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class="vector-toc-numb">2</span> <span>Babylonian sources</span> </div> </a> <ul id="toc-Babylonian_sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometry,_trigonometry_and_other_mathematical_techniques" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geometry,_trigonometry_and_other_mathematical_techniques"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Geometry, trigonometry and other mathematical techniques</span> </div> </a> <ul id="toc-Geometry,_trigonometry_and_other_mathematical_techniques-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lunar_and_solar_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lunar_and_solar_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Lunar and solar theory</span> </div> </a> <button aria-controls="toc-Lunar_and_solar_theory-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 Lunar and solar theory subsection</span> </button> <ul id="toc-Lunar_and_solar_theory-sublist" class="vector-toc-list"> <li id="toc-Motion_of_the_Moon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Motion_of_the_Moon"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Motion of the Moon</span> </div> </a> <ul id="toc-Motion_of_the_Moon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Orbit_of_the_Moon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Orbit_of_the_Moon"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Orbit of the Moon</span> </div> </a> <ul id="toc-Orbit_of_the_Moon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Apparent_motion_of_the_Sun" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Apparent_motion_of_the_Sun"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Apparent motion of the Sun</span> </div> </a> <ul id="toc-Apparent_motion_of_the_Sun-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Orbit_of_the_Sun" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Orbit_of_the_Sun"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Orbit of the Sun</span> </div> </a> <ul id="toc-Orbit_of_the_Sun-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Distance,_parallax,_size_of_the_Moon_and_the_Sun" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Distance,_parallax,_size_of_the_Moon_and_the_Sun"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Distance, parallax, size of the Moon and the Sun</span> </div> </a> <ul id="toc-Distance,_parallax,_size_of_the_Moon_and_the_Sun-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eclipses" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Eclipses"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Eclipses</span> </div> </a> <ul id="toc-Eclipses-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Astronomical_instruments_and_astrometry" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Astronomical_instruments_and_astrometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Astronomical instruments and astrometry</span> </div> </a> <ul id="toc-Astronomical_instruments_and_astrometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Star_catalog" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Star_catalog"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Star catalog</span> </div> </a> <button aria-controls="toc-Star_catalog-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 Star catalog subsection</span> </button> <ul id="toc-Star_catalog-sublist" class="vector-toc-list"> <li id="toc-Stellar_magnitude" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stellar_magnitude"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Stellar magnitude</span> </div> </a> <ul id="toc-Stellar_magnitude-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Coordinate_System" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Coordinate_System"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Coordinate System</span> </div> </a> <ul id="toc-Coordinate_System-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Celestial_globe" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Celestial_globe"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Celestial globe</span> </div> </a> <ul id="toc-Celestial_globe-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Arguments_for_and_against_Hipparchus's_star_catalog_in_the_Almagest" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Arguments_for_and_against_Hipparchus's_star_catalog_in_the_Almagest"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Arguments for and against Hipparchus's star catalog in the Almagest</span> </div> </a> <ul id="toc-Arguments_for_and_against_Hipparchus's_star_catalog_in_the_Almagest-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Precession_of_the_equinoxes_(146–127_BC)" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Precession_of_the_equinoxes_(146–127_BC)"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Precession of the equinoxes (146–127 BC)</span> </div> </a> <ul id="toc-Precession_of_the_equinoxes_(146–127_BC)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geography"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Geography</span> </div> </a> <ul id="toc-Geography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modern_speculation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Modern_speculation"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Modern speculation</span> </div> </a> <ul id="toc-Modern_speculation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legacy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legacy"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Legacy</span> </div> </a> <ul id="toc-Legacy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Translations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Translations"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Translations</span> </div> </a> <ul id="toc-Translations-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">12</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">13</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 class="vector-toc-numb">14</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Works_cited" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Works_cited"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>Works cited</span> </div> </a> <ul id="toc-Works_cited-sublist" class="vector-toc-list"> </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">16</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">17</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" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Hipparchus</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 75 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-75" 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">75 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Hipparchos" title="Hipparchos – Afrikaans" lang="af" hreflang="af" data-title="Hipparchos" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A3%D8%A8%D8%B1%D8%AE%D8%B4" title="أبرخش – Arabic" lang="ar" hreflang="ar" data-title="أبرخش" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Hiparco_de_Nicea" title="Hiparco de Nicea – Asturian" lang="ast" hreflang="ast" data-title="Hiparco de Nicea" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Hipparx" title="Hipparx – Azerbaijani" lang="az" hreflang="az" data-title="Hipparx" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B9%E0%A6%BF%E0%A6%AA%E0%A6%BE%E0%A6%B0%E0%A6%95%E0%A6%BE%E0%A6%B8" title="হিপারকাস – Bangla" lang="bn" hreflang="bn" data-title="হিপারকাস" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D1%96%D0%BF%D0%B0%D1%80%D1%85" title="Гіпарх – Belarusian" lang="be" hreflang="be" data-title="Гіпарх" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%93%D1%96%D0%BF%D0%B0%D1%80%D1%85" title="Гіпарх – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Гіпарх" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BF%D0%B0%D1%80%D1%85" title="Хипарх – Bulgarian" lang="bg" hreflang="bg" data-title="Хипарх" 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/Hiparc_de_Nicea" title="Hiparc de Nicea – Catalan" lang="ca" hreflang="ca" data-title="Hiparc de Nicea" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hipparchos" title="Hipparchos – Czech" lang="cs" hreflang="cs" data-title="Hipparchos" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hipparchos" title="Hipparchos – Danish" lang="da" hreflang="da" data-title="Hipparchos" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hipparchos_(Astronom)" title="Hipparchos (Astronom) – German" lang="de" hreflang="de" data-title="Hipparchos (Astronom)" 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%8A%CF%80%CF%80%CE%B1%CF%81%CF%87%CE%BF%CF%82_%CE%BF_%CE%A1%CF%8C%CE%B4%CE%B9%CE%BF%CF%82" title="Ίππαρχος ο Ρόδιος – Greek" lang="el" hreflang="el" data-title="Ίππαρχος ο Ρόδιος" 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/Hiparco_de_Nicea" title="Hiparco de Nicea – Spanish" lang="es" hreflang="es" data-title="Hiparco de Nicea" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Hiparko" title="Hiparko – Esperanto" lang="eo" hreflang="eo" data-title="Hiparko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Hiparko_Nizeakoa" title="Hiparko Nizeakoa – Basque" lang="eu" hreflang="eu" data-title="Hiparko Nizeakoa" 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%A7%D8%A8%D8%B1%D8%AE%D8%B3" title="ابرخس – Persian" lang="fa" hreflang="fa" data-title="ابرخس" 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/Hipparque_(astronome)" title="Hipparque (astronome) – French" lang="fr" hreflang="fr" data-title="Hipparque (astronome)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Hioparcas" title="Hioparcas – Irish" lang="ga" hreflang="ga" data-title="Hioparcas" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Hiparco" title="Hiparco – Galician" lang="gl" hreflang="gl" data-title="Hiparco" 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/%ED%9E%88%ED%8C%8C%EB%A5%B4%EC%BD%94%EC%8A%A4" title="히파르코스 – Korean" lang="ko" hreflang="ko" data-title="히파르코스" 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%80%D5%AB%D5%BA%D5%A1%D6%80%D6%84%D5%B8%D5%BD" title="Հիպարքոս – Armenian" lang="hy" hreflang="hy" data-title="Հիպարքոս" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B9%E0%A4%BF%E0%A4%AA%E0%A5%8D%E0%A4%AA%E0%A4%BE%E0%A4%B0%E0%A4%95%E0%A4%B8" title="हिप्पारकस – Hindi" lang="hi" hreflang="hi" data-title="हिप्पारकस" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://hr.wikipedia.org/wiki/Hiparh" title="Hiparh – Croatian" lang="hr" hreflang="hr" data-title="Hiparh" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hipparkhos" title="Hipparkhos – Indonesian" lang="id" hreflang="id" data-title="Hipparkhos" 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-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Hipparcho" title="Hipparcho – Interlingua" lang="ia" hreflang="ia" data-title="Hipparcho" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ipparco_di_Nicea" title="Ipparco di Nicea – Italian" lang="it" hreflang="it" data-title="Ipparco di Nicea" 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%94%D7%99%D7%A4%D7%A8%D7%9B%D7%95%D7%A1" title="היפרכוס – Hebrew" lang="he" hreflang="he" data-title="היפרכוס" 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%B0%E1%83%98%E1%83%9E%E1%83%90%E1%83%A0%E1%83%A5%E1%83%94" title="ჰიპარქე – Georgian" lang="ka" hreflang="ka" data-title="ჰიპარქე" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%93%D0%B8%D0%BF%D0%BF%D0%B0%D1%80%D1%85" title="Гиппарх – Kazakh" lang="kk" hreflang="kk" data-title="Гиппарх" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Hipparchos_wa_Nikaia" title="Hipparchos wa Nikaia – Swahili" lang="sw" hreflang="sw" data-title="Hipparchos wa Nikaia" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/H%C3%AEparxos" title="Hîparxos – Kurdish" lang="ku" hreflang="ku" data-title="Hîparxos" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B8%D0%BF%D0%BF%D0%B0%D1%80%D1%85" title="Гиппарх – Kyrgyz" lang="ky" hreflang="ky" data-title="Гиппарх" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Hipparchus" title="Hipparchus – Latin" lang="la" hreflang="la" data-title="Hipparchus" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Hiparhs" title="Hiparhs – Latvian" lang="lv" hreflang="lv" data-title="Hiparhs" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Hipparchos_vun_Nic%C3%A4a" title="Hipparchos vun Nicäa – Luxembourgish" lang="lb" hreflang="lb" data-title="Hipparchos vun Nicäa" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Hiparchas_(astronomas)" title="Hiparchas (astronomas) – Lithuanian" lang="lt" hreflang="lt" data-title="Hiparchas (astronomas)" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Hiparco" title="Hiparco – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Hiparco" 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/Hipparkhosz_(csillag%C3%A1sz)" title="Hipparkhosz (csillagász) – Hungarian" lang="hu" hreflang="hu" data-title="Hipparkhosz (csillagász)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BF%D0%B0%D1%80%D1%85" title="Хипарх – Macedonian" lang="mk" hreflang="mk" data-title="Хипарх" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Hipparque" title="Hipparque – Malagasy" lang="mg" hreflang="mg" data-title="Hipparque" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B9%E0%B4%BF%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B4%BE%E0%B5%BC%E0%B4%95%E0%B5%8D%E0%B4%95%E0%B4%B8%E0%B5%8D" title="ഹിപ്പാർക്കസ് – Malayalam" lang="ml" hreflang="ml" data-title="ഹിപ്പാർക്കസ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%B0%E1%83%98%E1%83%9E%E1%83%90%E1%83%A0%E1%83%A5%E1%83%94" title="ჰიპარქე – Mingrelian" lang="xmf" hreflang="xmf" data-title="ჰიპარქე" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%87%D9%8A%D8%A8%D8%A7%D8%B1%D8%AE%D9%88%D8%B3" title="هيبارخوس – Egyptian Arabic" lang="arz" hreflang="arz" data-title="هيبارخوس" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hipparchus_(astronoom)" title="Hipparchus (astronoom) – Dutch" lang="nl" hreflang="nl" data-title="Hipparchus (astronoom)" 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%92%E3%83%83%E3%83%91%E3%83%AB%E3%82%B3%E3%82%B9" title="ヒッパルコス – Japanese" lang="ja" hreflang="ja" data-title="ヒッパルコス" 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/Hipparkhos_(astronom)" title="Hipparkhos (astronom) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Hipparkhos (astronom)" 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/Hipparkhos" title="Hipparkhos – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Hipparkhos" 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-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Gipparx" title="Gipparx – Uzbek" lang="uz" hreflang="uz" data-title="Gipparx" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DB%81%D9%BE%D8%A7%D8%B1%D8%AE%D8%B3" title="ہپارخس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ہپارخس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%87%DB%90%D9%BE%D8%A7%D8%B1%D8%AE%D9%88%D8%B3" title="هېپارخوس – Pashto" lang="ps" hreflang="ps" data-title="هېپارخوس" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Hipparchos_z_Nikei" title="Hipparchos z Nikei – Polish" lang="pl" hreflang="pl" data-title="Hipparchos z Nikei" 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/Hiparco" title="Hiparco – Portuguese" lang="pt" hreflang="pt" data-title="Hiparco" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Hiparh" title="Hiparh – Romanian" lang="ro" hreflang="ro" data-title="Hiparh" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D0%B8%D0%BF%D0%BF%D0%B0%D1%80%D1%85" title="Гиппарх – Russian" lang="ru" hreflang="ru" data-title="Гиппарх" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-skr mw-list-item"><a href="https://skr.wikipedia.org/wiki/%D8%A7%D8%A8%D8%B1%D8%AE%D8%B3" title="ابرخس – Saraiki" lang="skr" hreflang="skr" data-title="ابرخس" data-language-autonym="سرائیکی" data-language-local-name="Saraiki" class="interlanguage-link-target"><span>سرائیکی</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Ipparcu" title="Ipparcu – Sicilian" lang="scn" hreflang="scn" data-title="Ipparcu" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Hipparchus" title="Hipparchus – Simple English" lang="en-simple" hreflang="en-simple" data-title="Hipparchus" 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/Hipparchos_z_Nikaie" title="Hipparchos z Nikaie – Slovak" lang="sk" hreflang="sk" data-title="Hipparchos z Nikaie" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://sl.wikipedia.org/wiki/Hiparh" title="Hiparh – Slovenian" lang="sl" hreflang="sl" data-title="Hiparh" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BF%D0%B0%D1%80%D1%85_%D1%81%D0%B0_%D0%A0%D0%BE%D0%B4%D0%BE%D1%81%D0%B0" title="Хипарх са Родоса – Serbian" lang="sr" hreflang="sr" data-title="Хипарх са Родоса" 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/Hiparh" title="Hiparh – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Hiparh" 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/Hipparkhos_Nikaialainen" title="Hipparkhos Nikaialainen – Finnish" lang="fi" hreflang="fi" data-title="Hipparkhos Nikaialainen" 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/Hipparchos" title="Hipparchos – Swedish" lang="sv" hreflang="sv" data-title="Hipparchos" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Hiparco" title="Hiparco – Tagalog" lang="tl" hreflang="tl" data-title="Hiparco" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B9%E0%AE%BF%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B8%E0%AF%8D" title="ஹிப்பார்க்கஸ் – Tamil" lang="ta" hreflang="ta" data-title="ஹிப்பார்க்கஸ்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AE%E0%B8%B4%E0%B8%9B%E0%B8%9B%E0%B8%B2%E0%B8%A3%E0%B9%8C%E0%B9%82%E0%B8%84%E0%B8%AA" title="ฮิปปาร์โคส – Thai" lang="th" hreflang="th" data-title="ฮิปปาร์โคส" 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/Hipparkos" title="Hipparkos – Turkish" lang="tr" hreflang="tr" data-title="Hipparkos" 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%93%D1%96%D0%BF%D0%BF%D0%B0%D1%80%D1%85" title="Гіппарх – Ukrainian" lang="uk" hreflang="uk" data-title="Гіппарх" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%A8%D8%B1%D8%AE%D8%B3" title="ابرخس – Urdu" lang="ur" hreflang="ur" data-title="ابرخس" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Hipparchus_(nh%C3%A0_thi%C3%AAn_v%C4%83n_h%E1%BB%8Dc)" title="Hipparchus (nhà thiên văn học) – Vietnamese" lang="vi" hreflang="vi" data-title="Hipparchus (nhà thiên văn học)" 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-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Hiparco_han_Nicea" title="Hiparco han Nicea – Waray" lang="war" hreflang="war" data-title="Hiparco han Nicea" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%96%9C%E5%B8%95%E6%81%B0%E6%96%AF" title="喜帕恰斯 – Wu" lang="wuu" hreflang="wuu" data-title="喜帕恰斯" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%96%9C%E5%B8%95%E6%81%B0%E6%96%AF" title="喜帕恰斯 – Cantonese" lang="yue" hreflang="yue" data-title="喜帕恰斯" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BE%9D%E5%B7%B4%E8%B0%B7" title="依巴谷 – Chinese" lang="zh" hreflang="zh" data-title="依巴谷" 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/Q159905#sitelinks-wikipedia" 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<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">2nd-century BC Greek astronomer, geographer and mathematician</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the Greek astronomer. For other uses, see <a href="/wiki/Hipparchus_(disambiguation)" class="mw-disambig" title="Hipparchus (disambiguation)">Hipparchus (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Hipparchus</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Head_of_Hipparchus_(cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Head_of_Hipparchus_%28cropped%29.jpg/220px-Head_of_Hipparchus_%28cropped%29.jpg" decoding="async" width="220" height="274" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Head_of_Hipparchus_%28cropped%29.jpg/330px-Head_of_Hipparchus_%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c6/Head_of_Hipparchus_%28cropped%29.jpg 2x" data-file-width="434" data-file-height="540" /></a></span><div class="infobox-caption">19th century engraving based on an <a href="/wiki/Engraved_gem" title="Engraved gem">engraved</a> <a href="/wiki/Amethyst" title="Amethyst">amethyst</a> from the <a href="/wiki/Poniatowski_gem" class="mw-redirect" title="Poniatowski gem">Poniatowski gem</a> collection<sup id="cite_ref-head-of-hipparchus_1-0" class="reference"><a href="#cite_note-head-of-hipparchus-1"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup></div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span title="circa">c.</span><span style="white-space:nowrap;"> 190</span> BC<br /><div style="display:inline" class="birthplace"><a href="/wiki/Nicaea" title="Nicaea">Nicaea</a>, <a href="/wiki/Kingdom_of_Bithynia" title="Kingdom of Bithynia">Kingdom of Bithynia</a><br />(modern-day <a href="/wiki/%C4%B0znik,_Bursa" class="mw-redirect" title="İznik, Bursa">İznik, Bursa</a>, Turkey)</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data"><span title="circa">c.</span><span style="white-space:nowrap;"> 120</span> BC (around age 70)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Rhodes" title="Rhodes">Rhodes</a>, <a href="/wiki/Roman_Republic" title="Roman Republic">Roman Republic</a><br />(modern-day Greece)</div></td></tr><tr><th scope="row" class="infobox-label">Occupations</th><td class="infobox-data role"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"><ul><li><a href="/wiki/Astronomer" title="Astronomer">Astronomer</a></li><li><a href="/wiki/Mathematician" title="Mathematician">Mathematician</a></li><li><a href="/wiki/Geographer" title="Geographer">Geographer</a></li></ul></div></td></tr></tbody></table> <p><b>Hipparchus</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="'h' in 'hi'">h</span><span title="/ɪ/: 'i' in 'kit'">ɪ</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="'p' in 'pie'">p</span><span title="/ɑːr/: 'ar' in 'far'">ɑːr</span><span title="'k' in 'kind'">k</span><span title="/ə/: 'a' in 'about'">ə</span><span title="'s' in 'sigh'">s</span></span>/</a></span></span>; <a href="/wiki/Ancient_Greek" title="Ancient Greek">Greek</a>: <span lang="grc"><a href="https://en.wiktionary.org/wiki/%E1%BC%BD%CF%80%CF%80%CE%B1%CF%81%CF%87%CE%BF%CF%82" class="extiw" title="wikt:Ἵππαρχος">Ἵππαρχος</a></span>, <span title="Ancient Greek transliteration" lang="grc-Latn"><i>Hípparkhos</i></span>; <span title="circa">c.</span><span style="white-space:nowrap;"> 190</span> – c.<span style="white-space:nowrap;"> 120</span> BC) was a <a href="/wiki/Ancient_Greek_astronomy" title="Ancient Greek astronomy">Greek astronomer</a>, <a href="/wiki/Geographer" title="Geographer">geographer</a>, and <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>. He is considered the founder of <a href="/wiki/Trigonometry" title="Trigonometry">trigonometry</a>,<sup id="cite_ref-linton2004_2-0" class="reference"><a href="#cite_note-linton2004-2"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> but is most famous for his incidental discovery of the <a href="/wiki/Precession_of_the_equinoxes" class="mw-redirect" title="Precession of the equinoxes">precession of the equinoxes</a>.<sup id="cite_ref-toomer1996_3-0" class="reference"><a href="#cite_note-toomer1996-3"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Hipparchus was born in <a href="/wiki/Nicaea" title="Nicaea">Nicaea</a>, <a href="/wiki/Bithynia" title="Bithynia">Bithynia</a>, and probably died on the island of <a href="/wiki/Rhodes" title="Rhodes">Rhodes</a>, Greece. He is known to have been a working astronomer between 162 and 127 BC.<sup id="cite_ref-mccluskey2000_4-0" class="reference"><a href="#cite_note-mccluskey2000-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of <a href="/wiki/Classical_antiquity" title="Classical antiquity">antiquity</a>.<sup id="cite_ref-willard1854_5-0" class="reference"><a href="#cite_note-willard1854-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> He was the first whose quantitative and accurate models for the motion of the <a href="/wiki/Sun" title="Sun">Sun</a> and <a href="/wiki/Moon" title="Moon">Moon</a> survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the <a href="/wiki/Babylonia" title="Babylonia">Babylonians</a> and by <a href="/wiki/Meton_of_Athens" title="Meton of Athens">Meton of Athens</a> (fifth century BC), <a href="/wiki/Timocharis" title="Timocharis">Timocharis</a>, <a href="/wiki/Aristyllus" title="Aristyllus">Aristyllus</a>, <a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus of Samos</a>, and <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a>, among others.<sup id="cite_ref-jones2017_7-0" class="reference"><a href="#cite_note-jones2017-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>He developed trigonometry and constructed <a href="/wiki/Trigonometric_tables" title="Trigonometric tables">trigonometric tables</a>, and he solved several problems of <a href="/wiki/Spherical_trigonometry" title="Spherical trigonometry">spherical trigonometry</a>. With his solar and <a href="/wiki/Lunar_theory" title="Lunar theory">lunar</a> theories and his trigonometry, he may have been the first to develop a reliable method to predict <a href="/wiki/Solar_eclipse" title="Solar eclipse">solar eclipses</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2024)">citation needed</span></a></i>]</sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Accuracy_dispute#Disputed_statement" title="Wikipedia:Accuracy dispute"><span title="The material near this tag is possibly inaccurate or nonfactual. (September 2024)">dubious</span></a> – <a href="/wiki/Talk:Hipparchus#Dubious" title="Talk:Hipparchus">discuss</a></i>]</sup> </p><p>His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first known comprehensive <a href="/wiki/Star_catalog" class="mw-redirect" title="Star catalog">star catalog</a> from the western world, and possibly the invention of the <a href="/wiki/Astrolabe" title="Astrolabe">astrolabe</a>, as well as of the <a href="/wiki/Armillary_sphere" title="Armillary sphere">armillary sphere</a> that he may have used in creating the star catalogue. Hipparchus is sometimes called the "father of astronomy",<sup id="cite_ref-newcomb1878_8-0" class="reference"><a href="#cite_note-newcomb1878-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-glashan1895_9-0" class="reference"><a href="#cite_note-glashan1895-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> a title conferred on him by <a href="/wiki/Jean_Baptiste_Joseph_Delambre" title="Jean Baptiste Joseph Delambre">Jean Baptiste Joseph Delambre</a> in 1817.<sup id="cite_ref-delambre1817_10-0" class="reference"><a href="#cite_note-delambre1817-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Life_and_work">Life and work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=1" title="Edit section: Life and work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hipparchus was born in Nicaea (<style data-mw-deduplicate="TemplateStyles:r1248666159">.mw-parser-output .tfd-dated{font-size:85%}.mw-parser-output .tfd-default{border-bottom:1px solid var(--border-color-base,#a2a9b1);clear:both;text-align:center}.mw-parser-output .tfd-tiny{font-weight:bold}.mw-parser-output .tfd-inline{border:1px solid var(--border-color-base,#a2a9b1)}.mw-parser-output .tfd-sidebar{border-bottom:1px solid var(--border-color-base,#a2a9b1);text-align:center;position:relative}@media(min-width:640px){.mw-parser-output .tfd-sidebar{clear:right;float:right;width:22em}}</style><span class="tfd tfd-dated tfd-tiny"><a href="/wiki/Wikipedia:Templates_for_discussion/Log/2024_November_12#Template:Lang-grc-gre" title="Wikipedia:Templates for discussion/Log/2024 November 12">‹See Tfd›</a></span><a href="/wiki/Greek_language" title="Greek language">Greek</a>: <span title="Ancient Greek (to 1453)-language text"><span lang="grc">Νίκαια</span></span>), in <a href="/wiki/Bithynia" title="Bithynia">Bithynia</a>. The exact dates of his life are not known, but <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a> attributes astronomical observations to him in the period from 147 to 127 BC, and some of these are stated as made in <a href="/wiki/Rhodes" title="Rhodes">Rhodes</a>; earlier observations since 162 BC might also have been made by him. His birth date (<span title="circa">c.</span><span style="white-space:nowrap;"> 190</span> BC) was calculated by <a href="/wiki/Jean_Baptiste_Joseph_Delambre" title="Jean Baptiste Joseph Delambre">Delambre</a> based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his observations from that year. Hipparchus obtained information from <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a> as well as <a href="/wiki/Babylon" title="Babylon">Babylon</a>, but it is not known when or if he visited these places. He is believed to have died on the island of Rhodes, where he seems to have spent most of his later life. </p><p>In the second and third centuries, <a href="/wiki/Coin" title="Coin">coins</a> were made in his honour in Bithynia that bear his name and show him with a <a href="/wiki/Globe" title="Globe">globe</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Relatively little of Hipparchus's direct work survives into modern times. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by <a href="/wiki/Aratus" title="Aratus">Aratus</a> was preserved by later copyists. Most of what is known about Hipparchus comes from <a href="/wiki/Strabo" title="Strabo">Strabo</a>'s <i><a href="/wiki/Geographica" title="Geographica">Geography</a></i> and <a href="/wiki/Pliny_the_Elder" title="Pliny the Elder">Pliny</a>'s <i><a href="/wiki/Natural_History_(Pliny)" title="Natural History (Pliny)">Natural History</a></i> in the first century; Ptolemy's second-century <i><a href="/wiki/Almagest" title="Almagest">Almagest</a></i>; and additional references to him in the fourth century by <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus</a> and <a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a> in their commentaries on the <i>Almagest</i>.<sup id="cite_ref-FOOTNOTEToomer1978_12-0" class="reference"><a href="#cite_note-FOOTNOTEToomer1978-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEJones2001_13-0" class="reference"><a href="#cite_note-FOOTNOTEJones2001-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Hipparchus's only preserved work is <i>Commentary on the Phaenomena of Eudoxus and Aratus</i> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1248666159"><span class="tfd tfd-dated tfd-tiny"><a href="/wiki/Wikipedia:Templates_for_discussion/Log/2024_November_12#Template:Lang-grc-gre" title="Wikipedia:Templates for discussion/Log/2024 November 12">‹See Tfd›</a></span><a href="/wiki/Greek_language" title="Greek language">Greek</a>: <span title="Ancient Greek (to 1453)-language text"><span lang="grc">Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις</span></span>). This is a highly critical commentary in the form of two books on a popular <a href="/wiki/Poem" class="mw-redirect" title="Poem">poem</a> by <a href="/wiki/Aratus" title="Aratus">Aratus</a> based on the work by <a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Hipparchus also made a list of his major works that apparently mentioned about fourteen books, but which is only known from references by later authors. His famous star catalog was incorporated into the one by Ptolemy and may be almost perfectly reconstructed by subtraction of two and two-thirds degrees from the longitudes of Ptolemy's stars <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2024)">citation needed</span></a></i>]</sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Accuracy_dispute#Disputed_statement" title="Wikipedia:Accuracy dispute"><span title="The material near this tag is possibly inaccurate or nonfactual. (September 2024)">dubious</span></a> – <a href="/wiki/Talk:Hipparchus#Dubious" title="Talk:Hipparchus">discuss</a></i>]</sup>. The first trigonometric table was apparently compiled by Hipparchus, who is consequently now known as "the father of trigonometry". </p> <div class="mw-heading mw-heading2"><h2 id="Babylonian_sources">Babylonian sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=2" title="Edit section: Babylonian sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Babylonian_astronomy" title="Babylonian astronomy">Babylonian astronomy</a></div> <p>Earlier Greek astronomers and mathematicians were influenced by Babylonian astronomy to some extent, for instance the period relations of the <a href="/wiki/Metonic_cycle" title="Metonic cycle">Metonic cycle</a> and <a href="/wiki/Saros_cycle" class="mw-redirect" title="Saros cycle">Saros cycle</a> may have come from Babylonian sources (see "<a href="/wiki/Babylonian_astronomical_diaries" title="Babylonian astronomical diaries">Babylonian astronomical diaries</a>"). Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically.<sup id="cite_ref-toomer1988_15-0" class="reference"><a href="#cite_note-toomer1988-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Eudoxus in the 4th century BC and <a href="/wiki/Timocharis" title="Timocharis">Timocharis</a> and <a href="/wiki/Aristillus" class="mw-redirect" title="Aristillus">Aristillus</a> in the 3rd century BC already divided the ecliptic in 360 parts (our <a href="/wiki/Degree_(angle)" title="Degree (angle)">degrees</a>, Greek: moira) of 60 <a href="/wiki/Arcminutes" class="mw-redirect" title="Arcminutes">arcminutes</a> and Hipparchus continued this tradition. It was only in Hipparchus's time (2nd century BC) when this division was introduced (probably by Hipparchus's contemporary Hypsikles) for all circles in mathematics. <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a> (3rd century BC), in contrast, used a simpler <a href="/wiki/Sexagesimal" title="Sexagesimal">sexagesimal</a> system dividing a circle into 60 parts. Hipparchus also adopted the Babylonian astronomical <i><a href="/wiki/Cubit" title="Cubit">cubit</a></i> unit (<a href="/wiki/Akkadian_language" title="Akkadian language">Akkadian</a> <i>ammatu</i>, Greek πῆχυς <i>pēchys</i>) that was equivalent to 2° or 2.5° ('large cubit').<sup id="cite_ref-bg1991_16-0" class="reference"><a href="#cite_note-bg1991-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>Hipparchus probably compiled a list of Babylonian astronomical observations; <a href="/wiki/Gerald_J._Toomer" title="Gerald J. Toomer">Gerald J. Toomer</a>, a historian of astronomy, has suggested that Ptolemy's knowledge of eclipse records and other Babylonian observations in the <i>Almagest</i> came from a list made by Hipparchus. Hipparchus's use of Babylonian sources has always been known in a general way, because of Ptolemy's statements, but the only text by Hipparchus that survives does not provide sufficient information to decide whether Hipparchus's knowledge (such as his usage of the units cubit and finger, degrees and minutes, or the concept of hour stars) was based on Babylonian practice.<sup id="cite_ref-hoffman-befunde_17-0" class="reference"><a href="#cite_note-hoffman-befunde-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> However, <a href="/wiki/Franz_Xaver_Kugler" title="Franz Xaver Kugler">Franz Xaver Kugler</a> demonstrated that the synodic and anomalistic periods that Ptolemy attributes to Hipparchus had already been used in Babylonian <a href="/wiki/Ephemerides" class="mw-redirect" title="Ephemerides">ephemerides</a>, specifically the collection of texts nowadays called "System B" (sometimes attributed to <a href="/wiki/Kidinnu" title="Kidinnu">Kidinnu</a>).<sup id="cite_ref-kugler1900_18-0" class="reference"><a href="#cite_note-kugler1900-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears (April 2023)">pages needed</span></a></i>]</sup> </p><p>Hipparchus's long <a href="/wiki/Orbital_period" title="Orbital period">draconitic</a> lunar period (5,458 months = 5,923 lunar nodal periods) also appears a few times in <a href="/wiki/Babylonian_astronomy" title="Babylonian astronomy">Babylonian records</a>.<sup id="cite_ref-aaboe1955_19-0" class="reference"><a href="#cite_note-aaboe1955-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> But the only such tablet explicitly dated, is post-Hipparchus so the direction of transmission is not settled by the tablets. </p> <div class="mw-heading mw-heading2"><h2 id="Geometry,_trigonometry_and_other_mathematical_techniques"><span id="Geometry.2C_trigonometry_and_other_mathematical_techniques"></span>Geometry, trigonometry and other mathematical techniques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=3" title="Edit section: Geometry, trigonometry and other mathematical techniques"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hipparchus was recognized as the first mathematician known to have possessed a <a href="/wiki/Trigonometric_table" class="mw-redirect" title="Trigonometric table">trigonometric table</a>, which he needed when computing the <a href="/wiki/Eccentricity_(orbit)" class="mw-redirect" title="Eccentricity (orbit)">eccentricity</a> of the <a href="/wiki/Orbit" title="Orbit">orbits</a> of the Moon and Sun. He tabulated values for the <a href="/wiki/Chord_(geometry)" title="Chord (geometry)">chord</a> function, which for a central angle in a circle gives the length of the straight line segment between the points where the angle intersects the circle. He may have computed this for a circle with a circumference of 21,600 units and a radius (rounded) of 3,438 units; this circle has a unit length for each arcminute along its perimeter. (This was “proven” by Toomer,<sup id="cite_ref-toomer1974-chordtable_20-0" class="reference"><a href="#cite_note-toomer1974-chordtable-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> but he later “cast doubt“ upon his earlier affirmation.<sup id="cite_ref-FOOTNOTEToomer1984215_21-0" class="reference"><a href="#cite_note-FOOTNOTEToomer1984215-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Other authors have argued that a circle of radius 3,600 units may instead have been used by Hipparchus.<sup id="cite_ref-klintberg2005_22-0" class="reference"><a href="#cite_note-klintberg2005-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>) He tabulated the chords for angles with increments of 7.5°. In modern terms, the chord subtended by a central angle in a circle of given radius <span class="texhtml mvar" style="font-style:italic;">R</span> equals <span class="texhtml mvar" style="font-style:italic;">R</span> times twice the <a href="/wiki/Sine" class="mw-redirect" title="Sine">sine</a> of half of the angle, i.e.: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {chord} \theta =2R\cdot \sin {\tfrac {1}{2}}\theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>chord</mi> <mo>⁡</mo> <mi>θ</mi> <mo>=</mo> <mn>2</mn> <mi>R</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {chord} \theta =2R\cdot \sin {\tfrac {1}{2}}\theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff343d70bb09dd8ab5e3cd298dee101f32141e20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:20.864ex; height:3.509ex;" alt="{\displaystyle \operatorname {chord} \theta =2R\cdot \sin {\tfrac {1}{2}}\theta }"></span></dd></dl> <p>The now-lost work in which Hipparchus is said to have developed his chord table, is called <i>Tōn en kuklōi eutheiōn</i> (<i>Of Lines Inside a Circle</i>) in <a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a>'s fourth-century commentary on section I.10 of the <i>Almagest</i>. Some claim the table of Hipparchus may have survived in astronomical treatises in India, such as the <i><a href="/wiki/Surya_Siddhanta" title="Surya Siddhanta">Surya Siddhanta</a></i>. Trigonometry was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques.<sup id="cite_ref-toomer1974-chordtable_20-1" class="reference"><a href="#cite_note-toomer1974-chordtable-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Hipparchus must have used a better approximation for <a href="/wiki/Pi" title="Pi"><span class="texhtml mvar" style="font-style:italic;">π</span></a> than the one given by <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> of between <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">3<span class="sr-only">+</span><span class="num">10</span>⁄<span class="den">71</span></span> (≈ 3.1408) and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">3<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">7</span></span> (≈ 3.1429). Perhaps he had the approximation later used by Ptolemy, <a href="/wiki/Sexagesimal" title="Sexagesimal">sexagesimal</a> 3;08,30 (≈ 3.1417) (<i>Almagest</i> VI.7). </p><p>Hipparchus could have constructed his chord table using the <a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a> and a theorem known to Archimedes. He also might have used the relationship between sides and diagonals of a <a href="/wiki/Cyclic_quadrilateral" title="Cyclic quadrilateral">cyclic quadrilateral</a>, today called <a href="/wiki/Ptolemy%27s_theorem" title="Ptolemy's theorem">Ptolemy's theorem</a> because its earliest extant source is a proof in the <i>Almagest</i> (I.10). </p><p>The <a href="/wiki/Stereographic_projection" title="Stereographic projection">stereographic projection</a> was ambiguously attributed to Hipparchus by <a href="/wiki/Synesius" title="Synesius">Synesius</a> (c. 400 AD), and on that basis Hipparchus is often credited with inventing it or at least knowing of it. However, some scholars believe this conclusion to be unjustified by available evidence.<sup id="cite_ref-synesius_23-0" class="reference"><a href="#cite_note-synesius-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> The oldest extant description of the stereographic projection is found in <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>'s <a href="/wiki/Planisphaerium" title="Planisphaerium"><i>Planisphere</i></a> (2nd century AD).<sup id="cite_ref-neugebauer1949_24-0" class="reference"><a href="#cite_note-neugebauer1949-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>Besides geometry, Hipparchus also used <a href="/wiki/Arithmetic" title="Arithmetic">arithmetic</a> techniques developed by the <a href="/wiki/Chaldea" title="Chaldea">Chaldeans</a>. He was one of the first Greek mathematicians to do this and, in this way, expanded the techniques available to astronomers and geographers. </p><p>There are several indications that Hipparchus knew spherical trigonometry, but the first surviving text discussing it is by <a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria">Menelaus of Alexandria</a> in the first century, who now, on that basis, commonly is credited with its discovery. (Previous to the finding of the proofs of Menelaus a century ago, Ptolemy was credited with the invention of spherical trigonometry.) Ptolemy later used spherical trigonometry to compute things such as the rising and setting points of the <a href="/wiki/Ecliptic" title="Ecliptic">ecliptic</a>, or to take account of the lunar <a href="/wiki/Parallax" title="Parallax">parallax</a>. If he did not use spherical trigonometry, Hipparchus may have used a globe for these tasks, reading values off coordinate grids drawn on it, or he may have made approximations from planar geometry, or perhaps used arithmetical approximations developed by the Chaldeans. </p> <div class="mw-heading mw-heading2"><h2 id="Lunar_and_solar_theory">Lunar and solar theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=4" title="Edit section: Lunar and solar theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:HipparchusConstruction.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/HipparchusConstruction.svg/400px-HipparchusConstruction.svg.png" decoding="async" width="400" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/HipparchusConstruction.svg/600px-HipparchusConstruction.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/HipparchusConstruction.svg/800px-HipparchusConstruction.svg.png 2x" data-file-width="777" data-file-height="194" /></a><figcaption>Geometric construction used by Hipparchus in his determination of the distances to the Sun and Moon</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Motion_of_the_Moon">Motion of the Moon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=5" title="Edit section: Motion of the Moon"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Lunar_theory" title="Lunar theory">Lunar theory</a> and <a href="/wiki/Orbit_of_the_Moon" title="Orbit of the Moon">Orbit of the Moon</a></div> <p>Hipparchus also studied the motion of the <a href="/wiki/Moon" title="Moon">Moon</a> and confirmed the accurate values for two periods of its motion that Chaldean astronomers are widely presumed to have possessed before him. The traditional value (from Babylonian System B) for the mean <a href="/wiki/Synodic_month" class="mw-redirect" title="Synodic month">synodic month</a> is 29 days; 31,50,8,20 (sexagesimal) = 29.5305941... days. Expressed as 29 days + 12 hours + <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.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="sfrac">⁠<span class="tion"><span class="num">793</span><span class="sr-only">/</span><span class="den">1080</span></span>⁠</span> hours this value has been used later in the <a href="/wiki/Hebrew_calendar" title="Hebrew calendar">Hebrew calendar</a>. The Chaldeans also knew that 251 <a href="/wiki/Synodic_month" class="mw-redirect" title="Synodic month">synodic months</a> ≈ 269 <a href="/wiki/Anomalistic_month" class="mw-redirect" title="Anomalistic month">anomalistic months</a>. Hipparchus used the multiple of this period by a factor of 17, because that interval is also an eclipse period, and is also close to an integer number of years (4,267 moons : 4,573 anomalistic periods : 4,630.53 nodal periods : 4,611.98 lunar orbits : 344.996 years : 344.982 solar orbits : 126,007.003 days : 126,351.985 rotations).<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> What was so exceptional and useful about the cycle was that all 345-year-interval eclipse pairs occur slightly more than 126,007 days apart within a tight range of only approximately ±<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> hour, guaranteeing (after division by 4,267) an estimate of the synodic month correct to one part in order of magnitude 10 million. </p><p>Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141 BC and 26 November 139 BC according to Toomer<sup id="cite_ref-toomer1980_26-0" class="reference"><a href="#cite_note-toomer1980-26"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup>) with eclipses from Babylonian records 345 years earlier (<i>Almagest</i> IV.2<sup id="cite_ref-FOOTNOTEJones2001_13-1" class="reference"><a href="#cite_note-FOOTNOTEJones2001-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>). </p><p>Later <a href="/wiki/Al-Biruni" title="Al-Biruni">al-Biruni</a> (<i>Qanun</i> VII.2.II) and <a href="/wiki/Nicolaus_Copernicus" title="Nicolaus Copernicus">Copernicus</a> (<i>de revolutionibus</i> IV.4) noted that the period of 4,267 moons is approximately five minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the timing methods of the Babylonians had an error of no fewer than eight minutes.<sup id="cite_ref-sf1993_27-0" class="reference"><a href="#cite_note-sf1993-27"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ssm1997_28-0" class="reference"><a href="#cite_note-ssm1997-28"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than to try to derive an improved value from his own observations. From modern ephemerides<sup id="cite_ref-ccf2002_29-0" class="reference"><a href="#cite_note-ccf2002-29"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> and taking account of the change in the length of the day (see <a href="/wiki/%CE%94T_(timekeeping)" title="ΔT (timekeeping)">ΔT</a>) we<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag possibly uses too-vague attribution or weasel words. (September 2024)">who?</span></a></i>]</sup> estimate that the error in the assumed length of the synodic month was less than 0.2 second in the fourth century BC and less than 0.1 second in Hipparchus's time. </p> <div class="mw-heading mw-heading3"><h3 id="Orbit_of_the_Moon">Orbit of the Moon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=6" title="Edit section: Orbit of the Moon"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It had been known for a long time that the motion of the Moon is not uniform: its speed varies. This is called its <i>anomaly</i> and it repeats with its own period; the <a href="/wiki/Anomalistic_month" class="mw-redirect" title="Anomalistic month">anomalistic month</a>. The Chaldeans took account of this arithmetically, and used a table giving the daily motion of the Moon according to the date within a long period. However, the Greeks preferred to think in geometrical models of the sky. At the end of the third century BC, <a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius of Perga</a> had proposed two models for lunar and planetary motion: </p> <ol><li>In the first, the Moon would move uniformly along a circle, but the Earth would be eccentric, i.e., at some distance of the center of the circle. So the apparent angular speed of the Moon (and its distance) would vary.</li> <li>The Moon would move uniformly (with some mean motion in anomaly) on a secondary circular orbit, called an <i>epicycle</i> that would move uniformly (with some mean motion in longitude) over the main circular orbit around the Earth, called <i>deferent</i>; see <a href="/wiki/Deferent_and_epicycle" title="Deferent and epicycle">deferent and epicycle</a>.</li></ol> <p>Apollonius demonstrated that these two models were in fact mathematically equivalent. However, all this was theory and had not been put to practice. Hipparchus is the first astronomer known to attempt to determine the relative proportions and actual sizes of these orbits. Hipparchus devised a geometrical method to find the parameters from three positions of the Moon at particular phases of its anomaly. In fact, he did this separately for the eccentric and the epicycle model. Ptolemy describes the details in the <i>Almagest</i> IV.11. Hipparchus used two sets of three lunar eclipse observations that he carefully selected to satisfy the requirements. The eccentric model he fitted to these eclipses from his Babylonian eclipse list: 22/23 December 383 BC, 18/19 June 382 BC, and 12/13 December 382 BC. The epicycle model he fitted to lunar eclipse observations made in Alexandria at 22 September 201 BC, 19 March 200 BC, and 11 September 200 BC. </p> <ul><li>For the eccentric model, Hipparchus found for the ratio between the radius of the <a href="/w/index.php?title=Eccenter&action=edit&redlink=1" class="new" title="Eccenter (page does not exist)">eccenter</a> and the distance between the center of the eccenter and the center of the ecliptic (i.e., the observer on Earth): 3144 : <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">327<span class="sr-only">+</span><span class="num">2</span>⁄<span class="den">3</span></span>;</li> <li>and for the epicycle model, the ratio between the radius of the deferent and the epicycle: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">3122<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> : <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">247<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> .</li></ul> <p>These figures are due to the cumbersome unit he used in his chord table and may partly be due to some sloppy rounding and calculation errors by Hipparchus, for which Ptolemy criticised him while also making rounding errors. A simpler alternate reconstruction<sup id="cite_ref-FOOTNOTEThurston2002_30-0" class="reference"><a href="#cite_note-FOOTNOTEThurston2002-30"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> agrees with all four numbers. Hipparchus found inconsistent results; he later used the ratio of the epicycle model (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">3122<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> : <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">247<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>), which is too small (60 : 4;45 sexagesimal). Ptolemy established a ratio of 60 : <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">5<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">4</span></span>.<sup id="cite_ref-toomer1968_31-0" class="reference"><a href="#cite_note-toomer1968-31"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> (The maximum angular deviation producible by this geometry is the arcsin of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">5<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">4</span></span> divided by 60, or approximately 5° 1', a figure that is sometimes therefore quoted as the equivalent of the Moon's <a href="/wiki/Equation_of_the_center" title="Equation of the center">equation of the center</a> in the Hipparchan model.) </p> <div class="mw-heading mw-heading3"><h3 id="Apparent_motion_of_the_Sun">Apparent motion of the Sun</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=7" title="Edit section: Apparent motion of the Sun"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Hipparchus" title="Special:EditPage/Hipparchus">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">July 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Before Hipparchus, <a href="/wiki/Meton" class="mw-redirect" title="Meton">Meton</a>, <a href="/wiki/Euctemon" title="Euctemon">Euctemon</a>, and their pupils at <a href="/wiki/Athens" title="Athens">Athens</a> had made a solstice observation (i.e., timed the moment of the summer <a href="/wiki/Solstice" title="Solstice">solstice</a>) on 27 June 432 BC (<a href="/wiki/Proleptic_Julian_calendar" title="Proleptic Julian calendar">proleptic Julian calendar</a>). <a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus of Samos</a> is said to have done so in 280 BC, and Hipparchus also had an observation by <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a>. He observed the summer solstices in 146 and 135 BC both accurately to a few hours, but observations of the moment of <a href="/wiki/Equinox" title="Equinox">equinox</a> were simpler, and he made twenty during his lifetime. Ptolemy gives an extensive discussion of Hipparchus's work on the length of the year in the <i>Almagest</i> III.1, and quotes many observations that Hipparchus made or used, spanning 162–128 BC, including an equinox timing by Hipparchus (at 24 March 146 BC at dawn) that differs by 5 hours from the observation made on <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a>'s large public <a href="/wiki/Equatorial_ring" title="Equatorial ring">equatorial ring</a> that same day (at 1 hour before noon). Ptolemy claims his solar observations were on a transit instrument set in the meridian. </p><p>At the end of his career, Hipparchus wrote a book entitled <i>Peri eniausíou megéthous</i> ("On the Length of the Year") regarding his results. The established value for the <a href="/wiki/Tropical_year" title="Tropical year">tropical year</a>, introduced by <a href="/wiki/Callippus" title="Callippus">Callippus</a> in or before 330 BC was <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">365<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">4</span></span> days.<sup id="cite_ref-leverington2003_32-0" class="reference"><a href="#cite_note-leverington2003-32"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Speculating a Babylonian origin for the Callippic year is difficult to defend, since Babylon did not observe solstices thus the only extant System B year length was based on Greek solstices (see below). Hipparchus's equinox observations gave varying results, but he points out (quoted in <i>Almagest</i> III.1(H195)) that the observation errors by him and his predecessors may have been as large as <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> day. He used old solstice observations and determined a difference of approximately one day in approximately 300 years. So he set the length of the tropical year to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">365<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">4</span></span> − <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">300</span></span> days (= 365.24666... days = 365 days 5 hours 55 min, which differs from the modern estimate of the value (including earth spin acceleration), in his time of approximately 365.2425 days, an error of approximately 6 min per year, an hour per decade, and ten hours per century. </p><p>Between the solstice observation of Meton and his own, there were 297 years spanning 108,478 days; this implies a tropical year of 365.24579... days = 365 days;14,44,51 (sexagesimal; = 365 days + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">14</span><span class="sr-only">/</span><span class="den">60</span></span>⁠</span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">44</span><span class="sr-only">/</span><span class="den">60<sup>2</sup></span></span>⁠</span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">51</span><span class="sr-only">/</span><span class="den">60<sup>3</sup></span></span>⁠</span>), a year length found on one of the few Babylonian clay tablets which explicitly specifies the System B month. Whether Babylonians knew of Hipparchus's work or the other way around is debatable. </p><p>Hipparchus also gave the value for the <a href="/wiki/Sidereal_year" title="Sidereal year">sidereal year</a> to be 365 + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">144</span></span>⁠</span> days (= 365.25694... days = 365 days 6 hours 10 min). Another value for the sidereal year that is attributed to Hipparchus (by the physician <a href="/wiki/Galen" title="Galen">Galen</a> in the second century AD) is 365 + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">288</span></span>⁠</span> days (= 365.25347... days = 365 days 6 hours 5 min), but this may be a corruption of another value attributed to a Babylonian source: 365 + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">144</span></span>⁠</span> days (= 365.25694... days = 365 days 6 hours 10 min). It is not clear whether Hipparchus got the value from Babylonian astronomers or calculated by himself.<sup id="cite_ref-FOOTNOTENeugebauer1975Vol._1,_pp._293,_294_33-0" class="reference"><a href="#cite_note-FOOTNOTENeugebauer1975Vol._1,_pp._293,_294-33"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Orbit_of_the_Sun">Orbit of the Sun</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=8" title="Edit section: Orbit of the Sun"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Before Hipparchus, astronomers knew that the lengths of the <a href="/wiki/Season" title="Season">seasons</a> are not equal. Hipparchus made observations of equinox and solstice, and according to Ptolemy (<i>Almagest</i> III.4) determined that spring (from spring equinox to summer solstice) lasted 94<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> days, and summer (from summer solstice to autumn equinox) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">92<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> days. This is inconsistent with a premise of the Sun moving around the Earth in a circle at uniform speed. Hipparchus's solution was to place the Earth not at the center of the Sun's motion, but at some distance from the center. This model described the apparent motion of the Sun fairly well. It is known today that the <a href="/wiki/Planet" title="Planet">planets</a>, including the Earth, move in approximate <a href="/wiki/Ellipse" title="Ellipse">ellipses</a> around the Sun, but this was not discovered until <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a> published his first two laws of planetary motion in 1609. The value for the <a href="/wiki/Eccentricity_(orbit)" class="mw-redirect" title="Eccentricity (orbit)">eccentricity</a> attributed to Hipparchus by Ptolemy is that the offset is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">24</span></span> of the radius of the orbit (which is a little too large), and the direction of the <a href="/wiki/Apogee" class="mw-redirect" title="Apogee">apogee</a> would be at longitude 65.5° from the <a href="/wiki/March_equinox" title="March equinox">vernal equinox</a>. Hipparchus may also have used other sets of observations, which would lead to different values. One of his two eclipse trios' solar longitudes are consistent with his having initially adopted inaccurate lengths for spring and summer of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">95<span class="sr-only">+</span><span class="num">3</span>⁄<span class="den">4</span></span> and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">91<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">4</span></span> days.<sup id="cite_ref-FOOTNOTEThurston2002p._67,_note_16_34-0" class="reference"><a href="#cite_note-FOOTNOTEThurston2002p._67,_note_16-34"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (September 2023)">failed verification</span></a></i>]</sup> His other triplet of solar positions is consistent with <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">94<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">4</span></span> and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">92<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> days,<sup id="cite_ref-FOOTNOTEJones2001_13-2" class="reference"><a href="#cite_note-FOOTNOTEJones2001-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEThurston2002note_14_35-0" class="reference"><a href="#cite_note-FOOTNOTEThurston2002note_14-35"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (September 2023)">failed verification</span></a></i>]</sup> an improvement on the results (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">94<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">92<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> days) attributed to Hipparchus by Ptolemy. Ptolemy made no change three centuries later, and expressed lengths for the autumn and winter seasons which were already implicit (as shown, e.g., by A. <a href="/wiki/Aaboe" class="mw-redirect" title="Aaboe">Aaboe</a>).<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (April 2023)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Distance,_parallax,_size_of_the_Moon_and_the_Sun"><span id="Distance.2C_parallax.2C_size_of_the_Moon_and_the_Sun"></span>Distance, parallax, size of the Moon and the Sun</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=9" title="Edit section: Distance, parallax, size of the Moon and the Sun"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/On_Sizes_and_Distances_(Hipparchus)" title="On Sizes and Distances (Hipparchus)">On Sizes and Distances (Hipparchus)</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:HipparchusEclipse.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/HipparchusEclipse.png/400px-HipparchusEclipse.png" decoding="async" width="400" height="230" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/3/32/HipparchusEclipse.png 1.5x" data-file-width="486" data-file-height="280" /></a><figcaption>Diagram used in reconstructing one of Hipparchus's methods of determining the distance to the Moon. This represents the Earth–Moon system during a partial solar eclipse at A (<a href="/wiki/Alexandria" title="Alexandria">Alexandria</a>) and a total solar eclipse at H (<a href="/wiki/Hellespont" class="mw-redirect" title="Hellespont">Hellespont</a>).</figcaption></figure> <p>Hipparchus also undertook to find the distances and sizes of the Sun and the Moon, in the now-lost work <i>On Sizes and Distances</i> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1248666159"><span class="tfd tfd-dated tfd-tiny"><a href="/wiki/Wikipedia:Templates_for_discussion/Log/2024_November_12#Template:Lang-grc-gre" title="Wikipedia:Templates for discussion/Log/2024 November 12">‹See Tfd›</a></span><a href="/wiki/Greek_language" title="Greek language">Greek</a>: <span title="Ancient Greek (to 1453)-language text"><span lang="grc">Περὶ μεγεθῶν καὶ ἀποστημάτων</span></span> <span title="Ancient Greek (to 1453)-language romanization"><i lang="grc-Latn">Peri megethon kai apostematon</i></span>). His work is mentioned in Ptolemy's <i>Almagest</i> V.11, and in a commentary thereon by <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus</a>; <a href="/wiki/Theon_of_Smyrna" title="Theon of Smyrna">Theon of Smyrna</a> (2nd century) also mentions the work, under the title <i>On Sizes and Distances of the Sun and Moon</i>. </p><p>Hipparchus measured the apparent diameters of the Sun and Moon with his <i><a href="/wiki/Alidade" title="Alidade">diopter</a></i>. Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. He found that at the <i><a href="/wiki/Mean" title="Mean">mean</a></i> distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into the circle, i.e., the mean apparent diameters are <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">360</span>⁄<span class="den">650</span></span> = 0°33′14″. </p><p>Like others before and after him, he also noticed that the Moon has a noticeable <a href="/wiki/Lunar_parallax" class="mw-redirect" title="Lunar parallax">parallax</a>, i.e., that it appears displaced from its calculated position (compared to the Sun or <a href="/wiki/Star" title="Star">stars</a>), and the difference is greater when closer to the horizon. He knew that this is because in the then-current models the Moon circles the center of the Earth, but the observer is at the surface—the Moon, Earth and observer form a triangle with a sharp angle that changes all the time. From the size of this parallax, the distance of the Moon as measured in Earth <a href="/wiki/Radius" title="Radius">radii</a> can be determined. For the Sun however, there was no observable parallax (we now know that it is about 8.8", several times smaller than the resolution of the unaided eye). </p><p>In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. He then analyzed a solar eclipse, which Toomer presumes to be the eclipse of 14 March 190 BC.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> It was total in the region of the <a href="/wiki/Hellespont" class="mw-redirect" title="Hellespont">Hellespont</a> (and in his birthplace, Nicaea); at the time Toomer proposes the Romans were preparing for war with <a href="/wiki/Antiochus_III" class="mw-redirect" title="Antiochus III">Antiochus III</a> in the area, and the eclipse is mentioned by <a href="/wiki/Livy" title="Livy">Livy</a> in his <i><a href="/wiki/Ab_Urbe_Condita_Libri" class="mw-redirect" title="Ab Urbe Condita Libri">Ab Urbe Condita Libri</a></i> VIII.2. It was also observed in Alexandria, where the Sun was reported to be obscured 4/5ths by the Moon. Alexandria and Nicaea are on the same meridian. Alexandria is at about 31° North, and the region of the Hellespont about 40° North. (It has been contended that authors like Strabo and Ptolemy had fairly decent values for these geographical positions, so Hipparchus must have known them too. However, Strabo's Hipparchus dependent latitudes for this region are at least 1° too high, and Ptolemy appears to copy them, placing Byzantium 2° high in latitude.) Hipparchus could draw a triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii. Because the eclipse occurred in the morning, the Moon was not in the <a href="/wiki/Meridian_(astronomy)" title="Meridian (astronomy)">meridian</a>, and it has been proposed that as a consequence the distance found by Hipparchus was a lower limit. In any case, according to Pappus, Hipparchus found that the least distance is 71 (from this eclipse), and the greatest 83 Earth radii. </p><p>In the second book, Hipparchus starts from the opposite extreme assumption: he assigns a (minimum) distance to the Sun of 490 Earth radii. This would correspond to a parallax of 7′, which is apparently the greatest parallax that Hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2′; <a href="/wiki/Tycho_Brahe" title="Tycho Brahe">Tycho Brahe</a> made naked eye observation with an accuracy down to 1′). In this case, the shadow of the Earth is a <a href="/wiki/Conical_surface" title="Conical surface">cone</a> rather than a <a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">cylinder</a> as under the first assumption. Hipparchus observed (at lunar eclipses) that at the mean distance of the Moon, the diameter of the shadow cone is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">2<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> lunar diameters. That apparent diameter is, as he had observed, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">360</span>⁄<span class="den">650</span></span> degrees. With these values and simple geometry, Hipparchus could determine the mean distance; because it was computed for a minimum distance of the Sun, it is the maximum mean distance possible for the Moon. With his value for the eccentricity of the orbit, he could compute the least and greatest distances of the Moon too. According to Pappus, he found a least distance of 62, a mean of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">67<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">3</span></span>, and consequently a greatest distance of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">72<span class="sr-only">+</span><span class="num">2</span>⁄<span class="den">3</span></span> Earth radii. With this method, as the parallax of the Sun decreases (i.e., its distance increases), the minimum limit for the mean distance is 59 Earth radii—exactly the mean distance that Ptolemy later derived. </p><p>Hipparchus thus had the problematic result that his minimum distance (from book 1) was greater than his maximum mean distance (from book 2). He was intellectually honest about this discrepancy, and probably realized that especially the first method is very sensitive to the accuracy of the observations and parameters. (In fact, modern calculations show that the size of the 189 BC solar eclipse at Alexandria must have been closer to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">9</span>⁄<span class="den">10</span></span>ths and not the reported <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">4</span>⁄<span class="den">5</span></span>ths, a fraction more closely matched by the degree of totality at Alexandria of eclipses occurring in 310 and 129 BC which were also nearly total in the Hellespont and are thought by many to be more likely possibilities for the eclipse Hipparchus used for his computations.) </p><p>Ptolemy later measured the lunar parallax directly (<i>Almagest</i> V.13), and used the second method of Hipparchus with lunar eclipses to compute the distance of the Sun (<i>Almagest</i> V.15). He criticizes Hipparchus for making contradictory assumptions, and obtaining conflicting results (<i>Almagest</i> V.11): but apparently he failed to understand Hipparchus's strategy to establish limits consistent with the observations, rather than a single value for the distance. His results were the best so far: the actual mean distance of the Moon is 60.3 Earth radii, within his limits from Hipparchus's second book. </p><p><a href="/wiki/Theon_of_Smyrna" title="Theon of Smyrna">Theon of Smyrna</a> wrote that according to Hipparchus, the Sun is 1,880 times the size of the Earth, and the Earth twenty-seven times the size of the Moon; apparently this refers to <a href="/wiki/Volume" title="Volume">volumes</a>, not <a href="/wiki/Diameter" title="Diameter">diameters</a>. From the geometry of book 2 it follows that the Sun is at 2,550 Earth radii, and the mean distance of the Moon is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">60<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> radii. Similarly, <a href="/wiki/Cleomedes" title="Cleomedes">Cleomedes</a> quotes Hipparchus for the sizes of the Sun and Earth as 1050:1; this leads to a mean lunar distance of 61 radii. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. </p><p>See Toomer (1974) for a more detailed discussion.<sup id="cite_ref-toomer1974-sunmoon_37-0" class="reference"><a href="#cite_note-toomer1974-sunmoon-37"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Eclipses">Eclipses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=10" title="Edit section: Eclipses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Pliny_the_Elder" title="Pliny the Elder">Pliny</a> (<i>Naturalis Historia</i> II.X) tells us that Hipparchus demonstrated that lunar eclipses can occur five months apart, and solar eclipses seven months (instead of the usual six months); and the Sun can be hidden twice in thirty days, but as seen by different nations. Ptolemy discussed this a century later at length in <i>Almagest</i> VI.6. The geometry, and the limits of the positions of Sun and Moon when a solar or lunar eclipse is possible, are explained in <i>Almagest</i> VI.5. Hipparchus apparently made similar calculations. The result that two solar eclipses can occur one month apart is important, because this can not be based on observations: one is visible on the northern and the other on the southern hemisphere—as Pliny indicates—and the latter was inaccessible to the Greek. </p><p>Prediction of a solar eclipse, i.e., exactly when and where it will be visible, requires a solid lunar theory and proper treatment of the lunar parallax. Hipparchus must have been the first to be able to do this. A rigorous treatment requires <a href="/wiki/Spherical_trigonometry" title="Spherical trigonometry">spherical trigonometry</a>, thus those who remain certain that Hipparchus lacked it must speculate that he may have made do with planar approximations. He may have discussed these things in <i>Perí tēs katá plátos mēniaías tēs selēnēs kinēseōs</i> ("On the monthly motion of the Moon in latitude"), a work mentioned in the <i><a href="/wiki/Suda" title="Suda">Suda</a></i>. </p><p>Pliny also remarks that "he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the Moon was eclipsed in the west while both luminaries were visible above the earth" (translation H. Rackham (1938), <a href="/wiki/Loeb_Classical_Library" title="Loeb Classical Library">Loeb Classical Library</a> 330 p. 207). Toomer argued that this must refer to the large total lunar eclipse of 26 November 139 BC, when over a clean sea horizon as seen from Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast.<sup id="cite_ref-toomer1980_26-1" class="reference"><a href="#cite_note-toomer1980-26"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> This would be the second eclipse of the 345-year interval that Hipparchus used to verify the traditional Babylonian periods: this puts a late date to the development of Hipparchus's lunar theory. We do not know what "exact reason" Hipparchus found for seeing the Moon eclipsed while apparently it was not in exact <a href="/wiki/Astronomical_opposition" class="mw-redirect" title="Astronomical opposition">opposition</a> to the Sun. Parallax lowers the altitude of the luminaries; refraction raises them, and from a high point of view the horizon is lowered. </p> <div class="mw-heading mw-heading2"><h2 id="Astronomical_instruments_and_astrometry">Astronomical instruments and astrometry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=11" title="Edit section: Astronomical instruments and astrometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hipparchus and his predecessors used various instruments for astronomical calculations and observations, such as the <a href="/wiki/Gnomon" title="Gnomon">gnomon</a>, the <a href="/wiki/Astrolabe" title="Astrolabe">astrolabe</a>, and the <a href="/wiki/Armillary_sphere" title="Armillary sphere">armillary sphere</a>. </p><p>Hipparchus is credited with the invention or improvement of several astronomical instruments, which were used for a long time for naked-eye observations. According to <a href="/wiki/Synesius" title="Synesius">Synesius</a> of Ptolemais (4th century) he made the first <i>astrolabion</i>: this may have been an <a href="/wiki/Armillary_sphere" title="Armillary sphere">armillary sphere</a> (which Ptolemy however says he constructed, in <i>Almagest</i> V.1); or the predecessor of the planar instrument called astrolabe (also mentioned by <a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a>). With an astrolabe Hipparchus was the first to be able to measure the geographical <a href="/wiki/Latitude" title="Latitude">latitude</a> and <a href="/wiki/Time" title="Time">time</a> by observing fixed stars. Previously this was done at daytime by measuring the shadow cast by a gnomon, by recording the length of the longest day of the year or with the portable instrument known as a <i><a href="/wiki/Scaphe" title="Scaphe">scaphe</a></i>. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Equatorial_ring.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Equatorial_ring.png/200px-Equatorial_ring.png" decoding="async" width="200" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Equatorial_ring.png/300px-Equatorial_ring.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/Equatorial_ring.png/400px-Equatorial_ring.png 2x" data-file-width="492" data-file-height="536" /></a><figcaption> <a href="/wiki/Equatorial_ring" title="Equatorial ring">Equatorial ring</a> of Hipparchus's time.</figcaption></figure> <p>Ptolemy mentions (<i>Almagest</i> V.14) that he used a similar instrument as Hipparchus, called <i><a href="/wiki/Dioptra" title="Dioptra">dioptra</a></i>, to measure the apparent diameter of the Sun and Moon. <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus of Alexandria</a> described it (in his commentary on the <i>Almagest</i> of that chapter), as did <a href="/wiki/Proclus" title="Proclus">Proclus</a> (<i>Hypotyposis</i> IV). It was a four-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon. </p><p>Hipparchus also observed solar <a href="/wiki/Equinox" title="Equinox">equinoxes</a>, which may be done with an <a href="/wiki/Equatorial_ring" title="Equatorial ring">equatorial ring</a>: its shadow falls on itself when the Sun is on the <a href="/wiki/Equator" title="Equator">equator</a> (i.e., in one of the equinoctial points on the <a href="/wiki/Ecliptic" title="Ecliptic">ecliptic</a>), but the shadow falls above or below the opposite side of the ring when the Sun is south or north of the equator. Ptolemy quotes (in <i>Almagest</i> III.1 (H195)) a description by Hipparchus of an equatorial ring in Alexandria; a little further he describes two such instruments present in Alexandria in his own time. </p><p>Hipparchus applied his knowledge of spherical angles to the problem of denoting locations on the Earth's surface. Before him a grid system had been used by <a href="/wiki/Dicaearchus" title="Dicaearchus">Dicaearchus</a> of <a href="/wiki/Messina,_Italy" class="mw-redirect" title="Messina, Italy">Messana</a>, but Hipparchus was the first to apply mathematical rigor to the determination of the <a href="/wiki/Latitude" title="Latitude">latitude</a> and <a href="/wiki/Longitude" title="Longitude">longitude</a> of places on the Earth. Hipparchus wrote a critique in three books on the work of the geographer <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a> of Cyrene (3rd century BC), called <i>Pròs tèn Eratosthénous geographían</i> ("Against the Geography of Eratosthenes"). It is known to us from <a href="/wiki/Strabo" title="Strabo">Strabo</a> of Amaseia, who in his turn criticised Hipparchus in his own <i>Geographia</i>. Hipparchus apparently made many detailed corrections to the locations and distances mentioned by Eratosthenes. It seems he did not introduce many improvements in methods, but he did propose a means to determine the <a href="/wiki/Geographic_coordinate_system" title="Geographic coordinate system">geographical longitudes</a> of different <a href="/wiki/City" title="City">cities</a> at <a href="/wiki/Lunar_eclipse" title="Lunar eclipse">lunar eclipses</a> (Strabo <i>Geographia</i> 1 January 2012). A lunar eclipse is visible simultaneously on half of the Earth, and the difference in longitude between places can be computed from the difference in local time when the eclipse is observed. His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical. </p> <div class="mw-heading mw-heading2"><h2 id="Star_catalog">Star catalog</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=12" title="Edit section: Star catalog"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Late in his career (possibly about 135 BC) Hipparchus compiled his star catalog. Scholars have been searching for it for centuries.<sup id="cite_ref-swerdlow1992_38-0" class="reference"><a href="#cite_note-swerdlow1992-38"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> In 2022, it was announced that a part of it was discovered in a medieval parchment manuscript, <a href="/wiki/Codex_Climaci_Rescriptus" title="Codex Climaci Rescriptus">Codex Climaci Rescriptus</a>, from <a href="/wiki/Saint_Catherine%27s_Monastery" title="Saint Catherine's Monastery">Saint Catherine's Monastery</a> in the <a href="/wiki/Sinai_Peninsula" title="Sinai Peninsula">Sinai Peninsula</a>, Egypt as hidden text (<a href="/wiki/Palimpsest" title="Palimpsest">palimpsest</a>).<sup id="cite_ref-gwz2022_39-0" class="reference"><a href="#cite_note-gwz2022-39"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:School_of_Athens_Raphael_detail_03.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/School_of_Athens_Raphael_detail_03.jpg/220px-School_of_Athens_Raphael_detail_03.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/School_of_Athens_Raphael_detail_03.jpg/330px-School_of_Athens_Raphael_detail_03.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/School_of_Athens_Raphael_detail_03.jpg/440px-School_of_Athens_Raphael_detail_03.jpg 2x" data-file-width="3000" data-file-height="2008" /></a><figcaption>The figure on the left may be Hipparchus, from <a href="/wiki/Raphael" title="Raphael">Raphael</a>’s fresco <i><a href="/wiki/The_School_of_Athens" title="The School of Athens">The School of Athens</a></i></figcaption></figure> <p>Hipparchus also constructed a celestial globe depicting the constellations, based on his observations. His interest in the <a href="/wiki/Fixed_star" class="mw-redirect" title="Fixed star">fixed stars</a> may have been inspired by the observation of a <a href="/wiki/Supernova" title="Supernova">supernova</a> (according to Pliny), or by his discovery of precession, according to Ptolemy, who says that Hipparchus could not reconcile his data with earlier observations made by <a href="/wiki/Timocharis" title="Timocharis">Timocharis</a> and <a href="/wiki/Aristillus" class="mw-redirect" title="Aristillus">Aristillus</a>. For more information see <a href="/wiki/Discovery_of_precession" class="mw-redirect" title="Discovery of precession">Discovery of precession</a>. In <a href="/wiki/Raphael" title="Raphael">Raphael</a>'s painting <i><a href="/wiki/The_School_of_Athens" title="The School of Athens">The School of Athens</a></i>, Hipparchus may be depicted holding his celestial globe, as the representative figure for astronomy. It is not certain that the figure is meant to represent him.<sup id="cite_ref-swerdlow1992_38-1" class="reference"><a href="#cite_note-swerdlow1992-38"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>Previously, <a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus of Cnidus</a> in the fourth century BC had described the stars and constellations in two books called <i>Phaenomena</i> and <i>Entropon</i>. <a href="/wiki/Aratus" title="Aratus">Aratus</a> wrote a poem called <i>Phaenomena</i> or <i>Arateia</i> based on Eudoxus's work. Hipparchus wrote a commentary on the <i>Arateia</i>—his only preserved work—which contains many stellar positions and times for rising, culmination, and setting of the constellations, and these are likely to have been based on his own measurements. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:19th_century_Hipparchus_engraving.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/19th_century_Hipparchus_engraving.jpg/220px-19th_century_Hipparchus_engraving.jpg" decoding="async" width="220" height="346" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/19th_century_Hipparchus_engraving.jpg/330px-19th_century_Hipparchus_engraving.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/19th_century_Hipparchus_engraving.jpg/440px-19th_century_Hipparchus_engraving.jpg 2x" data-file-width="1906" data-file-height="2996" /></a><figcaption>A 19th century artist's impression of Hipparchus<sup id="cite_ref-ks-engraving_41-0" class="reference"><a href="#cite_note-ks-engraving-41"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>According to Roman sources, Hipparchus made his measurements with a scientific instrument and he obtained the positions of roughly 850 stars. Pliny the Elder writes in book II, 24–26 of his Natural History:<sup id="cite_ref-FOOTNOTEHoffmann2017_42-0" class="reference"><a href="#cite_note-FOOTNOTEHoffmann2017-42"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>This same Hipparchus, who can never be sufficiently commended, ... discovered a new star that was produced in his own age, and, by observing its motions on the day in which it shone, he was led to doubt whether it does not often happen, that those stars have motion which we suppose to be fixed. And the same individual attempted, what might seem presumptuous even in a deity, viz. to number the stars for posterity and to express their relations by appropriate names; having previously devised instruments, by which he might mark the places and the magnitudes of each individual star. In this way it might be easily discovered, not only whether they were destroyed or produced, but whether they changed their relative positions, and likewise, whether they were increased or diminished; the heavens being thus left as an inheritance to any one, who might be found competent to complete his plan.</p></blockquote> <p>This passage reports that </p> <ul><li>Hipparchus was inspired by a newly emerging star</li> <li>he doubts on the stability of stellar brightnesses</li> <li>he observed with appropriate instruments (plural—it is not said that he observed everything with the same instrument)</li> <li>he made a catalogue of stars</li></ul> <p>It is unknown what instrument he used. The <a href="/wiki/Armillary_sphere" title="Armillary sphere">armillary sphere</a> was probably invented only later—maybe by Ptolemy 265 years after Hipparchus. The historian of science S. Hoffmann found clues that Hipparchus may have observed the longitudes and latitudes in different coordinate systems and, thus, with different instrumentation.<sup id="cite_ref-hoffman-befunde_17-1" class="reference"><a href="#cite_note-hoffman-befunde-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Right ascensions, for instance, could have been observed with a clock, while angular separations could have been measured with another device. </p> <div class="mw-heading mw-heading3"><h3 id="Stellar_magnitude">Stellar magnitude</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=13" title="Edit section: Stellar magnitude"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hipparchus is conjectured to have ranked the <a href="/wiki/Apparent_magnitude" title="Apparent magnitude">apparent magnitudes</a> of stars on a numerical scale from 1, the brightest, to 6, the faintest.<sup id="cite_ref-FOOTNOTEToomer1984[httpsarchiveorgdetailsptolemysalmagest0000ptolpage16_p.&nbsp;16]:_"The_magnitudes_range_(according_to_a_system_which_certainly_precedes_Ptolemy,_but_is_only_conjecturally_attributed_to_Hipparchus)_from_1_to_6.",_pp.&nbsp;341–399_43-0" class="reference"><a href="#cite_note-FOOTNOTEToomer1984[httpsarchiveorgdetailsptolemysalmagest0000ptolpage16_p.&nbsp;16]:_"The_magnitudes_range_(according_to_a_system_which_certainly_precedes_Ptolemy,_but_is_only_conjecturally_attributed_to_Hipparchus)_from_1_to_6.",_pp.&nbsp;341–399-43"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> This hypothesis is based on the vague statement by Pliny the Elder but cannot be proven by the data in Hipparchus's commentary on Aratus's poem. In this only work by his hand that has survived until today, he does not use the magnitude scale but estimates brightnesses unsystematically. However, this does not prove or disprove anything because the commentary might be an early work while the magnitude scale could have been introduced later.<sup id="cite_ref-hoffman-befunde_17-2" class="reference"><a href="#cite_note-hoffman-befunde-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Nevertheless, this system certainly precedes <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>, who used it extensively about AD 150.<sup id="cite_ref-FOOTNOTEToomer1984[httpsarchiveorgdetailsptolemysalmagest0000ptolpage16_p.&nbsp;16]:_"The_magnitudes_range_(according_to_a_system_which_certainly_precedes_Ptolemy,_but_is_only_conjecturally_attributed_to_Hipparchus)_from_1_to_6.",_pp.&nbsp;341–399_43-1" class="reference"><a href="#cite_note-FOOTNOTEToomer1984[httpsarchiveorgdetailsptolemysalmagest0000ptolpage16_p.&nbsp;16]:_"The_magnitudes_range_(according_to_a_system_which_certainly_precedes_Ptolemy,_but_is_only_conjecturally_attributed_to_Hipparchus)_from_1_to_6.",_pp.&nbsp;341–399-43"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> This system was made more precise and extended by <a href="/wiki/N._R._Pogson" title="N. R. Pogson">N. R. Pogson</a> in 1856, who placed the magnitudes on a logarithmic scale, making magnitude 1 stars 100 times brighter than magnitude 6 stars, thus each magnitude is <span class="nowrap"><sup style="margin-right: -0.5em; vertical-align: 0.8em;">5</sup>√<span style="border-top:1px solid; padding:0 0.1em;">100</span></span> or 2.512 times brighter than the next faintest magnitude.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Coordinate_System">Coordinate System</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=14" title="Edit section: Coordinate System"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is disputed which coordinate system(s) he used. Ptolemy's catalog in the <i><a href="/wiki/Almagest" title="Almagest">Almagest</a></i>, which is derived from Hipparchus's catalog, is given in <a href="/wiki/Ecliptic_coordinate_system" title="Ecliptic coordinate system">ecliptic coordinates</a>. Although Hipparchus strictly distinguishes between "signs" (30° section of the zodiac) and "constellations" in the zodiac, it is highly questionable whether or not he had an instrument to directly observe / measure units on the ecliptic.<sup id="cite_ref-hoffman-befunde_17-3" class="reference"><a href="#cite_note-hoffman-befunde-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEHoffmann2017_42-1" class="reference"><a href="#cite_note-FOOTNOTEHoffmann2017-42"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> He probably marked them as a unit on his celestial globe but the instrumentation for his observations is unknown.<sup id="cite_ref-hoffman-befunde_17-4" class="reference"><a href="#cite_note-hoffman-befunde-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Alm_signs%2Bconsts.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Alm_signs%2Bconsts.jpg/400px-Alm_signs%2Bconsts.jpg" decoding="async" width="400" height="54" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Alm_signs%2Bconsts.jpg/600px-Alm_signs%2Bconsts.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Alm_signs%2Bconsts.jpg/800px-Alm_signs%2Bconsts.jpg 2x" data-file-width="5742" data-file-height="773" /></a><figcaption>Ptolemy's constellation areas (blue polygons) and "signs" of the zodiac had different sizes and extends; it is highly likely Hipparchus considered these units the same. Reconstruction from the Almagest<sup id="cite_ref-FOOTNOTEHoffmann2017_42-2" class="reference"><a href="#cite_note-FOOTNOTEHoffmann2017-42"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>Delambre in his <span title="French-language text"><i lang="fr">Histoire de l'Astronomie Ancienne</i></span> (1817) concluded that Hipparchus knew and used the <a href="/wiki/Equatorial_coordinate_system" title="Equatorial coordinate system">equatorial coordinate system</a>, a conclusion challenged by <a href="/wiki/Otto_Neugebauer" class="mw-redirect" title="Otto Neugebauer">Otto Neugebauer</a> in his <i>History of Ancient Mathematical Astronomy</i> (1975). Hipparchus seems to have used a mix of <a href="/wiki/Ecliptic_coordinate_system" title="Ecliptic coordinate system">ecliptic coordinates</a> and <a href="/wiki/Equatorial_coordinate_system" title="Equatorial coordinate system">equatorial coordinates</a>: in his commentary on Eudoxus he provides stars' polar distance (equivalent to the <a href="/wiki/Declination" title="Declination">declination</a> in the equatorial system), right ascension (equatorial), longitude (ecliptic), polar longitude (hybrid), but not celestial latitude. This opinion was confirmed by the careful investigation of Hoffmann<sup id="cite_ref-FOOTNOTEHoffmann2017_42-3" class="reference"><a href="#cite_note-FOOTNOTEHoffmann2017-42"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> who independently studied the material, potential sources, techniques and results of Hipparchus and reconstructed his celestial globe and its making. </p><p>As with most of his work, Hipparchus's star catalog was adopted and perhaps expanded by Ptolemy, who has (since Brahe in 1598) been accused by some<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> of fraud for stating (<i>Syntaxis</i>, book 7, chapter 4) that he observed all 1025 stars—critics claim that, for almost every star, he used Hipparchus's data and precessed it to his own epoch <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac">2<span class="sr-only">+</span><span class="num">2</span>⁄<span class="den">3</span></span> centuries later by adding 2°40' to the longitude, using an erroneously small precession constant of 1° per century. This claim is highly exaggerated because it applies modern standards of citation to an ancient author. True is only that "the ancient star catalogue" that was initiated by Hipparchus in the second century BC, was reworked and improved multiple times in the 265 years to the Almagest (which is good scientific practise even today).<sup id="cite_ref-hoffmann2018_46-0" class="reference"><a href="#cite_note-hoffmann2018-46"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> Although the Almagest star catalogue is based upon Hipparchus's, it is not only a blind copy but enriched, enhanced, and thus (at least partially) re-observed.<sup id="cite_ref-hoffman-befunde_17-5" class="reference"><a href="#cite_note-hoffman-befunde-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Celestial_globe">Celestial globe</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=15" title="Edit section: Celestial globe"><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:HipparchsGlobus_smh2017.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/HipparchsGlobus_smh2017.png/220px-HipparchsGlobus_smh2017.png" decoding="async" width="220" height="130" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/HipparchsGlobus_smh2017.png/330px-HipparchsGlobus_smh2017.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/HipparchsGlobus_smh2017.png/440px-HipparchsGlobus_smh2017.png 2x" data-file-width="1576" data-file-height="932" /></a><figcaption>Reconstruction of Hipparchus's celestial globe according to ancient descriptions and the data in manuscripts by his hand (excellence cluster TOPOI, Berlin, 2015 - published in Hoffmann (2017)<sup id="cite_ref-FOOTNOTEHoffmann2017_42-4" class="reference"><a href="#cite_note-FOOTNOTEHoffmann2017-42"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup>).</figcaption></figure> <p>Hipparchus's celestial globe was an instrument similar to modern electronic computers.<sup id="cite_ref-FOOTNOTEHoffmann2017_42-5" class="reference"><a href="#cite_note-FOOTNOTEHoffmann2017-42"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> He used it to determine risings, settings and culminations (cf. also Almagest, book VIII, chapter 3). Therefore, his globe was mounted in a horizontal plane and had a meridian ring with a scale. In combination with a grid that divided the celestial equator into 24 hour lines (longitudes equalling our right ascension hours) the instrument allowed him to determine the hours. The ecliptic was marked and divided in 12 sections of equal length (the "signs", which he called <span title="Ancient Greek (to 1453)-language text"><i lang="grc-Latn">zodion</i></span> or <span title="Ancient Greek (to 1453)-language text"><i lang="grc-Latn">dodekatemoria</i></span> in order to distinguish them from constellations (<span title="Ancient Greek (to 1453)-language text"><i lang="grc-Latn">astron</i></span>). The globe was virtually reconstructed by a historian of science. </p> <div class="mw-heading mw-heading3"><h3 id="Arguments_for_and_against_Hipparchus's_star_catalog_in_the_Almagest"><span id="Arguments_for_and_against_Hipparchus.27s_star_catalog_in_the_Almagest"></span>Arguments for and against Hipparchus's star catalog in the Almagest</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=16" title="Edit section: Arguments for and against Hipparchus's star catalog in the Almagest"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For: </p> <ul><li>common errors in the reconstructed Hipparchian star catalogue and the Almagest suggest a direct transfer without re-observation within 265 years. There are 18 stars with common errors - for the other ~800 stars, the errors are not extant or within the error ellipse. That means, no further statement is allowed on these hundreds of stars.</li> <li>further statistical arguments</li></ul> <p>Against: </p> <ul><li>Unlike Ptolemy, Hipparchus did not use ecliptic coordinates to describe stellar positions.</li> <li>Hipparchus's catalogue is reported in Roman times to have enlisted about 850 stars but Ptolemy's catalogue has 1025 stars. Thus, somebody has added further entries.</li> <li>There are stars cited in the Almagest from Hipparchus that are missing in the Almagest star catalogue. Thus, by all the reworking within scientific progress in 265 years, not all of Hipparchus's stars made it into the Almagest version of the star catalogue.</li></ul> <p>Conclusion: Hipparchus's star catalogue is one of the sources of the Almagest star catalogue but not the only source.<sup id="cite_ref-hoffmann2018_46-1" class="reference"><a href="#cite_note-hoffmann2018-46"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Precession_of_the_equinoxes_(146–127_BC)"><span id="Precession_of_the_equinoxes_.28146.E2.80.93127_BC.29"></span>Precession of the equinoxes (146–127 BC)</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=17" title="Edit section: Precession of the equinoxes (146–127 BC)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Precession_(astronomy)" class="mw-redirect" title="Precession (astronomy)">Precession (astronomy)</a></div> <p>Hipparchus is generally recognized as discoverer of the <a href="/wiki/Precession" title="Precession">precession</a> of the <a href="/wiki/Equinox" title="Equinox">equinoxes</a> in 127 BC.<sup id="cite_ref-jones2010_47-0" class="reference"><a href="#cite_note-jones2010-47"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> His two books on precession, <i>On the Displacement of the Solstitial and Equinoctial Points</i> and <i>On the Length of the Year</i>, are both mentioned in the <i><a href="/wiki/Almagest" title="Almagest">Almagest</a></i> of Claudius <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>. According to Ptolemy, Hipparchus measured the longitude of <a href="/wiki/Spica" title="Spica">Spica</a> and <a href="/wiki/Regulus" title="Regulus">Regulus</a> and other bright stars. Comparing his measurements with data from his predecessors, <a href="/wiki/Timocharis" title="Timocharis">Timocharis</a> and <a href="/wiki/Aristillus" class="mw-redirect" title="Aristillus">Aristillus</a>, he concluded that Spica had moved 2° relative to the <a href="/wiki/September_equinox" title="September equinox">autumnal equinox</a>. He also compared the lengths of the <a href="/wiki/Tropical_year" title="Tropical year">tropical year</a> (the time it takes the Sun to return to an equinox) and the <a href="/wiki/Sidereal_year" title="Sidereal year">sidereal year</a> (the time it takes the Sun to return to a fixed star), and found a slight discrepancy. Hipparchus concluded that the equinoxes were moving ("precessing") through the zodiac, and that the rate of precession was not less than 1° in a century. </p> <div class="mw-heading mw-heading2"><h2 id="Geography">Geography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=18" title="Edit section: Geography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hipparchus's treatise <i>Against the Geography of Eratosthenes</i> in three books is not preserved.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> Most of our knowledge of it comes from <a href="/wiki/Strabo" title="Strabo">Strabo</a>, according to whom Hipparchus thoroughly and often unfairly criticized <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a>, mainly for internal contradictions and inaccuracy in determining positions of geographical localities. Hipparchus insists that a geographic map must be based only on astronomical measurements of <a href="/wiki/Latitude_and_longitude" class="mw-redirect" title="Latitude and longitude">latitudes and longitudes</a> and <a href="/wiki/Triangulation" title="Triangulation">triangulation</a> for finding unknown distances. In geographic theory and methods Hipparchus introduced three main innovations.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>He was the first to use the <a href="/wiki/Geographic_coordinate_system" title="Geographic coordinate system">grade grid</a>, to determine <a href="/wiki/Latitude" title="Latitude">geographic latitude</a> from star observations, and not only from the Sun's altitude, a method known long before him, and to suggest that <a href="/wiki/Longitude" title="Longitude">geographic longitude</a> could be determined by means of simultaneous observations of lunar eclipses in distant places. In the practical part of his work, the so-called "table of <a href="/wiki/Clime" title="Clime">climata</a>", Hipparchus listed latitudes for several tens of localities. In particular, he improved <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a>' values for the latitudes of <a href="/wiki/Athens" title="Athens">Athens</a>, <a href="/wiki/Sicily" title="Sicily">Sicily</a>, and <a href="/wiki/Comorin" class="mw-redirect" title="Comorin">southern extremity of India</a>.<sup id="cite_ref-shcheglov2010_50-0" class="reference"><a href="#cite_note-shcheglov2010-50"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-shcheglov2006_51-0" class="reference"><a href="#cite_note-shcheglov2006-51"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEShcheglov2007_52-0" class="reference"><a href="#cite_note-FOOTNOTEShcheglov2007-52"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> In calculating latitudes of <a href="/wiki/Clime" title="Clime">climata</a> (latitudes correlated with the length of the longest solstitial day), Hipparchus used an unexpectedly accurate value for <a href="/wiki/Axial_tilt" title="Axial tilt">the obliquity of the ecliptic</a>, 23°40' (the actual value in the second half of the second century BC was approximately 23°43'), whereas all other ancient authors knew only a roughly rounded value 24°, and even <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a> used a less accurate value, 23°51'.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p><p>Hipparchus opposed the view generally accepted in the <a href="/wiki/Hellenistic_period" title="Hellenistic period">Hellenistic period</a> that the <a href="/wiki/Atlantic_Ocean" title="Atlantic Ocean">Atlantic</a> and <a href="/wiki/Indian_Ocean" title="Indian Ocean">Indian Oceans</a> and the <a href="/wiki/Caspian_Sea" title="Caspian Sea">Caspian Sea</a> are parts of a single ocean. At the same time he extends the limits of the <a href="/wiki/Ecumene" title="Ecumene">oikoumene</a>, i.e. the inhabited part of the land, up to the <a href="/wiki/Equator" title="Equator">equator</a> and the <a href="/wiki/Arctic_Circle" title="Arctic Circle">Arctic Circle</a>.<sup id="cite_ref-shcheglov2007-thule_54-0" class="reference"><a href="#cite_note-shcheglov2007-thule-54"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> Hipparchus's ideas found their reflection in the <i><a href="/wiki/Geography_(Ptolemy)" title="Geography (Ptolemy)">Geography</a></i> of <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>. In essence, Ptolemy's work is an extended attempt to realize Hipparchus's vision of what geography ought to be. </p> <div class="mw-heading mw-heading2"><h2 id="Modern_speculation">Modern speculation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=19" title="Edit section: Modern speculation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hipparchus was in the international news in 2005, when it was again proposed (as in 1898) that the data on the <a href="/wiki/Celestial_globe" title="Celestial globe">celestial globe</a> of Hipparchus or in his star catalog may have been preserved in the only surviving large ancient celestial globe which depicts the constellations with moderate accuracy, the globe carried by the <a href="/wiki/Farnese_Atlas" title="Farnese Atlas">Farnese Atlas</a>.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> Evidence suggests that the Farnese globe may show constellations in the Aratean tradition and deviate from the constellations used by Hipparchus.<sup id="cite_ref-FOOTNOTEHoffmann2017_42-6" class="reference"><a href="#cite_note-FOOTNOTEHoffmann2017-42"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p><p>A line in Plutarch's <i>Table Talk</i> states that Hipparchus counted 103,049 compound propositions that can be formed from ten simple propositions. 103,049 is the tenth <a href="/wiki/Schr%C3%B6der%E2%80%93Hipparchus_number" title="Schröder–Hipparchus number">Schröder–Hipparchus number</a>, which counts the number of ways of adding one or more pairs of parentheses around consecutive subsequences of two or more items in any sequence of ten symbols. This has led to speculation that Hipparchus knew about <a href="/wiki/Enumerative_combinatorics" title="Enumerative combinatorics">enumerative combinatorics</a>, a field of mathematics that developed independently in modern mathematics.<sup id="cite_ref-stanley1997_57-0" class="reference"><a href="#cite_note-stanley1997-57"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-acerbi2003_58-0" class="reference"><a href="#cite_note-acerbi2003-58"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p><p>Hipparchos was suggested in a 2013 paper to have accidentally observed the planet <a href="/wiki/Uranus" title="Uranus">Uranus</a> in 128 BC and catalogued it as a star, over a millennium and a half before its formal discovery in 1781.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Legacy">Legacy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=20" title="Edit section: Legacy"><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:Hipparcos-testing-estec.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hipparcos-testing-estec.jpg/220px-Hipparcos-testing-estec.jpg" decoding="async" width="220" height="260" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hipparcos-testing-estec.jpg/330px-Hipparcos-testing-estec.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hipparcos-testing-estec.jpg/440px-Hipparcos-testing-estec.jpg 2x" data-file-width="1176" data-file-height="1390" /></a><figcaption><i>Hipparcos</i> satellite in the Large Solar Simulator, ESTEC, February 1988</figcaption></figure> <p>Hipparchus may be depicted opposite <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a> in <a href="/wiki/Raphael" title="Raphael">Raphael</a>'s 1509–1511 painting <i><a href="/wiki/The_School_of_Athens" title="The School of Athens">The School of Athens</a></i>, although this figure is usually identified as <a href="/wiki/Zoroaster" title="Zoroaster">Zoroaster</a>.<sup id="cite_ref-swerdlow1992_38-2" class="reference"><a href="#cite_note-swerdlow1992-38"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>The formal name for the <a href="/wiki/European_Space_Agency" title="European Space Agency">ESA</a>'s <a href="/wiki/Hipparcos" title="Hipparcos">Hipparcos Space Astrometry Mission</a> is High Precision Parallax Collecting Satellite, making a <a href="/wiki/Backronym" title="Backronym">backronym</a>, HiPParCoS, that echoes and commemorates the name of Hipparchus. </p><p>The lunar crater <a href="/wiki/Hipparchus_(lunar_crater)" title="Hipparchus (lunar crater)">Hipparchus</a>, the Martian crater <a href="/wiki/Hipparchus_(Martian_crater)" title="Hipparchus (Martian crater)">Hipparchus</a>, and the <a href="/wiki/Asteroid" title="Asteroid">asteroid</a> <a href="/wiki/4000_Hipparchus" title="4000 Hipparchus">4000 Hipparchus</a> are named after him. </p><p>He was inducted into the <a href="/wiki/International_Space_Hall_of_Fame" class="mw-redirect" title="International Space Hall of Fame">International Space Hall of Fame</a> in 2004.<sup id="cite_ref-ep4_60-0" class="reference"><a href="#cite_note-ep4-60"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Jean_Baptiste_Joseph_Delambre" title="Jean Baptiste Joseph Delambre">Jean Baptiste Joseph Delambre</a>, historian of astronomy, mathematical astronomer and director of the <a href="/wiki/Paris_Observatory" title="Paris Observatory">Paris Observatory</a>, in his history of astronomy in the 18th century (1821), considered Hipparchus along with <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a> and <a href="/wiki/James_Bradley" title="James Bradley">James Bradley</a> the greatest astronomers of all time.<sup id="cite_ref-delambre1827_61-0" class="reference"><a href="#cite_note-delambre1827-61"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> </p><p>The <i><a href="/wiki/Astronomers_Monument" title="Astronomers Monument">Astronomers Monument</a></i> at the <a href="/wiki/Griffith_Observatory" title="Griffith Observatory">Griffith Observatory</a> in Los Angeles, California, United States features a relief of Hipparchus as one of six of the greatest astronomers of all time and the only one from Antiquity.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a> had great respect for <a href="/wiki/Tycho_Brahe" title="Tycho Brahe">Tycho Brahe</a>'s methods and the accuracy of his observations, and considered him to be the new Hipparchus, who would provide the foundation for a restoration of the science of astronomy.<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Translations">Translations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=21" title="Edit section: Translations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><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 book cs1 cs1-prop-foreign-lang-source"><a href="/w/index.php?title=Ernst_Hugo_Berger&action=edit&redlink=1" class="new" title="Ernst Hugo Berger (page does not exist)">Berger, Ernst Hugo</a>, ed. (1869). <a rel="nofollow" class="external text" href="https://archive.org/details/diegeographisch03hippgoog/page/n5/mode/2up"><i>Die geographischen Fragmente des Hipparch</i></a> [<i>The Geographical Fragments of Hipparchus</i>] (in German). Leipzig: Teubner. <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/981902787">981902787</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Die+geographischen+Fragmente+des+Hipparch&rft.place=Leipzig&rft.pub=Teubner&rft.date=1869&rft_id=info%3Aoclcnum%2F981902787&rft.au=Hipparchus&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdiegeographisch03hippgoog%2Fpage%2Fn5%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Dicks, D. R., ed. (1960). <i>The Geographical Fragments of Hipparchus</i>. University of London classical studies. London: Athlone Press. <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/490381">490381</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Geographical+Fragments+of+Hipparchus&rft.place=London&rft.series=University+of+London+classical+studies&rft.pub=Athlone+Press&rft.date=1960&rft_id=info%3Aoclcnum%2F490381&rft.au=Hipparchus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source-2 cs1-prop-foreign-lang-source"><a href="/wiki/Karl_Manitius" title="Karl Manitius">Manitius, Karl</a>, ed. (1894). <a rel="nofollow" class="external text" href="https://archive.org/details/McGillLibrary-hssl_hipparchou-ton-aratou_QB41H561894-18575"><i>Hipparchou Tōn Aratou kai Eudoxou Phainomenōn exēgēseōs vivlia tria = Hipparchi in Arati et Eudoxi Phaenomena commentariorum libri tres</i></a> [<i>Hipparchus' Commentaries on the Phenomena of Aratus and Eudoxus in three books</i>] (in Ancient Greek and Latin). Leipzig: Teubner. <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/1127047584">1127047584</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hipparchou+T%C5%8Dn+Aratou+kai+Eudoxou+Phainomen%C5%8Dn+ex%C4%93g%C4%93se%C5%8Ds+vivlia+tria+%3D+Hipparchi+in+Arati+et+Eudoxi+Phaenomena+commentariorum+libri+tres&rft.place=Leipzig&rft.pub=Teubner&rft.date=1894&rft_id=info%3Aoclcnum%2F1127047584&rft.au=Hipparchus&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2FMcGillLibrary-hssl_hipparchou-ton-aratou_QB41H561894-18575&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source">Cusinato, Bruna; Vanin, Gabriele, eds. (2022) [2013]. <i>Commentari di Ipparco ai Fenomeni di Arato ed Eudosso</i> [<i>Hipparchus' Commentaries on the Phenomena of Aratus and Eudoxus</i>] (in Italian). Translation by Bruna Cusinato; Introduction and astronomical commentary by Gabriele Vanin (3rd ed.). <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2206.08243">2206.08243</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Commentari+di+Ipparco+ai+Fenomeni+di+Arato+ed+Eudosso&rft.edition=3rd&rft.date=2022&rft_id=info%3Aarxiv%2F2206.08243&rft.au=Hipparchus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span> Originally published in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Vanin, Gabriele (2013). <i>Catasterismi</i>. Feltre: Rheticus-DBS Zanetti. pp. 85–166.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Catasterismi&rft.place=Feltre&rft.pages=85-166&rft.pub=Rheticus-DBS+Zanetti&rft.date=2013&rft.aulast=Vanin&rft.aufirst=Gabriele&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></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=Hipparchus&action=edit&section=22" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus of Samos</a> (<a href="https://en.wiktionary.org/wiki/circa#English" class="extiw" title="wikt:circa">c.</a><span style="white-space:nowrap;"> 310</span> – c.<span style="white-space:nowrap;"> 230 BC</span>), a Greek mathematician who <a href="/wiki/On_the_Sizes_and_Distances_(Aristarchus)" title="On the Sizes and Distances (Aristarchus)">calculated</a> the distance from the Earth to the Sun.</li> <li><a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a> (<a href="https://en.wiktionary.org/wiki/circa#English" class="extiw" title="wikt:circa">c.</a><span style="white-space:nowrap;"> 276</span> – c.<span style="white-space:nowrap;"> 194/195 BC</span>), a Greek mathematician who <a href="/wiki/On_the_measure_of_the_Earth" class="mw-redirect" title="On the measure of the Earth">calculated</a> the circumference of the Earth and also the distance from the Earth to the Sun.</li> <li><a href="/wiki/Greek_mathematics" title="Greek mathematics">Greek mathematics</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> (Aristarchus)</a></li> <li><a href="/wiki/On_Sizes_and_Distances_(Hipparchus)" title="On Sizes and Distances (Hipparchus)"><i>On the Sizes and Distances</i> (Hipparchus)</a></li> <li><a href="/wiki/Posidonius" title="Posidonius">Posidonius</a> (<a href="https://en.wiktionary.org/wiki/circa#English" class="extiw" title="wikt:circa">c.</a><span style="white-space:nowrap;"> 135</span> – c.<span style="white-space:nowrap;"> 51 BC</span>), a Greek astronomer and mathematician who <a href="/wiki/Posidonius#Calculation_of_Earth's_circumference" title="Posidonius">calculated</a> the circumference of the Earth.</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=Hipparchus&action=edit&section=23" 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 reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-head-of-hipparchus-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-head-of-hipparchus_1-0">^</a></b></span> <span class="reference-text"><a href="/wiki/Stanis%C5%82aw_Poniatowski_(1754%E2%80%931833)" title="Stanisław Poniatowski (1754–1833)">Stanisław Poniatowski</a>'s collection of contemporary forgeries passed off as antique engraved gems included an amethyst depicting Hipparchus with a star and the subject's name, which was included in a Christie's 1839 auction. From Poniatowski (1833), p. 52: <span title="French-language text"><span lang="fr">"... Dans le champ de cette pierre on voit une étoile et en beaux caractères le nom du sujet. <i>Améthyste</i>."</span></span> [In the field of this stone we see a star and in beautiful characters the name of the subject. <i>Amethyst</i>.]<sup id="cite_ref-gem_64-0" class="reference"><a href="#cite_note-gem-64"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> <div class="paragraphbreak" style="margin-top:0.5em"></div> This engraving was used for the title page of <a href="/wiki/William_Henry_Smyth" title="William Henry Smyth">William Henry Smyth</a>'s 1844 book, as suggested by an 1842 letter Smyth sent to the <i>National Institute for the Promotion of Science</i>, which described "the head of Hipparchus, from the Poniatowski-gem, intended as a vignette illustration of his work".<sup id="cite_ref-smyth_65-0" class="reference"><a href="#cite_note-smyth-65"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> The engraving has subsequently been repeatedly copied and re-used as a representation of Hipparchus, for instance in a 1965 Greek <a href="/wiki/Postage_stamp" title="Postage stamp">postage stamp</a> commemorating the <a href="/wiki/Eugenides_Foundation" title="Eugenides Foundation">Eugenides Planetarium</a> in Athens.<sup id="cite_ref-wilson1989_66-0" class="reference"><a href="#cite_note-wilson1989-66"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text">These figures use modern <a href="/wiki/Dynamical_time" class="mw-redirect" title="Dynamical time">dynamical time</a>, not the solar time of Hipparchus's era. E.g., the true 4267-month interval was nearer 126,007 days plus a little over half an hour.</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=Hipparchus&action=edit&section=24" title="Edit section: References"><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 reflist-columns references-column-width" style="column-width: 30em ;"> <ol class="references"> <li id="cite_note-linton2004-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-linton2004_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLinton2004" class="citation book cs1">Linton, C. M. (2004). <i>From Eudoxus to Einstein: a history of mathematical astronomy</i>. Cambridge University Press. p. 52. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-82750-8" title="Special:BookSources/978-0-521-82750-8"><bdi>978-0-521-82750-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=From+Eudoxus+to+Einstein%3A+a+history+of+mathematical+astronomy&rft.pages=52&rft.pub=Cambridge+University+Press&rft.date=2004&rft.isbn=978-0-521-82750-8&rft.aulast=Linton&rft.aufirst=C.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-toomer1996-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-toomer1996_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToomer1996" class="citation book cs1"><a href="/wiki/Gerald_J._Toomer" title="Gerald J. Toomer">Toomer, Gerald J.</a> (1996). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/astronomybeforet0000unse/page/n81/">"Ptolemy and his Greek Predecessors"</a></span>. In Walker, Christopher B. F. (ed.). <i>Astronomy before the Telescope</i>. London: The British Museum Press. p. 81. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7141-1746-1" title="Special:BookSources/978-0-7141-1746-1"><bdi>978-0-7141-1746-1</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/1391175189">1391175189</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Ptolemy+and+his+Greek+Predecessors&rft.btitle=Astronomy+before+the+Telescope&rft.place=London&rft.pages=81&rft.pub=The+British+Museum+Press&rft.date=1996&rft_id=info%3Aoclcnum%2F1391175189&rft.isbn=978-0-7141-1746-1&rft.aulast=Toomer&rft.aufirst=Gerald+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fastronomybeforet0000unse%2Fpage%2Fn81%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-mccluskey2000-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-mccluskey2000_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcCluskey2000" class="citation book cs1">McCluskey, Stephen C. (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PsLArVtOsPYC"><i>Astronomies and cultures in early medieval Europe</i></a>. Cambridge University Press. p. 22. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-77852-7" title="Special:BookSources/978-0-521-77852-7"><bdi>978-0-521-77852-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astronomies+and+cultures+in+early+medieval+Europe&rft.pages=22&rft.pub=Cambridge+University+Press&rft.date=2000&rft.isbn=978-0-521-77852-7&rft.aulast=McCluskey&rft.aufirst=Stephen+C.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPsLArVtOsPYC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-willard1854-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-willard1854_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWillard1854" class="citation book cs1">Willard, Emma (1854). <a rel="nofollow" class="external text" href="https://archive.org/details/astronographyora00will/page/246/"><i>Astronography, or Astronomical Geography</i></a>. Troy, New York: Merriam, Moore & Co. p. 246.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astronography%2C+or+Astronomical+Geography&rft.place=Troy%2C+New+York&rft.pages=246&rft.pub=Merriam%2C+Moore+%26+Co&rft.date=1854&rft.aulast=Willard&rft.aufirst=Emma&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fastronographyora00will%2Fpage%2F246%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></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">Denison Olmsted, Outlines of a Course of Lectures on Meteorology and Astronomy, pp 22</span> </li> <li id="cite_note-jones2017-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-jones2017_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJones2017" class="citation encyclopaedia cs1">Jones, Alexander Raymond (2017). <a rel="nofollow" class="external text" href="https://www.britannica.com/biography/Hipparchus-Greek-astronomer">"Hipparchus"</a>. <i>Encyclopaedia Britannica</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 August</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hipparchus&rft.btitle=Encyclopaedia+Britannica&rft.date=2017&rft.aulast=Jones&rft.aufirst=Alexander+Raymond&rft_id=https%3A%2F%2Fwww.britannica.com%2Fbiography%2FHipparchus-Greek-astronomer&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-newcomb1878-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-newcomb1878_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewcomb1878" class="citation book cs1"><a href="/wiki/Simon_Newcomb" title="Simon Newcomb">Newcomb, Simon</a> (1878). <a rel="nofollow" class="external text" href="https://archive.org/details/albertatest_01376/page/5/"><i>Popular Astronomy</i></a>. New York: Harper. p. 5. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-665-01376-8" title="Special:BookSources/978-0-665-01376-8"><bdi>978-0-665-01376-8</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/612980386">612980386</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Popular+Astronomy&rft.place=New+York&rft.pages=5&rft.pub=Harper&rft.date=1878&rft_id=info%3Aoclcnum%2F612980386&rft.isbn=978-0-665-01376-8&rft.aulast=Newcomb&rft.aufirst=Simon&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Falbertatest_01376%2Fpage%2F5%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-glashan1895-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-glashan1895_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGlashan1895" class="citation journal cs1">Glashan, J. C. (1895). <a rel="nofollow" class="external text" href="https://hdl.handle.net/2027/mdp.39015059411960?urlappend=%3Bseq=237">"Celestial Mechanics: Ptolemy, Copernicus and Newton"</a>. <i>University of Toronto Quarterly</i>. <b>2</b> (1): 49. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/2027%2Fmdp.39015059411960?urlappend=%3Bseq=237">2027/mdp.39015059411960</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/0042-0247">0042-0247</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/1011693113">1011693113</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=University+of+Toronto+Quarterly&rft.atitle=Celestial+Mechanics%3A+Ptolemy%2C+Copernicus+and+Newton&rft.volume=2&rft.issue=1&rft.pages=49&rft.date=1895&rft_id=info%3Ahdl%2F2027%2Fmdp.39015059411960%3Furlappend%3D%253Bseq%3D237&rft.issn=0042-0247&rft_id=info%3Aoclcnum%2F1011693113&rft.aulast=Glashan&rft.aufirst=J.+C.&rft_id=https%3A%2F%2Fhdl.handle.net%2F2027%2Fmdp.39015059411960%3Furlappend%3D%253Bseq%3D237&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-delambre1817-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-delambre1817_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDelambre1817" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Jean_Baptiste_Joseph_Delambre" title="Jean Baptiste Joseph Delambre">Delambre, Jean Baptiste Joseph</a> (1817). <a rel="nofollow" class="external text" href="https://archive.org/details/histoiredelastro01dela_0/page/n64/mode/1up"><i>Histoire de l'astronomie ancienne</i></a> [<i>History of Ancient Astronomy</i>] (in French). Vol. 1. Paris: Ve Courcier. p. lxi. <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/594550435">594550435</a>. <q>Hipparque, le vrai père de l'Astronomie</q> [Hipparchus, the true father of Astronomy]</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Histoire+de+l%27astronomie+ancienne&rft.place=Paris&rft.pages=lxi&rft.pub=Ve+Courcier&rft.date=1817&rft_id=info%3Aoclcnum%2F594550435&rft.aulast=Delambre&rft.aufirst=Jean+Baptiste+Joseph&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoiredelastro01dela_0%2Fpage%2Fn64%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</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="http://snible.org/coins/hn/bithynia.html">"Ancient coinage of Bithynia"</a>. <i>snible.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">26 April</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=snible.org&rft.atitle=Ancient+coinage+of+Bithynia&rft_id=http%3A%2F%2Fsnible.org%2Fcoins%2Fhn%2Fbithynia.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEToomer1978-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEToomer1978_12-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFToomer1978">Toomer 1978</a>.</span> </li> <li id="cite_note-FOOTNOTEJones2001-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEJones2001_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEJones2001_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEJones2001_13-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFJones2001">Jones 2001</a>.</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">Modern editions: <a href="#CITEREFManitius1894">Manitius 1894</a> (Ancient Greek and Latin), <a href="#CITEREFCusinatoVanin2022">Cusinato & Vanin 2022</a> (Italian)</span> </li> <li id="cite_note-toomer1988-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-toomer1988_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToomer1988" class="citation book cs1"><a href="/wiki/Gerald_J._Toomer" title="Gerald J. Toomer">Toomer, Gerald J.</a> (1988). "Hipparchus and Babylonian Astronomy". In Leichty, Erle; Ellis, Maria deJ. (eds.). <i>A Scientific Humanist: studies in memory of Abraham Sachs</i>. Philadelphia: Samuel Noah Kramer Fund, Univ. Museum. pp. 353–362. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-934718-90-5" title="Special:BookSources/978-0-934718-90-5"><bdi>978-0-934718-90-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hipparchus+and+Babylonian+Astronomy&rft.btitle=A+Scientific+Humanist%3A+studies+in+memory+of+Abraham+Sachs&rft.place=Philadelphia&rft.pages=353-362&rft.pub=Samuel+Noah+Kramer+Fund%2C+Univ.+Museum&rft.date=1988&rft.isbn=978-0-934718-90-5&rft.aulast=Toomer&rft.aufirst=Gerald+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-bg1991-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-bg1991_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBowenGoldstein1991" class="citation journal cs1">Bowen, A.C.; Goldstein, B.R. (1991). "The Introduction of Dated Observations and Precise Measurement in Greek Astronomy". <i>Archive for History of Exact Sciences</i>. <b>43</b> (2): 104. <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/1991AHES...43...93G">1991AHES...43...93G</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=The+Introduction+of+Dated+Observations+and+Precise+Measurement+in+Greek+Astronomy&rft.volume=43&rft.issue=2&rft.pages=104&rft.date=1991&rft_id=info%3Abibcode%2F1991AHES...43...93G&rft.aulast=Bowen&rft.aufirst=A.C.&rft.au=Goldstein%2C+B.R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-hoffman-befunde-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-hoffman-befunde_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-hoffman-befunde_17-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-hoffman-befunde_17-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-hoffman-befunde_17-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-hoffman-befunde_17-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-hoffman-befunde_17-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"> <a href="#CITEREFHoffmann2017">Hoffmann 2017</a>, Ch. 6 "Befunde", pp. 661–676, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><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%2F978-3-658-18683-8_6">10.1007/978-3-658-18683-8_6</a></span> </li> <li id="cite_note-kugler1900-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-kugler1900_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKugler1900" class="citation book cs1">Kugler, Franz Xaver (1900). <a rel="nofollow" class="external text" href="https://archive.org/details/diebabylonische00stragoog/"><i>Die Babylonische Mondrechnung</i></a> [<i>The Babylonian lunar computation</i>]. Freiburg im Breisgau: Herder.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Die+Babylonische+Mondrechnung&rft.place=Freiburg+im+Breisgau&rft.pub=Herder&rft.date=1900&rft.aulast=Kugler&rft.aufirst=Franz+Xaver&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdiebabylonische00stragoog%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-aaboe1955-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-aaboe1955_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAaboe1955" class="citation journal cs1"><a href="/wiki/Asger_Aaboe" title="Asger Aaboe">Aaboe, Asger</a> (1955). "On the Babylonian origin of some Hipparchian parameters". <i>Centaurus</i>. <b>4</b> (2): 122–125. <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/1955Cent....4..122A">1955Cent....4..122A</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.1600-0498.1955.tb00619.x">10.1111/j.1600-0498.1955.tb00619.x</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=On+the+Babylonian+origin+of+some+Hipparchian+parameters&rft.volume=4&rft.issue=2&rft.pages=122-125&rft.date=1955&rft_id=info%3Adoi%2F10.1111%2Fj.1600-0498.1955.tb00619.x&rft_id=info%3Abibcode%2F1955Cent....4..122A&rft.aulast=Aaboe&rft.aufirst=Asger&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span>. On p. 124, Aaboe identifies the Hipparchian equation <span class="nowrap">5458 syn. mo. =</span> <span class="nowrap">5923 drac. mo.</span> with the equation of <span class="nowrap">1,30,58 syn. mo. =</span> <span class="nowrap">1,38,43 drac. mo.</span> (written in <a href="/wiki/Sexagesimal" title="Sexagesimal">sexagesimal</a>), citing <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeugebauer1955" class="citation book cs1"><a href="/wiki/Otto_E._Neugebauer" title="Otto E. Neugebauer">Neugebauer, Otto E.</a> (1955). <i>Astronomical Cuneiform Texts</i>. Vol. 1. London: Lund Humphries. p. 73.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astronomical+Cuneiform+Texts&rft.place=London&rft.pages=73&rft.pub=Lund+Humphries&rft.date=1955&rft.aulast=Neugebauer&rft.aufirst=Otto+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-toomer1974-chordtable-20"><span class="mw-cite-backlink">^ <a href="#cite_ref-toomer1974-chordtable_20-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-toomer1974-chordtable_20-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToomer1974" class="citation journal cs1"><a href="/wiki/Gerald_J._Toomer" title="Gerald J. Toomer">Toomer, Gerald J.</a> (1974). "The Chord Table of Hipparchus and the Early History of Greek Trigonometry". <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/0008-8994">0008-8994</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/5155644322">5155644322</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_id=info%3Aoclcnum%2F5155644322&rft.issn=0008-8994&rft_id=info%3Adoi%2F10.1111%2Fj.1600-0498.1974.tb00205.x&rft_id=info%3Abibcode%2F1974Cent...18....6T&rft.aulast=Toomer&rft.aufirst=Gerald+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEToomer1984215-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEToomer1984215_21-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFToomer1984">Toomer 1984</a>, p. 215.</span> </li> <li id="cite_note-klintberg2005-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-klintberg2005_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKlintberg2005" class="citation journal cs1">Klintberg, Bo C. (2005). <a rel="nofollow" class="external text" href="http://www.insa.ndl.iitkgp.ac.in/xmlui/handle/1234567/1708">"Hipparchus's 3600′-Based Chord Table and Its Place in the History of Ancient Greek and Indian Trigonometry"</a>. <i>Indian Journal of History of Science</i>. <b>40</b> (2): 169–203.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Indian+Journal+of+History+of+Science&rft.atitle=Hipparchus%27s+3600%E2%80%B2-Based+Chord+Table+and+Its+Place+in+the+History+of+Ancient+Greek+and+Indian+Trigonometry&rft.volume=40&rft.issue=2&rft.pages=169-203&rft.date=2005&rft.aulast=Klintberg&rft.aufirst=Bo+C.&rft_id=http%3A%2F%2Fwww.insa.ndl.iitkgp.ac.in%2Fxmlui%2Fhandle%2F1234567%2F1708&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-synesius-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-synesius_23-0">^</a></b></span> <span class="reference-text"><a href="/wiki/Synesius" title="Synesius">Synesius</a> wrote in a letter describing an instrument involving the stereographic projection: "Hipparchus long ago hinted at the unfolding of a spherical surface [on a plane], so as to keep a proper proportion between the given ratios in the different figures, and he was in fact the first to apply himself to this subject. I, however (if it is not presumptuous to make so great a claim), have followed it to its uttermost conclusion, and have perfected it, although for most of the intervening time the problem had been neglected; for the great Ptolemy and the divine band of his successors were content to make only such use of it as sufficed for the night-clock by means of the sixteen stars, which were the only ones that Hipparchus rearranged and entered on his instrument." Translation from <a href="#CITEREFDicks1960">Dicks 1960</a>, fragment 63 pp. 102–103. <div class="paragraphbreak" style="margin-top:0.5em"></div> Dicks concludes (commentary on fragment 63, pp. 194–207): "Whether Synesius' evidence can be accepted at its face value depends on the view taken as to the strength of the objections raised above. On the whole, it would seem that the value of his testimony has been greatly exaggerated, and its unsatisfactory nature on so many points insufficiently emphasized. At any rate, the 'instrument' he sent to Paeonius was either a modified astrolabic clock of the Vitruvian type or a simple celestial map, and not a planispheric astrolabe. Furthermore, on the evidence available we are not, in my opinion, justified in attributing to Hipparchus a knowledge of either stereographic projection or the planispheric astrolabe."</span> </li> <li id="cite_note-neugebauer1949-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-neugebauer1949_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeugebauer1949" class="citation journal cs1"><a href="/wiki/Otto_Neugebauer" class="mw-redirect" title="Otto Neugebauer">Neugebauer, Otto</a> (1949). "The Early History of the Astrolabe". <i>Isis</i>. <b>40</b> (3): 240–256. <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%2F349045">10.1086/349045</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/227240">227240</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:144350543">144350543</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=The+Early+History+of+the+Astrolabe&rft.volume=40&rft.issue=3&rft.pages=240-256&rft.date=1949&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A144350543%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F227240%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1086%2F349045&rft.aulast=Neugebauer&rft.aufirst=Otto&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-toomer1980-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-toomer1980_26-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-toomer1980_26-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToomer1980" class="citation journal cs1"><a href="/wiki/Gerald_J._Toomer" title="Gerald J. Toomer">Toomer, Gerald J.</a> (1980). "Hipparchus' Empirical Basis for his Lunar Mean Motions". <i>Centaurus</i>. <b>24</b> (1): 97–109. <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/1980Cent...24...97T">1980Cent...24...97T</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.1600-0498.1980.tb00367.x">10.1111/j.1600-0498.1980.tb00367.x</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=Hipparchus%27+Empirical+Basis+for+his+Lunar+Mean+Motions&rft.volume=24&rft.issue=1&rft.pages=97-109&rft.date=1980&rft_id=info%3Adoi%2F10.1111%2Fj.1600-0498.1980.tb00367.x&rft_id=info%3Abibcode%2F1980Cent...24...97T&rft.aulast=Toomer&rft.aufirst=Gerald+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-sf1993-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-sf1993_27-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStephensonFatoohi1993" class="citation journal cs1">Stephenson, F. Richard; Fatoohi, Louay J. (1993). <a rel="nofollow" class="external text" href="https://articles.adsabs.harvard.edu/full/1993JHA....24..255S">"Lunar Eclipse Times Recorded in Babylonian History"</a>. <i>Journal for the History of Astronomy</i>. <b>24</b> (4): 255–267. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F002182869302400402">10.1177/002182869302400402</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/0021-8286">0021-8286</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/812872940">812872940</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+for+the+History+of+Astronomy&rft.atitle=Lunar+Eclipse+Times+Recorded+in+Babylonian+History&rft.volume=24&rft.issue=4&rft.pages=255-267&rft.date=1993&rft_id=info%3Aoclcnum%2F812872940&rft.issn=0021-8286&rft_id=info%3Adoi%2F10.1177%2F002182869302400402&rft.aulast=Stephenson&rft.aufirst=F.+Richard&rft.au=Fatoohi%2C+Louay+J.&rft_id=https%3A%2F%2Farticles.adsabs.harvard.edu%2Ffull%2F1993JHA....24..255S&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-ssm1997-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-ssm1997_28-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSteeleStephensonMorrison1997" class="citation journal cs1">Steele, J. M.; Stephenson, F. R.; Morrison, L. V. (1997). <a rel="nofollow" class="external text" href="https://articles.adsabs.harvard.edu/full/1997JHA....28..337S">"The Accuracy of Eclipse Times Measured by the Babylonians"</a>. <i>Journal for the History of Astronomy</i>. <b>28</b> (4): 337–345. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F002182869702800404">10.1177/002182869702800404</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/0021-8286">0021-8286</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/5723829772">5723829772</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+for+the+History+of+Astronomy&rft.atitle=The+Accuracy+of+Eclipse+Times+Measured+by+the+Babylonians&rft.volume=28&rft.issue=4&rft.pages=337-345&rft.date=1997&rft_id=info%3Aoclcnum%2F5723829772&rft.issn=0021-8286&rft_id=info%3Adoi%2F10.1177%2F002182869702800404&rft.aulast=Steele&rft.aufirst=J.+M.&rft.au=Stephenson%2C+F.+R.&rft.au=Morrison%2C+L.+V.&rft_id=https%3A%2F%2Farticles.adsabs.harvard.edu%2Ffull%2F1997JHA....28..337S&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-ccf2002-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-ccf2002_29-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChaprontChapront-TouzéFrancou2002" class="citation journal cs1">Chapront, J.; Chapront-Touzé, M.; Francou, G. (2002). <a rel="nofollow" class="external text" href="https://doi.org/10.1051%2F0004-6361%3A20020420">"A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements"</a>. <i>Astronomy & Astrophysics</i>. <b>387</b> (2): 700–709. <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/2002A&A...387..700C">2002A&A...387..700C</a>. <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/10.1051%2F0004-6361%3A20020420">10.1051/0004-6361:20020420</a></span>. <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:55131241">55131241</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+%26+Astrophysics&rft.atitle=A+new+determination+of+lunar+orbital+parameters%2C+precession+constant+and+tidal+acceleration+from+LLR+measurements&rft.volume=387&rft.issue=2&rft.pages=700-709&rft.date=2002&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A55131241%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1051%2F0004-6361%3A20020420&rft_id=info%3Abibcode%2F2002A%26A...387..700C&rft.aulast=Chapront&rft.aufirst=J.&rft.au=Chapront-Touz%C3%A9%2C+M.&rft.au=Francou%2C+G.&rft_id=https%3A%2F%2Fdoi.org%2F10.1051%252F0004-6361%253A20020420&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEThurston2002-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEThurston2002_30-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFThurston2002">Thurston 2002</a>.</span> </li> <li id="cite_note-toomer1968-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-toomer1968_31-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToomer1968" class="citation journal cs1"><a href="/wiki/Gerald_J._Toomer" title="Gerald J. Toomer">Toomer, Gerald J.</a> (1968). "The Size of the Lunar Epicycle According to Hipparchus". <i>Centaurus</i>. <b>12</b> (3): 145–150. <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/1968Cent...12..145T">1968Cent...12..145T</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.1600-0498.1968.tb00087.x">10.1111/j.1600-0498.1968.tb00087.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/0008-8994">0008-8994</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/4656032977">4656032977</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+Size+of+the+Lunar+Epicycle+According+to+Hipparchus&rft.volume=12&rft.issue=3&rft.pages=145-150&rft.date=1968&rft_id=info%3Aoclcnum%2F4656032977&rft.issn=0008-8994&rft_id=info%3Adoi%2F10.1111%2Fj.1600-0498.1968.tb00087.x&rft_id=info%3Abibcode%2F1968Cent...12..145T&rft.aulast=Toomer&rft.aufirst=Gerald+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-leverington2003-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-leverington2003_32-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeverington2003" class="citation book cs1">Leverington, David (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6Hpi202ybn8C&pg=PA30"><i>Babylon to Voyager and Beyond: A History of Planetary Astronomy</i></a>. Cambridge University Press. p. 30. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521808408" title="Special:BookSources/9780521808408"><bdi>9780521808408</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Babylon+to+Voyager+and+Beyond%3A+A+History+of+Planetary+Astronomy&rft.pages=30&rft.pub=Cambridge+University+Press&rft.date=2003&rft.isbn=9780521808408&rft.aulast=Leverington&rft.aufirst=David&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D6Hpi202ybn8C%26pg%3DPA30&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTENeugebauer1975Vol._1,_pp._293,_294-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTENeugebauer1975Vol._1,_pp._293,_294_33-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFNeugebauer1975">Neugebauer 1975</a>, Vol. 1, pp. 293, 294.</span> </li> <li id="cite_note-FOOTNOTEThurston2002p._67,_note_16-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEThurston2002p._67,_note_16_34-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFThurston2002">Thurston 2002</a>, p. 67, note 16.</span> </li> <li id="cite_note-FOOTNOTEThurston2002note_14-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEThurston2002note_14_35-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFThurston2002">Thurston 2002</a>, note 14.</span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</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://eclipse.gsfc.nasa.gov/SEcat5/SE-0199--0100.html">"Five Millennium Catalog of Solar Eclipses"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150425070114/http://eclipse.gsfc.nasa.gov/SEcat5/SE-0199--0100.html">Archived</a> from the original on 25 April 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">11 August</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Five+Millennium+Catalog+of+Solar+Eclipses&rft_id=http%3A%2F%2Feclipse.gsfc.nasa.gov%2FSEcat5%2FSE-0199--0100.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span>, #04310, Fred Espenak, NASA/GSFC</span> </li> <li id="cite_note-toomer1974-sunmoon-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-toomer1974-sunmoon_37-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToomer1974" class="citation journal cs1"><a href="/wiki/Gerald_J._Toomer" title="Gerald J. Toomer">Toomer, Gerald J.</a> (1974). "Hipparchus on the Distances of the Sun and Moon". <i>Archive for History of Exact Sciences</i>. <b>14</b> (2): 126–142. <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%2FBF00329826">10.1007/BF00329826</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:122093782">122093782</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=Hipparchus+on+the+Distances+of+the+Sun+and+Moon&rft.volume=14&rft.issue=2&rft.pages=126-142&rft.date=1974&rft_id=info%3Adoi%2F10.1007%2FBF00329826&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122093782%23id-name%3DS2CID&rft.aulast=Toomer&rft.aufirst=Gerald+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-swerdlow1992-38"><span class="mw-cite-backlink">^ <a href="#cite_ref-swerdlow1992_38-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-swerdlow1992_38-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-swerdlow1992_38-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSwerdlow1992" class="citation journal cs1">Swerdlow, N. M. (1992). "The Enigma of Ptolemy's Catalogue of Stars". <i>Journal for the History of Astronomy</i>. <b>23</b> (3): 173–183. <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/1992JHA....23..173S">1992JHA....23..173S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F002182869202300303">10.1177/002182869202300303</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:116612700">116612700</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+for+the+History+of+Astronomy&rft.atitle=The+Enigma+of+Ptolemy%27s+Catalogue+of+Stars&rft.volume=23&rft.issue=3&rft.pages=173-183&rft.date=1992&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A116612700%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1177%2F002182869202300303&rft_id=info%3Abibcode%2F1992JHA....23..173S&rft.aulast=Swerdlow&rft.aufirst=N.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-gwz2022-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-gwz2022_39-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGysemberghWilliamsZingg2022" class="citation journal cs1">Gysembergh, Victor; Williams, Peter J.; Zingg, Emanuel (2022). <a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F00218286221128289">"New evidence for Hipparchus' Star Catalog revealed by multispectral imaging"</a>. <i>Journal for the History of Astronomy</i>. <b>53</b> (4): 383–393. <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/2022JHA....53..383G">2022JHA....53..383G</a>. <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/10.1177%2F00218286221128289">10.1177/00218286221128289</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+for+the+History+of+Astronomy&rft.atitle=New+evidence+for+Hipparchus%27+Star+Catalog+revealed+by+multispectral+imaging&rft.volume=53&rft.issue=4&rft.pages=383-393&rft.date=2022&rft_id=info%3Adoi%2F10.1177%2F00218286221128289&rft_id=info%3Abibcode%2F2022JHA....53..383G&rft.aulast=Gysembergh&rft.aufirst=Victor&rft.au=Williams%2C+Peter+J.&rft.au=Zingg%2C+Emanuel&rft_id=https%3A%2F%2Fdoi.org%2F10.1177%252F00218286221128289&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarchant2022" class="citation journal cs1">Marchant, Jo (18 October 2022). <a rel="nofollow" class="external text" href="https://www.nature.com/articles/d41586-022-03296-1">"First known map of night sky found hidden in Medieval parchment"</a>. <i>Nature News</i>. <b>610</b> (7933): 613–614. <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/2022Natur.610..613M">2022Natur.610..613M</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%2Fd41586-022-03296-1">10.1038/d41586-022-03296-1</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/36258126">36258126</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:252994351">252994351</a><span class="reference-accessdate">. Retrieved <span class="nowrap">22 October</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+News&rft.atitle=First+known+map+of+night+sky+found+hidden+in+Medieval+parchment&rft.volume=610&rft.issue=7933&rft.pages=613-614&rft.date=2022-10-18&rft_id=info%3Adoi%2F10.1038%2Fd41586-022-03296-1&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A252994351%23id-name%3DS2CID&rft_id=info%3Apmid%2F36258126&rft_id=info%3Abibcode%2F2022Natur.610..613M&rft.aulast=Marchant&rft.aufirst=Jo&rft_id=https%3A%2F%2Fwww.nature.com%2Farticles%2Fd41586-022-03296-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-ks-engraving-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-ks-engraving_41-0">^</a></b></span> <span class="reference-text"> Image by Charles Kreutzberger and Louis Sargent, printed in: <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFiguier1866" class="citation book cs1">Figuier, Louis (1866). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=eTo-AAAAcAAJ&pg=PA283-IA2"><i>Vies des savants illustres</i></a>. Librairie Internationale. p. 284.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vies+des+savants+illustres&rft.pages=284&rft.pub=Librairie+Internationale&rft.date=1866&rft.aulast=Figuier&rft.aufirst=Louis&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DeTo-AAAAcAAJ%26pg%3DPA283-IA2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span> Reprinted with artists' signatures trimmed in: <div class="paragraphbreak" style="margin-top:0.5em"></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYaggyHaines1880" class="citation book cs1">Yaggy, Levy W.; Haines, Thomas L. (1880). <a rel="nofollow" class="external text" href="https://archive.org/details/museumofantiquit00yagg_0/page/745/mode/1up"><i>Museum of Antiquity</i></a>. Western Publishing House. p. 745.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Museum+of+Antiquity&rft.pages=745&rft.pub=Western+Publishing+House&rft.date=1880&rft.aulast=Yaggy&rft.aufirst=Levy+W.&rft.au=Haines%2C+Thomas+L.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmuseumofantiquit00yagg_0%2Fpage%2F745%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span> </p> </span></li> <li id="cite_note-FOOTNOTEHoffmann2017-42"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEHoffmann2017_42-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHoffmann2017_42-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHoffmann2017_42-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHoffmann2017_42-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHoffmann2017_42-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHoffmann2017_42-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHoffmann2017_42-6"><sup><i><b>g</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFHoffmann2017">Hoffmann 2017</a>.</span> </li> <li id="cite_note-FOOTNOTEToomer1984[httpsarchiveorgdetailsptolemysalmagest0000ptolpage16_p.&nbsp;16]:_"The_magnitudes_range_(according_to_a_system_which_certainly_precedes_Ptolemy,_but_is_only_conjecturally_attributed_to_Hipparchus)_from_1_to_6.",_pp.&nbsp;341–399-43"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEToomer1984[httpsarchiveorgdetailsptolemysalmagest0000ptolpage16_p.&nbsp;16]:_"The_magnitudes_range_(according_to_a_system_which_certainly_precedes_Ptolemy,_but_is_only_conjecturally_attributed_to_Hipparchus)_from_1_to_6.",_pp.&nbsp;341–399_43-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEToomer1984[httpsarchiveorgdetailsptolemysalmagest0000ptolpage16_p.&nbsp;16]:_"The_magnitudes_range_(according_to_a_system_which_certainly_precedes_Ptolemy,_but_is_only_conjecturally_attributed_to_Hipparchus)_from_1_to_6.",_pp.&nbsp;341–399_43-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFToomer1984">Toomer 1984</a>, <a rel="nofollow" class="external text" href="https://archive.org/details/ptolemysalmagest0000ptol/page/16/">p. 16</a>: "The magnitudes range (according to a system which certainly precedes Ptolemy, but is only conjecturally attributed to Hipparchus) from 1 to 6.", pp. 341–399.</span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPogson1856" class="citation journal cs1"><a href="/wiki/Norman_Robert_Pogson" class="mw-redirect" title="Norman Robert Pogson">Pogson, N. R.</a> (1856). <a rel="nofollow" class="external text" href="http://articles.adsabs.harvard.edu//full/seri/MNRAS/0017//0000012.000.html">"Magnitudes of Thirty-six of the Minor Planets for the first day of each month of the year 1857"</a>. <i><a href="/wiki/Monthly_Notices_of_the_Royal_Astronomical_Society" title="Monthly Notices of the Royal Astronomical Society">MNRAS</a></i>. <b>17</b>: 12. <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/1856MNRAS..17...12P">1856MNRAS..17...12P</a>. <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/10.1093%2Fmnras%2F17.1.12">10.1093/mnras/17.1.12</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=MNRAS&rft.atitle=Magnitudes+of+Thirty-six+of+the+Minor+Planets+for+the+first+day+of+each+month+of+the+year+1857&rft.volume=17&rft.pages=12&rft.date=1856&rft_id=info%3Adoi%2F10.1093%2Fmnras%2F17.1.12&rft_id=info%3Abibcode%2F1856MNRAS..17...12P&rft.aulast=Pogson&rft.aufirst=N.+R.&rft_id=http%3A%2F%2Farticles.adsabs.harvard.edu%2F%2Ffull%2Fseri%2FMNRAS%2F0017%2F%2F0000012.000.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1977" class="citation book cs1">Newton, Robert Russell (1977). <a rel="nofollow" class="external text" href="https://archive.org/details/crime-of-cladius-ptolemy"><i>The Crime of Claudius Ptolemy</i></a>. Baltimore, MD: Johns Hopkins University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8018-1990-2" title="Special:BookSources/978-0-8018-1990-2"><bdi>978-0-8018-1990-2</bdi></a> – via <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Crime+of+Claudius+Ptolemy&rft.place=Baltimore%2C+MD&rft.pub=Johns+Hopkins+University+Press&rft.date=1977&rft.isbn=978-0-8018-1990-2&rft.aulast=Newton&rft.aufirst=Robert+Russell&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcrime-of-cladius-ptolemy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-hoffmann2018-46"><span class="mw-cite-backlink">^ <a href="#cite_ref-hoffmann2018_46-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-hoffmann2018_46-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoffmann2018" class="citation journal cs1">Hoffmann, Susanne M. (2018). <a rel="nofollow" class="external text" href="https://www.maajournal.com/index.php/maa/article/view/738">"The Genesis of Hipparchus' Celestial Globe"</a>. <i>Mediterranean Archaeology and Archaeometry</i>. <b>18</b> (4): 281. <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/2241-8121">2241-8121</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mediterranean+Archaeology+and+Archaeometry&rft.atitle=The+Genesis+of+Hipparchus%27+Celestial+Globe&rft.volume=18&rft.issue=4&rft.pages=281&rft.date=2018&rft.issn=2241-8121&rft.aulast=Hoffmann&rft.aufirst=Susanne+M.&rft_id=https%3A%2F%2Fwww.maajournal.com%2Findex.php%2Fmaa%2Farticle%2Fview%2F738&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-jones2010-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-jones2010_47-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJones2010" class="citation book cs1">Jones, Alexander (2010). "Ancient Rejection and Adoption of Ptolemy's Frame of Reference for Longitudes". In Jones, Alexander (ed.). <i>Ptolemy in Perspective</i>. Archimedes. Vol. 23. Springer. p. 36. <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%2F978-90-481-2788-7_2">10.1007/978-90-481-2788-7_2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-481-2787-0" title="Special:BookSources/978-90-481-2787-0"><bdi>978-90-481-2787-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Ancient+Rejection+and+Adoption+of+Ptolemy%27s+Frame+of+Reference+for+Longitudes&rft.btitle=Ptolemy+in+Perspective&rft.series=Archimedes&rft.pages=36&rft.pub=Springer&rft.date=2010&rft_id=info%3Adoi%2F10.1007%2F978-90-481-2788-7_2&rft.isbn=978-90-481-2787-0&rft.aulast=Jones&rft.aufirst=Alexander&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text">Editions of fragments: <a href="#CITEREFBerger1869">Berger 1869</a> (Latin), <a href="#CITEREFDicks1960">Dicks 1960</a> (English).</span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text">On Hipparchus's geography see: <a href="#CITEREFBerger1869">Berger 1869</a>; <a href="#CITEREFDicks1960">Dicks 1960</a>; <a href="#CITEREFNeugebauer1975">Neugebauer 1975</a>, <a rel="nofollow" class="external text" href="https://archive.org/details/historyofancient0000neug/page/332/">pp. 332–338</a>; <a href="#CITEREFShcheglov2007">Shcheglov 2007</a>.</span> </li> <li id="cite_note-shcheglov2010-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-shcheglov2010_50-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShcheglov2010" class="citation journal cs1">Shcheglov, Dmitriy A. (2010). <a rel="nofollow" class="external text" href="https://grbs.library.duke.edu/index.php/grbs/article/view/361">"Hipparchus on the Latitude of Southern India"</a>. <i>Greek, Roman, and Byzantine Studies</i>. <b>45</b> (4): 359–380. <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/0017-3916">0017-3916</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/7179548964">7179548964</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Greek%2C+Roman%2C+and+Byzantine+Studies&rft.atitle=Hipparchus+on+the+Latitude+of+Southern+India&rft.volume=45&rft.issue=4&rft.pages=359-380&rft.date=2010&rft_id=info%3Aoclcnum%2F7179548964&rft.issn=0017-3916&rft.aulast=Shcheglov&rft.aufirst=Dmitriy+A.&rft_id=https%3A%2F%2Fgrbs.library.duke.edu%2Findex.php%2Fgrbs%2Farticle%2Fview%2F361&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-shcheglov2006-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-shcheglov2006_51-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShcheglov2006" class="citation journal cs1">Shcheglov, Dmitriy A. (2006). "Eratosthenes' Parallel of Rhodes and the History of the System of Climata". <i>Klio</i>. <b>88</b> (2). Walter de Gruyter: 351–359. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1524%2Fklio.2006.88.2.351">10.1524/klio.2006.88.2.351</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/2192-7669">2192-7669</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/7003041189">7003041189</a>. <a href="/wiki/Academia.edu" title="Academia.edu">Academia</a>:<a rel="nofollow" class="external text" href="https://www.academia.edu/191065">191065</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Klio&rft.atitle=Eratosthenes%27+Parallel+of+Rhodes+and+the+History+of+the+System+of+Climata&rft.volume=88&rft.issue=2&rft.pages=351-359&rft.date=2006&rft_id=info%3Aoclcnum%2F7003041189&rft.issn=2192-7669&rft_id=info%3Adoi%2F10.1524%2Fklio.2006.88.2.351&rft.aulast=Shcheglov&rft.aufirst=Dmitriy+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEShcheglov2007-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEShcheglov2007_52-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFShcheglov2007">Shcheglov 2007</a>.</span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text">Diller A. (1934). "Geographical Latitudes in Eratosthenes, Hipparchus and Posidonius". <i>Klio</i> 27.3: 258–269; cf. <a href="#CITEREFShcheglov2007">Shcheglov 2007</a>, pp. 177–180.</span> </li> <li id="cite_note-shcheglov2007-thule-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-shcheglov2007-thule_54-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1">Shcheglov, D.A. (2007). "Ptolemy's Latitude of Thule and the Map Projection in the Pre-Ptolemaic Geography". <i>Antike Naturwissenschaft und Ihre Rezeption (AKAN)</i>. <b>17</b>: 121–151 (esp. 132–139). <a href="/wiki/Academia.edu" title="Academia.edu">Academia</a>:<a rel="nofollow" class="external text" href="https://www.academia.edu/213001">213001</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Antike+Naturwissenschaft+und+Ihre+Rezeption+%28AKAN%29&rft.atitle=Ptolemy%27s+Latitude+of+Thule+and+the+Map+Projection+in+the+Pre-Ptolemaic+Geography&rft.volume=17&rft.pages=121-151+%28esp.+132-139%29&rft.date=2007&rft.aulast=Shcheglov&rft.aufirst=D.A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchaefer2005" class="citation journal cs1">Schaefer, Bradley Elliott (2005). <a rel="nofollow" class="external text" href="https://digitalcommons.lsu.edu/physics_astronomy_pubs/4735">"The epoch of the constellations on the Farnese Atlas and their origin in Hipparchus's lost catalogue"</a>. <i>Journal for the History of Astronomy</i>. <b>36</b> (2): 167–196. <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/2005JHA....36..167S">2005JHA....36..167S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F002182860503600202">10.1177/002182860503600202</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:15431718">15431718</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+for+the+History+of+Astronomy&rft.atitle=The+epoch+of+the+constellations+on+the+Farnese+Atlas+and+their+origin+in+Hipparchus%27s+lost+catalogue&rft.volume=36&rft.issue=2&rft.pages=167-196&rft.date=2005&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15431718%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1177%2F002182860503600202&rft_id=info%3Abibcode%2F2005JHA....36..167S&rft.aulast=Schaefer&rft.aufirst=Bradley+Elliott&rft_id=https%3A%2F%2Fdigitalcommons.lsu.edu%2Fphysics_astronomy_pubs%2F4735&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuke2006" class="citation journal cs1 cs1-prop-long-vol">Duke, Dennis W. (February 2006). "Analysis of the Farnese Globe". <i>Journal for the History of Astronomy</i>. 37, Part 1 (126): 87–100. <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/2006JHA....37...87D">2006JHA....37...87D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F002182860603700107">10.1177/002182860603700107</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:36841784">36841784</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+for+the+History+of+Astronomy&rft.atitle=Analysis+of+the+Farnese+Globe&rft.volume=37%2C+Part+1&rft.issue=126&rft.pages=87-100&rft.date=2006-02&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A36841784%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1177%2F002182860603700107&rft_id=info%3Abibcode%2F2006JHA....37...87D&rft.aulast=Duke&rft.aufirst=Dennis+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-stanley1997-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-stanley1997_57-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStanley1997" class="citation journal cs1"><a href="/wiki/Richard_P._Stanley" title="Richard P. Stanley">Stanley, Richard P.</a> (1997). <a rel="nofollow" class="external text" href="http://www-math.mit.edu/~rstan/papers/hip.pdf">"Hipparchus, Plutarch, Schröder, and Hough"</a> <span class="cs1-format">(PDF)</span>. <i>The American Mathematical Monthly</i>. <b>104</b> (4): 344–350. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2974582">10.2307/2974582</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2974582">2974582</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=Hipparchus%2C+Plutarch%2C+Schr%C3%B6der%2C+and+Hough&rft.volume=104&rft.issue=4&rft.pages=344-350&rft.date=1997&rft_id=info%3Adoi%2F10.2307%2F2974582&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2974582%23id-name%3DJSTOR&rft.aulast=Stanley&rft.aufirst=Richard+P.&rft_id=http%3A%2F%2Fwww-math.mit.edu%2F~rstan%2Fpapers%2Fhip.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-acerbi2003-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-acerbi2003_58-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAcerbi2003" class="citation journal cs1">Acerbi, F. (2003). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110721023220/http://stl.recherche.univ-lille3.fr/sitespersonnels/acerbi/acerbipub5.pdf">"On the shoulders of Hipparchus: A reappraisal of ancient Greek combinatorics"</a> <span class="cs1-format">(PDF)</span>. <i>Archive for History of Exact Sciences</i>. <b>57</b> (6): 465–502. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00407-003-0067-0">10.1007/s00407-003-0067-0</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:122758966">122758966</a>. Archived from <a rel="nofollow" class="external text" href="http://stl.recherche.univ-lille3.fr/sitespersonnels/acerbi/acerbipub5.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 21 July 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=On+the+shoulders+of+Hipparchus%3A+A+reappraisal+of+ancient+Greek+combinatorics&rft.volume=57&rft.issue=6&rft.pages=465-502&rft.date=2003&rft_id=info%3Adoi%2F10.1007%2Fs00407-003-0067-0&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122758966%23id-name%3DS2CID&rft.aulast=Acerbi&rft.aufirst=F.&rft_id=http%3A%2F%2Fstl.recherche.univ-lille3.fr%2Fsitespersonnels%2Facerbi%2Facerbipub5.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRené_Bourtembourg2013" class="citation journal cs1">René Bourtembourg (2013). "Was Uranus Observed by Hipparchos?". <i>Journal for the History of Astronomy</i>. <b>44</b> (4): 377–387. <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/2013JHA....44..377B">2013JHA....44..377B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F002182861304400401">10.1177/002182861304400401</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:122482074">122482074</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+for+the+History+of+Astronomy&rft.atitle=Was+Uranus+Observed+by+Hipparchos%3F&rft.volume=44&rft.issue=4&rft.pages=377-387&rft.date=2013&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122482074%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1177%2F002182861304400401&rft_id=info%3Abibcode%2F2013JHA....44..377B&rft.au=Ren%C3%A9+Bourtembourg&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-ep4-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-ep4_60-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.newspapers.com/clip/29988299/el_paso_times/">"X-Prize Group Founder to Speak at Induction"</a>. <i>El Paso Times</i>. El Paso, Texas. 17 October 2004. p. 59.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=El+Paso+Times&rft.atitle=X-Prize+Group+Founder+to+Speak+at+Induction&rft.pages=59&rft.date=2004-10-17&rft_id=https%3A%2F%2Fwww.newspapers.com%2Fclip%2F29988299%2Fel_paso_times%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-delambre1827-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-delambre1827_61-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDelambre1827" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Jean_Baptiste_Joseph_Delambre" title="Jean Baptiste Joseph Delambre">Delambre, Jean Baptiste Joseph</a> (1827). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ps1WS1-5_dYC&pg=PA413"><i>Histoire de l'astronomie au dix-huitième siècle</i></a> [<i>History of astronomy in the 18th century</i>] (in French). Paris: Bachelier. p. 413 (see also <span class="nowrap">pp. xvii</span> and 420).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Histoire+de+l%27astronomie+au+dix-huiti%C3%A8me+si%C3%A8cle&rft.place=Paris&rft.pages=413+%28see+also+%3Cspan+class%3D%22nowrap%22%3Epp.+xvii%3C%2Fspan%3E+and+420%29&rft.pub=Bachelier&rft.date=1827&rft.aulast=Delambre&rft.aufirst=Jean+Baptiste+Joseph&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dps1WS1-5_dYC%26pg%3DPA413&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://griffithobservatory.org/exhibits/astronomers-monument-sundial/">"Astronomers Monument & Sundial"</a>. <i>Griffith Observatory</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Astronomers+Monument+%26+Sundial&rft.btitle=Griffith+Observatory&rft_id=https%3A%2F%2Fgriffithobservatory.org%2Fexhibits%2Fastronomers-monument-sundial%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> <li id="cite_note-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-63">^</a></b></span> <span class="reference-text">Christianson, J. R. (2000). <i>On Tycho's Island: Tycho Brahe and His Assistants, 1570–1601</i>. Cambridge: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, p 304.</span> </li> <li id="cite_note-gem-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-gem_64-0">^</a></b></span> <span class="reference-text"> "Head of Hipparchus", CARC:<a rel="nofollow" class="external text" href="https://www.beazley.ox.ac.uk/record/1AB583C8-C0E7-4D77-B9E7-9167C2BC80C5">1839-881</a>, described in Poniatowski's 1830–1833 catalog <i>Catalogue des pierres gravées antiques</i> (VIII.2.60, <a rel="nofollow" class="external text" href="https://polona.pl/item-view/2aab1313-ee74-4932-b53a-f37c66aa49c0?page=136">vol. 1, p. 105</a>, <a rel="nofollow" class="external text" href="https://polona.pl/item-view/7f06b3df-503a-43d8-b2d7-7d9661255993?page=51">vol. 2, p. 52</a>) and included in <a href="/wiki/Christie%27s" title="Christie's">Christie's</a> 1839 auction (<i>A catalogue of the very celebrated collection of antique gems of the Prince Poniatowski</i> ..., No. 881), with whereabouts since unknown.</span> </li> <li id="cite_note-smyth-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-smyth_65-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://archive.org/details/bulletinofprocee01usan/page/258/">"Stated Meeting, September 12, 1842"</a>. Letters and Communications. <i>Bulletin of the Proceedings of the National Institute for the Promotion of Science</i>. <b>3</b>: 258. 1845.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+Proceedings+of+the+National+Institute+for+the+Promotion+of+Science&rft.atitle=Stated+Meeting%2C+September+12%2C+1842&rft.volume=3&rft.pages=258&rft.date=1845&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbulletinofprocee01usan%2Fpage%2F258%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmyth1844" class="citation book cs1"><a href="/wiki/William_Henry_Smyth" title="William Henry Smyth">Smyth, William Henry</a> (1844). <a rel="nofollow" class="external text" href="https://archive.org/details/cycleofcelestial02smytrich/page/n10/mode/1up"><i>A Cycle of Celestial Objects, for the use of naval, military, and private astronomers</i></a>. Vol. 2. London: J.W. Parker. Title page. <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/1042977120">1042977120</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Cycle+of+Celestial+Objects%2C+for+the+use+of+naval%2C+military%2C+and+private+astronomers&rft.place=London&rft.pages=Title+page&rft.pub=J.W.+Parker&rft.date=1844&rft_id=info%3Aoclcnum%2F1042977120&rft.aulast=Smyth&rft.aufirst=William+Henry&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcycleofcelestial02smytrich%2Fpage%2Fn10%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span> </p> </span></li> <li id="cite_note-wilson1989-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-wilson1989_66-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilson1989" class="citation journal cs1">Wilson, Robin (1989). "Stamp corner". <i><a href="/wiki/The_Mathematical_Intelligencer" title="The Mathematical Intelligencer">The Mathematical Intelligencer</a></i>. <b>11</b> (1): 72. <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%2Fbf03023779">10.1007/bf03023779</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:189887329">189887329</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=Stamp+corner&rft.volume=11&rft.issue=1&rft.pages=72&rft.date=1989&rft_id=info%3Adoi%2F10.1007%2Fbf03023779&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A189887329%23id-name%3DS2CID&rft.aulast=Wilson&rft.aufirst=Robin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Works_cited">Works cited</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hipparchus&action=edit&section=25" title="Edit section: Works cited"><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="CITEREFBerger1869" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/w/index.php?title=Ernst_Hugo_Berger&action=edit&redlink=1" class="new" title="Ernst Hugo Berger (page does not exist)">Berger, Ernst Hugo</a>, ed. (1869). <a rel="nofollow" class="external text" href="https://archive.org/details/diegeographisch03hippgoog/page/n5/mode/2up"><i>Die geographischen Fragmente des Hipparch</i></a> [<i>The Geographical Fragments of Hipparchus</i>] (in German). Leipzig: Teubner. <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/981902787">981902787</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Die+geographischen+Fragmente+des+Hipparch&rft.place=Leipzig&rft.pub=Teubner&rft.date=1869&rft_id=info%3Aoclcnum%2F981902787&rft.au=Hipparchus&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdiegeographisch03hippgoog%2Fpage%2Fn5%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCusinatoVanin2022" class="citation book cs1 cs1-prop-foreign-lang-source">Cusinato, Bruna; Vanin, Gabriele, eds. (2022) [2013]. <i>Commentari di Ipparco ai Fenomeni di Arato ed Eudosso</i> [<i>Hipparchus' Commentaries on the Phenomena of Aratus and Eudoxus</i>] (in Italian). Translation by Bruna Cusinato; Introduction and astronomical commentary by Gabriele Vanin (3rd ed.). <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2206.08243">2206.08243</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Commentari+di+Ipparco+ai+Fenomeni+di+Arato+ed+Eudosso&rft.edition=3rd&rft.date=2022&rft_id=info%3Aarxiv%2F2206.08243&rft.au=Hipparchus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDicks1960" class="citation book cs1">Dicks, D. R., ed. (1960). <i>The Geographical Fragments of Hipparchus</i>. University of London classical studies. London: Athlone Press. <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/490381">490381</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Geographical+Fragments+of+Hipparchus&rft.place=London&rft.series=University+of+London+classical+studies&rft.pub=Athlone+Press&rft.date=1960&rft_id=info%3Aoclcnum%2F490381&rft.au=Hipparchus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoffmann2017" class="citation book cs1 cs1-prop-foreign-lang-source">Hoffmann, Susanne M. (2017). <i>Hipparchs Himmelsglobus: Ein Bindeglied in der babylonisch-griechischen Astrometrie?</i> [<i>Hipparchus' Celestial Globe: A Link in Babylonian-Greek Astrometry?</i>] (in German). Wiesbaden: Springer. <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%2F978-3-658-18683-8">10.1007/978-3-658-18683-8</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-658-18683-8" title="Special:BookSources/978-3-658-18683-8"><bdi>978-3-658-18683-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hipparchs+Himmelsglobus%3A+Ein+Bindeglied+in+der+babylonisch-griechischen+Astrometrie%3F&rft.place=Wiesbaden&rft.pub=Springer&rft.date=2017&rft_id=info%3Adoi%2F10.1007%2F978-3-658-18683-8&rft.isbn=978-3-658-18683-8&rft.aulast=Hoffmann&rft.aufirst=Susanne+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJones2001" class="citation encyclopaedia cs1">Jones, Alexander (2001). <a rel="nofollow" class="external text" href="https://archive.org/details/encyclopedia-of-astronomy-and-astrophysics-4-volumes-2001/page/n1719/mode/2up">"Hipparchus"</a>. In Murdin, Paul (ed.). <i>Encyclopedia of Astronomy and Astrophysics</i>. Bristol: Institute of Physics Pub. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-333-75088-9" title="Special:BookSources/978-0-333-75088-9"><bdi>978-0-333-75088-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1193410336">1193410336</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hipparchus&rft.btitle=Encyclopedia+of+Astronomy+and+Astrophysics&rft.place=Bristol&rft.pub=Institute+of+Physics+Pub.&rft.date=2001&rft_id=info%3Aoclcnum%2F1193410336&rft.isbn=978-0-333-75088-9&rft.aulast=Jones&rft.aufirst=Alexander&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fencyclopedia-of-astronomy-and-astrophysics-4-volumes-2001%2Fpage%2Fn1719%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFManitius1894" class="citation book cs1 cs1-prop-foreign-lang-source-2 cs1-prop-foreign-lang-source"><a href="/wiki/Karl_Manitius" title="Karl Manitius">Manitius, Karl</a>, ed. (1894). <a rel="nofollow" class="external text" href="https://archive.org/details/McGillLibrary-hssl_hipparchou-ton-aratou_QB41H561894-18575"><i>Hipparchou Tōn Aratou kai Eudoxou Phainomenōn exēgēseōs vivlia tria = Hipparchi in Arati et Eudoxi Phaenomena commentariorum libri tres</i></a> [<i>Hipparchus' Commentaries on the Phenomena of Aratus and Eudoxus in three books</i>] (in Ancient Greek and Latin). Leipzig: Teubner. <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/1127047584">1127047584</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hipparchou+T%C5%8Dn+Aratou+kai+Eudoxou+Phainomen%C5%8Dn+ex%C4%93g%C4%93se%C5%8Ds+vivlia+tria+%3D+Hipparchi+in+Arati+et+Eudoxi+Phaenomena+commentariorum+libri+tres&rft.place=Leipzig&rft.pub=Teubner&rft.date=1894&rft_id=info%3Aoclcnum%2F1127047584&rft.au=Hipparchus&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2FMcGillLibrary-hssl_hipparchou-ton-aratou_QB41H561894-18575&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeugebauer1975" class="citation book cs1"><a href="/wiki/Otto_E._Neugebauer" title="Otto E. Neugebauer">Neugebauer, Otto E.</a> (1975). <i>A History of Ancient Mathematical Astronomy</i>. Berlin: Springer. <span class="nowrap"><a rel="nofollow" class="external text" href="https://archive.org/details/historyofancient0000neug">Part 1</a></span>, <span class="nowrap"><a rel="nofollow" class="external text" href="https://archive.org/details/historyofancient0000neug_v8q1">Part 2</a></span>, <span class="nowrap"><a rel="nofollow" class="external text" href="https://archive.org/details/historyofancient0000neug_z6r9">Part 3</a></span>.</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+Ancient+Mathematical+Astronomy&rft.place=Berlin&rft.pages=%3Cspan+class%3D%22nowrap%22%3EPart+1%3C%2Fspan%3E%2C+%3Cspan+class%3D%22nowrap%22%3EPart+2%3C%2Fspan%3E%2C+%3Cspan+class%3D%22nowrap%22%3EPart+3%3C%2Fspan%3E&rft.pub=Springer&rft.date=1975&rft.aulast=Neugebauer&rft.aufirst=Otto+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToomer1984" class="citation book cs1"><a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a> (1984). <a href="/wiki/Gerald_J._Toomer" title="Gerald J. Toomer">Toomer, Gerald J.</a> (ed.). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/ptolemysalmagest0000ptol/"><i>Ptolemy's Almagest</i></a></span>. London: Duckworth. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780387912202" title="Special:BookSources/9780387912202"><bdi>9780387912202</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ptolemy%27s+Almagest&rft.place=London&rft.pub=Duckworth&rft.date=1984&rft.isbn=9780387912202&rft.au=Ptolemy&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fptolemysalmagest0000ptol%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShcheglov2007" class="citation journal cs1">Shcheglov, Dmitry A. (2007). "Hipparchus' Table of Climata and Ptolemy's Geography". <i>Orbis Terrarum</i>. <b>9</b>: 159–192. <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/1385-285X">1385-285X</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/34941672">34941672</a>. <a href="/wiki/Academia.edu" title="Academia.edu">Academia</a>:<a rel="nofollow" class="external text" href="https://www.academia.edu/">214134 214134</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Orbis+Terrarum&rft.atitle=Hipparchus%27+Table+of+Climata+and+Ptolemy%27s+Geography&rft.volume=9&rft.pages=159-192&rft.date=2007&rft_id=info%3Aoclcnum%2F34941672&rft.issn=1385-285X&rft.aulast=Shcheglov&rft.aufirst=Dmitry+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThurston2002" class="citation journal cs1">Thurston, Hugh (2002). "Greek Mathematical Astronomy Reconsidered". <i>Isis</i>. <b>93</b> (1): 58–69. <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%2F343242">10.1086/343242</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/0021-1753">0021-1753</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/10.1086/343242">10.1086/343242</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/907786460">907786460</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:145527182">145527182</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=Greek+Mathematical+Astronomy+Reconsidered&rft.volume=93&rft.issue=1&rft.pages=58-69&rft.date=2002&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F10.1086%2F343242%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1086%2F343242&rft_id=info%3Aoclcnum%2F907786460&rft.issn=0021-1753&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A145527182%23id-name%3DS2CID&rft.aulast=Thurston&rft.aufirst=Hugh&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToomer1978" class="citation book cs1 cs1-prop-long-vol"><a href="/wiki/Gerald_J._Toomer" title="Gerald J. Toomer">Toomer, Gerald J.</a> (1978). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/dictionaryofscie1516char/page/n224/mode/1up">"Hipparchus"</a></span>. In Gillispie, C. C. (ed.). <i>Dictionary of Scientific Biography</i>. Vol. 15 (Supplement I, Adams–Sejszner). Scribner. pp. 207–224.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hipparchus&rft.btitle=Dictionary+of+Scientific+Biography&rft.pages=207-224&rft.pub=Scribner&rft.date=1978&rft.aulast=Toomer&rft.aufirst=Gerald+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdictionaryofscie1516char%2Fpage%2Fn224%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li></ul> <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=Hipparchus&action=edit&section=26" 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="CITEREFClerke1911" class="citation encyclopaedia cs1"><a href="/wiki/Agnes_Mary_Clerke" title="Agnes Mary Clerke">Clerke, Agnes Mary</a> (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Hipparchus"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Hipparchus">"Hipparchus" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 13 (11th ed.). p. 516.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hipparchus&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=516&rft.edition=11th&rft.date=1911&rft.aulast=Clerke&rft.aufirst=Agnes+Mary&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDreyer1953" class="citation book cs1"><a href="/wiki/John_Louis_Emil_Dreyer" title="John Louis Emil Dreyer">Dreyer, John L.E.</a> (1953). <i>A History of Astronomy from Thales to Kepler</i>. New York: Dover.</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+Astronomy+from+Thales+to+Kepler&rft.place=New+York&rft.pub=Dover&rft.date=1953&rft.aulast=Dreyer&rft.aufirst=John+L.E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeath1921" class="citation book cs1"><a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Heath, Thomas</a> (1921). <i>A History of Greek Mathematics</i>. Oxford: Clarendon. <span class="nowrap"><a rel="nofollow" class="external text" href="https://archive.org/details/historyofgreekma01heat/">Vol. 1</a></span>, <span class="nowrap"><a rel="nofollow" class="external text" href="https://archive.org/details/historyofgreekma00heat/">Vol. 2</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Greek+Mathematics&rft.place=Oxford&rft.pages=%3Cspan+class%3D%22nowrap%22%3EVol.+1%3C%2Fspan%3E%2C+%3Cspan+class%3D%22nowrap%22%3EVol.+2%3C%2Fspan%3E&rft.pub=Clarendon&rft.date=1921&rft.aulast=Heath&rft.aufirst=Thomas&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLloyd1973" class="citation book cs1"><a href="/wiki/G._E._R._Lloyd" title="G. E. R. Lloyd">Lloyd, G.E.R.</a> (1973). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/greekscienceafte00lloy"><i>Greek science after Aristotle</i></a></span>. New York: Norton. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-04371-6" title="Special:BookSources/978-0-393-04371-6"><bdi>978-0-393-04371-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Greek+science+after+Aristotle&rft.place=New+York&rft.pub=Norton&rft.date=1973&rft.isbn=978-0-393-04371-6&rft.aulast=Lloyd&rft.aufirst=G.E.R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgreekscienceafte00lloy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeugebauer1956" class="citation book cs1"><a href="/wiki/Otto_E._Neugebauer" title="Otto E. Neugebauer">Neugebauer, Otto E.</a> (1956). "Notes on Hipparchus". In Weinberg, Saul S (ed.). <i>The Aegean and the Near East: Studies Presented to Hetty Goldman</i>. Locust Valley, NY: J.J. Augustin.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Notes+on+Hipparchus&rft.btitle=The+Aegean+and+the+Near+East%3A+Studies+Presented+to+Hetty+Goldman&rft.place=Locust+Valley%2C+NY&rft.pub=J.J.+Augustin&rft.date=1956&rft.aulast=Neugebauer&rft.aufirst=Otto+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Hipparchus.html">"Hipparchus"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hipparchus&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FHipparchus.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThomson1948" class="citation book cs1">Thomson, J. Oliver (1948). <i>History of Ancient Geography</i>. Cambridge University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=History+of+Ancient+Geography&rft.pub=Cambridge+University+Press&rft.date=1948&rft.aulast=Thomson&rft.aufirst=J.+Oliver&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHipparchus" 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=Hipparchus&action=edit&section=27" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output 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template">e</abbr></a></li></ul></div><div id="Ancient_Greek_mathematics" style="font-size:114%;margin:0 4em"><a href="/wiki/Greek_mathematics" title="Greek mathematics">Ancient Greek mathematics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_Greek_mathematicians" title="List of Greek mathematicians">Mathematicians</a><br /><a href="/wiki/Timeline_of_ancient_Greek_mathematicians" title="Timeline of ancient Greek mathematicians">(timeline)</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anaxagoras" title="Anaxagoras">Anaxagoras</a></li> <li><a href="/wiki/Anthemius_of_Tralles" title="Anthemius of Tralles">Anthemius</a></li> <li><a href="/wiki/Archytas" title="Archytas">Archytas</a></li> <li><a href="/wiki/Aristaeus_the_Elder" title="Aristaeus the Elder">Aristaeus the Elder</a></li> <li><a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus</a></li> <li><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a></li> <li><a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius</a></li> <li><a href="/wiki/Archimedes" title="Archimedes">Archimedes</a></li> <li><a href="/wiki/Autolycus_of_Pitane" title="Autolycus of Pitane">Autolycus</a></li> <li><a href="/wiki/Bion_of_Abdera" title="Bion of Abdera">Bion</a></li> <li><a href="/wiki/Bryson_of_Heraclea" title="Bryson of Heraclea">Bryson</a></li> <li><a href="/wiki/Callippus" title="Callippus">Callippus</a></li> <li><a href="/wiki/Carpus_of_Antioch" title="Carpus of Antioch">Carpus</a></li> <li><a href="/wiki/Chrysippus" title="Chrysippus">Chrysippus</a></li> <li><a href="/wiki/Cleomedes" title="Cleomedes">Cleomedes</a></li> <li><a href="/wiki/Conon_of_Samos" title="Conon of Samos">Conon</a></li> <li><a href="/wiki/Ctesibius" title="Ctesibius">Ctesibius</a></li> <li><a href="/wiki/Democritus" title="Democritus">Democritus</a></li> <li><a href="/wiki/Dicaearchus" title="Dicaearchus">Dicaearchus</a></li> <li><a href="/wiki/Diocles_(mathematician)" title="Diocles (mathematician)">Diocles</a></li> <li><a href="/wiki/Diophantus" title="Diophantus">Diophantus</a></li> <li><a href="/wiki/Dinostratus" title="Dinostratus">Dinostratus</a></li> <li><a href="/wiki/Dionysodorus" title="Dionysodorus">Dionysodorus</a></li> <li><a href="/wiki/Domninus_of_Larissa" title="Domninus of Larissa">Domninus</a></li> <li><a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a></li> <li><a href="/wiki/Eudemus_of_Rhodes" title="Eudemus of Rhodes">Eudemus</a></li> <li><a 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 class="mw-selflink selflink">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_Greek_astronomy" style="padding:3px"><table class="nowraplinks 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_Greek_astronomy" title="Template:Ancient Greek astronomy"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Ancient_Greek_astronomy" title="Template talk:Ancient Greek astronomy"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Ancient_Greek_astronomy" title="Special:EditPage/Template:Ancient Greek astronomy"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Ancient_Greek_astronomy" style="font-size:114%;margin:0 4em"><a href="/wiki/Ancient_Greek_astronomy" title="Ancient Greek astronomy">Ancient Greek astronomy</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_ancient_Greek_astronomers" title="List of ancient Greek astronomers">Astronomers</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aglaonice" title="Aglaonice">Aglaonice</a></li> <li><a href="/wiki/Agrippa_(astronomer)" title="Agrippa (astronomer)">Agrippa</a></li> <li><a href="/wiki/Anaximander" title="Anaximander">Anaximander</a></li> <li><a href="/wiki/Andronicus_of_Cyrrhus" title="Andronicus of 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 class="mw-selflink selflink">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 href="/wiki/Metonic_cycle" title="Metonic cycle">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 style="padding:0 0.25em"> <ul><li><a href="/wiki/European_science_in_the_Middle_Ages" title="European science in the Middle Ages">Medieval European science</a></li> <li><a href="/wiki/Indian_astronomy" title="Indian astronomy">Indian astronomy</a></li> <li><a href="/wiki/Astronomy_in_the_medieval_Islamic_world" title="Astronomy in the medieval Islamic world">Medieval Islamic astronomy</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_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" title="Special:EditPage/Template:Ancient Greece topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Ancient_Greece" style="font-size:114%;margin:0 4em"><a href="/wiki/Ancient_Greece" title="Ancient Greece">Ancient Greece</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Timeline_of_ancient_Greece" title="Timeline of ancient Greece">Timeline</a></li></ul> </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="HistoryGeography" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/wiki/History_of_Greece" title="History of Greece">History</a></li><li><a href="/wiki/Regions_of_ancient_Greece" title="Regions of ancient 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 href="/wiki/Greek_mathematics" title="Greek mathematics">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 0.25em"> <ul><li><a href="/wiki/List_of_ancient_Greek_cities" title="List of ancient Greek cities">Cities</a> <ul><li><a href="/wiki/List_of_cities_in_ancient_Epirus" title="List of cities in ancient Epirus">in Epirus</a></li></ul></li> <li><a href="/wiki/List_of_ancient_Greeks" title="List of ancient Greeks">People</a></li> <li><a href="/wiki/List_of_Greek_place_names" title="List of Greek place names">Place names</a></li> <li><a href="/wiki/List_of_stoae" title="List of stoae">Stoae</a></li> <li><a href="/wiki/List_of_Ancient_Greek_temples" title="List of Ancient Greek temples">Temples</a></li> <li><a href="/wiki/List_of_ancient_Greek_theatres" title="List of ancient Greek theatres">Theatres</a></li></ul> </div></td></tr></tbody></table><div></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:Ancient_Greece" title="Category:Ancient Greece">Category</a></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a></span> <a href="/wiki/Portal:Ancient_Greece" title="Portal:Ancient Greece">Portal</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Outline"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Global_thinking.svg/10px-Global_thinking.svg.png" decoding="async" width="10" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Global_thinking.svg/15px-Global_thinking.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Global_thinking.svg/21px-Global_thinking.svg.png 2x" data-file-width="130" data-file-height="200" /></span></span> <a href="/wiki/Outline_of_ancient_Greece" title="Outline of ancient Greece">Outline</a></li></ul> </div></td></tr></tbody></table></div> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 0}.mw-parser-output .portal-bar-related{font-size:100%;justify-content:flex-start}.mw-parser-output .portal-bar-unbordered{padding:0 1.7em;margin-left:0}.mw-parser-output .portal-bar-header{margin:0 1em 0 0.5em;flex:0 0 auto;min-height:24px}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;flex:0 1 auto;padding:0.15em 0;column-gap:1em;align-items:baseline;margin:0;list-style:none}.mw-parser-output .portal-bar-content-related{margin:0;list-style:none}.mw-parser-output .portal-bar-item{display:inline-block;margin:0.15em 0.2em;min-height:24px;line-height:24px}@media screen and (max-width:768px){.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;flex-flow:column wrap;align-items:baseline}.mw-parser-output .portal-bar-header{text-align:center;flex:0;padding-left:0.5em;margin:0 auto}.mw-parser-output .portal-bar-related{font-size:100%;align-items:flex-start}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;align-items:center;flex:0;column-gap:1em;border-top:1px solid #a2a9b1;margin:0 auto;list-style:none}.mw-parser-output .portal-bar-content-related{border-top:none;margin:0;list-style:none}}.mw-parser-output .navbox+link+.portal-bar,.mw-parser-output .navbox+style+.portal-bar,.mw-parser-output .navbox+link+.portal-bar-bordered,.mw-parser-output .navbox+style+.portal-bar-bordered,.mw-parser-output .sister-bar+link+.portal-bar,.mw-parser-output .sister-bar+style+.portal-bar,.mw-parser-output .portal-bar+.navbox-styles+.navbox,.mw-parser-output .portal-bar+.navbox-styles+.sister-bar{margin-top:-1px}</style><div class="portal-bar noprint metadata noviewer portal-bar-bordered" role="navigation" aria-label="Portals"><span class="portal-bar-header"><a href="/wiki/Wikipedia:Contents/Portals" title="Wikipedia:Contents/Portals">Portals</a>:</span><ul class="portal-bar-content"><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/19px-P_vip.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/28px-P_vip.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/37px-P_vip.svg.png 2x" data-file-width="1911" data-file-height="1944" /></span></span> </span><a href="/wiki/Portal:Biography" title="Portal:Biography">Biography</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Terra.png/19px-Terra.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Terra.png/29px-Terra.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Terra.png/38px-Terra.png 2x" data-file-width="600" data-file-height="600" /></span></span> </span><a href="/wiki/Portal:Geography" title="Portal:Geography">Geography</a></li><li class="portal-bar-item"><span class="nowrap"><span 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/19px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/29px-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/38px-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</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/19px-Crab_Nebula.jpg" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/29px-Crab_Nebula.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/38px-Crab_Nebula.jpg 2x" data-file-width="3864" data-file-height="3864" /></span></span> </span><a href="/wiki/Portal:Astronomy" title="Portal:Astronomy">Astronomy</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:He1523a.jpg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/16px-He1523a.jpg" decoding="async" width="16" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/25px-He1523a.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/33px-He1523a.jpg 2x" data-file-width="180" data-file-height="207" /></a></span> </span><a href="/wiki/Portal:Stars" title="Portal:Stars">Stars</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/21px-Earth-moon.jpg" decoding="async" width="21" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/32px-Earth-moon.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/42px-Earth-moon.jpg 2x" data-file-width="3000" data-file-height="2400" /></span></span> </span><a href="/wiki/Portal:Outer_space" title="Portal:Outer space">Outer space</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Solar_system.jpg/15px-Solar_system.jpg" decoding="async" width="15" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Solar_system.jpg/23px-Solar_system.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Solar_system.jpg/30px-Solar_system.jpg 2x" data-file-width="4500" data-file-height="5600" /></span></span> </span><a href="/wiki/Portal:Solar_System" title="Portal:Solar System">Solar System</a></li></ul></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"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q159905#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" 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"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q159905#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q159905#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/0000000107855341">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/302240082">VIAF</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/17570519">2</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/3521159820942514000009">3</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/52151776732418010777">4</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/412145857098422922241">5</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/14161271961247440068">6</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/305858661">7</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/2186153063164019320004">8</a></span></li></ul></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/1824102/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJbM4RwTpcTMxgGV4qpByd">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/100499651">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/no91008369">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb13521687n">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb13521687n">BnF data</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Hipparchus"><a rel="nofollow" class="external text" href="https://opac.sbn.it/nome/SBLV285514">Italy</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35765179">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX1588034">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p06973996X">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/95002236">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.nlg.gr/cgi-bin/koha/opac-authoritiesdetail.pl?authid=160182">Greece</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/vs69fvnd5c7dpv0">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810586661305606">Poland</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810583115805606">2</a></span></li></ul></li><li><span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8034&url_prefix=https://opac.vatlib.it/auth/detail/&id=495/17914">Vatican</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007262754505171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA14388047?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:hipparchus-of-nicaea.">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/210698">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/1077177">Trove</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd100499651.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/100499651">DDB</a></span></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><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/05977682X">IdRef</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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[\"CITEREFJones2001\"] = 1,\n [\"CITEREFJones2010\"] = 1,\n [\"CITEREFJones2017\"] = 1,\n [\"CITEREFKlintberg2005\"] = 1,\n [\"CITEREFKugler1900\"] = 1,\n [\"CITEREFLeverington2003\"] = 1,\n [\"CITEREFLinton2004\"] = 1,\n [\"CITEREFLloyd1973\"] = 1,\n [\"CITEREFManitius1894\"] = 1,\n [\"CITEREFMarchant2022\"] = 1,\n [\"CITEREFMcCluskey2000\"] = 1,\n [\"CITEREFNeugebauer1949\"] = 1,\n [\"CITEREFNeugebauer1955\"] = 1,\n [\"CITEREFNeugebauer1956\"] = 1,\n [\"CITEREFNeugebauer1975\"] = 1,\n [\"CITEREFNewcomb1878\"] = 1,\n [\"CITEREFNewton1977\"] = 1,\n [\"CITEREFPogson1856\"] = 1,\n [\"CITEREFRené_Bourtembourg2013\"] = 1,\n [\"CITEREFSchaefer2005\"] = 1,\n [\"CITEREFShcheglov2006\"] = 1,\n [\"CITEREFShcheglov2007\"] = 1,\n [\"CITEREFShcheglov2010\"] = 1,\n [\"CITEREFSmyth1844\"] = 1,\n [\"CITEREFStanley1997\"] = 1,\n [\"CITEREFSteeleStephensonMorrison1997\"] = 1,\n [\"CITEREFStephensonFatoohi1993\"] = 1,\n [\"CITEREFSwerdlow1992\"] = 1,\n [\"CITEREFThomson1948\"] = 1,\n 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