geometry)">Chord</a></li> <li><a href="/wiki/Circles_of_Apollonius" title="Circles of Apollonius">Circles of Apollonius</a> <ul><li><a href="/wiki/Apollonian_circles" title="Apollonian circles">Apollonian circles</a></li> <li><a href="/wiki/Apollonian_gasket" title="Apollonian gasket">Apollonian gasket</a></li></ul></li> <li><a href="/wiki/Circumscribed_circle" title="Circumscribed circle">Circumscribed circle</a></li> <li><a href="/wiki/Commensurability_(mathematics)" title="Commensurability (mathematics)">Commensurability</a></li> <li><a href="/wiki/Diophantine_equation" title="Diophantine equation">Diophantine equation</a></li> <li><a href="https://en.wikiquote.org/wiki/Doctrine_of_proportion_(mathematics)" class="extiw" title="wikiquote:Doctrine of proportion (mathematics)">Doctrine of proportionality</a></li> <li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a></li> <li><a href="/wiki/Golden_ratio" title="Golden ratio">Golden ratio</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a></li> <li><a href="/wiki/Incircle_and_excircles_of_a_triangle" class="mw-redirect" title="Incircle and excircles of a triangle">Incircle and excircles of a triangle</a></li> <li><a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">Method of exhaustion</a></li> <li><a href="/wiki/Parallel_postulate" title="Parallel postulate">Parallel postulate</a></li> <li><a href="/wiki/Platonic_solid" title="Platonic solid">Platonic solid</a></li> <li><a href="/wiki/Lune_of_Hippocrates" title="Lune of Hippocrates">Lune of Hippocrates</a></li> <li><a href="/wiki/Quadratrix_of_Hippias" title="Quadratrix of Hippias">Quadratrix of Hippias</a></li> <li><a href="/wiki/Regular_polygon" title="Regular polygon">Regular polygon</a></li> <li><a href="/wiki/Straightedge_and_compass_construction" title="Straightedge and compass construction">Straightedge and compass construction</a></li> <li><a href="/wiki/Triangle_center" title="Triangle center">Triangle center</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Results</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">In <a href="/wiki/Euclid%27s_elements" class="mw-redirect" title="Euclid's elements">Elements</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Angle_bisector_theorem" title="Angle bisector theorem">Angle bisector theorem</a></li> <li><a href="/wiki/Exterior_angle_theorem" title="Exterior angle theorem">Exterior angle theorem</a></li> <li><a href="/wiki/Euclidean_algorithm" title="Euclidean algorithm">Euclidean algorithm</a></li> <li><a href="/wiki/Euclid%27s_theorem" title="Euclid's theorem">Euclid's theorem</a></li> <li><a href="/wiki/Geometric_mean_theorem" title="Geometric mean theorem">Geometric mean theorem</a></li> <li><a href="/wiki/Greek_geometric_algebra" class="mw-redirect" title="Greek geometric algebra">Greek geometric algebra</a></li> <li><a href="/wiki/Hinge_theorem" title="Hinge theorem">Hinge theorem</a></li> <li><a href="/wiki/Inscribed_angle_theorem" class="mw-redirect" title="Inscribed angle theorem">Inscribed angle theorem</a></li> <li><a href="/wiki/Intercept_theorem" title="Intercept theorem">Intercept theorem</a></li> <li><a href="/wiki/Intersecting_chords_theorem" title="Intersecting chords theorem">Intersecting chords theorem</a></li> <li><a href="/wiki/Intersecting_secants_theorem" title="Intersecting secants theorem">Intersecting secants theorem</a></li> <li><a href="/wiki/Law_of_cosines" title="Law of cosines">Law of cosines</a></li> <li><a href="/wiki/Pons_asinorum" title="Pons asinorum">Pons asinorum</a></li> <li><a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a></li> <li><a href="/wiki/Tangent-secant_theorem" class="mw-redirect" title="Tangent-secant theorem">Tangent-secant theorem</a></li> <li><a href="/wiki/Thales%27s_theorem" title="Thales's theorem">Thales's theorem</a></li> <li><a href="/wiki/Theorem_of_the_gnomon" title="Theorem of the gnomon">Theorem of the gnomon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Apollonius_of_Tyana" title="Apollonius of Tyana">Apollonius</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Apollonius%27s_theorem" title="Apollonius's theorem">Apollonius's theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aristarchus%27s_inequality" title="Aristarchus's inequality">Aristarchus's inequality</a></li> <li><a href="/wiki/Crossbar_theorem" title="Crossbar theorem">Crossbar theorem</a></li> <li><a href="/wiki/Heron%27s_formula" title="Heron's formula">Heron's formula</a></li> <li><a href="/wiki/Irrational_number" title="Irrational number">Irrational numbers</a></li> <li><a href="/wiki/Law_of_sines" title="Law of sines">Law of sines</a></li> <li><a href="/wiki/Menelaus%27s_theorem" title="Menelaus's theorem">Menelaus's theorem</a></li> <li><a href="/wiki/Pappus%27s_area_theorem" title="Pappus's area theorem">Pappus's area theorem</a></li> <li><a href="/wiki/Diophantus_II.VIII" title="Diophantus II.VIII">Problem II.8 of Arithmetica</a></li> <li><a href="/wiki/Ptolemy%27s_inequality" title="Ptolemy's inequality">Ptolemy's inequality</a></li> <li><a href="/wiki/Ptolemy%27s_table_of_chords" title="Ptolemy's table of chords">Ptolemy's table of chords</a></li> <li><a href="/wiki/Ptolemy%27s_theorem" title="Ptolemy's theorem">Ptolemy's theorem</a></li> <li><a href="/wiki/Spiral_of_Theodorus" title="Spiral of Theodorus">Spiral of Theodorus</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Centers</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cyrene,_Libya" title="Cyrene, Libya">Cyrene</a></li> <li><a href="/wiki/Musaeum" class="mw-redirect" title="Musaeum">Mouseion of Alexandria</a></li> <li><a href="/wiki/Platonic_Academy" title="Platonic Academy">Platonic Academy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ancient_Greek_astronomy" title="Ancient Greek astronomy">Ancient Greek astronomy</a></li> <li><a href="/wiki/Attic_numerals" title="Attic numerals">Attic numerals</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a></li> <li><a href="/wiki/Latin_translations_of_the_12th_century" title="Latin translations of the 12th century">Latin translations of the 12th century</a></li> <li><a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">Non-Euclidean geometry</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy of mathematics</a></li> <li><a href="/wiki/Neusis_construction" title="Neusis construction">Neusis construction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">History of</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/A_History_of_Greek_Mathematics" title="A History of Greek Mathematics">A History of Greek Mathematics</a> <ul><li>by <a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Thomas Heath</a></li></ul></li> <li><a href="/wiki/History_of_algebra" title="History of algebra">algebra</a> <ul><li><a href="/wiki/Timeline_of_algebra" title="Timeline of algebra">timeline</a></li></ul></li> <li><a href="/wiki/History_of_arithmetic" class="mw-redirect" title="History of arithmetic">arithmetic</a> <ul><li><a href="/wiki/Timeline_of_numerals_and_arithmetic" title="Timeline of numerals and arithmetic">timeline</a></li></ul></li> <li><a href="/wiki/History_of_calculus" title="History of calculus">calculus</a> <ul><li><a href="/wiki/Timeline_of_calculus_and_mathematical_analysis" title="Timeline of calculus and mathematical analysis">timeline</a></li></ul></li> <li><a href="/wiki/History_of_geometry" title="History of geometry">geometry</a> <ul><li><a href="/wiki/Timeline_of_geometry" title="Timeline of geometry">timeline</a></li></ul></li> <li><a href="/wiki/History_of_logic" title="History of logic">logic</a> <ul><li><a href="/wiki/Timeline_of_mathematical_logic" title="Timeline of mathematical logic">timeline</a></li></ul></li> <li><a href="/wiki/History_of_mathematics" title="History of mathematics">mathematics</a> <ul><li><a href="/wiki/Timeline_of_mathematics" title="Timeline of mathematics">timeline</a></li></ul></li> <li><a href="/wiki/History_of_numbers" class="mw-redirect" title="History of numbers">numbers</a> <ul><li><a href="/wiki/Prehistoric_counting" class="mw-redirect" title="Prehistoric counting">prehistoric counting</a></li></ul></li> <li><a href="/wiki/History_of_ancient_numeral_systems" title="History of ancient numeral systems">numeral systems</a> <ul><li><a href="/wiki/List_of_numeral_systems" title="List of numeral systems">list</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other cultures</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Arabian/Islamic</a></li> <li><a href="/wiki/Babylonian_mathematics" title="Babylonian mathematics">Babylonian</a></li> <li><a href="/wiki/Chinese_mathematics" title="Chinese mathematics">Chinese</a></li> <li><a href="/wiki/Ancient_Egyptian_mathematics" title="Ancient Egyptian mathematics">Egyptian</a></li> <li><a href="/wiki/Mathematics_of_the_Incas" title="Mathematics of the Incas">Incan</a></li> <li><a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian</a></li> <li><a href="/wiki/Japanese_mathematics" title="Japanese mathematics">Japanese</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/17px-Parthenon_from_west.jpg" decoding="async" width="17" height="13" class="mw-file-element" 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class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> <script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.eqiad.main-58c4b96c94-whjqb","wgBackendResponseTime":222,"wgPageParseReport":{"limitreport":{"cputime":"1.566","walltime":"2.013","ppvisitednodes":{"value":16551,"limit":1000000},"postexpandincludesize":{"value":209290,"limit":2097152},"templateargumentsize":{"value":21912,"limit":2097152},"expansiondepth":{"value":15,"limit":100},"expensivefunctioncount":{"value":20,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":192504,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 1767.854 1 -total"," 20.80% 367.713 145 Template:Sfn"," 14.43% 255.168 1 Template:Infobox_scientist"," 8.69% 153.701 11 Template:Langx"," 6.95% 122.891 2 Template:Reflist"," 5.83% 102.979 1 Template:Subject_bar"," 5.64% 99.775 1 Template:Transl"," 5.03% 88.990 1 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