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class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Mathematical basis</span> </div> </a> <ul id="toc-Mathematical_basis-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">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-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 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Available in 37 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-37" 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">37 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%AF%D9%88%D8%B1%D8%A9_%D9%85%D9%8A%D8%AA%D9%88%D9%86%D9%8A%D8%A9" title="دورة ميتونية – Arabic" lang="ar" hreflang="ar" data-title="دورة ميتونية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%BD%D0%B0%D1%9E_%D1%86%D1%8B%D0%BA%D0%BB" title="Метонаў цыкл – Belarusian" lang="be" hreflang="be" data-title="Метонаў цыкл" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%BD%D0%B8%D1%87%D0%B5%D0%BD_%D1%86%D0%B8%D0%BA%D1%8A%D0%BB" title="Метоничен цикъл – Bulgarian" lang="bg" hreflang="bg" data-title="Метоничен цикъл" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cicle_met%C3%B2nic" title="Cicle metònic – Catalan" lang="ca" hreflang="ca" data-title="Cicle metònic" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Meton-Zyklus" title="Meton-Zyklus – German" lang="de" hreflang="de" data-title="Meton-Zyklus" 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%A3%CE%B5%CE%BB%CE%B7%CE%BD%CE%B9%CE%B1%CE%BA%CF%8C%CF%82_%CE%BA%CF%8D%CE%BA%CE%BB%CE%BF%CF%82" title="Σεληνιακός κύκλος – Greek" lang="el" hreflang="el" data-title="Σεληνιακός κύκλος" 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/Ciclo_met%C3%B3nico" title="Ciclo metónico – Spanish" lang="es" hreflang="es" data-title="Ciclo metónico" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D9%88%D8%B1%D9%87_%D9%85%D8%AA%D9%88%D9%86%DB%8C" title="دوره متونی – Persian" lang="fa" hreflang="fa" data-title="دوره متونی" 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/Cycle_m%C3%A9tonique" title="Cycle métonique – French" lang="fr" hreflang="fr" data-title="Cycle métonique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Ciclo_met%C3%B3nico" title="Ciclo metónico – Galician" lang="gl" hreflang="gl" data-title="Ciclo metónico" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A9%94%ED%86%A4_%EC%A3%BC%EA%B8%B0" title="메톤 주기 – Korean" lang="ko" hreflang="ko" data-title="메톤 주기" 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%A5%D5%BF%D5%B8%D5%B6%D5%AB_%D6%81%D5%AB%D5%AF%D5%AC" title="Մետոնի ցիկլ – Armenian" lang="hy" hreflang="hy" data-title="Մետոնի ցիկլ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/Okirikiri_Metonic" title="Okirikiri Metonic – Igbo" lang="ig" hreflang="ig" data-title="Okirikiri Metonic" data-language-autonym="Igbo" data-language-local-name="Igbo" class="interlanguage-link-target"><span>Igbo</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Siklus_metonik" title="Siklus metonik – Indonesian" lang="id" hreflang="id" data-title="Siklus metonik" 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/Ciclo_metonico" title="Ciclo metonico – Italian" lang="it" hreflang="it" data-title="Ciclo metonico" 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%97%D7%96%D7%95%D7%A8_%D7%9E%D7%98%D7%95%D7%A0%D7%99" title="מחזור מטוני – Hebrew" lang="he" hreflang="he" data-title="מחזור מטוני" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%94%E1%83%A2%E1%83%9D%E1%83%9C%E1%83%98%E1%83%A1_%E1%83%AA%E1%83%98%E1%83%99%E1%83%9A%E1%83%98" title="მეტონის ციკლი – Georgian" lang="ka" hreflang="ka" data-title="მეტონის ციკლი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Met%C3%B3n-ciklus" title="Metón-ciklus – Hungarian" lang="hu" hreflang="hu" data-title="Metón-ciklus" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Tsingerin%27_i_Met%C3%B4na" title="Tsingerin' i Metôna – Malagasy" lang="mg" hreflang="mg" data-title="Tsingerin' i Metôna" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Cyclus_van_Meton" title="Cyclus van Meton – Dutch" lang="nl" hreflang="nl" data-title="Cyclus van Meton" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%A1%E3%83%88%E3%83%B3%E5%91%A8%E6%9C%9F" title="メトン周期 – Japanese" lang="ja" hreflang="ja" data-title="メトン周期" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Meton-syklus" title="Meton-syklus – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Meton-syklus" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Meton-syklus" title="Meton-syklus – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Meton-syklus" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Cykl_Metona" title="Cykl Metona – Polish" lang="pl" hreflang="pl" data-title="Cykl Metona" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ciclo_met%C3%B3nico" title="Ciclo metónico – Portuguese" lang="pt" hreflang="pt" data-title="Ciclo metónico" 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%B5%D1%82%D0%BE%D0%BD%D0%BE%D0%B2_%D1%86%D0%B8%D0%BA%D0%BB" title="Метонов цикл – Russian" lang="ru" hreflang="ru" data-title="Метонов цикл" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Kalendari_i_Metonit" title="Kalendari i Metonit – Albanian" lang="sq" hreflang="sq" data-title="Kalendari i Metonit" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Metonic_cycle" title="Metonic cycle – Simple English" lang="en-simple" hreflang="en-simple" data-title="Metonic cycle" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Met%C3%B3nov_cyklus" title="Metónov cyklus – Slovak" lang="sk" hreflang="sk" data-title="Metónov cyklus" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Metonski_ciklus" title="Metonski ciklus – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Metonski ciklus" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Metonin_jakso" title="Metonin jakso – Finnish" lang="fi" hreflang="fi" data-title="Metonin jakso" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Metons_cykel" title="Metons cykel – Swedish" lang="sv" hreflang="sv" data-title="Metons cykel" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A7%E0%B8%B1%E0%B8%8F%E0%B8%88%E0%B8%B1%E0%B8%81%E0%B8%A3%E0%B9%80%E0%B8%A1%E0%B8%95%E0%B8%AD%E0%B8%99" title="วัฏจักรเมตอน – Thai" lang="th" hreflang="th" data-title="วัฏจักรเมตอน" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Meton_d%C3%B6ng%C3%BCs%C3%BC" title="Meton döngüsü – Turkish" lang="tr" hreflang="tr" data-title="Meton döngüsü" 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%9C%D0%B5%D1%82%D0%BE%D0%BD%D1%96%D0%B2_%D1%86%D0%B8%D0%BA%D0%BB" title="Метонів цикл – Ukrainian" lang="uk" hreflang="uk" data-title="Метонів цикл" 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/Chu_k%E1%BB%B3_Meton" title="Chu kỳ Meton – Vietnamese" lang="vi" hreflang="vi" data-title="Chu kỳ Meton" 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/%E9%BB%98%E5%86%AC%E7%AB%A0" title="默冬章 – Chinese" lang="zh" hreflang="zh" data-title="默冬章" 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 class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q285682#sitelinks-wikipedia" title="Edit 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class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CLM_14456_70v71r.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/CLM_14456_70v71r.jpg/320px-CLM_14456_70v71r.jpg" decoding="async" width="320" height="247" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/CLM_14456_70v71r.jpg/480px-CLM_14456_70v71r.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/CLM_14456_70v71r.jpg/640px-CLM_14456_70v71r.jpg 2x" data-file-width="2000" data-file-height="1546" /></a><figcaption>Depiction of the 19 years of the Metonic cycle as a wheel, with the Julian date of the Easter New Moon, from a 9th-century computistic manuscript made in <a href="/wiki/St._Emmeram%27s_Abbey" class="mw-redirect" title="St. Emmeram's Abbey">St. Emmeram's Abbey</a> (<a href="/wiki/Codex_latinus_monacensis" class="mw-redirect" title="Codex latinus monacensis">Clm</a> 14456, fol. 71r)</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Christmas_full_moons_1711-2300.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Christmas_full_moons_1711-2300.gif/220px-Christmas_full_moons_1711-2300.gif" decoding="async" width="220" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Christmas_full_moons_1711-2300.gif/330px-Christmas_full_moons_1711-2300.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Christmas_full_moons_1711-2300.gif/440px-Christmas_full_moons_1711-2300.gif 2x" data-file-width="480" data-file-height="459" /></a><figcaption>For example, by the 19-year Metonic cycle, the full moon repeats on or near <a href="/wiki/Christmas" title="Christmas">Christmas</a> between 1711 and 2300.<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> A small horizontal <a href="/wiki/Libration" title="Libration">libration</a> is visible comparing their appearances. A red color shows full moons that are also <a href="/wiki/Lunar_eclipse" title="Lunar eclipse">lunar eclipses</a>.</figcaption></figure> <p>The <b>Metonic cycle</b> or <b>enneadecaeteris</b> (from <a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: <span lang="grc">ἐννεακαιδεκαετηρίς</span>, from ἐννεακαίδεκα, "nineteen") is a period of almost exactly 19 years after which the <a href="/wiki/Lunar_phases" class="mw-redirect" title="Lunar phases">lunar phases</a> recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 <a href="/wiki/Synodic_month" class="mw-redirect" title="Synodic month">synodic months</a> is just 2 hours, 4 minutes and 58 seconds longer than 19 <a href="/wiki/Tropical_year" title="Tropical year">tropical years</a>. <a href="/wiki/Meton_of_Athens" title="Meton of Athens">Meton of Athens</a>, in the 5th century BC, judged the cycle to be a whole number of days, 6,940.<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> Using these whole numbers facilitates the construction of a <a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">lunisolar calendar</a>. </p><p>A tropical year (about 365.24 days) is longer than 12 lunar months (about 354.36 days) and shorter than 13 of them (about 383.90 days). In a <b>Metonic calendar</b> (a type of <a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">lunisolar calendar</a>), there are twelve years of 12 lunar months and seven years of 13 lunar months. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Application_in_traditional_calendars">Application in traditional calendars</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Metonic_cycle&action=edit&section=1" title="Edit section: Application in traditional calendars"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <a href="/wiki/Babylonian_calendar" title="Babylonian calendar">Babylonian</a> and <a href="/wiki/Hebrew_calendar" title="Hebrew calendar">Hebrew</a> <a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">lunisolar calendars</a>, the years 3, 6, 8, 11, 14, 17, and 19 are the long (13-month) years of the Metonic cycle. This cycle forms the basis of the Greek and Hebrew calendars. A 19-year cycle is used for the <a href="/wiki/Computus" class="mw-redirect" title="Computus">computation of the date of Easter</a> each year. </p><p>The Babylonians applied the 19-year cycle from the late sixth century BC.<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> </p><p>According to <a href="/wiki/Livy" title="Livy">Livy</a>, the second king of Rome, <a href="/wiki/Numa_Pompilius" title="Numa Pompilius">Numa Pompilius</a> (reigned 715–673 BC), inserted <a href="/wiki/Intercalation_(timekeeping)" title="Intercalation (timekeeping)">intercalary</a> months in such a way that "in the twentieth year the days should fall in with the same position of the sun from which they had started".<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> As "the twentieth year" takes place nineteen years after "the first year", this seems to indicate that the Metonic cycle was applied to Numa's calendar. </p><p><a href="/wiki/Diodorus_Siculus" title="Diodorus Siculus">Diodorus Siculus</a> reports that <a href="/wiki/Apollo" title="Apollo">Apollo</a> is said to have visited the <a href="/wiki/Hyperborea" title="Hyperborea">Hyperboreans</a> once every 19 years.<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> </p><p>The Metonic cycle has been implemented in the <a href="/wiki/Antikythera_mechanism" title="Antikythera mechanism">Antikythera mechanism</a> which offers unexpected evidence for the popularity of the calendar based on it.<sup id="cite_ref-freeth-08_7-0" class="reference"><a href="#cite_note-freeth-08-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The (19-year) Metonic cycle is a <b>lunisolar</b> cycle, as is the (76-year) <a href="/wiki/Callippic_cycle" title="Callippic cycle">Callippic cycle</a>.<sup id="cite_ref-FOOTNOTENothaft2012168_8-0" class="reference"><a href="#cite_note-FOOTNOTENothaft2012168-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> An important example of an application of the Metonic cycle in the <a href="/wiki/Julian_calendar" title="Julian calendar">Julian calendar</a> is the 19-year <b>lunar</b> cycle insofar as provided with a Metonic structure.<sup id="cite_ref-FOOTNOTEMcCarthyBreen200317_9-0" class="reference"><a href="#cite_note-FOOTNOTEMcCarthyBreen200317-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Meton introduced the 19 year cycle to the <a href="/wiki/Attic_calendar" title="Attic calendar">Attic calendar</a> in 432 BC. In the following century, <a href="/wiki/Callippus" title="Callippus">Callippus</a> developed the Callippic cycle of four 19-year periods for a 76-year cycle with a mean year of exactly 365.25 days. </p><p>Around AD 260 the Alexandrian <a href="/wiki/Computus" class="mw-redirect" title="Computus">computist</a> <a href="/wiki/Anatolius_of_Laodicea" title="Anatolius of Laodicea">Anatolius</a>, who became bishop of Laodicea in AD 268, was the first to devise a method for determining the date of Easter Sunday.<sup id="cite_ref-FOOTNOTEDeclercq200065–66_10-0" class="reference"><a href="#cite_note-FOOTNOTEDeclercq200065–66-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> However, it was some later, somewhat different, version of the Metonic 19-year lunar cycle which, as the basic structure of <a href="/wiki/Dionysius_Exiguus" title="Dionysius Exiguus">Dionysius Exiguus</a>' and also of <a href="/wiki/Bede" title="Bede">Bede</a>'s Easter table, would ultimately prevail throughout <a href="/wiki/Christendom" title="Christendom">Christendom</a>,<sup id="cite_ref-FOOTNOTEDeclercq200066_11-0" class="reference"><a href="#cite_note-FOOTNOTEDeclercq200066-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> at least until in the year 1582, when the <a href="/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian calendar</a> was introduced. </p><p>The <a href="/wiki/Coligny_calendar" title="Coligny calendar">Coligny calendar</a> is a Celtic lunisolar calendar using the Metonic cycle. The bronze plaque on which it was found dates from c. AD 200, but the internal evidence points to the calendar itself being several centuries older, created in the Iron Age or late Bronze Age.<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> </p><p>The Metonic cycle is thought to be numerically encoded on the <a href="/wiki/Berlin_Gold_Hat" title="Berlin Gold Hat">Berlin Gold Hat</a> from central Europe, dating from c. 1000-800 BC.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><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><sup id="cite_ref-:0_16-0" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Runic_calendar" title="Runic calendar">Runic calendar</a> is a <a href="/wiki/Perpetual_calendar" title="Perpetual calendar">perpetual calendar</a> based on the 19-year-long Metonic cycle. It is also known as a Rune staff or Runic Almanac. This calendar does not rely on knowledge of the duration of the tropical year or of the occurrence of leap years. It is set at the beginning of each year by observing the first full moon after the winter solstice. The oldest one known, and the only one from the Middle Ages, is the <a href="/w/index.php?title=Nyk%C3%B6ping_staff&action=edit&redlink=1" class="new" title="Nyköping staff (page does not exist)">Nyköping staff</a>, which is believed to date from the 13th century. </p><p>The <a href="/wiki/Bah%C3%A1%27%C3%AD_calendar" class="mw-redirect" title="Bahá'í calendar">Bahá'í calendar</a>, established during the middle of the 19th century, is also based on cycles of 19 solar years. </p> <div class="mw-heading mw-heading3"><h3 id="Hebrew_calendar">Hebrew calendar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Metonic_cycle&action=edit&section=2" title="Edit section: Hebrew calendar"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <b>Small Maḥzor</b> (<a href="/wiki/Hebrew_language" title="Hebrew language">Hebrew</a> מחזור, <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">pronounced</span> <span class="IPA nowrap" lang="he-Latn-fonipa"><a href="/wiki/Help:IPA/Hebrew" title="Help:IPA/Hebrew">[maχˈzor]</a></span>, meaning "cycle") is a 19-year cycle in the <a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">lunisolar calendar</a> system used by the <a href="/wiki/Jewish_people" class="mw-redirect" title="Jewish people">Jewish people</a>. It is similar to, but slightly different in usage from, the Greek Metonic cycle (being based on a month of <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac">29<span class="sr-only">+</span><span class="num">13753</span>⁄<span class="den">25920</span></span> days, giving a cycle of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027" /><span class="frac">6939<span class="sr-only">+</span><span class="num">3575</span>⁄<span class="den">5184</span></span> ≈ 6939.69 days<sup id="cite_ref-Tondering_17-0" class="reference"><a href="#cite_note-Tondering-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>), and likely derived from or alongside the much earlier <a href="/wiki/Babylonian_calendar" title="Babylonian calendar">Babylonian</a> calendar.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Polynesia">Polynesia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Metonic_cycle&action=edit&section=3" title="Edit section: Polynesia"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is possible that the Polynesian kilo-hoku (astronomers) discovered the Metonic cycle in the same way Meton had, by trying to make the month fit the year.<sup id="cite_ref-FOOTNOTEJohnson2001238_19-0" class="reference"><a href="#cite_note-FOOTNOTEJohnson2001238-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematical_basis">Mathematical basis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Metonic_cycle&action=edit&section=4" title="Edit section: Mathematical basis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Metonic cycle is the most accurate cycle of time (in a timespan of less than 100 years) for synchronizing the <a href="/wiki/Tropical_year" title="Tropical year">tropical year</a> and the lunar month (<a href="/wiki/Synodic_month" class="mw-redirect" title="Synodic month">synodic month</a>), when the method of synchronizing is the <a href="/wiki/Intercalation_(timekeeping)" title="Intercalation (timekeeping)">intercalation</a> of a thirteenth lunar month in a calendar year from time to time.<sup id="cite_ref-FOOTNOTERichards199894–96_20-0" class="reference"><a href="#cite_note-FOOTNOTERichards199894–96-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> The traditional lunar year of 12 synodic months is about 354 days, approximately eleven days short of the solar year. Thus, every 2 to 3 years there is a discrepancy of 22 to 33 days, or a full synodic month. For example, if the winter solstice and the new moon coincide, it takes 19 tropical years for the coincidence to recur. The mathematical logic is this: </p> <ul><li>A tropical year lasts 365.2422 days.<sup id="cite_ref-FOOTNOTEglossary2022s.v._year,_tropical_21-0" class="reference"><a href="#cite_note-FOOTNOTEglossary2022s.v._year,_tropical-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> <dl><dd>a span of 19 tropical years (365.2422 × 19) lasts 6,939.602 days</dd></dl></li></ul> <p>That duration is almost the same as 235 synodic months: </p> <ul><li>A synodic month lasts 29.53059 days.<sup id="cite_ref-FOOTNOTERichards2013587_22-0" class="reference"><a href="#cite_note-FOOTNOTERichards2013587-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <dl><dd>a span of 235 synodic months (29.53059 × 235) lasts 6,939.689 days</dd></dl></li></ul> <p>Thus the algorithm is correct to 0.087 days (2 hours, 5 minutes and 16 seconds). </p><p>For a <a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">lunisolar calendar</a> to 'catch up' to this discrepancy and thus maintain seasonal consistency, seven <a href="/wiki/Intercalation_(timekeeping)" title="Intercalation (timekeeping)">intercalary months</a> are added (one at a time), at intervals of every 2–3 years during the course of 19 solar years. Thus twelve of those years have 12 lunar months and seven have 13 months. </p> <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=Metonic_cycle&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Octaeteris" title="Octaeteris">Octaeteris</a> (8-year cycle of antiquity)</li> <li><a href="/wiki/Callippic_cycle" title="Callippic cycle">Callippic cycle</a> (76-year cycle from 330 BC)</li> <li><a href="/wiki/Hipparchic_cycle" title="Hipparchic cycle">Hipparchic cycle</a> (304-year cycle from 2nd century BC)</li> <li><a href="/wiki/Saros_cycle" class="mw-redirect" title="Saros cycle">Saros cycle</a> of eclipses</li> <li><a href="/wiki/Attic_calendar" title="Attic calendar">Attic</a> and <a href="/wiki/Byzantine_calendar" title="Byzantine calendar">Byzantine calendar</a></li> <li><a href="/wiki/Julian_day" title="Julian day">Julian day</a></li> <li><a href="/wiki/Date_of_Easter" title="Date of Easter">Date of Easter</a> ("the Computus")</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Metonic_cycle&action=edit&section=6" title="Edit section: Notes"><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"> <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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.nasa.gov/feature/goddard/rare-full-moon-on-christmas-day">"Rare Full Moon on Christmas Day"</a>. <i>NASA</i>. 17 December 2015. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231108031712/https://www.nasa.gov/solar-system/rare-full-moon-on-christmas-day/">Archived</a> from the original on 8 November 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=NASA&rft.atitle=Rare+Full+Moon+on+Christmas+Day&rft.date=2015-12-17&rft_id=https%3A%2F%2Fwww.nasa.gov%2Ffeature%2Fgoddard%2Frare-full-moon-on-christmas-day&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" 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="CITEREFSkilling2015" class="citation news cs1">Skilling, Tom (20 December 2015). <a rel="nofollow" class="external text" href="http://www.chicagotribune.com/news/weather/ct-wea-1221-asktom-20151220-column.html">"Ask Tom: How unusual is a full moon on Christmas Day?"</a>. <i><a href="/wiki/Chicago_Tribune" title="Chicago Tribune">Chicago Tribune</a></i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151222054149/http://www.chicagotribune.com/news/weather/ct-wea-1221-asktom-20151220-column.html">Archived</a> from the original on 22 December 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Chicago+Tribune&rft.atitle=Ask+Tom%3A+How+unusual+is+a+full+moon+on+Christmas+Day%3F&rft.date=2015-12-20&rft.aulast=Skilling&rft.aufirst=Tom&rft_id=http%3A%2F%2Fwww.chicagotribune.com%2Fnews%2Fweather%2Fct-wea-1221-asktom-20151220-column.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><sup>needs citation</sup></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://webspace.science.uu.nl/~gent0113/babylon/babycal.htm">"The Babylonian Calendar"</a>. <i>Mathematical Institute</i>. Utrecht University. July 2021. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230902103953/https://webspace.science.uu.nl/~gent0113/babylon/babycal.htm">Archived</a> from the original on 2 September 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Mathematical+Institute&rft.atitle=The+Babylonian+Calendar&rft.date=2021-07&rft_id=https%3A%2F%2Fwebspace.science.uu.nl%2F~gent0113%2Fbabylon%2Fbabycal.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Livy, <a href="/wiki/Ab_Urbe_Condita" class="mw-redirect" title="Ab Urbe Condita">Ab Urbe Condita</a>, I, XIX, 6.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Diodorus Siculus, <i>Bibl. Hist.</i> <a rel="nofollow" class="external text" href="https://archive.org/details/diodorusofsicily02dioduoft/page/40/mode/2up">II.47</a>.</span> </li> <li id="cite_note-freeth-08-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-freeth-08_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFreethJonesSteeleBitsakis2008" class="citation journal cs1">Freeth, Tony; Jones, Alexander; Steele, John M.; Bitsakis, Yanis (31 July 2008). <a rel="nofollow" class="external text" href="http://www.antikythera-mechanism.gr/system/files/Antikythera_Nature2008_submitted.pdf">"Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism"</a> <span class="cs1-format">(PDF)</span>. <i>Nature</i>. <b>454</b> (7204): <span class="nowrap">614–</span>7. <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/2008Natur.454..614F">2008Natur.454..614F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnature07130">10.1038/nature07130</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/18668103">18668103</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:4400693">4400693</a><span class="reference-accessdate">. Retrieved <span class="nowrap">20 May</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Calendars+with+Olympiad+display+and+eclipse+prediction+on+the+Antikythera+Mechanism&rft.volume=454&rft.issue=7204&rft.pages=%3Cspan+class%3D%22nowrap%22%3E614-%3C%2Fspan%3E7&rft.date=2008-07-31&rft_id=info%3Adoi%2F10.1038%2Fnature07130&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4400693%23id-name%3DS2CID&rft_id=info%3Apmid%2F18668103&rft_id=info%3Abibcode%2F2008Natur.454..614F&rft.aulast=Freeth&rft.aufirst=Tony&rft.au=Jones%2C+Alexander&rft.au=Steele%2C+John+M.&rft.au=Bitsakis%2C+Yanis&rft_id=http%3A%2F%2Fwww.antikythera-mechanism.gr%2Fsystem%2Ffiles%2FAntikythera_Nature2008_submitted.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTENothaft2012168-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTENothaft2012168_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFNothaft2012">Nothaft 2012</a>, p. 168.</span> </li> <li id="cite_note-FOOTNOTEMcCarthyBreen200317-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMcCarthyBreen200317_9-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMcCarthyBreen2003">McCarthy & Breen 2003</a>, p. 17.</span> </li> <li id="cite_note-FOOTNOTEDeclercq200065–66-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDeclercq200065–66_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDeclercq2000">Declercq 2000</a>, pp. 65–66.</span> </li> <li id="cite_note-FOOTNOTEDeclercq200066-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDeclercq200066_11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDeclercq2000">Declercq 2000</a>, p. 66.</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="CITEREFOlmsted2001" class="citation journal cs1">Olmsted, Garrett (2001). <a rel="nofollow" class="external text" href="https://www.academia.edu/62011364">"A Definitive Reconstructed Text of the Coligny Calendar"</a>. <i>Journal of Indo-European Studies</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Indo-European+Studies&rft.atitle=A+Definitive+Reconstructed+Text+of+the+Coligny+Calendar&rft.date=2001&rft.aulast=Olmsted&rft.aufirst=Garrett&rft_id=https%3A%2F%2Fwww.academia.edu%2F62011364&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://artsandculture.google.com/story/DAVRgpAwHmLsLw?hl=en">"Life and Belief During the Bronze Age" Neues Museum, Berlin"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">13 March</span> 2022</span>. <q>What is especially fascinating is the ornamentation on the [Berlin gold hat] in which a complex counting system is encoded, enabling calendar calculations, especially the 19-year cycle of the sun and the moon. ... The star at the tip symbolises the sun, with the sickles and eye patterns representing the moon and Venus, while the circular ornaments can equally be interpreted as depictions of the sun or the moon. … The cycle of the sun determines day and nigh and the seasons, while the moon determines the division of the year into months and days. But the lunar year is eleven days shorter than the solar year. Even as early as the 2nd millennium BC intercalary days were inserted to bring the solar and lunar cycles into alignment. This knowledge is reflected in the ornamentation of the Gold Hat. The stamped patterns should be read as a calendar. For instance, the number of circles in certain decorative areas equals the twelve lunar periods of 354 days. If the patterns in other decorative areas are added, this gives the 365 days of the solar year. It takes 19 years for the solar year and the lunar year to align again. In the ornamentation of the hat the fact is encoded that seven lunar months need to be inserted into the 19-year cycle. Other calculations can be made as well, such as the dates of eclipses of the moon. (…) The golden hats show that astronomical knowledge was combined with cult activities… They were apparently worn over several generation and at some point buried in the ground in a sacred act to protect them from desecration and to place them in the realm of the gods. It seems that Bronze Age rulers combined worldly and spiritual power.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Life+and+Belief+During+the+Bronze+Age%22+Neues+Museum%2C+Berlin&rft_id=https%3A%2F%2Fartsandculture.google.com%2Fstory%2FDAVRgpAwHmLsLw%3Fhl%3Den&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://artsandculture.google.com/asset/golden-ceremonial-hat-berlin-gold-hat-artist-unknown/hAGC3knXgLdPZg?hl=en">"Golden Ceremonial Hat ("Berlin Gold Hat")"</a>. Neues Museum Berlin. <q>One particularly impressive piece of evidence for early man's astronomical knowledge is the Bronze Age Berlin gold hat, unique in its size and preservation. The sun, evoked by the gold coloration and the pattern of rays at the top of the hat, creates day, night and the seasons by apparently circling the earth. The moon, represented several times on the hat, marks out months and weeks. The number and arrangement of the ornaments is not random; it allows a nineteen-year lunisolar cycle of 228 solar months and 235 lunar months to be calculated. Someone who knew how to read these ornaments would be able to calculate the shifts between the solar year and the lunar year, predict lunar eclipses, and set fixed dates for significant events. … Over half a millennium before the astronomer and mathematician Meton in 432 BC calculated the shifts in the lunisolar cycle, they were already known to the educated elite of the Bronze Age. The golden hat may have been worn by a ruler with a religious role on ceremonial occasions. Other Bronze Age items prove that astronomical knowledge was often preserved in coded form on valuable and sacred objects.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Golden+Ceremonial+Hat+%28%22Berlin+Gold+Hat%22%29&rft.pub=Neues+Museum+Berlin&rft_id=https%3A%2F%2Fartsandculture.google.com%2Fasset%2Fgolden-ceremonial-hat-berlin-gold-hat-artist-unknown%2FhAGC3knXgLdPZg%3Fhl%3Den&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMenghin2008" class="citation journal cs1">Menghin, Wilfried (2008). <a rel="nofollow" class="external text" href="https://journals.ub.uni-heidelberg.de/index.php/apa/issue/view/5045">"Zahlensymbolik und digitales Rechnersystem in der Ornamentik des Berliner Goldhutes"</a>. <i>Acta Praehistorica et Archaeologica</i>. <b>40</b>: <span class="nowrap">157–</span>169. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.11588%2Fapa.2008.0.71505">10.11588/apa.2008.0.71505</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Praehistorica+et+Archaeologica&rft.atitle=Zahlensymbolik+und+digitales+Rechnersystem+in+der+Ornamentik+des+Berliner+Goldhutes&rft.volume=40&rft.pages=%3Cspan+class%3D%22nowrap%22%3E157-%3C%2Fspan%3E169&rft.date=2008&rft_id=info%3Adoi%2F10.11588%2Fapa.2008.0.71505&rft.aulast=Menghin&rft.aufirst=Wilfried&rft_id=https%3A%2F%2Fjournals.ub.uni-heidelberg.de%2Findex.php%2Fapa%2Fissue%2Fview%2F5045&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></span> </li> <li id="cite_note-:0-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://archive.org/details/goldundkultderbr0000unse"><i>Gold und Kult der Bronzezeit</i></a>. Germanisches Nationalmuseum, Nuremberg. 2003. pp. <span class="nowrap">220–</span>237. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-926982-95-0" title="Special:BookSources/3-926982-95-0"><bdi>3-926982-95-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gold+und+Kult+der+Bronzezeit&rft.pages=%3Cspan+class%3D%22nowrap%22%3E220-%3C%2Fspan%3E237&rft.pub=Germanisches+Nationalmuseum%2C+Nuremberg&rft.date=2003&rft.isbn=3-926982-95-0&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgoldundkultderbr0000unse&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></span> </li> <li id="cite_note-Tondering-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Tondering_17-0">^</a></b></span> <span class="reference-text">The month is 29.5 days and 793 "parts", where a part is 1/18 of a minute. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFTønderingTøndering" class="citation web cs1">Tøndering, Trine; Tøndering, Claus. <a rel="nofollow" class="external text" href="https://www.tondering.dk/claus/cal/hebrew.php#newmoon">"Calendar FAQ: the Hebrew calendar: New moon"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Calendar+FAQ%3A+the+Hebrew+calendar%3A+New+moon&rft.aulast=T%C3%B8ndering&rft.aufirst=Trine&rft.au=T%C3%B8ndering%2C+Claus&rft_id=https%3A%2F%2Fwww.tondering.dk%2Fclaus%2Fcal%2Fhebrew.php%23newmoon&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span> This comes to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027" /><span class="frac">29<span class="sr-only">+</span><span class="num">13753</span>⁄<span class="den">25920</span></span> days. Multiplying this by 235 gives the length of the cycle.</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/topic/Jewish-religious-year">"Jewish religious year | Cycle, Holidays, & Facts | Britannica"</a>. <i>www.britannica.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">14 November</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.britannica.com&rft.atitle=Jewish+religious+year+%7C+Cycle%2C+Holidays%2C+%26+Facts+%7C+Britannica&rft_id=https%3A%2F%2Fwww.britannica.com%2Ftopic%2FJewish-religious-year&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEJohnson2001238-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEJohnson2001238_19-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFJohnson2001">Johnson 2001</a>, p. 238.</span> </li> <li id="cite_note-FOOTNOTERichards199894–96-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERichards199894–96_20-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRichards1998">Richards (1998)</a>, pp. 94–96.</span> </li> <li id="cite_note-FOOTNOTEglossary2022s.v._year,_tropical-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEglossary2022s.v._year,_tropical_21-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFglossary2022">glossary (2022)</a>, s.v. year, tropical.</span> </li> <li id="cite_note-FOOTNOTERichards2013587-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERichards2013587_22-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRichards2013">Richards (2013)</a>, p. 587.</span> </li> </ol></div></div> <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=Metonic_cycle&action=edit&section=7" title="Edit section: References"><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="CITEREFDeclercq2000" class="citation book cs1">Declercq, Georges (2000). <i>Anno Domini: The Origins of the Christian Era</i>. Turnhout. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9782503510507" title="Special:BookSources/9782503510507"><bdi>9782503510507</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Anno+Domini%3A+The+Origins+of+the+Christian+Era&rft.pub=Turnhout&rft.date=2000&rft.isbn=9782503510507&rft.aulast=Declercq&rft.aufirst=Georges&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFglossary2022" class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20201021173505/http://asa.hmnao.com/SecM/Glossary.html">"Glossary"</a>. <i>The Astronomical Almanac Online!</i>. Washington, DC: United States Naval Observatory. 2022. Archived from <a rel="nofollow" class="external text" href="http://asa.hmnao.com/SecM/Glossary.html">the original</a> on 21 October 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">30 March</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Astronomical+Almanac+Online%21&rft.atitle=Glossary&rft.date=2022&rft_id=http%3A%2F%2Fasa.hmnao.com%2FSecM%2FGlossary.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHannah2005" class="citation book cs1">Hannah, Robert (2005). <i>Greek & Roman Calendars: Construction of Time in the Classical World</i>. London: Duckworth.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Greek+%26+Roman+Calendars%3A+Construction+of+Time+in+the+Classical+World&rft.place=London&rft.pub=Duckworth&rft.date=2005&rft.aulast=Hannah&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJohnson2001" class="citation book cs1">Johnson, Rubellite Kawena (2001). <i>Essays in Hawaiian Literature Part 1 Origin Myths and Migration traditions</i>. author.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essays+in+Hawaiian+Literature+Part+1+Origin+Myths+and+Migration+traditions&rft.pub=author&rft.date=2001&rft.aulast=Johnson&rft.aufirst=Rubellite+Kawena&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMcCarthyBreen2003" class="citation book cs1">McCarthy, Daniel P.; Breen, Aidan (2003). <i>The ante-Nicene Christian Pasch | </i>De ratione paschali:<i> The Paschal tract of Anatolius, bishop of Laodicea</i>. Dublin: Four Courts Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781851826971" title="Special:BookSources/9781851826971"><bdi>9781851826971</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/367715096">367715096</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+ante-Nicene+Christian+Pasch+%7C+De+ratione+paschali%3A+The+Paschal+tract+of+Anatolius%2C+bishop+of+Laodicea&rft.place=Dublin&rft.pub=Four+Courts+Press&rft.date=2003&rft_id=info%3Aoclcnum%2F367715096&rft.isbn=9781851826971&rft.aulast=McCarthy&rft.aufirst=Daniel+P.&rft.au=Breen%2C+Aidan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFNothaft2012" class="citation book cs1">Nothaft, C Philipp E. (2012). <i>Dating the Passion: The Life of Jesus and the Emergence of Scientific Chronology (200–1600</i>. Leiden: BRILL. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9789004212190" title="Special:BookSources/9789004212190"><bdi>9789004212190</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dating+the+Passion%3A+The+Life+of+Jesus+and+the+Emergence+of+Scientific+Chronology+%28200%26ndash%3B1600&rft.place=Leiden&rft.pub=BRILL&rft.date=2012&rft.isbn=9789004212190&rft.aulast=Nothaft&rft.aufirst=C+Philipp+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRichards1998" class="citation book cs1">Richards, E. G. (1998). <i>Mapping Time: The Calendar and its History</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0192862051" title="Special:BookSources/978-0192862051"><bdi>978-0192862051</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mapping+Time%3A+The+Calendar+and+its+History&rft.pub=Oxford+University+Press&rft.date=1998&rft.isbn=978-0192862051&rft.aulast=Richards&rft.aufirst=E.+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRichards2013" class="citation book cs1">Richards, E. G. (2013). "Calendars". In Urban, Sean E.; Seidelmann, P. Kenneth (eds.). <i>Explanatory Supplement to the Astronomical Almanac</i> (3rd ed.). Mill Valley, CA: University Science Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-891389-85-6" title="Special:BookSources/978-1-891389-85-6"><bdi>978-1-891389-85-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Calendars&rft.btitle=Explanatory+Supplement+to+the+Astronomical+Almanac&rft.place=Mill+Valley%2C+CA&rft.edition=3rd&rft.pub=University+Science+Books&rft.date=2013&rft.isbn=978-1-891389-85-6&rft.aulast=Richards&rft.aufirst=E.+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWatkins1954" class="citation book cs1">Watkins, Harold (1954). <i>Time Counts: The Story of the Calendars</i>. New York: Philosophical Library.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Time+Counts%3A+The+Story+of+the+Calendars&rft.place=New+York&rft.pub=Philosophical+Library&rft.date=1954&rft.aulast=Watkins&rft.aufirst=Harold&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMetonic+cycle" 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=Metonic_cycle&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Metonic_cycle" class="extiw" title="commons:Category:Metonic cycle">Metonic cycle</a> at Wikimedia Commons</li> <li><a rel="nofollow" class="external text" href="http://jqjacobs.net/astro/eclipse.html#metonic">Eclipses, Cosmic Clockwork of the Ancients</a></li> <li><a rel="nofollow" class="external text" href="https://www.thomasweibel.ch/meton/">Meton</a>, Virtual Mechanical Lunar Phase and Eclipse Calculator</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output 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.navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /></div><div role="navigation" class="navbox" aria-labelledby="Chronology382" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Chronology" title="Template:Chronology"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Chronology" title="Template talk:Chronology"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Chronology" title="Special:EditPage/Template:Chronology"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Chronology382" style="font-size:114%;margin:0 4em"><a href="/wiki/Chronology" title="Chronology">Chronology</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;background:#cc9;">Key topics</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/Archaeology" title="Archaeology">Archaeology</a></li> <li><a href="/wiki/Astronomy" title="Astronomy">Astronomy</a></li> <li><a href="/wiki/Geology" title="Geology">Geology</a></li> <li><a href="/wiki/History" title="History">History</a> <ul><li><a href="/wiki/Big_History" title="Big History">Big History</a></li></ul></li> <li><a href="/wiki/Paleontology" title="Paleontology">Paleontology</a></li> <li><a href="/wiki/Time" title="Time">Time</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;background:#cc9;"><div class="hlist"><ul><li><a href="/wiki/Periodization" title="Periodization">Periods</a></li><li><a href="/wiki/Era" title="Era">Eras</a></li><li><a href="/wiki/Epoch_(reference_date)" class="mw-redirect" title="Epoch (reference date)">Epochs</a></li></ul></div></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:8.0em;font-weight:normal;background:#cc9;"><a href="/wiki/Calendar_era" title="Calendar era">Calendar eras</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Holocene_calendar" title="Holocene calendar">Human Era</a></li> <li><i><a href="/wiki/Ab_urbe_condita" title="Ab urbe condita">Ab urbe condita</a></i></li> <li><a href="/wiki/Anno_Domini" title="Anno Domini">Anno Domini</a> / <a href="/wiki/Common_Era" title="Common Era">Common Era</a></li> <li><a href="/wiki/Anno_Mundi" title="Anno Mundi">Anno Mundi</a></li> <li><a href="/wiki/Bosporan_era" title="Bosporan era">Bosporan era</a></li> <li><a href="/wiki/Bostran_era" title="Bostran era">Bostran era</a></li> <li><a href="/wiki/Byzantine_calendar" title="Byzantine calendar">Byzantine era</a></li> <li><a href="/wiki/Seleucid_era" title="Seleucid era">Seleucid era</a></li> <li><a href="/wiki/Era_of_Caesar_(Iberian_Peninsula)" class="mw-redirect" title="Era of Caesar (Iberian Peninsula)">Era of Caesar (Iberia)</a></li> <li><a href="/wiki/Before_present" class="mw-redirect" title="Before present">Before present</a></li> <li><a href="/wiki/Islamic_calendar" title="Islamic calendar">Hijri</a></li> <li><a href="/wiki/Egyptian_chronology" title="Egyptian chronology">Egyptian</a></li> <li><a href="/wiki/Sothic_cycle" title="Sothic cycle">Sothic cycle</a></li> <li><a href="/wiki/Hindu_units_of_time" title="Hindu units of time">Hindu units of time</a> (<a href="/wiki/Yuga" title="Yuga">Yuga</a>)</li> <li><a href="/wiki/Mesoamerican_calendars" title="Mesoamerican calendars">Mesoamerican</a> <ul><li><a href="/wiki/Mesoamerican_Long_Count_calendar" title="Mesoamerican Long Count calendar">Long Count</a></li> <li><a href="/wiki/Maya_calendar#Short_Count" title="Maya calendar">Short Count</a></li> <li><a href="/wiki/Tzolk%27in" class="mw-redirect" title="Tzolk'in">Tzolk'in</a></li> <li><a href="/wiki/Haab%27" class="mw-redirect" title="Haab'">Haab'</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:8.0em;font-weight:normal;background:#cc9;"><a href="/wiki/Regnal_year" title="Regnal year">Regnal year</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anka_year" title="Anka year">Anka year</a></li> <li><a href="/wiki/Canon_of_Kings" title="Canon of Kings">Canon of Kings</a></li> <li><a href="/wiki/Regnal_years_of_English_and_British_monarchs" title="Regnal years of English and British monarchs">English and British regnal year</a></li> <li><a href="/wiki/Category:Regnal_lists" title="Category:Regnal lists">Lists of kings</a></li> <li><a href="/wiki/Limmu" title="Limmu">Limmu</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:8.0em;font-weight:normal;background:#cc9;"><a href="/wiki/Regnal_year" title="Regnal year">Era names</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chinese_era_name" title="Chinese era name">Chinese</a></li> <li><a href="/wiki/Japanese_era_name" title="Japanese era name">Japanese</a></li> <li><a href="/wiki/Korean_era_name" title="Korean era name">Korean</a></li> <li><a href="/wiki/Vietnamese_era_name" title="Vietnamese era name">Vietnamese</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;background:#cc9;"><a href="/wiki/Calendar" title="Calendar">Calendars</a></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:8.0em;font-weight:normal;background:#cc9;">Pre-Julian / Julian</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Roman_calendar" title="Roman calendar">Pre-Julian Roman</a></li> <li><a href="/wiki/Julian_calendar" title="Julian calendar">Original Julian</a></li> <li><a href="/wiki/Proleptic_Julian_calendar" title="Proleptic Julian calendar">Proleptic Julian</a></li> <li><a href="/wiki/Revised_Julian_calendar" title="Revised Julian calendar">Revised Julian</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:8.0em;font-weight:normal;background:#cc9;">Gregorian</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian</a></li> <li><a href="/wiki/Proleptic_Gregorian_calendar" title="Proleptic Gregorian calendar">Proleptic Gregorian</a></li> <li><a href="/wiki/Old_Style_and_New_Style_dates" title="Old Style and New Style dates">Old Style and New Style dates</a></li> <li><a href="/wiki/Adoption_of_the_Gregorian_calendar" title="Adoption of the Gregorian calendar">Adoption of the Gregorian calendar</a></li> <li><a href="/wiki/Dual_dating" title="Dual dating">Dual dating</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:8.0em;font-weight:normal;background:#cc9;">Astronomical</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">Lunisolar</a> (<a href="/wiki/Hebrew_calendar" title="Hebrew calendar">Hebrew</a>, <a href="/wiki/Hindu_calendar" title="Hindu calendar">Hindu</a>)</li> <li><a href="/wiki/Solar_calendar" title="Solar calendar">Solar</a></li> <li><a href="/wiki/Lunar_calendar" title="Lunar calendar">Lunar</a> (<a href="/wiki/Islamic_calendar" title="Islamic calendar">Islamic</a>)</li> <li><a href="/wiki/Astronomical_year_numbering" title="Astronomical year numbering">Astronomical year numbering</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:8.0em;font-weight:normal;background:#cc9;">Others</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sexagenary_cycle" title="Sexagenary cycle">Chinese sexagenary cycle</a></li> <li><a href="/wiki/Geologic_Calendar" title="Geologic Calendar">Geologic Calendar</a></li> <li><a href="/wiki/Iranian_calendars" title="Iranian calendars">Iranian</a></li> <li><a href="/wiki/ISO_week_date" title="ISO week date">ISO week date</a></li> <li><a href="/wiki/Mesoamerican_calendars" title="Mesoamerican calendars">Mesoamerican</a> <ul><li><a href="/wiki/Maya_calendar" title="Maya calendar">Maya</a></li> <li><a href="/wiki/Aztec_calendar" title="Aztec calendar">Aztec</a></li></ul></li> <li><a href="/wiki/Winter_count" title="Winter count">Winter count</a></li> <li><a href="/wiki/New_Earth_Time" title="New Earth Time">New Earth Time</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;background:#cc9;"><a href="/wiki/Astronomical_chronology" title="Astronomical chronology">Astronomic time</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0;background:#fff;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cosmic_Calendar" title="Cosmic Calendar">Cosmic Calendar</a></li> <li><a href="/wiki/Ephemeris" title="Ephemeris">Ephemeris</a></li> <li><a href="/wiki/Galactic_year" title="Galactic year">Galactic year</a></li> <li><a class="mw-selflink selflink">Metonic cycle</a></li> <li><a href="/wiki/Milankovitch_cycles" title="Milankovitch cycles">Milankovitch cycles</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;background:#cc9;"><a href="/wiki/Geologic_time_scale" title="Geologic time scale">Geologic time</a></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:8.0em;font-weight:normal;background:#cc9;">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Deep_time" title="Deep time">Deep time</a></li> <li><a href="/wiki/Geological_history_of_Earth" title="Geological history of Earth">Geological history of Earth</a></li> <li><a href="/wiki/Geologic_time_scale#Terminology" title="Geologic time scale">Geological time units</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:8.0em;font-weight:normal;background:#cc9;">Standards</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Global_Standard_Stratigraphic_Age" title="Global Standard Stratigraphic Age">Global Standard Stratigraphic Age (GSSA)</a></li> <li><a href="/wiki/Global_Boundary_Stratotype_Section_and_Point" title="Global Boundary Stratotype Section and Point">Global Boundary Stratotype Section and Point (GSSP)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:8.0em;font-weight:normal;background:#cc9;">Methods</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chronostratigraphy" title="Chronostratigraphy">Chronostratigraphy</a></li> <li><a href="/wiki/Geochronology" title="Geochronology">Geochronology</a></li> <li><a href="/wiki/Isotope_geochemistry" title="Isotope geochemistry">Isotope geochemistry</a></li> <li><a href="/wiki/Law_of_superposition" title="Law of superposition">Law of superposition</a></li> <li><a href="/wiki/Luminescence_dating" title="Luminescence dating">Luminescence dating</a></li> <li><a href="/wiki/Samarium%E2%80%93neodymium_dating" title="Samarium–neodymium dating">Samarium–neodymium dating</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;background:#cc9;"><a href="/wiki/Chronological_dating" title="Chronological dating">Chronological<br />dating</a></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:8.0em;font-weight:normal;background:#cc9;"><a href="/wiki/Absolute_dating" title="Absolute dating">Absolute dating</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amino_acid_dating" title="Amino acid dating">Amino acid racemisation</a></li> <li><a href="/wiki/Archaeomagnetic_dating" title="Archaeomagnetic dating">Archaeomagnetic dating</a></li> <li><a href="/wiki/Dendrochronology" title="Dendrochronology">Dendrochronology</a></li> <li><a href="/wiki/Ice_core" title="Ice core">Ice core</a></li> <li><a href="/wiki/Incremental_dating" title="Incremental dating">Incremental dating</a></li> <li><a href="/wiki/Lichenometry" title="Lichenometry">Lichenometry</a></li> <li><a href="/wiki/Paleomagnetism" title="Paleomagnetism">Paleomagnetism</a></li> <li><a href="/wiki/Radiometric_dating" title="Radiometric dating">Radiometric dating</a> <ul><li><a href="/wiki/Lead%E2%80%93lead_dating" title="Lead–lead dating">Lead–lead</a></li> <li><a href="/wiki/K%E2%80%93Ar_dating" title="K–Ar dating">Potassium–argon</a></li> <li><a href="/wiki/Radiocarbon_dating" title="Radiocarbon dating">Radiocarbon</a></li> <li><a href="/wiki/Uranium%E2%80%93lead_dating" title="Uranium–lead dating">Uranium–lead</a></li></ul></li> <li><a href="/wiki/Tephrochronology" title="Tephrochronology">Tephrochronology</a></li> <li><a href="/wiki/Luminescence_dating" title="Luminescence dating">Luminescence dating</a></li> <li><a href="/wiki/Thermoluminescence_dating" title="Thermoluminescence dating">Thermoluminescence dating</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:8.0em;font-weight:normal;background:#cc9;"><a href="/wiki/Relative_dating" title="Relative dating">Relative dating</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Fluorine_absorption_dating" title="Fluorine absorption dating">Fluorine absorption</a></li> <li><a href="/wiki/Nitrogen_dating" title="Nitrogen dating">Nitrogen dating</a></li> <li><a href="/wiki/Obsidian_hydration_dating" title="Obsidian hydration dating">Obsidian hydration</a></li> <li><a href="/wiki/Seriation_(archaeology)" title="Seriation (archaeology)">Seriation</a></li> <li><a href="/wiki/Stratigraphy_(archaeology)" title="Stratigraphy (archaeology)">Stratigraphy</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;background:#cc9;">Genetic methods</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/Molecular_clock" title="Molecular clock">Molecular clock</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;background:#cc9;">Linguistic methods</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/Glottochronology" title="Glottochronology">Glottochronology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;background:#cc9;">Related topics</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/Chronicle" title="Chronicle">Chronicle</a></li> <li><a href="/wiki/New_Chronology_(Fomenko)" class="mw-redirect" title="New Chronology (Fomenko)">New Chronology</a></li> <li><a href="/wiki/Synchronoptic_view" title="Synchronoptic view">Synchronoptic view</a></li> <li><a href="/wiki/Timeline" title="Timeline">Timeline</a></li> <li><a href="/wiki/Year_zero" title="Year zero">Year zero</a></li> <li><a href="/wiki/Floruit" title="Floruit">Floruit</a></li> <li><a href="/wiki/Terminus_post_quem" title="Terminus post quem">Terminus post quem</a></li> <li><a href="/wiki/ASPRO_chronology" title="ASPRO chronology">ASPRO chronology</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" 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Cyrrhus">Andronicus</a></li> <li><a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius</a></li> <li><a href="/wiki/Aratus" title="Aratus">Aratus</a></li> <li><a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus</a></li> <li><a href="/wiki/Aristyllus" title="Aristyllus">Aristyllus</a></li> <li><a href="/wiki/Attalus_of_Rhodes" title="Attalus of Rhodes">Attalus</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/Callippus" title="Callippus">Callippus</a></li> <li><a href="/wiki/Cleomedes" title="Cleomedes">Cleomedes</a></li> <li><a href="/wiki/Cleostratus" title="Cleostratus">Cleostratus</a></li> <li><a href="/wiki/Conon_of_Samos" title="Conon of Samos">Conon</a></li> <li><a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a></li> <li><a href="/wiki/Euctemon" title="Euctemon">Euctemon</a></li> <li><a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus</a></li> <li><a href="/wiki/Geminus" title="Geminus">Geminus</a></li> <li><a href="/wiki/Heraclides_Ponticus" title="Heraclides Ponticus">Heraclides</a></li> <li><a href="/wiki/Hicetas" title="Hicetas">Hicetas</a></li> <li><a href="/wiki/Hipparchus" title="Hipparchus">Hipparchus</a></li> <li><a href="/wiki/Hippocrates_of_Chios" title="Hippocrates of Chios">Hippocrates of Chios</a></li> <li><a href="/wiki/Hypsicles" title="Hypsicles">Hypsicles</a></li> <li><a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria">Menelaus</a></li> <li><a href="/wiki/Meton_of_Athens" title="Meton of Athens">Meton</a></li> <li><a href="/wiki/Oenopides" title="Oenopides">Oenopides</a></li> <li><a href="/wiki/Philip_of_Opus" title="Philip of Opus">Philip of Opus</a></li> <li><a href="/wiki/Philolaus" title="Philolaus">Philolaus</a></li> <li><a href="/wiki/Posidonius" title="Posidonius">Posidonius</a></li> <li><a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a></li> <li><a href="/wiki/Pytheas" title="Pytheas">Pytheas</a></li> <li><a href="/wiki/Seleucus_of_Seleucia" title="Seleucus of Seleucia">Seleucus</a></li> <li><a href="/wiki/Sosigenes_of_Alexandria" class="mw-redirect" title="Sosigenes of Alexandria">Sosigenes of Alexandria</a></li> <li><a href="/wiki/Sosigenes_the_Peripatetic" title="Sosigenes the Peripatetic">Sosigenes the Peripatetic</a></li> <li><a href="/wiki/Strabo" title="Strabo">Strabo</a></li> <li><a href="/wiki/Thales_of_Miletus" title="Thales of Miletus">Thales</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/Timocharis" title="Timocharis">Timocharis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Works</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Almagest" title="Almagest"><i>Almagest</i> <span style="font-size: 85%;">(Ptolemy)</span></a></li> <li><a href="/wiki/Catasterismi" title="Catasterismi"><i>Catasterismi</i> <span style="font-size: 85%;">(Eratosthenes)</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/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_the_Heavens" title="On the Heavens"><i>On the Heavens</i> <span style="font-size: 85%;">(Aristotle)</span></a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Instruments</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/Antikythera_mechanism" title="Antikythera mechanism">Antikythera mechanism</a></li> <li><a href="/wiki/Armillary_sphere" title="Armillary sphere">Armillary sphere</a></li> <li><a href="/wiki/Astrolabe" title="Astrolabe">Astrolabe</a></li> <li><a href="/wiki/Dioptra" title="Dioptra">Dioptra</a></li> <li><a href="/wiki/Equatorial_ring" title="Equatorial ring">Equatorial ring</a></li> <li><a href="/wiki/Gnomon" title="Gnomon">Gnomon</a></li> <li><a href="/wiki/Mural_instrument" title="Mural instrument">Mural instrument</a></li> <li><a href="/wiki/Triquetrum_(astronomy)" title="Triquetrum (astronomy)">Triquetrum</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</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/Callippic_cycle" title="Callippic cycle">Callippic cycle</a></li> <li><a href="/wiki/Celestial_spheres" title="Celestial spheres">Celestial spheres</a></li> <li><a href="/wiki/Circle_of_latitude" title="Circle of latitude">Circle of latitude</a></li> <li><a href="/wiki/Counter-Earth" title="Counter-Earth">Counter-Earth</a></li> <li><a href="/wiki/Deferent_and_epicycle" title="Deferent and epicycle">Deferent and epicycle</a></li> <li><a href="/wiki/Equant" title="Equant">Equant</a></li> <li><a href="/wiki/Geocentric_model" title="Geocentric model">Geocentrism</a></li> <li><a href="/wiki/Heliocentrism" title="Heliocentrism">Heliocentrism</a></li> <li><a href="/wiki/Hipparchic_cycle" title="Hipparchic cycle">Hipparchic cycle</a></li> <li><a href="/wiki/Inferior_and_superior_planets" title="Inferior and superior planets">Inferior and superior planets</a></li> <li><a class="mw-selflink selflink">Metonic cycle</a></li> <li><a href="/wiki/Octaeteris" title="Octaeteris">Octaeteris</a></li> <li><a href="/wiki/Solstice" title="Solstice">Solstice</a></li> <li><a href="/wiki/Spherical_Earth" title="Spherical Earth">Spherical Earth</a></li> <li><a href="/wiki/Sublunary_sphere" title="Sublunary sphere">Sublunary sphere</a></li> <li><a href="/wiki/Zodiac" title="Zodiac">Zodiac</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Influences</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/Babylonian_astronomy" title="Babylonian astronomy">Babylonian astronomy</a></li> <li><a href="/wiki/Egyptian_astronomy" title="Egyptian astronomy">Egyptian astronomy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Influenced</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div 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