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id="toc-Transmission_and_the_manuscript_tradition" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Transmission_and_the_manuscript_tradition"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Transmission and the manuscript tradition</span> </div> </a> <ul id="toc-Transmission_and_the_manuscript_tradition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-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"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Note</span> </div> </a> <ul id="toc-Note-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"> <span class="vector-toc-numb">7.2</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </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"> <span class="vector-toc-numb">9</span> <span>External links</span> </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" > <input type="checkbox" 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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 31 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-31" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">31 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA_%D8%B9%D9%86%D8%AF_%D8%A7%D9%84%D8%A5%D8%BA%D8%B1%D9%8A%D9%82" title="الرياضيات عند الإغريق – Arabic" lang="ar" hreflang="ar" data-title="الرياضيات عند الإغريق" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%95_%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="গ্রিক গণিত – Bangla" lang="bn" hreflang="bn" data-title="গ্রিক গণিত" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Matem%C3%A0tiques_de_l%27antiga_Gr%C3%A8cia" title="Matemàtiques de l'antiga Grècia – Catalan" lang="ca" hreflang="ca" data-title="Matemàtiques de l'antiga Grècia" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Griechische_Mathematik" title="Griechische Mathematik – German" lang="de" hreflang="de" data-title="Griechische Mathematik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BB%CE%BB%CE%B7%CE%BD%CE%B9%CE%BA%CE%AC_%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC" title="Ελληνικά μαθηματικά – Greek" lang="el" hreflang="el" data-title="Ελληνικά μαθηματικά" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Matem%C3%A1tica_griega" title="Matemática griega – Spanish" lang="es" hreflang="es" data-title="Matemática griega" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Greziar_matematika" title="Greziar matematika – Basque" lang="eu" hreflang="eu" data-title="Greziar matematika" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA_%DB%8C%D9%88%D9%86%D8%A7%D9%86%DB%8C" title="ریاضیات یونانی – Persian" lang="fa" hreflang="fa" data-title="ریاضیات یونانی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Math%C3%A9matiques_de_la_Gr%C3%A8ce_antique" title="Mathématiques de la Grèce antique – French" lang="fr" hreflang="fr" data-title="Mathématiques de la Grèce antique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B7%B8%EB%A6%AC%EC%8A%A4_%EC%88%98%ED%95%99" title="그리스 수학 – Korean" lang="ko" hreflang="ko" data-title="그리스 수학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1%D5%B6_%D5%80%D5%AB%D5%B6_%D5%80%D5%B8%D6%82%D5%B6%D5%A1%D5%BD%D5%BF%D5%A1%D5%B6%D5%B8%D6%82%D5%B4" title="Մաթեմատիկան Հին Հունաստանում – Armenian" lang="hy" hreflang="hy" data-title="Մաթեմատիկան Հին Հունաստանում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Matematika_Yunani" title="Matematika Yunani – Indonesian" lang="id" hreflang="id" data-title="Matematika Yunani" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Matematica_greco-ellenistica" title="Matematica greco-ellenistica – Italian" lang="it" hreflang="it" data-title="Matematica greco-ellenistica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94_%D7%91%D7%99%D7%95%D7%95%D7%9F_%D7%94%D7%A2%D7%AA%D7%99%D7%A7%D7%94" title="מתמטיקה ביוון העתיקה – Hebrew" lang="he" hreflang="he" data-title="מתמטיקה ביוון העתיקה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%95%D0%B6%D0%B5%D0%BB%D0%B3%D1%96_%D0%93%D1%80%D0%B5%D0%BA%D0%B8%D1%8F%D0%B4%D0%B0%D2%93%D1%8B_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Ежелгі Грекиядағы математика – Kazakh" lang="kk" hreflang="kk" data-title="Ежелгі Грекиядағы математика" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Matematica_elinica" title="Matematica elinica – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Matematica elinica" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/G%C3%B6r%C3%B6g_matematika" title="Görög matematika – Hungarian" lang="hu" hreflang="hu" data-title="Görög matematika" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B5%8D%E0%B4%B0%E0%B5%80%E0%B4%95%E0%B5%8D%E0%B4%95%E0%B5%8D_%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%B6%E0%B4%BE%E0%B4%B8%E0%B5%8D%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%82" title="ഗ്രീക്ക് ഗണിതശാസ്ത്രം – Malayalam" lang="ml" hreflang="ml" data-title="ഗ്രീക്ക് ഗണിതശാസ്ത്രം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Matematik_Yunani" title="Matematik Yunani – Malay" lang="ms" hreflang="ms" data-title="Matematik Yunani" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Oud-Griekse_wiskunde" title="Oud-Griekse wiskunde – Dutch" lang="nl" hreflang="nl" data-title="Oud-Griekse wiskunde" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Gresk_matematikk" title="Gresk matematikk – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Gresk matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Matem%C3%A1tica_da_Gr%C3%A9cia_Antiga" title="Matemática da Grécia Antiga – Portuguese" lang="pt" hreflang="pt" data-title="Matemática da Grécia Antiga" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%B2_%D0%94%D1%80%D0%B5%D0%B2%D0%BD%D0%B5%D0%B9_%D0%93%D1%80%D0%B5%D1%86%D0%B8%D0%B8" title="Математика в Древней Греции – Russian" lang="ru" hreflang="ru" data-title="Математика в Древней Греции" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/Greek_mathematics" title="Greek mathematics – Sinhala" lang="si" hreflang="si" data-title="Greek mathematics" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Greek_mathematics" title="Greek mathematics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Greek mathematics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%80%D0%BE%D0%B3%D1%80%D1%87%D0%BA%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Старогрчка математика – Serbian" lang="sr" hreflang="sr" data-title="Старогрчка математика" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Gr%C4%8Dka_matematika" title="Grčka matematika – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Grčka matematika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Yunan_matemati%C4%9Fi" title="Yunan matematiği – Turkish" lang="tr" hreflang="tr" data-title="Yunan matematiği" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B0%D0%B2%D0%BD%D1%8C%D0%BE%D0%B3%D1%80%D0%B5%D1%86%D1%8C%D0%BA%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Давньогрецька математика – Ukrainian" lang="uk" hreflang="uk" data-title="Давньогрецька математика" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/To%C3%A1n_h%E1%BB%8Dc_Hy_L%E1%BA%A1p" title="Toán học Hy Lạp – Vietnamese" lang="vi" hreflang="vi" data-title="Toán học Hy Lạp" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8F%A4%E5%B8%8C%E8%85%8A%E6%95%B0%E5%AD%A6" title="古希腊数学 – Chinese" lang="zh" hreflang="zh" data-title="古希腊数学" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Mathematics of Ancient Greeks</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pythagoras_Euclid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Pythagoras_Euclid.svg/170px-Pythagoras_Euclid.svg.png" decoding="async" width="170" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Pythagoras_Euclid.svg/255px-Pythagoras_Euclid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Pythagoras_Euclid.svg/340px-Pythagoras_Euclid.svg.png 2x" data-file-width="398" data-file-height="420" /></a><figcaption>An illustration of <a href="/wiki/Euclid" title="Euclid">Euclid</a>'s proof of the <a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a></figcaption></figure><p><b>Greek mathematics</b> refers to <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> texts and ideas stemming from the <a href="/wiki/Archaic_Greece" title="Archaic Greece">Archaic</a> through the <a href="/wiki/Hellenistic_period" title="Hellenistic period">Hellenistic</a> and <a href="/wiki/Roman_Empire" title="Roman Empire">Roman</a> periods, mostly from the 5th century BC to the 6th century AD, around the shores of the <a href="/wiki/Mediterranean_Sea" title="Mediterranean Sea">Mediterranean</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Greek mathematicians lived in cities spread over the entire region, from <a href="/wiki/Anatolia" title="Anatolia">Anatolia</a> to <a href="/wiki/Italy" title="Italy">Italy</a> and <a href="/wiki/North_Africa" title="North Africa">North Africa</a>, but were united by <a href="/wiki/Culture_of_Greece" title="Culture of Greece">Greek culture</a> and the <a href="/wiki/Greek_language" title="Greek language">Greek language</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The development of mathematics as a theoretical discipline and the use of <a href="/wiki/Deductive_reasoning" title="Deductive reasoning">deductive reasoning</a> in <a href="/wiki/Mathematical_proof" title="Mathematical proof">proofs</a> is an important difference between Greek mathematics and those of preceding civilizations.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Origins_and_etymology">Origins and etymology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=1" title="Edit section: Origins and etymology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Greek <i>mathēmatikē</i> ("mathematics") derives from the <a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: <span lang="grc"><span lang="grc"><a href="https://en.wiktionary.org/wiki/%CE%BC%CE%AC%CE%B8%CE%B7%CE%BC%CE%B1#Ancient_Greek" class="extiw" title="wikt:μάθημα">μάθημα</a></span></span>, <small><a href="/wiki/Romanization_of_Ancient_Greek" class="mw-redirect" title="Romanization of Ancient Greek">romanized</a>: </small><span title="Ancient Greek-language romanization"><i lang="grc-Latn">máthēma</i></span>, <style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style><span class="IPA-label IPA-label-small"><a href="/wiki/Attic_Greek_language" class="mw-redirect" title="Attic Greek language">Attic Greek</a>:</span> <span class="IPA nowrap" lang="grc-Latn-fonipa"><a href="/wiki/Help:IPA/Greek" title="Help:IPA/Greek">[má.tʰɛː.ma]</a></span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1177148991"><span class="IPA-label IPA-label-small"><a href="/wiki/Koin%C4%93_Greek_language" class="mw-redirect" title="Koinē Greek language">Koinē Greek</a>:</span> <span class="IPA nowrap" lang="grc-Latn-fonipa"><a href="/wiki/Help:IPA" title="Help:IPA">[ˈma.θi.ma]</a></span>, from the verb <i>manthanein</i>, "to learn". Strictly speaking, a <i>máthēma</i> could be any branch of learning, or anything learnt; however, since antiquity certain <i>mathēmata</i> (mainly arithmetic, geometry, astronomy, and harmonics) were granted special status.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The origins of Greek mathematics are not well documented.<sup id="cite_ref-LH_8-0" class="reference"><a href="#cite_note-LH-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The earliest advanced civilizations in <a href="/wiki/Greece" title="Greece">Greece</a> and <a href="/wiki/Europe" title="Europe">Europe</a> were the <a href="/wiki/Minoan_civilization" title="Minoan civilization">Minoan</a> and later <a href="/wiki/Mycenaean_Greece" title="Mycenaean Greece">Mycenaean</a> civilizations, both of which flourished during the 2nd millennium BC. While these civilizations possessed writing and were capable of advanced engineering, including four-story palaces with drainage and <a href="/wiki/Beehive_tomb" title="Beehive tomb">beehive tombs</a>, they left behind no mathematical documents. </p><p>Though no direct evidence is available, it is generally thought that the neighboring <a href="/wiki/Babylonia" title="Babylonia">Babylonian</a> and <a href="/wiki/Ancient_Egypt" title="Ancient Egypt">Egyptian</a> civilizations had an influence on the younger Greek tradition.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-høyrup_11-0" class="reference"><a href="#cite_note-høyrup-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-LH_8-1" class="reference"><a href="#cite_note-LH-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Unlike the flourishing of <a href="/wiki/Greek_literature" title="Greek literature">Greek literature</a> in the span of 800 to 600 BC, not much is known about Greek mathematics in this early period—nearly all of the information was passed down through later authors, beginning in the mid-4th century BC.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Boyer_2nd_ed_43-61_13-0" class="reference"><a href="#cite_note-Boyer_2nd_ed_43-61-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Archaic_and_Classical_periods">Archaic and Classical periods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=2" title="Edit section: Archaic and Classical periods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cropped_image_of_Pythagoras_from_Raphael%27s_School_of_Athens.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Cropped_image_of_Pythagoras_from_Raphael%27s_School_of_Athens.jpg/170px-Cropped_image_of_Pythagoras_from_Raphael%27s_School_of_Athens.jpg" decoding="async" width="170" height="184" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Cropped_image_of_Pythagoras_from_Raphael%27s_School_of_Athens.jpg/255px-Cropped_image_of_Pythagoras_from_Raphael%27s_School_of_Athens.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/Cropped_image_of_Pythagoras_from_Raphael%27s_School_of_Athens.jpg/340px-Cropped_image_of_Pythagoras_from_Raphael%27s_School_of_Athens.jpg 2x" data-file-width="744" data-file-height="806" /></a><figcaption><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a> with a tablet of ratios, detail from <i><a href="/wiki/The_School_of_Athens" title="The School of Athens">The School of Athens</a></i> by <a href="/wiki/Raphael" title="Raphael">Raphael</a> (1509)</figcaption></figure> <p>Greek mathematics allegedly began with <a href="/wiki/Thales_of_Miletus" title="Thales of Miletus">Thales of Miletus</a> (c. 624–548 BC). Very little is known about his life, although it is generally agreed that he was one of the <a href="/wiki/Seven_Wise_Men_of_Greece" class="mw-redirect" title="Seven Wise Men of Greece">Seven Wise Men of Greece</a>. According to <a href="/wiki/Proclus" title="Proclus">Proclus</a>, he traveled to Babylon from where he learned mathematics and other subjects, coming up with the proof of what is now called <a href="/wiki/Thales%27s_theorem" title="Thales's theorem">Thales' Theorem</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>An equally enigmatic figure is <a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras of Samos</a> (c. 580–500 BC), who supposedly visited Egypt and Babylon,<sup id="cite_ref-Boyer_2nd_ed_43-61_13-1" class="reference"><a href="#cite_note-Boyer_2nd_ed_43-61-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Heath_36-111_16-0" class="reference"><a href="#cite_note-Heath_36-111-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> and ultimately settled in <a href="/wiki/Crotone" title="Crotone">Croton</a>, <a href="/wiki/Magna_Graecia" title="Magna Graecia">Magna Graecia</a>, where he started a kind of brotherhood. <a href="/wiki/Pythagoreanism" title="Pythagoreanism">Pythagoreans</a> supposedly believed that "all is number" and were keen in looking for mathematical relations between numbers and things.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Pythagoras himself was given credit for many later discoveries, including the construction of the <a href="/wiki/Platonic_solid" title="Platonic solid">five regular solids</a>. However, Aristotle refused to attribute anything specifically to Pythagoras and only discussed the work of the Pythagoreans as a group.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Almost half of the material in <a href="/wiki/Euclid" title="Euclid">Euclid</a>'s <i><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Elements</a></i> is customarily attributed to the Pythagoreans, including the discovery of irrationals, attributed to <a href="/wiki/Hippasus" title="Hippasus">Hippasus</a> (c. 530–450 BC) and <a href="/wiki/Theodorus_of_Cyrene" title="Theodorus of Cyrene">Theodorus</a> (fl. 450 BC).<sup id="cite_ref-:0_20-0" class="reference"><a href="#cite_note-:0-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> The greatest mathematician associated with the group, however, may have been <a href="/wiki/Archytas" title="Archytas">Archytas</a> (c. 435-360 BC), who solved the problem of <a href="/wiki/Doubling_the_cube" title="Doubling the cube">doubling the cube</a>, identified the <a href="/wiki/Harmonic_mean" title="Harmonic mean">harmonic mean</a>, and possibly contributed to <a href="/wiki/Optics" title="Optics">optics</a> and <a href="/wiki/Mechanics" title="Mechanics">mechanics</a>.<sup id="cite_ref-:0_20-1" class="reference"><a href="#cite_note-:0-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Other mathematicians active in this period, not fully affiliated with any school, include <a href="/wiki/Hippocrates_of_Chios" title="Hippocrates of Chios">Hippocrates of Chios</a> (c. 470–410 BC), <a href="/wiki/Theaetetus_(mathematician)" title="Theaetetus (mathematician)">Theaetetus</a> (c. 417–369 BC), and <a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus</a> (c. 408–355 BC). </p><p>Greek mathematics also drew the attention of philosophers during the <a href="/wiki/Classical_Greece" title="Classical Greece">Classical period</a>. <a href="/wiki/Plato" title="Plato">Plato</a> (c. 428–348 BC), the founder of the <a href="/wiki/Platonic_Academy" title="Platonic Academy">Platonic Academy</a>, mentions mathematics in several of his dialogues.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> While not considered a mathematician, Plato seems to have been influenced by <a href="/wiki/Pythagoreanism" title="Pythagoreanism">Pythagorean</a> ideas about number and believed that the elements of matter could be broken down into geometric solids.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> He also believed that geometrical proportions bound the <a href="/wiki/Cosmos" title="Cosmos">cosmos</a> together rather than physical or mechanical forces.<sup id="cite_ref-:2_24-0" class="reference"><a href="#cite_note-:2-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> (c. 384–322 BC), the founder of the <a href="/wiki/Peripatetic_school" title="Peripatetic school">Peripatetic school</a>, often used mathematics to illustrate many of his theories, as when he used geometry in his theory of the rainbow and the theory of proportions in his analysis of motion.<sup id="cite_ref-:2_24-1" class="reference"><a href="#cite_note-:2-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Much of the knowledge about ancient Greek mathematics in this period is thanks to records referenced by Aristotle in his own works.<sup id="cite_ref-Boyer_2nd_ed_43-61_13-2" class="reference"><a href="#cite_note-Boyer_2nd_ed_43-61-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Hellenistic_and_Roman_periods">Hellenistic and Roman periods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=3" title="Edit section: Hellenistic and Roman periods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/170px-P._Oxy._I_29.jpg" decoding="async" width="170" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/P._Oxy._I_29.jpg/255px-P._Oxy._I_29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/P._Oxy._I_29.jpg/340px-P._Oxy._I_29.jpg 2x" data-file-width="1694" data-file-height="1032" /></a><figcaption>A fragment from <a href="/wiki/Euclid" title="Euclid">Euclid</a>'s <i><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Elements</a></i> (c. 300 BC), considered the most influential mathematics textbook of all time<sup id="cite_ref-Boyer_1991_loc=Euclid_of_Alexandria_p._119_26-0" class="reference"><a href="#cite_note-Boyer_1991_loc=Euclid_of_Alexandria_p._119-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The <a href="/wiki/Hellenistic_period" title="Hellenistic period">Hellenistic era</a> began in the late 4th century BC, following <a href="/wiki/Alexander_the_Great" title="Alexander the Great">Alexander the Great's</a> conquest of the <a href="/wiki/Eastern_Mediterranean" title="Eastern Mediterranean">Eastern Mediterranean</a>, <a href="/wiki/Ancient_Egypt" title="Ancient Egypt">Egypt</a>, <a href="/wiki/Mesopotamia" title="Mesopotamia">Mesopotamia</a>, the <a href="/wiki/Iranian_plateau" title="Iranian plateau">Iranian plateau</a>, <a href="/wiki/Central_Asia" title="Central Asia">Central Asia</a>, and parts of <a href="/wiki/India" title="India">India</a>, leading to the spread of the Greek language and culture across these regions. Greek became the <i><a href="/wiki/Lingua_franca" title="Lingua franca">lingua franca</a></i> of scholarship throughout the Hellenistic world, and the mathematics of the Classical period merged with <a href="/wiki/Egyptian_mathematics" class="mw-redirect" title="Egyptian mathematics">Egyptian</a> and <a href="/wiki/Babylonian_mathematics" title="Babylonian mathematics">Babylonian mathematics</a> to give rise to Hellenistic mathematics.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>Greek mathematics<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> reached its acme during the Hellenistic and early <a href="/wiki/Roman_Empire" title="Roman Empire">Roman periods</a>, and much of the work represented by authors such as <a href="/wiki/Euclid" title="Euclid">Euclid</a> (fl. 300 BC), <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> (c. 287–212 BC), <a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius</a> (c. 240–190 BC), <a href="/wiki/Hipparchus" title="Hipparchus">Hipparchus</a> (c. 190–120 BC), and <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a> (c. 100–170 AD) was of a very advanced level and rarely mastered outside a small circle.<sup id="cite_ref-:3_30-0" class="reference"><a href="#cite_note-:3-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Examples of <a href="/wiki/Applied_mathematics" title="Applied mathematics">applied mathematics</a> around this time include the construction of analogue computers like the <a href="/wiki/Antikythera_mechanism" title="Antikythera mechanism">Antikythera mechanism</a>,<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> the accurate measurement of the <a href="/wiki/Circumference_of_the_Earth" class="mw-redirect" title="Circumference of the Earth">circumference of the Earth</a> by <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a> (276–194 BC), and the mathematical and mechanical works of <a href="/wiki/Heron_of_Alexandria" class="mw-redirect" title="Heron of Alexandria">Heron</a> (c. 10–70 AD).<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>Several centers of learning appeared during the Hellenistic period, of which the most important one was the <a href="/wiki/Musaeum" class="mw-redirect" title="Musaeum">Mouseion</a> in <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a>, <a href="/wiki/Ancient_Egypt" title="Ancient Egypt">Egypt</a>, which attracted scholars from across the Hellenistic world (mostly Greek, but also <a href="/wiki/Egyptians" title="Egyptians">Egyptian</a>, <a href="/wiki/Jew" class="mw-redirect" title="Jew">Jewish</a>, <a href="/wiki/Persian_people" class="mw-redirect" title="Persian people">Persian</a>, among others).<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> Although few in number, Hellenistic mathematicians actively communicated with each other; publication consisted of passing and copying someone's work among colleagues.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p><p>Later mathematicians in the Roman era include <a href="/wiki/Diophantus" title="Diophantus">Diophantus</a> (c. 214–298 AD), who wrote on <a href="/wiki/Polygonal_number" title="Polygonal number">polygonal numbers</a> and a work in pre-modern algebra (<i><a href="/wiki/Arithmetica" title="Arithmetica">Arithmetica</a></i>),<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus of Alexandria</a> (c. 290–350 AD), who compiled many important results in the <i>Collection</i>,<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a> (c. 335–405 AD) and his daughter <a href="/wiki/Hypatia" title="Hypatia">Hypatia</a> (c. 370–415 AD), who edited Ptolemy's <i><a href="/wiki/Almagest" title="Almagest">Almagest</a></i> and other works,<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Eutocius_of_Ascalon" title="Eutocius of Ascalon">Eutocius of Ascalon</a> (<abbr>c.</abbr> 480–540 AD), who wrote commentaries on treatises by Archimedes and Apollonius.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Although none of these mathematicians, save perhaps Diophantus, had notable original works, they are distinguished for their commentaries and expositions. These commentaries have preserved valuable extracts from works which have perished, or historical allusions which, in the absence of original documents, are precious because of their rarity.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p><p>Most of the mathematical texts written in Greek survived through the copying of manuscripts over the centuries. While some fragments dating from antiquity have been found above all in <a href="/wiki/Egypt" title="Egypt">Egypt</a>, as a rule they do not add anything significant to our knowledge of Greek mathematics preserved in the manuscript tradition.<sup id="cite_ref-:3_30-1" class="reference"><a href="#cite_note-:3-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Achievements">Achievements</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=4" title="Edit section: Achievements"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Greek mathematics constitutes an important period in the history of <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>: fundamental in respect of <a href="/wiki/Geometry" title="Geometry">geometry</a> and for the idea of <a href="/wiki/Formal_proof" title="Formal proof">formal proof</a>.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> Greek mathematicians also contributed to <a href="/wiki/Number_theory" title="Number theory">number theory</a>, <a href="/wiki/Theoretical_astronomy" title="Theoretical astronomy">mathematical astronomy</a>, <a href="/wiki/Combinatorics" title="Combinatorics">combinatorics</a>, <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a>, and, at times, approached ideas close to the <a href="/wiki/Integral_calculus" class="mw-redirect" title="Integral calculus">integral calculus</a>.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus of Cnidus</a> developed a theory of proportion that bears resemblance to the modern theory of <a href="/wiki/Real_number" title="Real number">real numbers</a> using the <a href="/wiki/Dedekind_cut" title="Dedekind cut">Dedekind cut</a>, developed by <a href="/wiki/Richard_Dedekind" title="Richard Dedekind">Richard Dedekind</a>, who acknowledged Eudoxus as inspiration.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Euclid" title="Euclid">Euclid</a>, who presumably wrote on optics, astronomy, and harmonics, collected many previous mathematical results and theorems in the <i><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Elements</a></i>, a canon of geometry and elementary number theory for many centuries.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria">Menelaus</a>, a later geometer and astronomer, wrote a standard work on <a href="/wiki/Spherical_geometry" title="Spherical geometry">spherical geometry</a> in the style of the <i>Elements</i>, the <i>Spherics</i>, arguably considered the first treatise in <a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean geometry</a>.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> made use of a technique dependent on a form of <a href="/wiki/Proof_by_contradiction" title="Proof by contradiction">proof by contradiction</a> to reach answers to problems with an arbitrary degree of accuracy, while specifying the limits within which the answers lay. Known as the <a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">method of exhaustion</a>, Archimedes employed it in several of his works, including an approximation to <a href="/wiki/Pi" title="Pi"><span class="texhtml mvar" style="font-style:italic;">π</span></a> (<i><a href="/wiki/Measurement_of_a_Circle" title="Measurement of a Circle">Measurement of the Circle</a></i>),<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> and a proof that the area enclosed by a <a href="/wiki/Parabola" title="Parabola">parabola</a> and a straight line is <span class="nowrap">4/3</span> times the area of a <a href="/wiki/Triangle" title="Triangle">triangle</a> with equal base and height (<i><a href="/wiki/Quadrature_of_the_Parabola" title="Quadrature of the Parabola">Quadrature of the Parabola</a></i>).<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> Archimedes also showed that the number of grains of sand filling the universe was not uncountable, devising his own counting scheme based on the <a href="/wiki/Myriad" title="Myriad">myriad</a>, which denoted 10,000 (<i><a href="/wiki/The_Sand-Reckoner" class="mw-redirect" title="The Sand-Reckoner">The Sand-Reckoner</a></i>).<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> </p><p>The most characteristic product of Greek mathematics may be the theory of <a href="/wiki/Conic_section" title="Conic section">conic sections</a>, which was largely developed in the <a href="/wiki/Hellenistic_period" title="Hellenistic period">Hellenistic period</a>, starting with the work of <a href="/wiki/Menaechmus" title="Menaechmus">Menaechmus</a> and perfected primarily under Apollonius in his work <i><a href="/wiki/On_Conic_Sections" class="mw-redirect" title="On Conic Sections">Conics</a></i>.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> The methods employed in these works made no explicit use of <a href="/wiki/Algebra" title="Algebra">algebra</a>, nor <a href="/wiki/Trigonometry" title="Trigonometry">trigonometry</a>, the latter appearing around the time of <a href="/wiki/Hipparchus" title="Hipparchus">Hipparchus</a>.<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </p><p>Ancient Greek mathematics was not limited to theoretical works but was also used in other activities, such as business transactions and in land mensuration, as evidenced by extant texts where <a href="/wiki/Numerical_analysis" title="Numerical analysis">computational procedures</a> and practical considerations took more of a central role.<sup id="cite_ref-høyrup_11-1" class="reference"><a href="#cite_note-høyrup-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Transmission_and_the_manuscript_tradition">Transmission and the manuscript tradition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=5" title="Edit section: Transmission and the manuscript tradition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Diophantus-cover.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Diophantus-cover.png/170px-Diophantus-cover.png" decoding="async" width="170" height="266" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Diophantus-cover.png/255px-Diophantus-cover.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Diophantus-cover.png/340px-Diophantus-cover.png 2x" data-file-width="828" data-file-height="1295" /></a><figcaption>Cover of Diophantus' <i><a href="/wiki/Arithmetica" title="Arithmetica">Arithmetica</a></i> in Latin</figcaption></figure> <p>Although the earliest <a href="/wiki/Greek_language" title="Greek language">Greek</a> mathematical texts that have been found were written after the Hellenistic period, most are considered to be copies of works written during and before the Hellenistic period.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> The two major sources are </p> <ul><li><a href="/wiki/Constantinople#Culture" title="Constantinople">Byzantine codices</a>, written some 500 to 1500 years after their originals, and</li> <li><a href="/wiki/Syriac_language" title="Syriac language">Syriac</a> or <a href="/wiki/Graeco-Arabic_translation_movement" title="Graeco-Arabic translation movement">Arabic translations</a> of Greek works and <a href="/wiki/Latin_translations_of_the_12th_century" title="Latin translations of the 12th century">Latin translations</a> of the Arabic versions.</li></ul> <p>Despite the lack of original manuscripts, the dates for some Greek mathematicians are more certain than the dates of surviving Babylonian or Egyptian sources because a number of overlapping chronologies exist, though many dates remain uncertain. </p><p><a href="/wiki/Reviel_Netz" title="Reviel Netz">Netz</a> (2011) has counted 144 ancient authors in the mathematical or exact sciences, from whom only 29 works are extant in Greek: <a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus</a>, <a href="/wiki/Autolycus_of_Pitane" title="Autolycus of Pitane">Autolycus</a>, <a href="/wiki/Philo_of_Byzantium" title="Philo of Byzantium">Philo of Byzantium</a>, <a href="/wiki/Biton_of_Pergamon" title="Biton of Pergamon">Biton</a>, <a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius</a>, <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a>, <a href="/wiki/Euclid" title="Euclid">Euclid</a>, <a href="/wiki/Theodosius_of_Bithynia" title="Theodosius of Bithynia">Theodosius</a>, <a href="/wiki/Hypsicles" title="Hypsicles">Hypsicles</a>, <a href="/wiki/Athenaeus_Mechanicus" title="Athenaeus Mechanicus">Athenaeus</a>, <a href="/wiki/Geminus" title="Geminus">Geminus</a>, <a href="/wiki/Hero_of_Alexandria" title="Hero of Alexandria">Heron</a>, <a href="/wiki/Apollodorus_of_Damascus" title="Apollodorus of Damascus">Apollodorus</a>, <a href="/wiki/Theon_of_Smyrna" title="Theon of Smyrna">Theon of Smyrna</a>, <a href="/wiki/Cleomedes" title="Cleomedes">Cleomedes</a>, <a href="/wiki/Nicomachus" title="Nicomachus">Nicomachus</a>, <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>, <a href="/wiki/Gaudentius_(music_theorist)" title="Gaudentius (music theorist)">Gaudentius</a>, <a href="/wiki/Anatolius_of_Laodicea" title="Anatolius of Laodicea">Anatolius</a>, <a href="/wiki/Aristides_Quintilian" class="mw-redirect" title="Aristides Quintilian">Aristides Quintilian</a>, <a href="/wiki/Porphyry_(philosopher)" title="Porphyry (philosopher)">Porphyry</a>, <a href="/wiki/Diophantus" title="Diophantus">Diophantus</a>, <a href="/wiki/Alypius_of_Alexandria" title="Alypius of Alexandria">Alypius</a>, <a href="/wiki/Heliodorus_of_Larissa" title="Heliodorus of Larissa">Damianus</a>, <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus</a>, <a href="/wiki/Serenus_of_Antino%C3%B6polis" title="Serenus of Antinoöpolis">Serenus</a>, <a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a>, <a href="/wiki/Anthemius_of_Tralles" title="Anthemius of Tralles">Anthemius</a>, and <a href="/wiki/Eutocius" class="mw-redirect" title="Eutocius">Eutocius</a>.<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> </p><p>The following works are extant only in Arabic translations:<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Apollonius, <i>Conics</i> books V to VII</li> <li>Apollonius, <i>Cutting Off of a Ratio</i></li> <li>Archimedes, <i><a href="/wiki/Book_of_Lemmas" title="Book of Lemmas">Book of Lemmas</a></i></li> <li>Archimedes, <i>Construction of the Regular Heptagon</i></li> <li><a href="/wiki/Diocles_(mathematician)" title="Diocles (mathematician)">Diocles</a>, <i>On Burning Mirrors</i></li> <li>Diophantus, <i><a href="/wiki/Arithmetica" title="Arithmetica">Arithmetica</a></i> books IV to VII</li> <li>Euclid, <i>On Divisions of Figures</i></li> <li>Euclid, <i>On Weights</i></li> <li>Heron, <i>Catoptrica</i></li> <li>Heron, <i>Mechanica</i></li> <li><a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria">Menelaus</a>, <i>Sphaerica</i></li> <li>Pappus, <i>Commentary on Euclid's Elements book X</i></li> <li>Ptolemy, <i><a href="/wiki/Optics_(Ptolemy)" title="Optics (Ptolemy)">Optics</a></i> (extant in Latin from an Arabic translation of the Greek)</li> <li>Ptolemy, <i><a href="/wiki/Planisphaerium" title="Planisphaerium">Planisphaerium</a></i></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1259569809">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output 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mathematicians</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Note">Note</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=8" title="Edit section: Note"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Inclusive of astronomy, harmonics, optics, and mechanics.</span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=9" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><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 id="CITEREFSidoli2020" class="citation journal cs1">Sidoli, Nathan (2020). Taub, Liba (ed.). <a rel="nofollow" class="external text" href="http://individual.utoronto.ca/acephalous/Sidoli_2020_Ancient_Greek_Mathematics.pdf">"Ancient Greek Mathematics"</a> <span class="cs1-format">(PDF)</span>. <i>The Cambridge Companion to Ancient Greek and Roman Science</i>: 190–191. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2F9781316136096.010">10.1017/9781316136096.010</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-316-13609-6" title="Special:BookSources/978-1-316-13609-6"><bdi>978-1-316-13609-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Cambridge+Companion+to+Ancient+Greek+and+Roman+Science&rft.atitle=Ancient+Greek+Mathematics&rft.pages=190-191&rft.date=2020&rft_id=info%3Adoi%2F10.1017%2F9781316136096.010&rft.isbn=978-1-316-13609-6&rft.aulast=Sidoli&rft.aufirst=Nathan&rft_id=http%3A%2F%2Findividual.utoronto.ca%2Facephalous%2FSidoli_2020_Ancient_Greek_Mathematics.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNetz2002" class="citation web cs1">Netz, Reviel (2002). <a rel="nofollow" class="external text" href="https://academic.oup.com/book/9389/chapter-abstract/156223875?redirectedFrom=fulltext&login=false">"Greek mathematics: A group picture"</a>. <i>Science and Mathematics in Ancient Greek Culture</i>. pp. 196–216<span class="reference-accessdate">. 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Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-852937-8" title="Special:BookSources/978-0-19-852937-8"><bdi>978-0-19-852937-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Greeks+and+origins&rft.btitle=A+History+of+Mathematics%3A+From+Mesopotamia+to+Modernity&rft.pub=Oxford+University+Press&rft.date=2005&rft.isbn=978-0-19-852937-8&rft.aulast=Hodgkin&rft.aufirst=Luke&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryofmathema0000hodg&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKnorr1981" class="citation book cs1">Knorr, W. (1981). <i>On the early history of axiomatics: The interaction of mathematics and philosophy in Greek Antiquity</i>. D. Reidel Publishing Co. pp. 145–186.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=On+the+early+history+of+axiomatics%3A+The+interaction+of+mathematics+and+philosophy+in+Greek+Antiquity.&rft.pages=145-186&rft.pub=D.+Reidel+Publishing+Co.&rft.date=1981&rft.aulast=Knorr&rft.aufirst=W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span> Theory Change, Ancient Axiomatics, and Galileo's Methodology, Vol. 1</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKahn1991" class="citation book cs1">Kahn, C. H. (1991). <i>Some remarks on the origins of Greek science and philosophy</i>. 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(1990). <a rel="nofollow" class="external text" href="http://webhotel4.ruc.dk/~jensh/Publications/1990%7bg%7d_Undercurrents.PDF"><i><span></span></i>"Sub-scientific mathematics: Undercurrents and missing links in the mathematical technology of the Hellenistic and Roman world"<i><span></span></i></a> <span class="cs1-format">(PDF)</span> (Unpublished manuscript, written for <i><a href="/wiki/Aufstieg_und_Niedergang_der_r%C3%B6mischen_Welt" title="Aufstieg und Niedergang der römischen Welt">Aufstieg und Niedergang der römischen Welt</a></i>).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%22Sub-scientific+mathematics%3A+Undercurrents+and+missing+links+in+the+mathematical+technology+of+the+Hellenistic+and+Roman+world%22&rft.date=1990&rft.aulast=H%C3%B8yrup&rft.aufirst=J.&rft_id=http%3A%2F%2Fwebhotel4.ruc.dk%2F~jensh%2FPublications%2F1990%257bg%257d_Undercurrents.PDF&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZhmud2008" class="citation book cs1">Zhmud, Leonid (2008-08-22). <a rel="nofollow" class="external text" href="https://www.degruyter.com/document/doi/10.1515/9783110194326/html"><i>The Origin of the History of Science in Classical Antiquity</i></a>. Peripatoi. De Gruyter. pp. 23–44. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1515%2F9783110194326">10.1515/9783110194326</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-11-019432-6" title="Special:BookSources/978-3-11-019432-6"><bdi>978-3-11-019432-6</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+Origin+of+the+History+of+Science+in+Classical+Antiquity&rft.series=Peripatoi&rft.pages=23-44&rft.pub=De+Gruyter&rft.date=2008-08-22&rft_id=info%3Adoi%2F10.1515%2F9783110194326&rft.isbn=978-3-11-019432-6&rft.aulast=Zhmud&rft.aufirst=Leonid&rft_id=https%3A%2F%2Fwww.degruyter.com%2Fdocument%2Fdoi%2F10.1515%2F9783110194326%2Fhtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-Boyer_2nd_ed_43-61-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Boyer_2nd_ed_43-61_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Boyer_2nd_ed_43-61_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Boyer_2nd_ed_43-61_13-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Boyer & Merzbach (2011) pp. 40–89.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPanchenko1993" class="citation journal cs1">Panchenko, D. 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(1974). <a rel="nofollow" class="external text" href="https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1600-0498.1974.tb00205.x">"The Chord Table of Hipparchus and the Early History of Greek Trigonometry"</a>. <i>Centaurus</i>. <b>18</b> (1): 6–28. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1974Cent...18....6T">1974Cent...18....6T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1600-0498.1974.tb00205.x">10.1111/j.1600-0498.1974.tb00205.x</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1600-0498">1600-0498</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Centaurus&rft.atitle=The+Chord+Table+of+Hipparchus+and+the+Early+History+of+Greek+Trigonometry&rft.volume=18&rft.issue=1&rft.pages=6-28&rft.date=1974&rft.issn=1600-0498&rft_id=info%3Adoi%2F10.1111%2Fj.1600-0498.1974.tb00205.x&rft_id=info%3Abibcode%2F1974Cent...18....6T&rft.aulast=Toomer&rft.aufirst=G.+J.&rft_id=https%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2Fabs%2F10.1111%2Fj.1600-0498.1974.tb00205.x&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuke2011" class="citation journal cs1">Duke, D. (2011). <a rel="nofollow" class="external text" href="https://people.sc.fsu.edu/~dduke/earlytrig12.pdf">"The very early history of trigonometry"</a> <span class="cs1-format">(PDF)</span>. <i>DIO: The International Journal of Scientific History</i>. <b>17</b>: 34–42.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=DIO%3A+The+International+Journal+of+Scientific+History&rft.atitle=The+very+early+history+of+trigonometry.&rft.volume=17&rft.pages=34-42&rft.date=2011&rft.aulast=Duke&rft.aufirst=D.&rft_id=https%3A%2F%2Fpeople.sc.fsu.edu%2F~dduke%2Fearlytrig12.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRobbins1934" class="citation journal cs1">Robbins, F. E. (1934). <a rel="nofollow" class="external text" href="https://www.journals.uchicago.edu/doi/10.1086/346874">"Greco-Egyptian Arithmetical Problems: P. Mich. 4966"</a>. <i>Isis</i>. <b>22</b> (1): 95–103. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F346874">10.1086/346874</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:144052363">144052363</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=Greco-Egyptian+Arithmetical+Problems%3A+P.+Mich.+4966&rft.volume=22&rft.issue=1&rft.pages=95-103&rft.date=1934&rft_id=info%3Adoi%2F10.1086%2F346874&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A144052363%23id-name%3DS2CID&rft.aulast=Robbins&rft.aufirst=F.+E.&rft_id=https%3A%2F%2Fwww.journals.uchicago.edu%2Fdoi%2F10.1086%2F346874&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ_J_O'Connor_and_E_F_Robertson1999" class="citation web cs1">J J O'Connor and E F Robertson (October 1999). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20000130113411/http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Greek_sources_1.html">"How do we know about Greek mathematics?"</a>. <i>The MacTutor History of Mathematics archive</i>. University of St. Andrews. Archived from <a rel="nofollow" class="external text" href="http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Greek_sources_1.html">the original</a> on 30 January 2000<span class="reference-accessdate">. Retrieved <span class="nowrap">18 April</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+MacTutor+History+of+Mathematics+archive&rft.atitle=How+do+we+know+about+Greek+mathematics%3F&rft.date=1999-10&rft.au=J+J+O%27Connor+and+E+F+Robertson&rft_id=http%3A%2F%2Fwww-groups.dcs.st-and.ac.uk%2F~history%2FHistTopics%2FGreek_sources_1.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-67">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNetz2011" class="citation journal cs1 cs1-prop-foreign-lang-source">Netz, Reviel (27 September 2011). <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00048-011-0057-2">"The Bibliosphere of Ancient Science (Outside of Alexandria)"</a>. <i>NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin</i> (in German). <b>19</b> (3): 239–269. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00048-011-0057-2">10.1007/s00048-011-0057-2</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1420-9144">1420-9144</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/21946891">21946891</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:21519829">21519829</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=NTM+Zeitschrift+f%C3%BCr+Geschichte+der+Wissenschaften%2C+Technik+und+Medizin&rft.atitle=The+Bibliosphere+of+Ancient+Science+%28Outside+of+Alexandria%29&rft.volume=19&rft.issue=3&rft.pages=239-269&rft.date=2011-09-27&rft.issn=1420-9144&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A21519829%23id-name%3DS2CID&rft_id=info%3Apmid%2F21946891&rft_id=info%3Adoi%2F10.1007%2Fs00048-011-0057-2&rft.aulast=Netz&rft.aufirst=Reviel&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%252Fs00048-011-0057-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-68">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLorch2001" class="citation journal cs1">Lorch, Richard (June 2001). <a rel="nofollow" class="external text" href="https://epub.ub.uni-muenchen.de/15929/">"Greek-Arabic-Latin: The Transmission of Mathematical Texts in the Middle Ages"</a>. <i>Science in Context</i>. <b>14</b> (1–2): 313–331. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0269889701000114">10.1017/S0269889701000114</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:146539132">146539132</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science+in+Context&rft.atitle=Greek-Arabic-Latin%3A+The+Transmission+of+Mathematical+Texts+in+the+Middle+Ages&rft.volume=14&rft.issue=1%E2%80%932&rft.pages=313-331&rft.date=2001-06&rft_id=info%3Adoi%2F10.1017%2FS0269889701000114&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A146539132%23id-name%3DS2CID&rft.aulast=Lorch&rft.aufirst=Richard&rft_id=https%3A%2F%2Fepub.ub.uni-muenchen.de%2F15929%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-69"><span class="mw-cite-backlink"><b><a href="#cite_ref-69">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToomer1984" class="citation journal cs1">Toomer, G. J. (January 1984). "Lost greek mathematical works in arabic translation". <i>The Mathematical Intelligencer</i>. <b>6</b> (2): 32–38. <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%2FBF03024153">10.1007/BF03024153</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Mathematical+Intelligencer&rft.atitle=Lost+greek+mathematical+works+in+arabic+translation&rft.volume=6&rft.issue=2&rft.pages=32-38&rft.date=1984-01&rft_id=info%3Adoi%2F10.1007%2FBF03024153&rft.aulast=Toomer&rft.aufirst=G.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=10" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoyerMerzbach2011" class="citation cs2"><a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer">Boyer, Carl B.</a>; <a href="/wiki/Uta_Merzbach" title="Uta Merzbach">Merzbach, Uta C.</a> (2011), <a rel="nofollow" class="external text" href="https://www.wiley.com/en-us/A+History+of+Mathematics%2C+3rd+Edition-p-9780470525487"><i>A History of Mathematics</i></a> (3rd 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=3rd&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=2011&rft.isbn=978-0-471-54397-8&rft.aulast=Boyer&rft.aufirst=Carl+B.&rft.au=Merzbach%2C+Uta+C.&rft_id=https%3A%2F%2Fwww.wiley.com%2Fen-us%2FA%2BHistory%2Bof%2BMathematics%252C%2B3rd%2BEdition-p-9780470525487&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJean_Christianidis2004" class="citation cs2">Jean Christianidis, ed. (2004), <i>Classics in the History of Greek Mathematics</i>, Kluwer Academic Publishers, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-0081-2" title="Special:BookSources/978-1-4020-0081-2"><bdi>978-1-4020-0081-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classics+in+the+History+of+Greek+Mathematics&rft.pub=Kluwer+Academic+Publishers&rft.date=2004&rft.isbn=978-1-4020-0081-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCooke1997" class="citation cs2">Cooke, Roger (1997), <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema0000cook"><i>The History of Mathematics: A Brief Course</i></a>, Wiley-Interscience, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-18082-1" title="Special:BookSources/978-0-471-18082-1"><bdi>978-0-471-18082-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+History+of+Mathematics%3A+A+Brief+Course&rft.pub=Wiley-Interscience&rft.date=1997&rft.isbn=978-0-471-18082-1&rft.aulast=Cooke&rft.aufirst=Roger&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryofmathema0000cook&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDerbyshire2006" class="citation cs2"><a href="/wiki/John_Derbyshire" title="John Derbyshire">Derbyshire, John</a> (2006), <a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780309096577"><i>Unknown Quantity: A Real And Imaginary History of Algebra</i></a>, Joseph Henry Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-309-09657-7" title="Special:BookSources/978-0-309-09657-7"><bdi>978-0-309-09657-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Unknown+Quantity%3A+A+Real+And+Imaginary+History+of+Algebra&rft.pub=Joseph+Henry+Press&rft.date=2006&rft.isbn=978-0-309-09657-7&rft.aulast=Derbyshire&rft.aufirst=John&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fisbn_9780309096577&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStillwell2004" class="citation cs2"><a href="/wiki/John_Stillwell" title="John Stillwell">Stillwell, John</a> (2004), <i>Mathematics and its History</i> (2nd ed.), Springer Science + Business Media Inc., <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-95336-6" title="Special:BookSources/978-0-387-95336-6"><bdi>978-0-387-95336-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+and+its+History&rft.edition=2nd&rft.pub=Springer+Science+%2B+Business+Media+Inc.&rft.date=2004&rft.isbn=978-0-387-95336-6&rft.aulast=Stillwell&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBurton1997" class="citation cs2">Burton, David M. (1997), <i>The History of Mathematics: An Introduction</i> (3rd ed.), The McGraw-Hill Companies, Inc., <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-009465-9" title="Special:BookSources/978-0-07-009465-9"><bdi>978-0-07-009465-9</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+History+of+Mathematics%3A+An+Introduction&rft.edition=3rd&rft.pub=The+McGraw-Hill+Companies%2C+Inc.&rft.date=1997&rft.isbn=978-0-07-009465-9&rft.aulast=Burton&rft.aufirst=David+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeath1981" class="citation cs2"><a href="/wiki/T._L._Heath" class="mw-redirect" title="T. L. Heath">Heath, Thomas Little</a> (1981) [First published 1921], <i><a href="/wiki/A_History_of_Greek_Mathematics" title="A History of Greek Mathematics">A History of Greek Mathematics</a></i>, Dover publications, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-24073-2" title="Special:BookSources/978-0-486-24073-2"><bdi>978-0-486-24073-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Greek+Mathematics&rft.pub=Dover+publications&rft.date=1981&rft.isbn=978-0-486-24073-2&rft.aulast=Heath&rft.aufirst=Thomas+Little&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeath2003" class="citation cs2"><a href="/wiki/T._L._Heath" class="mw-redirect" title="T. L. Heath">Heath, Thomas Little</a> (2003) [First published 1931], <i>A Manual of Greek Mathematics</i>, Dover publications, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-43231-1" title="Special:BookSources/978-0-486-43231-1"><bdi>978-0-486-43231-1</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+Manual+of+Greek+Mathematics&rft.pub=Dover+publications&rft.date=2003&rft.isbn=978-0-486-43231-1&rft.aulast=Heath&rft.aufirst=Thomas+Little&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></li> <li>Sing, Robert; van Berkel Tazuko; Osborne, Robin (2021), <i><a rel="nofollow" class="external text" href="https://brill.com/display/title/60496">Numbers and Numeracy in the Greek Polis</a></i>, Brill, ISBN 978-90-04-46722-4</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSzabo1978" class="citation cs2">Szabo, Arpad (1978) [First published 1978], <i>The Beginnings of Greek Mathematics</i>, Reidel & Akademiai Kiado, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-963-05-1416-3" title="Special:BookSources/978-963-05-1416-3"><bdi>978-963-05-1416-3</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+Beginnings+of+Greek+Mathematics&rft.pub=Reidel+%26+Akademiai+Kiado&rft.date=1978&rft.isbn=978-963-05-1416-3&rft.aulast=Szabo&rft.aufirst=Arpad&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGreek+mathematics" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Greek_mathematics&action=edit&section=11" 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mathematics</a> (<a href="/wiki/Timeline_of_mathematics" title="Timeline of mathematics">timeline</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">By topic</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/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>Algorithms <ul><li><a href="/wiki/Timeline_of_algorithms" title="Timeline of algorithms">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> <li><a href="/wiki/History_of_Grandi%27s_series" title="History of Grandi's series">Grandi's series</a></li></ul></li> <li>Category theory <ul><li><a href="/wiki/Timeline_of_category_theory_and_related_mathematics" title="Timeline of category theory and related mathematics">timeline</a></li> <li><a href="/wiki/History_of_topos_theory" title="History of topos theory">Topos theory</a></li></ul></li> <li><a href="/wiki/History_of_combinatorics" title="History of combinatorics">Combinatorics</a></li> <li><a href="/wiki/History_of_the_function_concept" title="History of the function concept">Functions</a> <ul><li><a href="/wiki/History_of_logarithms" title="History of logarithms">Logarithms</a></li></ul></li> <li><a href="/wiki/History_of_geometry" title="History of geometry">Geometry</a> <ul><li><a href="/wiki/History_of_trigonometry" title="History of trigonometry">Trigonometry</a></li> <li><a href="/wiki/Timeline_of_geometry" title="Timeline of geometry">timeline</a></li></ul></li> <li><a href="/wiki/History_of_group_theory" title="History of group theory">Group theory</a></li> <li><a href="/wiki/History_of_information_theory" title="History of information theory">Information theory</a> <ul><li><a href="/wiki/Timeline_of_information_theory" title="Timeline of information theory">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_mathematical_notation" title="History of mathematical notation">Math notation</a></li> <li>Number theory <ul><li><a href="/wiki/Timeline_of_number_theory" title="Timeline of number theory">timeline</a></li></ul></li> <li><a href="/wiki/History_of_statistics" title="History of statistics">Statistics</a> <ul><li><a href="/wiki/Timeline_of_probability_and_statistics" title="Timeline of probability and statistics">timeline</a></li> <li><a href="/wiki/History_of_probability" title="History of probability">Probability</a></li></ul></li> <li>Topology <ul><li><a href="/wiki/History_of_manifolds_and_varieties" title="History of manifolds and varieties">Manifolds</a> <ul><li><a href="/wiki/Timeline_of_manifolds" title="Timeline of manifolds">timeline</a></li></ul></li> <li><a href="/wiki/History_of_the_separation_axioms" title="History of the separation axioms">Separation axioms</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Numeral systems</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/Prehistoric_counting" title="Prehistoric counting">Prehistoric</a></li> <li><a href="/wiki/History_of_ancient_numeral_systems" title="History of ancient numeral systems">Ancient</a></li> <li><a href="/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_system" title="History of the Hindu–Arabic numeral system">Hindu-Arabic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By ancient 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/Babylonian_mathematics" title="Babylonian mathematics">Mesopotamia</a></li> <li><a href="/wiki/Ancient_Egyptian_mathematics" title="Ancient Egyptian mathematics">Ancient Egypt</a></li> <li><a class="mw-selflink selflink">Ancient Greece</a></li> <li><a href="/wiki/Chinese_mathematics" title="Chinese mathematics">China</a></li> <li><a href="/wiki/Indian_mathematics" title="Indian mathematics">India</a></li> <li><a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Medieval Islamic world</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Controversies</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/Brouwer%E2%80%93Hilbert_controversy" title="Brouwer–Hilbert controversy">Brouwer–Hilbert</a></li> <li><a href="/wiki/Controversy_over_Cantor%27s_theory" title="Controversy over Cantor's theory">Over Cantor's theory</a></li> <li><a href="/wiki/Leibniz%E2%80%93Newton_calculus_controversy" title="Leibniz–Newton calculus controversy">Leibniz–Newton</a></li> <li><a href="/wiki/Hobbes%E2%80%93Wallis_controversy" title="Hobbes–Wallis controversy">Hobbes–Wallis</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>Women in mathematics <ul><li><a href="/wiki/Timeline_of_women_in_mathematics" title="Timeline of women in mathematics">timeline</a></li></ul></li> <li><a href="/wiki/Approximations_of_%CF%80" title="Approximations of π">Approximations of π</a> <ul><li><a href="/wiki/Chronology_of_computation_of_%CF%80" title="Chronology of computation of π">timeline</a></li></ul></li> <li><a href="/wiki/Future_of_mathematics" title="Future of mathematics">Future of mathematics</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><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" /></span></span> <a href="/wiki/Category:History_of_mathematics" title="Category:History of mathematics">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_mathematics" style="padding:3px"><table class="nowraplinks mw-collapsible uncollapsed 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 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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 href="/wiki/Euclid" title="Euclid">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_(philosopher)" title="Porphyry (philosopher)">Porphyry</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><i><a href="/wiki/Almagest" title="Almagest">Almagest</a></i></li> <li><a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a></li> <li><i><a href="/wiki/Arithmetica" title="Arithmetica">Arithmetica</a></i></li> <li><a href="/wiki/Apollonius_of_Perga#Conics" title="Apollonius of Perga"><i>Conics</i> <span style="font-size:85%;">(Apollonius)</span></a></li> <li><i><a href="/wiki/Catoptrics" title="Catoptrics">Catoptrics</a></i></li> <li><a href="/wiki/Data_(Euclid)" class="mw-redirect" title="Data (Euclid)"><i>Data</i> <span style="font-size:85%;">(Euclid)</span></a></li> <li><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements"><i>Elements</i> <span style="font-size:85%;">(Euclid)</span></a></li> <li><i><a href="/wiki/Measurement_of_a_Circle" title="Measurement of a Circle">Measurement of a Circle</a></i></li> <li><i><a href="/wiki/On_Conoids_and_Spheroids" title="On Conoids and Spheroids">On Conoids and Spheroids</a></i></li> <li><a href="/wiki/On_the_Sizes_and_Distances_(Aristarchus)" title="On the Sizes and Distances (Aristarchus)"><i>On the Sizes and Distances</i> <span style="font-size:85%;">(Aristarchus)</span></a></li> <li><a href="/wiki/On_Sizes_and_Distances_(Hipparchus)" title="On Sizes and Distances (Hipparchus)"><i>On Sizes and Distances</i> <span style="font-size:85%;">(Hipparchus)</span></a></li> <li><a href="/wiki/Autolycus_of_Pitane" title="Autolycus of Pitane"><i>On the Moving Sphere</i> <span style="font-size:85%;">(Autolycus)</span></a></li> <li><a href="/wiki/Euclid%27s_Optics" title="Euclid's Optics"><i>Optics</i> <span style="font-size:85%;">(Euclid)</span></a></li> <li><i><a href="/wiki/On_Spirals" title="On Spirals">On Spirals</a></i></li> <li><i><a href="/wiki/On_the_Sphere_and_Cylinder" title="On the Sphere and Cylinder">On the Sphere and Cylinder</a></i></li> <li><i><a href="/wiki/Ostomachion" title="Ostomachion">Ostomachion</a></i></li> <li><i><a href="/wiki/Planisphaerium" title="Planisphaerium">Planisphaerium</a></i></li> <li><a href="/wiki/Theodosius%27_Spherics" title="Theodosius' Spherics"><i>Spherics</i> <span style="font-size:85%;">(Theodosius)</span></a></li> <li><a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria"><i>Spherics</i> <span style="font-size:85%;">(Menelaus)</span></a></li> <li><i><a href="/wiki/The_Quadrature_of_the_Parabola" class="mw-redirect" title="The Quadrature of the Parabola">The Quadrature of the Parabola</a></i></li> <li><i><a href="/wiki/The_Sand_Reckoner" title="The Sand Reckoner">The Sand Reckoner</a></i></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<br />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"><i>Elements</i></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 <i>Arithmetica</i></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><i><a href="/wiki/A_History_of_Greek_Mathematics" title="A History of Greek Mathematics">A History of Greek Mathematics</a></i> <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" 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><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/16px-Parthenon_from_west.jpg" decoding="async" width="16" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/24px-Parthenon_from_west.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/32px-Parthenon_from_west.jpg 2x" data-file-width="2048" data-file-height="1536" /></span></span> </span><a href="/wiki/Portal:Ancient_Greece" title="Portal:Ancient Greece">Ancient Greece portal</a></b> •  <b><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/16px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/24px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/32px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></b></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_Greece" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse 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_Greece_topics" title="Template:Ancient Greece topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Ancient_Greece_topics" title="Template talk:Ancient Greece topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Ancient_Greece_topics" 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Greece">Geography</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Periods</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/Cycladic_culture" title="Cycladic culture">Cycladic civilization</a></li> <li><a href="/wiki/Minoan_civilization" title="Minoan civilization">Minoan civilization</a></li> <li><a href="/wiki/Mycenaean_Greece" title="Mycenaean Greece">Mycenaean Greece</a></li> <li><a href="/wiki/Greek_Dark_Ages" title="Greek Dark Ages">Greek Dark Ages</a></li> <li><a href="/wiki/Archaic_Greece" title="Archaic Greece">Archaic Greece</a></li> <li><a href="/wiki/Classical_Greece" title="Classical Greece">Classical Greece</a></li> <li><a href="/wiki/Hellenistic_Greece" title="Hellenistic Greece">Hellenistic Greece</a></li> <li><a href="/wiki/Greece_in_the_Roman_era" title="Greece in the Roman era">Roman Greece</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Regions_of_ancient_Greece" title="Regions of ancient Greece">Geography</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/Aegean_Sea" title="Aegean Sea">Aegean Sea</a></li> <li><a href="/wiki/Aeolis" title="Aeolis">Aeolis</a></li> <li><a href="/wiki/Crete" title="Crete">Crete</a></li> <li><a href="/wiki/Cyrenaica" title="Cyrenaica">Cyrenaica</a></li> <li><a href="/wiki/Cyprus" title="Cyprus">Cyprus</a></li> <li><a href="/wiki/Doric_Hexapolis" title="Doric Hexapolis">Doris</a></li> <li><a href="/wiki/Epirus" title="Epirus">Epirus</a></li> <li><a href="/wiki/Dardanelles" title="Dardanelles">Hellespont</a></li> <li><a href="/wiki/Ionia" title="Ionia">Ionia</a></li> <li><a href="/wiki/Ionian_Sea" title="Ionian Sea">Ionian Sea</a></li> <li><a href="/wiki/Macedonia_(region)" title="Macedonia (region)">Macedonia</a></li> <li><a href="/wiki/Magna_Graecia" title="Magna Graecia">Magna Graecia</a></li> <li><a href="/wiki/Peloponnese" title="Peloponnese">Peloponnesus</a></li> <li><a href="/wiki/Pontus_(region)" title="Pontus (region)">Pontus</a></li> <li><a href="/wiki/Crimea" title="Crimea">Taurica</a></li> <li><a href="/wiki/Colonies_in_antiquity" title="Colonies in antiquity">Ancient Greek colonies</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="City_statesPoliticsMilitary" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/wiki/Polis" title="Polis">City states</a></li><li><a href="/wiki/Ancient_Greece#Politics_and_society" title="Ancient Greece">Politics</a></li><li><a href="/wiki/Ancient_Greek_warfare" title="Ancient Greek warfare">Military</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Polis" title="Polis">City states</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/Ancient_Argos" class="mw-redirect" title="Ancient Argos">Argos</a></li> <li><a href="/wiki/Classical_Athens" title="Classical Athens">Athens</a></li> <li><a href="/wiki/Byzantium" title="Byzantium">Byzantion</a></li> <li><a href="/wiki/Chalcis" title="Chalcis">Chalcis</a></li> <li><a href="/wiki/Ancient_Corinth" title="Ancient Corinth">Corinth</a></li> <li><a href="/wiki/Ephesus" title="Ephesus">Ephesus</a></li> <li><a href="/wiki/Miletus" title="Miletus">Miletus</a></li> <li><a href="/wiki/Pergamon" title="Pergamon">Pergamon</a></li> <li><a href="/wiki/Eretria" title="Eretria">Eretria</a></li> <li><a href="/wiki/Corfu" title="Corfu">Kerkyra</a></li> <li><a href="/wiki/Larissa" title="Larissa">Larissa</a></li> <li><a href="/wiki/Megalopolis,_Greece" title="Megalopolis, Greece">Megalopolis</a></li> <li><a href="/wiki/Thebes,_Greece" title="Thebes, Greece">Thebes</a></li> <li><a href="/wiki/Megara" title="Megara">Megara</a></li> <li><a href="/wiki/Rhodes" title="Rhodes">Rhodes</a></li> <li><a href="/wiki/Samos" title="Samos">Samos</a></li> <li><a href="/wiki/Sparta" title="Sparta">Sparta</a></li> <li><a href="/wiki/Lissus_(Crete)" title="Lissus (Crete)">Lissus (Crete)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Kingdoms</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/Kingdom_of_Bithynia" title="Kingdom of Bithynia">Bithynia</a></li> <li><a href="/wiki/Kingdom_of_Cappadocia" title="Kingdom of Cappadocia">Cappadocia</a></li> <li><a href="/wiki/Epirus_(ancient_state)" title="Epirus (ancient state)">Epirus</a></li> <li><a href="/wiki/Greco-Bactrian_Kingdom" title="Greco-Bactrian Kingdom">Greco-Bactrian Kingdom</a></li> <li><a href="/wiki/Indo-Greek_Kingdom" title="Indo-Greek Kingdom">Indo-Greek Kingdom</a></li> <li><a href="/wiki/Macedonia_(ancient_kingdom)" title="Macedonia (ancient kingdom)">Macedonia</a></li> <li><a href="/wiki/Kingdom_of_Pergamon" title="Kingdom of Pergamon">Pergamon</a></li> <li><a href="/wiki/Kingdom_of_Pontus" title="Kingdom of Pontus">Pontus</a></li> <li><a href="/wiki/Ptolemaic_Kingdom" title="Ptolemaic Kingdom">Ptolemaic Kingdom</a></li> <li><a href="/wiki/Seleucid_Empire" title="Seleucid Empire">Seleucid Empire</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Federation" title="Federation">Federations</a>/<br /><a href="/wiki/Confederation" title="Confederation">Confederations</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/Doric_Hexapolis" title="Doric Hexapolis">Doric Hexapolis</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 1100</span> – c.<span style="white-space:nowrap;"> 560 BC</span>)</li> <li><a href="/wiki/Italiotes#Italiote_League" title="Italiotes">Italiote League</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 800</span>–389 BC)</li> <li><a href="/wiki/Ionian_League" title="Ionian League">Ionian League</a> (c. 650–404 BC)</li> <li><a href="/wiki/Peloponnesian_League" title="Peloponnesian League">Peloponnesian League</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 550</span>–366 BC)</li> <li><a href="/wiki/Amphictyonic_League" class="mw-redirect" title="Amphictyonic League">Amphictyonic League</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 595</span>–279 BC)</li> <li><a href="/wiki/Acarnanian_League" title="Acarnanian League">Acarnanian League</a> (c. 500–31 BC)</li> <li><a href="/wiki/Greco-Persian_Wars" title="Greco-Persian Wars">Hellenic League</a> (499–449 BC)</li> <li><a href="/wiki/Delian_League" title="Delian League">Delian League</a> (478–404 BC)</li> <li><a href="/wiki/Chalcidian_League" title="Chalcidian League">Chalcidian League</a> (430–348 BC)</li> <li><a href="/wiki/Boeotia#Boeotian_League" title="Boeotia">Boeotian League</a> (c. 424–c. 395 BC)</li> <li><a href="/wiki/Aetolian_League" title="Aetolian League">Aetolian League</a> (c. 400–188 BC)</li> <li><a href="/wiki/Second_Athenian_League" title="Second Athenian League">Second Athenian League</a> (378–355 BC)</li> <li><a href="/wiki/Thessalian_League" title="Thessalian League">Thessalian League</a> (374–196 BC)</li> <li><a href="/wiki/Arcadian_League" title="Arcadian League">Arcadian League</a> (370–c. 230 BC)</li> <li><a href="/wiki/Epirote_League" title="Epirote League">Epirote League</a> (370–168 BC)</li> <li><a href="/wiki/League_of_Corinth" title="League of Corinth">League of Corinth</a> (338–322 BC)</li> <li><a href="/wiki/Euboean_League" title="Euboean League">Euboean League</a> (c. 300 BC–c. 300 AD)</li> <li><a href="/wiki/Achaean_League" title="Achaean League">Achaean League</a> (280–146 BC)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ancient_Greece#Politics_and_society" title="Ancient Greece">Politics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boule_(ancient_Greece)" title="Boule (ancient Greece)">Boule</a></li> <li><a href="/wiki/Free_city_(classical_antiquity)" title="Free city (classical antiquity)">Free city</a></li> <li><a href="/wiki/Koinon" title="Koinon">Koinon</a></li> <li><a href="/wiki/Proxeny" title="Proxeny">Proxeny</a></li> <li><a href="/wiki/Stasis_(ancient_Greece)" title="Stasis (ancient Greece)">Stasis</a></li> <li><a href="/wiki/Tagus_(title)" title="Tagus (title)">Tagus</a></li> <li><a href="/wiki/Tyrant" title="Tyrant">Tyrant</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Athenian_democracy" title="Athenian democracy">Athenian</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/Agora" title="Agora">Agora</a></li> <li><a href="/wiki/Areopagus" title="Areopagus">Areopagus</a></li> <li><a href="/wiki/Ecclesia_(ancient_Athens)" class="mw-redirect" title="Ecclesia (ancient Athens)">Ecclesia</a></li> <li><a href="/wiki/Graphe_paranomon" title="Graphe paranomon">Graphe paranomon</a></li> <li><a href="/wiki/Heliaia" title="Heliaia">Heliaia</a></li> <li><a href="/wiki/Ostracism" title="Ostracism">Ostracism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Spartan_Constitution" title="Spartan Constitution">Spartan</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/Ecclesia_(Sparta)" title="Ecclesia (Sparta)">Ekklesia</a></li> <li><a href="/wiki/Ephor" title="Ephor">Ephor</a></li> <li><a href="/wiki/Gerousia" title="Gerousia">Gerousia</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Macedonia_(ancient_kingdom)" title="Macedonia (ancient kingdom)">Macedon</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/Synedrion" title="Synedrion">Synedrion</a></li> <li><a href="/wiki/Koinon_of_Macedonians" class="mw-redirect" title="Koinon of Macedonians">Koinon</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ancient_Greek_warfare" title="Ancient Greek warfare">Military</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/List_of_wars_involving_Greece" title="List of wars involving Greece">Wars</a></li> <li><a href="/wiki/Athenian_military" title="Athenian military">Athenian military</a> <ul><li><a href="/wiki/Scythian_archers" title="Scythian archers">Scythian archers</a></li></ul></li> <li><a href="/wiki/Antigonid_Macedonian_army" title="Antigonid Macedonian army">Antigonid Macedonian army</a></li> <li><a href="/wiki/Ancient_Macedonian_army" title="Ancient Macedonian army">Army of Macedon</a></li> <li><a href="/wiki/Ballista" title="Ballista">Ballista</a></li> <li><a href="/wiki/Cretan_archers" title="Cretan archers">Cretan archers</a></li> <li><a href="/wiki/Hellenistic_armies" title="Hellenistic armies">Hellenistic armies</a></li> <li><a href="/wiki/Hippeis" title="Hippeis">Hippeis</a></li> <li><a href="/wiki/Hoplite" title="Hoplite">Hoplite</a></li> <li><a href="/wiki/Companion_cavalry" title="Companion cavalry">Hetairoi</a></li> <li><a href="/wiki/Macedonian_phalanx" title="Macedonian phalanx">Macedonian phalanx</a></li> <li><a href="/wiki/Military_of_Mycenaean_Greece" title="Military of Mycenaean Greece">Military of Mycenaean Greece</a></li> <li><a href="/wiki/Phalanx" title="Phalanx">Phalanx</a></li> <li><a href="/wiki/Peltast" title="Peltast">Peltast</a></li> <li><a href="/wiki/Pezhetairos" title="Pezhetairos">Pezhetairos</a></li> <li><a href="/wiki/Sarissa" title="Sarissa">Sarissa</a></li> <li><a href="/wiki/Sacred_Band_of_Thebes" title="Sacred Band of Thebes">Sacred Band of Thebes</a></li> <li><a href="/wiki/Sciritae" title="Sciritae">Sciritae</a></li> <li><a href="/wiki/Seleucid_army" title="Seleucid army">Seleucid army</a></li> <li><a href="/wiki/Spartan_army" title="Spartan army">Spartan army</a></li> <li><a href="/wiki/Strategos" title="Strategos">Strategos</a></li> <li><a href="/wiki/Toxotai" title="Toxotai">Toxotai</a></li> <li><a href="/wiki/Xiphos" title="Xiphos">Xiphos</a></li> <li><a href="/wiki/Xyston" title="Xyston">Xyston</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="People" style="font-size:114%;margin:0 4em"><a href="/wiki/Category:Ancient_Greeks" title="Category:Ancient Greeks">People</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td class="navbox-abovebelow" colspan="2"><div id="List_of_ancient_Greeks"><a href="/wiki/List_of_ancient_Greeks" title="List of ancient Greeks">List of ancient Greeks</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Lists_of_rulers_of_Greece#Antiquity" class="mw-redirect" title="Lists of rulers of Greece">Rulers</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/List_of_kings_of_Argos" title="List of kings of Argos">Kings of Argos</a></li> <li><a href="/wiki/Eponymous_archon" title="Eponymous archon">Archons of Athens</a></li> <li><a href="/wiki/List_of_kings_of_Athens" title="List of kings of Athens">Kings of Athens</a></li> <li><a href="/wiki/List_of_rulers_of_Commagene" class="mw-redirect" title="List of rulers of Commagene">Kings of Commagene</a></li> <li><a href="/wiki/Diadochi" title="Diadochi">Diadochi</a></li> <li><a href="/wiki/List_of_kings_of_Macedonia" title="List of kings of Macedonia">Kings of Macedonia</a></li> <li><a href="/wiki/List_of_rulers_of_Thrace_and_Dacia" class="mw-redirect" title="List of rulers of Thrace and Dacia">Kings of Paionia</a></li> <li><a href="/wiki/Attalid_dynasty" class="mw-redirect" title="Attalid dynasty">Attalid kings of Pergamon</a></li> <li><a href="/wiki/List_of_kings_of_Pontus" class="mw-redirect" title="List of kings of Pontus">Kings of Pontus</a></li> <li><a href="/wiki/Ptolemaic_dynasty" title="Ptolemaic dynasty">Ptolemaic dynasty</a></li> <li><a href="/wiki/Seleucid_dynasty" title="Seleucid dynasty">Seleucid dynasty</a></li> <li><a href="/wiki/List_of_kings_of_Sparta" title="List of kings of Sparta">Kings of Sparta</a></li> <li><a href="/wiki/List_of_tyrants_of_Syracuse" title="List of tyrants of Syracuse">Tyrants of Syracuse</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Artists & scholars</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_ancient_Greek_astronomers" title="List of ancient Greek astronomers">Astronomers</a></li> <li><a href="/wiki/List_of_Graeco-Roman_geographers" title="List of Graeco-Roman geographers">Geographers</a></li> <li><a href="/wiki/List_of_ancient_Greek_historians" title="List of ancient Greek historians">Historians</a></li> <li><a href="/wiki/List_of_ancient_Greek_mathematicians" title="List of ancient Greek mathematicians">Mathematicians</a></li> <li><a href="/wiki/List_of_ancient_Greek_philosophers" title="List of ancient Greek philosophers">Philosophers</a></li> <li><a href="/wiki/List_of_ancient_Greek_playwrights" title="List of ancient Greek playwrights">Playwrights</a></li> <li><a href="/wiki/List_of_ancient_Greek_poets" title="List of ancient Greek poets">Poets</a></li> <li><a href="/wiki/Seven_Sages_of_Greece" title="Seven Sages of Greece">Seven Sages</a></li> <li><a href="/wiki/List_of_ancient_Greek_writers" title="List of ancient Greek writers">Writers</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ancient_Greek_philosophy" title="Ancient Greek philosophy">Philosophers</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/Anaxagoras" title="Anaxagoras">Anaxagoras</a></li> <li><a href="/wiki/Anaximander" title="Anaximander">Anaximander</a></li> <li><a href="/wiki/Anaximenes_of_Miletus" title="Anaximenes of Miletus">Anaximenes</a></li> <li><a href="/wiki/Antisthenes" title="Antisthenes">Antisthenes</a></li> <li><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a></li> <li><a href="/wiki/Democritus" title="Democritus">Democritus</a></li> <li><a href="/wiki/Diogenes" title="Diogenes">Diogenes of Sinope</a></li> <li><a href="/wiki/Empedocles" title="Empedocles">Empedocles</a></li> <li><a href="/wiki/Epicurus" title="Epicurus">Epicurus</a></li> <li><a href="/wiki/Gorgias" title="Gorgias">Gorgias</a></li> <li><a href="/wiki/Heraclitus" title="Heraclitus">Heraclitus</a></li> <li><a href="/wiki/Hypatia" title="Hypatia">Hypatia</a></li> <li><a href="/wiki/Leucippus" title="Leucippus">Leucippus</a></li> <li><a href="/wiki/Parmenides" title="Parmenides">Parmenides</a></li> <li><a href="/wiki/Plato" title="Plato">Plato</a></li> <li><a href="/wiki/Protagoras" title="Protagoras">Protagoras</a></li> <li><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li> <li><a href="/wiki/Socrates" title="Socrates">Socrates</a></li> <li><a href="/wiki/Thales_of_Miletus" title="Thales of Miletus">Thales</a></li> <li><a href="/wiki/Zeno_of_Elea" title="Zeno of Elea">Zeno</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ancient_Greek_literature" title="Ancient Greek literature">Authors</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/Aeschylus" title="Aeschylus">Aeschylus</a></li> <li><a href="/wiki/Aesop" title="Aesop">Aesop</a></li> <li><a href="/wiki/Alcaeus_of_Mytilene" class="mw-redirect" title="Alcaeus of Mytilene">Alcaeus</a></li> <li><a href="/wiki/Archilochus" title="Archilochus">Archilochus</a></li> <li><a href="/wiki/Aristophanes" title="Aristophanes">Aristophanes</a></li> <li><a href="/wiki/Bacchylides" title="Bacchylides">Bacchylides</a></li> <li><a href="/wiki/Euripides" title="Euripides">Euripides</a></li> <li><a href="/wiki/Herodotus" title="Herodotus">Herodotus</a></li> <li><a href="/wiki/Hesiod" title="Hesiod">Hesiod</a></li> <li><a href="/wiki/Hipponax" title="Hipponax">Hipponax</a></li> <li><a href="/wiki/Homer" title="Homer">Homer</a></li> <li><a href="/wiki/Ibycus" title="Ibycus">Ibycus</a></li> <li><a href="/wiki/Lucian" title="Lucian">Lucian</a></li> <li><a href="/wiki/Menander" title="Menander">Menander</a></li> <li><a href="/wiki/Mimnermus" title="Mimnermus">Mimnermus</a></li> <li><a href="/wiki/Panyassis" title="Panyassis">Panyassis</a></li> <li><a href="/wiki/Philocles" title="Philocles">Philocles</a></li> <li><a href="/wiki/Pindar" title="Pindar">Pindar</a></li> <li><a href="/wiki/Plutarch" title="Plutarch">Plutarch</a></li> <li><a href="/wiki/Polybius" title="Polybius">Polybius</a></li> <li><a href="/wiki/Sappho" title="Sappho">Sappho</a></li> <li><a href="/wiki/Simonides_of_Ceos" title="Simonides of Ceos">Simonides</a></li> <li><a href="/wiki/Sophocles" title="Sophocles">Sophocles</a></li> <li><a href="/wiki/Stesichorus" title="Stesichorus">Stesichorus</a></li> <li><a href="/wiki/Theognis_of_Megara" title="Theognis of Megara">Theognis</a></li> <li><a href="/wiki/Thucydides" title="Thucydides">Thucydides</a></li> <li><a href="/wiki/Timocreon" title="Timocreon">Timocreon</a></li> <li><a href="/wiki/Tyrtaeus" title="Tyrtaeus">Tyrtaeus</a></li> <li><a href="/wiki/Xenophon" title="Xenophon">Xenophon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Others</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/List_of_ancient_Athenian_statesmen" class="mw-redirect" title="List of ancient Athenian statesmen">Athenian statesmen</a></li> <li><a href="/wiki/List_of_ancient_Greek_lawgivers" title="List of ancient Greek lawgivers">Lawgivers</a></li> <li><a href="/wiki/List_of_ancient_Olympic_victors" title="List of ancient Olympic victors">Olympic victors</a></li> <li><a href="/wiki/List_of_ancient_Greek_tyrants" title="List of ancient Greek tyrants">Tyrants</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By culture</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_ancient_Greek_tribes" title="List of ancient Greek tribes">Ancient Greek tribes</a></li> <li><a href="/wiki/List_of_Thracian_Greeks" title="List of Thracian Greeks">Thracian Greeks</a></li> <li><a href="/wiki/List_of_ancient_Macedonians" title="List of ancient Macedonians">Ancient Macedonians</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="SocietyCulture" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/wiki/Ancient_Greece#Politics_and_society" title="Ancient Greece">Society</a></li><li><a href="/wiki/Culture_of_Greece" title="Culture of Greece">Culture</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ancient_Greece#Politics_and_society" title="Ancient Greece">Society</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/Agriculture_in_ancient_Greece" title="Agriculture in ancient Greece">Agriculture</a></li> <li><a href="/wiki/Ancient_Greek_calendars" title="Ancient Greek calendars">Calendar</a></li> <li><a href="/wiki/Clothing_in_ancient_Greece" title="Clothing in ancient Greece">Clothing</a></li> <li><a href="/wiki/Ancient_Greek_coinage" title="Ancient Greek coinage">Coinage</a></li> <li><a href="/wiki/Ancient_Greek_cuisine" title="Ancient Greek cuisine">Cuisine</a></li> <li><a href="/wiki/Economy_of_ancient_Greece" title="Economy of ancient Greece">Economy</a></li> <li><a href="/wiki/Paideia" title="Paideia">Education</a></li> <li><a href="/wiki/Emporium_(antiquity)" title="Emporium (antiquity)">Emporium</a></li> <li><a href="/wiki/Euergetism" title="Euergetism">Euergetism</a></li> <li><a href="/wiki/Athenian_festivals" title="Athenian festivals">Festivals</a></li> <li><a href="/wiki/Ancient_Greek_folklore" title="Ancient Greek folklore">Folklore</a></li> <li><a href="/wiki/Homosexuality_in_ancient_Greece" title="Homosexuality in ancient Greece">Homosexuality</a></li> <li><a href="/wiki/Ancient_Greek_law" title="Ancient Greek law">Law</a></li> <li><a href="/wiki/Ancient_Olympic_Games" title="Ancient Olympic Games">Olympic Games</a></li> <li><a href="/wiki/Pederasty_in_ancient_Greece" title="Pederasty in ancient Greece">Pederasty</a></li> <li><a href="/wiki/Ancient_Greek_philosophy" title="Ancient Greek philosophy">Philosophy</a></li> <li><a href="/wiki/Prostitution_in_ancient_Greece" title="Prostitution in ancient Greece">Prostitution</a></li> <li><a href="/wiki/Ancient_Greek_religion" title="Ancient Greek religion">Religion</a></li> <li><a href="/wiki/Slavery_in_ancient_Greece" title="Slavery in ancient Greece">Slavery</a></li> <li><a href="/wiki/Ancient_Greek_warfare" title="Ancient Greek warfare">Warfare</a></li> <li><a href="/wiki/Marriage_in_ancient_Greece" title="Marriage in ancient Greece">Wedding customs</a></li> <li><a href="/wiki/Ancient_Greece_and_wine" title="Ancient Greece and wine">Wine</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ancient_Greek_art" title="Ancient Greek art">Arts</a> and science</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/Ancient_Greek_architecture" title="Ancient Greek architecture">Architecture</a> <ul><li><a href="/wiki/Greek_Revival_architecture" title="Greek Revival architecture">Greek Revival architecture</a></li></ul></li> <li><a href="/wiki/Ancient_Greek_astronomy" title="Ancient Greek astronomy">Astronomy</a></li> <li><a href="/wiki/Ancient_Greek_literature" title="Ancient Greek literature">Literature</a></li> <li><a class="mw-selflink selflink">Mathematics</a></li> <li><a href="/wiki/Ancient_Greek_medicine" title="Ancient Greek medicine">Medicine</a></li> <li><a href="/wiki/Music_of_ancient_Greece" title="Music of ancient Greece">Music</a> <ul><li><a href="/wiki/Musical_system_of_ancient_Greece" title="Musical system of ancient Greece">Musical system</a></li></ul></li> <li><a href="/wiki/Pottery_of_ancient_Greece" title="Pottery of ancient Greece">Pottery</a></li> <li><a href="/wiki/Ancient_Greek_sculpture" title="Ancient Greek sculpture">Sculpture</a></li> <li><a href="/wiki/Ancient_Greek_technology" title="Ancient Greek technology">Technology</a></li> <li><a href="/wiki/Theatre_of_ancient_Greece" title="Theatre of ancient Greece">Theatre</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ancient_Greek_religion" title="Ancient Greek religion">Religion</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><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_funeral_and_burial_practices" title="Ancient Greek funeral and burial practices">Funeral and burial practices</a></li> <li><a href="/wiki/Greek_mythology" title="Greek mythology">Mythology</a> <ul><li><a href="/wiki/List_of_Greek_mythological_figures" title="List of Greek mythological figures">mythological figures</a></li></ul></li> <li><a href="/wiki/Ancient_Greek_temple" title="Ancient Greek temple">Temple</a></li> <li><a href="/wiki/Twelve_Olympians" title="Twelve Olympians">Twelve Olympians</a></li> <li><a href="/wiki/Greek_underworld" title="Greek underworld">Underworld</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;text-align:left;">Sacred places</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/Eleusis" class="mw-redirect" title="Eleusis">Eleusis</a></li> <li><a href="/wiki/Delphi" title="Delphi">Delphi</a></li> <li><a href="/wiki/Delos" title="Delos">Delos</a></li> <li><a href="/wiki/Dion,_Pieria" title="Dion, Pieria">Dion</a></li> <li><a href="/wiki/Dodona" title="Dodona">Dodona</a></li> <li><a href="/wiki/Mount_Olympus" title="Mount Olympus">Mount Olympus</a></li> <li><a href="/wiki/Olympia,_Greece" title="Olympia, Greece">Olympia</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Structures</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Athenian_Treasury" title="Athenian Treasury">Athenian Treasury</a></li> <li><a href="/wiki/Lion_Gate" title="Lion Gate">Lion Gate</a></li> <li><a href="/wiki/Long_Walls" title="Long Walls">Long Walls</a></li> <li><a href="/wiki/Philippeion" title="Philippeion">Philippeion</a></li> <li><a href="/wiki/Theatre_of_Dionysus" title="Theatre of Dionysus">Theatre of Dionysus</a></li> <li><a href="/wiki/Tunnel_of_Eupalinos" title="Tunnel of Eupalinos">Tunnel of Eupalinos</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Ancient_Greek_temple" title="Ancient Greek temple">Temples</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/Temple_of_Aphaea" class="mw-redirect" title="Temple of Aphaea">Aphaea</a></li> <li><a href="/wiki/Temple_of_Artemis" title="Temple of Artemis">Artemis</a></li> <li><a href="/wiki/Temple_of_Athena_Nike" title="Temple of Athena Nike">Athena Nike</a></li> <li><a href="/wiki/Erechtheion" title="Erechtheion">Erechtheion</a></li> <li><a href="/wiki/Temple_of_Hephaestus" title="Temple of Hephaestus">Hephaestus</a></li> <li><a href="/wiki/Temple_of_Hera,_Olympia" title="Temple of Hera, Olympia">Hera, Olympia</a></li> <li><a href="/wiki/Parthenon" title="Parthenon">Parthenon</a></li> <li><a href="/wiki/Samothrace_temple_complex" title="Samothrace temple complex">Samothrace</a></li> <li><a href="/wiki/Temple_of_Zeus,_Olympia" title="Temple of Zeus, Olympia">Zeus, Olympia</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ancient_Greek" title="Ancient Greek">Language</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/Proto-Greek_language" title="Proto-Greek language">Proto-Greek</a></li> <li><a href="/wiki/Mycenaean_Greek" title="Mycenaean Greek">Mycenaean</a></li> <li><a href="/wiki/Homeric_Greek" title="Homeric Greek">Homeric</a></li> <li><a href="/wiki/Ancient_Greek_dialects" title="Ancient Greek dialects">Dialects</a> <ul><li><a href="/wiki/Aeolic_Greek" title="Aeolic Greek">Aeolic</a></li> <li><a href="/wiki/Arcadocypriot_Greek" title="Arcadocypriot Greek">Arcadocypriot</a></li> <li><a href="/wiki/Attic_Greek" title="Attic Greek">Attic</a></li> <li><a href="/wiki/Doric_Greek" title="Doric Greek">Doric</a></li> <li><a href="/wiki/Epirote_Greek" title="Epirote Greek">Epirote</a></li> <li><a href="/wiki/Ionic_Greek" title="Ionic Greek">Ionic</a></li> <li><a href="/wiki/Locrian_Greek" title="Locrian Greek">Locrian</a></li> <li><a href="/wiki/Ancient_Macedonian_language" title="Ancient Macedonian language">Macedonian</a></li> <li><a href="/wiki/Pamphylian_Greek" title="Pamphylian Greek">Pamphylian</a></li></ul></li> <li><a href="/wiki/Koine_Greek" title="Koine Greek">Koine</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/History_of_the_Greek_alphabet" title="History of the Greek alphabet">Writing</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/Linear_A" title="Linear A">Linear A</a></li> <li><a href="/wiki/Linear_B" title="Linear B">Linear B</a></li> <li><a href="/wiki/Cypriot_syllabary" title="Cypriot syllabary">Cypriot syllabary</a></li> <li><a href="/wiki/Greek_alphabet" title="Greek alphabet">Greek alphabet</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a></li> <li><a href="/wiki/Attic_numerals" title="Attic numerals">Attic numerals</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Greek_colonisation" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/wiki/Greek_colonisation" title="Greek colonisation">Greek colonisation</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Magna_Graecia" title="Magna Graecia">Magna Graecia</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Mainland<br />Italy</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/Lecce" title="Lecce">Alision</a></li> <li><a href="/wiki/Brindisi" title="Brindisi">Brentesion</a></li> <li><a href="/wiki/Caulonia_(ancient_city)" title="Caulonia (ancient city)">Caulonia</a></li> <li><a href="/wiki/Casabona" title="Casabona">Chone</a></li> <li><a href="/wiki/Crotone" title="Crotone">Croton</a></li> <li><a href="/wiki/Cumae" title="Cumae">Cumae</a></li> <li><a href="/wiki/Velia" title="Velia">Elea</a></li> <li><a href="/wiki/Heraclea_Lucania" title="Heraclea Lucania">Heraclea Lucania</a></li> <li><a href="/wiki/Vibo_Valentia" title="Vibo Valentia">Hipponion</a></li> <li><a href="/wiki/Otranto" title="Otranto">Hydrus</a></li> <li><a href="/wiki/Krimisa" title="Krimisa">Krimisa</a></li> <li><a href="/wiki/La%C3%BCs" title="Laüs">Laüs</a></li> <li><a href="/wiki/Locri" title="Locri">Locri</a></li> <li><a href="/wiki/Medma" title="Medma">Medma</a></li> <li><a href="/wiki/Metauros" title="Metauros">Metauros</a></li> <li><a href="/wiki/Metapontum" title="Metapontum">Metapontion</a></li> <li><a href="/wiki/Naples" title="Naples">Neápolis</a></li> <li><a href="/wiki/Pandosia_(Lucania)" title="Pandosia (Lucania)">Pandosia (Lucania)</a></li> <li><a href="/wiki/Paestum" title="Paestum">Poseidonia</a></li> <li><a href="/wiki/Policastro_Bussentino" title="Policastro Bussentino">Pixous</a></li> <li><a href="/wiki/Reggio_Calabria" title="Reggio Calabria">Rhegion</a></li> <li><a href="/wiki/Scylletium" title="Scylletium">Scylletium</a></li> <li><a href="/wiki/Siris_(Magna_Graecia)" class="mw-redirect" title="Siris (Magna Graecia)">Siris</a></li> <li><a href="/wiki/Sybaris" title="Sybaris">Sybaris</a></li> <li><a href="/wiki/Sybaris_on_the_Traeis" title="Sybaris on the Traeis">Sybaris on the Traeis</a></li> <li><a href="/wiki/Taranto" title="Taranto">Taras</a></li> <li><a href="/wiki/Terina_(ancient_city)" title="Terina (ancient city)">Terina</a></li> <li><a href="/wiki/Thurii" title="Thurii">Thurii</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Sicily" title="Sicily">Sicily</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/Agrigento" title="Agrigento">Akragas</a></li> <li><a href="/wiki/Akrai" title="Akrai">Akrai</a></li> <li><a href="/wiki/Akrillai" title="Akrillai">Akrillai</a></li> <li><a href="/wiki/Apollonia_(Sicily)" title="Apollonia (Sicily)">Apollonia</a></li> <li><a href="/wiki/Caronia" title="Caronia">Calacte</a></li> <li><a href="/wiki/Casmenae" title="Casmenae">Casmenae</a></li> <li><a href="/wiki/Catania" title="Catania">Catana</a></li> <li><a href="/wiki/Gela" title="Gela">Gela</a></li> <li><a href="/wiki/Helorus" title="Helorus">Helorus</a></li> <li><a href="/wiki/Enna" title="Enna">Henna</a></li> <li><a href="/wiki/Heraclea_Minoa" title="Heraclea Minoa">Heraclea Minoa</a></li> <li><a href="/wiki/Himera" title="Himera">Himera</a></li> <li><a href="/wiki/Hybla_Gereatis" title="Hybla Gereatis">Hybla Gereatis</a></li> <li><a href="/wiki/Hybla_Heraea" title="Hybla Heraea">Hybla Heraea</a></li> <li><a href="/wiki/Kamarina,_Sicily" title="Kamarina, Sicily">Kamarina</a></li> <li><a href="/wiki/Lentini" title="Lentini">Leontinoi</a></li> <li><a href="/wiki/Megara_Hyblaea" title="Megara Hyblaea">Megara Hyblaea</a></li> <li><a href="/wiki/Messina" title="Messina">Messana</a></li> <li><a href="/wiki/Naxos_(Sicily)" title="Naxos (Sicily)">Naxos</a></li> <li><a href="/wiki/Segesta" title="Segesta">Segesta</a></li> <li><a href="/wiki/Selinunte" title="Selinunte">Selinous</a></li> <li><a href="/wiki/Syracuse,_Sicily" title="Syracuse, Sicily">Syracuse</a></li> <li><a href="/wiki/Taormina" title="Taormina">Tauromenion</a></li> <li><a href="/wiki/Sciacca" title="Sciacca">Thermae</a></li> <li><a href="/wiki/Tindari" title="Tindari">Tyndaris</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Aeolian_Islands" title="Aeolian Islands">Aeolian Islands</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/Salina,_Sicily" title="Salina, Sicily">Didyme</a></li> <li><a href="/wiki/Panarea" title="Panarea">Euonymos</a></li> <li><a href="/wiki/Alicudi" title="Alicudi">Ereikousa</a></li> <li><a href="/wiki/Basiluzzo" title="Basiluzzo">Hycesia</a></li> <li><a href="/wiki/Lipari" title="Lipari">Lipara/Meligounis</a></li> <li><a href="/wiki/Filicudi" title="Filicudi">Phoenicusa</a></li> <li><a href="/wiki/Stromboli" title="Stromboli">Strongyle</a></li> <li><a href="/wiki/Vulcano" title="Vulcano">Therassía</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Cyrenaica" title="Cyrenaica">Cyrenaica</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/Bayda,_Libya" title="Bayda, Libya">Balagrae</a></li> <li><a href="/wiki/Barca_(ancient_city)" title="Barca (ancient city)">Barca</a></li> <li><a href="/wiki/Benghazi" title="Benghazi">Berenice</a></li> <li><a href="/wiki/Cyrene,_Libya" title="Cyrene, Libya">Cyrene</a> (<a href="/wiki/Apollonia,_Cyrenaica" class="mw-redirect" title="Apollonia, Cyrenaica">Apollonia</a>)</li> <li><a href="/wiki/Ptolemais,_Cyrenaica" title="Ptolemais, Cyrenaica">Ptolemais</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Iberian_Peninsula" title="Iberian Peninsula">Iberian Peninsula</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/Lucentum" title="Lucentum">Akra Leuke</a></li> <li><a href="/wiki/Villajoyosa" title="Villajoyosa">Alonis</a></li> <li><a href="/wiki/Emp%C3%BAries" title="Empúries">Emporion</a></li> <li><a href="/wiki/Elche" title="Elche">Helike</a></li> <li><a href="/wiki/D%C3%A9nia" title="Dénia">Hemeroscopion</a></li> <li><a href="/wiki/Aljaraque" title="Aljaraque">Kalathousa</a></li> <li><a href="/wiki/Sant_Mart%C3%AD_d%27Emp%C3%BAries" title="Sant Martí d'Empúries">Kypsela</a></li> <li><a href="/wiki/Mainake_(Greek_settlement)" title="Mainake (Greek settlement)">Mainake</a></li> <li><a href="/wiki/El_Puerto_de_Santa_Mar%C3%ADa" title="El Puerto de Santa María">Menestheus's Limin</a></li> <li><a href="/wiki/Santa_Pola" title="Santa Pola">Illicitanus Limin/Portus Illicitanus</a></li> <li><a href="/wiki/Roses,_Girona" class="mw-redirect" title="Roses, Girona">Rhode</a></li> <li><a href="/wiki/Salou" title="Salou">Salauris</a></li> <li><a href="/wiki/Sagunto" title="Sagunto">Zacynthos</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Illyria" title="Illyria">Illyria</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/Aspalathos" class="mw-redirect" title="Aspalathos">Aspalathos</a></li> <li><a href="/wiki/Apollonia_(Illyria)" title="Apollonia (Illyria)">Apollonia</a></li> <li><a href="/wiki/Vlor%C3%AB#Early_history" title="Vlorë">Aulon</a></li> <li><a href="/wiki/Epidamnos" title="Epidamnos">Epidamnos</a></li> <li><a href="/wiki/Epidaurum" title="Epidaurum">Epidauros</a></li> <li><a href="/wiki/Issa_(polis)" class="mw-redirect" title="Issa (polis)">Issa</a></li> <li><a href="/wiki/Melaina_Korkyra" class="mw-redirect" title="Melaina Korkyra">Melaina Korkyra</a></li> <li><a href="/wiki/Nymphaeum_(Illyria)" title="Nymphaeum (Illyria)">Nymphaion</a></li> <li><a href="/wiki/Oricum" title="Oricum">Orikon</a></li> <li><a href="/wiki/Pharos_(polis)" class="mw-redirect" title="Pharos (polis)">Pharos</a></li> <li><a href="/wiki/Tragurion" class="mw-redirect" title="Tragurion">Tragurion</a></li> <li><a href="/wiki/Thronion_(Illyria)" title="Thronion (Illyria)">Thronion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Black_Sea" title="Black Sea">Black Sea</a><br />basin</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">North<br />coast</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/Akra_(Crimmerian_Bosporus)" class="mw-redirect" title="Akra (Crimmerian Bosporus)">Akra</a></li> <li><a href="/wiki/Berezan_Island" title="Berezan Island">Borysthenes</a></li> <li><a href="/wiki/Charax,_Crimea" title="Charax, Crimea">Charax</a></li> <li><a href="/wiki/Chersonesus" title="Chersonesus">Chersonesus</a></li> <li><a href="/wiki/Sukhumi" title="Sukhumi">Dioscurias</a></li> <li><a href="/wiki/Anapa" title="Anapa">Gorgippia</a></li> <li><a href="/wiki/Tmutarakan" title="Tmutarakan">Hermonassa</a></li> <li><a href="/wiki/Kalos_Limen" title="Kalos Limen">Kalos Limen</a></li> <li><a href="/wiki/Kepoi" title="Kepoi">Kepoi</a></li> <li><a href="/wiki/Yevpatoria" title="Yevpatoria">Kerkinitis</a></li> <li><a href="/wiki/Kimmerikon" title="Kimmerikon">Kimmerikon</a></li> <li><a href="/wiki/Myrmekion" class="mw-redirect" title="Myrmekion">Myrmekion</a></li> <li><a href="/wiki/Nikonion" class="mw-redirect" title="Nikonion">Nikonion</a></li> <li><a href="/wiki/Nymphaion_(Crimea)" title="Nymphaion (Crimea)">Nymphaion</a></li> <li><a href="/wiki/Olbia_(Pontic)" class="mw-redirect" title="Olbia (Pontic)">Olbia</a></li> <li><a href="/wiki/Pantikapaion" title="Pantikapaion">Pantikapaion</a></li> <li><a href="/wiki/Phanagoria" title="Phanagoria">Phanagoria</a></li> <li><a href="/wiki/Pitsunda" title="Pitsunda">Pityus</a></li> <li><a href="/wiki/Tanais" title="Tanais">Tanais</a></li> <li><a href="/wiki/Feodosia" title="Feodosia">Theodosia</a></li> <li><a href="/wiki/Tyras" title="Tyras">Tyras</a></li> <li><a href="/wiki/Tyritake" class="mw-redirect" title="Tyritake">Tyritake</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">South<br />coast</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/Abonoteichos" title="Abonoteichos">Abonoteichos</a></li> <li><a href="/wiki/Samsun" title="Samsun">Amisos</a></li> <li><a href="/wiki/Pomorie" title="Pomorie">Anchialos</a></li> <li><a href="/wiki/Sozopol" title="Sozopol">Apollonia</a></li> <li><a href="/wiki/Pazar,_Rize" title="Pazar, Rize">Athina</a></li> <li><a href="/wiki/Batumi" title="Batumi">Bathus</a></li> <li><a href="/wiki/Balchik" title="Balchik">Dionysopolis</a></li> <li><a href="/wiki/Ordu" title="Ordu">Cotyora</a></li> <li><a href="/wiki/Cytorus" title="Cytorus">Cytorus</a></li> <li><a href="/wiki/Eupatoria_(Pontus)" title="Eupatoria (Pontus)">Eupatoria</a></li> <li><a href="/wiki/Heraclea_Pontica" title="Heraclea Pontica">Heraclea</a></li> <li><a href="/wiki/Giresun" title="Giresun">Kerasous</a></li> <li><a href="/wiki/Nesebar" title="Nesebar">Mesambria</a></li> <li><a href="/wiki/Varna,_Bulgaria" title="Varna, Bulgaria">Odessos</a></li> <li><a href="/wiki/%C3%9Cnye" title="Ünye">Oinòe</a></li> <li><a href="/wiki/Phasis_(town)" title="Phasis (town)">Phasis</a></li> <li><a href="/wiki/Fatsa" title="Fatsa">Polemonion</a></li> <li><a href="/wiki/Rize" title="Rize">Rhizos</a></li> <li><a href="/wiki/K%C4%B1y%C4%B1k%C3%B6y" title="Kıyıköy">Salmydessus</a></li> <li><a href="/wiki/Amasra" title="Amasra">Sesamus</a></li> <li><a href="/wiki/Sinop,_Turkey" title="Sinop, Turkey">Sinope</a></li> <li><a href="/wiki/Terme" title="Terme">Thèrmae</a></li> <li><a href="/wiki/Tium" title="Tium">Tium</a></li> <li><a href="/wiki/Trabzon" title="Trabzon">Trapezous</a></li> <li><a href="/wiki/Tripolis_(Pontus)" title="Tripolis (Pontus)">Tripolis</a></li> <li><a href="/wiki/Zaliche" title="Zaliche">Zaliche</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Lists" style="font-size:114%;margin:0 4em">Lists</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 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alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-59bf896c4b-tgnn9","wgBackendResponseTime":139,"wgPageParseReport":{"limitreport":{"cputime":"1.260","walltime":"1.534","ppvisitednodes":{"value":5966,"limit":1000000},"postexpandincludesize":{"value":325678,"limit":2097152},"templateargumentsize":{"value":1636,"limit":2097152},"expansiondepth":{"value":13,"limit":100},"expensivefunctioncount":{"value":5,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":277445,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 1282.444 1 -total"," 45.17% 579.307 2 Template:Reflist"," 20.45% 262.215 28 Template:Cite_journal"," 12.10% 155.237 12 Template:Navbox"," 9.88% 126.703 1 Template:Langx"," 7.14% 91.533 7 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