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class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Career"> <div class="vector-toc-text"> 1.2 Career </div> </a> <ul id="toc-Career-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Death" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Death"> <div class="vector-toc-text"> 1.3 Death </div> </a> <ul id="toc-Death-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Discoveries_and_inventions" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Discoveries_and_inventions"> <div class="vector-toc-text"> 2 Discoveries and inventions </div> </a> <button aria-controls="toc-Discoveries_and_inventions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Discoveries and inventions subsection </button> <ul id="toc-Discoveries_and_inventions-sublist" class="vector-toc-list"> <li id="toc-Archimedes'_principle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Archimedes'_principle"> <div class="vector-toc-text"> 2.1 Archimedes' principle </div> </a> <ul id="toc-Archimedes'_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Law_of_the_lever" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Law_of_the_lever"> <div class="vector-toc-text"> 2.2 Law of the lever </div> </a> <ul id="toc-Law_of_the_lever-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Archimedes'_screw" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Archimedes'_screw"> <div class="vector-toc-text"> 2.3 Archimedes' screw </div> </a> <ul id="toc-Archimedes'_screw-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Archimedes'_claw" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Archimedes'_claw"> <div class="vector-toc-text"> 2.4 Archimedes' claw </div> </a> <ul id="toc-Archimedes'_claw-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heat_ray" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heat_ray"> <div class="vector-toc-text"> 2.5 Heat ray </div> </a> <ul id="toc-Heat_ray-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Astronomical_instruments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Astronomical_instruments"> <div class="vector-toc-text"> 2.6 Astronomical instruments </div> </a> <ul id="toc-Astronomical_instruments-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mathematics" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Mathematics"> <div class="vector-toc-text"> 3 Mathematics </div> </a> <button aria-controls="toc-Mathematics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Mathematics subsection </button> <ul id="toc-Mathematics-sublist" class="vector-toc-list"> <li id="toc-Method_of_exhaustion" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Method_of_exhaustion"> <div class="vector-toc-text"> 3.1 Method of exhaustion </div> </a> <ul id="toc-Method_of_exhaustion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Archimedean_property" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Archimedean_property"> <div class="vector-toc-text"> 3.2 Archimedean property </div> </a> <ul id="toc-Archimedean_property-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_infinite_series" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_infinite_series"> <div class="vector-toc-text"> 3.3 The infinite series </div> </a> <ul id="toc-The_infinite_series-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Myriad_of_myriads" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Myriad_of_myriads"> <div class="vector-toc-text"> 3.4 Myriad of myriads </div> </a> <ul id="toc-Myriad_of_myriads-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Writings" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Writings"> <div class="vector-toc-text"> 4 Writings </div> </a> <button aria-controls="toc-Writings-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Writings subsection </button> <ul id="toc-Writings-sublist" class="vector-toc-list"> <li id="toc-Surviving_works" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Surviving_works"> <div class="vector-toc-text"> 4.1 Surviving works </div> </a> <ul id="toc-Surviving_works-sublist" class="vector-toc-list"> <li id="toc-Measurement_of_a_Circle" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Measurement_of_a_Circle"> <div class="vector-toc-text"> 4.1.1 Measurement of a Circle </div> </a> <ul id="toc-Measurement_of_a_Circle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_Sand_Reckoner" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#The_Sand_Reckoner"> <div class="vector-toc-text"> 4.1.2 The Sand Reckoner </div> </a> <ul id="toc-The_Sand_Reckoner-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-On_the_Equilibrium_of_Planes" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#On_the_Equilibrium_of_Planes"> <div class="vector-toc-text"> 4.1.3 On the Equilibrium of Planes </div> </a> <ul id="toc-On_the_Equilibrium_of_Planes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quadrature_of_the_Parabola" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Quadrature_of_the_Parabola"> <div class="vector-toc-text"> 4.1.4 Quadrature of the Parabola </div> </a> <ul id="toc-Quadrature_of_the_Parabola-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-On_the_Sphere_and_Cylinder" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#On_the_Sphere_and_Cylinder"> <div class="vector-toc-text"> 4.1.5 On the Sphere and Cylinder </div> </a> <ul id="toc-On_the_Sphere_and_Cylinder-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-On_Spirals" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#On_Spirals"> <div class="vector-toc-text"> 4.1.6 On Spirals </div> </a> <ul id="toc-On_Spirals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-On_Conoids_and_Spheroids" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#On_Conoids_and_Spheroids"> <div class="vector-toc-text"> 4.1.7 On Conoids and Spheroids </div> </a> <ul id="toc-On_Conoids_and_Spheroids-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-On_Floating_Bodies" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#On_Floating_Bodies"> <div class="vector-toc-text"> 4.1.8 On Floating Bodies </div> </a> <ul id="toc-On_Floating_Bodies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ostomachion" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ostomachion"> <div class="vector-toc-text"> 4.1.9 Ostomachion </div> </a> <ul id="toc-Ostomachion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_cattle_problem" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#The_cattle_problem"> <div class="vector-toc-text"> 4.1.10 The cattle problem </div> </a> <ul id="toc-The_cattle_problem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_Method_of_Mechanical_Theorems" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#The_Method_of_Mechanical_Theorems"> <div class="vector-toc-text"> 4.1.11 The Method of Mechanical Theorems </div> </a> <ul id="toc-The_Method_of_Mechanical_Theorems-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Apocryphal_works" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Apocryphal_works"> <div class="vector-toc-text"> 4.2 Apocryphal works </div> </a> <ul id="toc-Apocryphal_works-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Archimedes_Palimpsest" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Archimedes_Palimpsest"> <div class="vector-toc-text"> 4.3 Archimedes Palimpsest </div> </a> <ul id="toc-Archimedes_Palimpsest-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Legacy" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Legacy"> <div class="vector-toc-text"> 5 Legacy </div> </a> <button aria-controls="toc-Legacy-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Legacy subsection </button> <ul id="toc-Legacy-sublist" class="vector-toc-list"> <li id="toc-Mathematics_and_physics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mathematics_and_physics"> <div class="vector-toc-text"> 5.1 Mathematics and physics </div> </a> <ul id="toc-Mathematics_and_physics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Honors_and_commemorations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Honors_and_commemorations"> <div class="vector-toc-text"> 5.2 Honors and commemorations </div> </a> <ul id="toc-Honors_and_commemorations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 6 See also </div> </a> <button aria-controls="toc-See_also-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle See also subsection </button> <ul id="toc-See_also-sublist" class="vector-toc-list"> <li id="toc-Concepts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Concepts"> <div class="vector-toc-text"> 6.1 Concepts </div> </a> <ul id="toc-Concepts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-People" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#People"> <div class="vector-toc-text"> 6.2 People </div> </a> <ul id="toc-People-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 7 References </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle References subsection </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> 7.1 Notes </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> 7.2 Citations </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> 8 Further reading </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"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 9 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Archimedes</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 187 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-187" aria-hidden="true" > 187 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Archimedes" title="Archimedes – Afrikaans" lang="af" hreflang="af" data-title="Archimedes" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Archimedes" title="Archimedes – Alemannic" lang="gsw" hreflang="gsw" data-title="Archimedes" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target">Alemannisch</a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%88%AD%E1%8A%AA%E1%88%9C%E1%8B%B4%E1%88%B5" title="አርኪሜዴስ – Amharic" lang="am" hreflang="am" data-title="አርኪሜዴስ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target">አማርኛ</a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A4%BF%E0%A4%AE%E0%A4%BF%E0%A4%A1%E0%A5%80%E0%A4%9C" title="आर्किमिडीज – Angika" lang="anp" hreflang="anp" data-title="आर्किमिडीज" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target">अंगिका</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A3%D8%B1%D8%AE%D9%85%D9%8A%D8%AF%D8%B3" title="أرخميدس – Arabic" lang="ar" hreflang="ar" data-title="أرخميدس" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Arquimedes" title="Arquimedes – Aragonese" lang="an" hreflang="an" data-title="Arquimedes" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-roa-rup mw-list-item"><a href="https://roa-rup.wikipedia.org/wiki/Arhimede" title="Arhimede – Aromanian" lang="rup" hreflang="rup" data-title="Arhimede" data-language-autonym="Armãneashti" data-language-local-name="Aromanian" class="interlanguage-link-target">Armãneashti</a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%86%E0%A7%B0%E0%A7%8D%E0%A6%95%E0%A6%BF%E0%A6%AE%E0%A6%BF%E0%A6%A1%E0%A6%BF%E0%A6%9B" title="আৰ্কিমিডিছ – Assamese" lang="as" hreflang="as" data-title="আৰ্কিমিডিছ" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target">অসমীয়া</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Arqu%C3%ADmedes" title="Arquímedes – Asturian" lang="ast" hreflang="ast" data-title="Arquímedes" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-awa mw-list-item"><a href="https://awa.wikipedia.org/wiki/%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A5%80%E0%A4%AE%E0%A4%BF%E0%A4%A1%E0%A5%80%E0%A4%9C" title="आर्कीमिडीज – Awadhi" lang="awa" hreflang="awa" data-title="आर्कीमिडीज" data-language-autonym="अवधी" data-language-local-name="Awadhi" class="interlanguage-link-target">अवधी</a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Arqu%C3%ADmedes" title="Arquímedes – Guarani" lang="gn" hreflang="gn" data-title="Arquímedes" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" class="interlanguage-link-target">Avañe'ẽ</a></li><li class="interlanguage-link interwiki-av mw-list-item"><a href="https://av.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Avaric" lang="av" hreflang="av" data-title="Архимед" data-language-autonym="Авар" data-language-local-name="Avaric" class="interlanguage-link-target">Авар</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Arximed" title="Arximed – Azerbaijani" lang="az" hreflang="az" data-title="Arximed" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D8%B1%D8%B4%D9%85%DB%8C%D8%AF%D9%88%D8%B3" title="ارشمیدوس – South Azerbaijani" lang="azb" hreflang="azb" data-title="ارشمیدوس" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target">تۆرکجه</a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/Archim%C3%A9d%C3%A9s" title="Archimédés – Balinese" lang="ban" hreflang="ban" data-title="Archimédés" data-language-autonym="Basa Bali" data-language-local-name="Balinese" class="interlanguage-link-target">Basa Bali</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%86%E0%A6%B0%E0%A7%8D%E0%A6%95%E0%A6%BF%E0%A6%AE%E0%A6%BF%E0%A6%A1%E0%A6%BF%E0%A6%B8" title="আর্কিমিডিস – Bangla" lang="bn" hreflang="bn" data-title="আর্কিমিডিস" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Archimedes" title="Archimedes – Minnan" lang="nan" hreflang="nan" data-title="Archimedes" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-map-bms mw-list-item"><a href="https://map-bms.wikipedia.org/wiki/Archimedes" title="Archimedes – Banyumasan" lang="jv-x-bms" hreflang="jv-x-bms" data-title="Archimedes" data-language-autonym="Basa Banyumasan" data-language-local-name="Banyumasan" class="interlanguage-link-target">Basa Banyumasan</a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Bashkir" lang="ba" hreflang="ba" data-title="Архимед" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target">Башҡортса</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D1%96%D0%BC%D0%B5%D0%B4" title="Архімед – Belarusian" lang="be" hreflang="be" data-title="Архімед" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D1%96%D0%BC%D1%8D%D0%B4" title="Архімэд – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Архімэд" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target">Беларуская (тарашкевіца)</a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A4%AE%E0%A5%87%E0%A4%A1%E0%A5%80%E0%A4%B8%E0%A4%BC" title="आर्कमेडीस़ – Bhojpuri" lang="bh" hreflang="bh" data-title="आर्कमेडीस़" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target">भोजपुरी</a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Archimedes" title="Archimedes – Central Bikol" lang="bcl" hreflang="bcl" data-title="Archimedes" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target">Bikol Central</a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Archimedes" title="Archimedes – Bislama" lang="bi" hreflang="bi" data-title="Archimedes" data-language-autonym="Bislama" data-language-local-name="Bislama" class="interlanguage-link-target">Bislama</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Bulgarian" lang="bg" hreflang="bg" data-title="Архимед" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Archimedes" title="Archimedes – Bavarian" lang="bar" hreflang="bar" data-title="Archimedes" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target">Boarisch</a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A8%E0%BD%A2%E0%BC%8B%E0%BD%81%E0%BD%B2%E0%BC%8B%E0%BD%98%E0%BD%BA%E0%BD%A0%E0%BD%B4%E0%BC%8B%E0%BD%8F%E0%BD%BA%E0%BC%8B%E0%BD%A6%E0%BD%B2%E0%BC%8D" title="ཨར་ཁི་མེའུ་ཏེ་སི། – Tibetan" lang="bo" hreflang="bo" data-title="ཨར་ཁི་མེའུ་ཏེ་སི།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target">བོད་ཡིག</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Arhimed" title="Arhimed – Bosnian" lang="bs" hreflang="bs" data-title="Arhimed" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Arc%27himedes" title="Arc'himedes – Breton" lang="br" hreflang="br" data-title="Arc'himedes" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target">Brezhoneg</a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Архимед" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target">Буряад</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Arquimedes" title="Arquimedes – Catalan" lang="ca" hreflang="ca" data-title="Arquimedes" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Chuvash" lang="cv" hreflang="cv" data-title="Архимед" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Archimedes" title="Archimedes – Cebuano" lang="ceb" hreflang="ceb" data-title="Archimedes" data-language-autonym="Cebuano" data-language-local-name="Cebuano" class="interlanguage-link-target">Cebuano</a></li><li class="interlanguage-link interwiki-cs badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://cs.wikipedia.org/wiki/Archim%C3%A9d%C3%A9s" title="Archimédés – Czech" lang="cs" hreflang="cs" data-title="Archimédés" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-tum mw-list-item"><a href="https://tum.wikipedia.org/wiki/Archimedes" title="Archimedes – Tumbuka" lang="tum" hreflang="tum" data-title="Archimedes" data-language-autonym="ChiTumbuka" data-language-local-name="Tumbuka" class="interlanguage-link-target">ChiTumbuka</a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Archimede" title="Archimede – Corsican" lang="co" hreflang="co" data-title="Archimede" data-language-autonym="Corsu" data-language-local-name="Corsican" class="interlanguage-link-target">Corsu</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Archimedes" title="Archimedes – Welsh" lang="cy" hreflang="cy" data-title="Archimedes" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Danish" lang="da" hreflang="da" data-title="Arkimedes" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Archimedes" title="Archimedes – German" lang="de" hreflang="de" data-title="Archimedes" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Archimedes" title="Archimedes – Estonian" lang="et" hreflang="et" data-title="Archimedes" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%B9%CE%BC%CE%AE%CE%B4%CE%B7%CF%82" title="Αρχιμήδης – Greek" lang="el" hreflang="el" data-title="Αρχιμήδης" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Erzya" lang="myv" hreflang="myv" data-title="Архимед" data-language-autonym="Эрзянь" data-language-local-name="Erzya" class="interlanguage-link-target">Эрзянь</a></li><li class="interlanguage-link interwiki-es badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://es.wikipedia.org/wiki/Arqu%C3%ADmedes" title="Arquímedes – Spanish" lang="es" hreflang="es" data-title="Arquímedes" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Arkimedo" title="Arkimedo – Esperanto" lang="eo" hreflang="eo" data-title="Arkimedo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Arqu%C3%ADmedi" title="Arquímedi – Extremaduran" lang="ext" hreflang="ext" data-title="Arquímedi" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target">Estremeñu</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Basque" lang="eu" hreflang="eu" data-title="Arkimedes" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%B1%D8%B4%D9%85%DB%8C%D8%AF%D8%B3" title="ارشمیدس – Persian" lang="fa" hreflang="fa" data-title="ارشمیدس" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Archimedes" title="Archimedes – Fiji Hindi" lang="hif" hreflang="hif" data-title="Archimedes" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target">Fiji Hindi</a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Faroese" lang="fo" hreflang="fo" data-title="Arkimedes" data-language-autonym="Føroyskt" data-language-local-name="Faroese" class="interlanguage-link-target">Føroyskt</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Archim%C3%A8de" title="Archimède – French" lang="fr" hreflang="fr" data-title="Archimède" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Archimedes" title="Archimedes – Western Frisian" lang="fy" hreflang="fy" data-title="Archimedes" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target">Frysk</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Aircim%C3%A9id%C3%A9as" title="Airciméidéas – Irish" lang="ga" hreflang="ga" data-title="Airciméidéas" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Archimedes" title="Archimedes – Scottish Gaelic" lang="gd" hreflang="gd" data-title="Archimedes" data-language-autonym="Gàidhlig" data-language-local-name="Scottish Gaelic" class="interlanguage-link-target">Gàidhlig</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Arqu%C3%ADmedes" title="Arquímedes – Galician" lang="gl" hreflang="gl" data-title="Arquímedes" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7" title="阿基米德 – Gan" lang="gan" hreflang="gan" data-title="阿基米德" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target">贛語</a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%86%E0%AA%B0%E0%AB%8D%E0%AA%95%E0%AA%BF%E0%AA%AE%E0%AB%80%E0%AA%A1%E0%AB%80%E0%AA%9D" title="આર્કિમીડીઝ – Gujarati" lang="gu" hreflang="gu" data-title="આર્કિમીડીઝ" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target">ગુજરાતી</a></li><li class="interlanguage-link interwiki-gom mw-list-item"><a href="https://gom.wikipedia.org/wiki/%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A4%BF%E0%A4%AE%E0%A4%BF%E0%A4%A1%E0%A5%80%E0%A4%9C" title="आर्किमिडीज – Goan Konkani" lang="gom" hreflang="gom" data-title="आर्किमिडीज" data-language-autonym="गोंयची कोंकणी / Gõychi Konknni" data-language-local-name="Goan Konkani" class="interlanguage-link-target">गोंयची कोंकणी / Gõychi Konknni</a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Archimedes" title="Archimedes – Hakka Chinese" lang="hak" hreflang="hak" data-title="Archimedes" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target">客家語 / Hak-kâ-ngî</a></li><li class="interlanguage-link interwiki-ko badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ko.wikipedia.org/wiki/%EC%95%84%EB%A5%B4%ED%82%A4%EB%A9%94%EB%8D%B0%EC%8A%A4" title="아르키메데스 – Korean" lang="ko" hreflang="ko" data-title="아르키메데스" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Arkimidus" title="Arkimidus – Hausa" lang="ha" hreflang="ha" data-title="Arkimidus" data-language-autonym="Hausa" data-language-local-name="Hausa" class="interlanguage-link-target">Hausa</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D6%80%D6%84%D5%AB%D5%B4%D5%A5%D5%A4%D5%A5%D5%BD" title="Արքիմեդես – Armenian" lang="hy" hreflang="hy" data-title="Արքիմեդես" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A4%BF%E0%A4%AE%E0%A4%BF%E0%A4%A1%E0%A5%80%E0%A4%9C%E0%A4%BC" title="आर्किमिडीज़ – Hindi" lang="hi" hreflang="hi" data-title="आर्किमिडीज़" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Arhimed" title="Arhimed – Croatian" lang="hr" hreflang="hr" data-title="Arhimed" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-gor mw-list-item"><a href="https://gor.wikipedia.org/wiki/Archimedes" title="Archimedes – Gorontalo" lang="gor" hreflang="gor" data-title="Archimedes" data-language-autonym="Bahasa Hulontalo" data-language-local-name="Gorontalo" class="interlanguage-link-target">Bahasa Hulontalo</a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Ido" lang="io" hreflang="io" data-title="Arkimedes" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target">Ido</a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Iloko" lang="ilo" hreflang="ilo" data-title="Arkimedes" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target">Ilokano</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Archimedes" title="Archimedes – Indonesian" lang="id" hreflang="id" data-title="Archimedes" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Archimedes" title="Archimedes – Interlingua" lang="ia" hreflang="ia" data-title="Archimedes" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target">Interlingua</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Ark%C3%ADmedes" title="Arkímedes – Icelandic" lang="is" hreflang="is" data-title="Arkímedes" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://it.wikipedia.org/wiki/Archimede" title="Archimede – Italian" lang="it" hreflang="it" data-title="Archimede" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A8%D7%9B%D7%99%D7%9E%D7%93%D7%A1" title="ארכימדס – Hebrew" lang="he" hreflang="he" data-title="ארכימדס" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Arkhim%C3%A9d%C3%A8s" title="Arkhimédès – Javanese" lang="jv" hreflang="jv" data-title="Arkhimédès" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target">Jawa</a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Archim%C3%A8de" title="Archimède – Kabiye" lang="kbp" hreflang="kbp" data-title="Archimède" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target">Kabɩyɛ</a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%86%E0%B2%B0%E0%B3%8D%E0%B2%95%E0%B2%BF%E0%B2%AE%E0%B2%BF%E0%B2%A1%E0%B3%80%E0%B2%B8%E0%B3%8D" title="ಆರ್ಕಿಮಿಡೀಸ್ – Kannada" lang="kn" hreflang="kn" data-title="ಆರ್ಕಿಮಿಡೀಸ್" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-pam mw-list-item"><a href="https://pam.wikipedia.org/wiki/Archimedes" title="Archimedes – Pampanga" lang="pam" hreflang="pam" data-title="Archimedes" data-language-autonym="Kapampangan" data-language-local-name="Pampanga" class="interlanguage-link-target">Kapampangan</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%A0%E1%83%A5%E1%83%98%E1%83%9B%E1%83%94%E1%83%93%E1%83%94" title="არქიმედე – Georgian" lang="ka" hreflang="ka" data-title="არქიმედე" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Kazakh" lang="kk" hreflang="kk" data-title="Архимед" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Archimedes" title="Archimedes – Cornish" lang="kw" hreflang="kw" data-title="Archimedes" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target">Kernowek</a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Archimedes" title="Archimedes – Swahili" lang="sw" hreflang="sw" data-title="Archimedes" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target">Kiswahili</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Archimedes" title="Archimedes – Haitian Creole" lang="ht" hreflang="ht" data-title="Archimedes" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Archim%C3%A8d" title="Archimèd – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Archimèd" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target">Kriyòl gwiyannen</a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Ar%C5%9F%C3%AEmed" title="Arşîmed – Kurdish" lang="ku" hreflang="ku" data-title="Arşîmed" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target">Kurdî</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Kyrgyz" lang="ky" hreflang="ky" data-title="Архимед" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Archimedes" title="Archimedes – Latin" lang="la" hreflang="la" data-title="Archimedes" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Arhim%C4%93ds" title="Arhimēds – Latvian" lang="lv" hreflang="lv" data-title="Arhimēds" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Archimedes" title="Archimedes – Luxembourgish" lang="lb" hreflang="lb" data-title="Archimedes" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target">Lëtzebuergesch</a></li><li class="interlanguage-link interwiki-lez mw-list-item"><a href="https://lez.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Lezghian" lang="lez" hreflang="lez" data-title="Архимед" data-language-autonym="Лезги" data-language-local-name="Lezghian" class="interlanguage-link-target">Лезги</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Archimedas" title="Archimedas – Lithuanian" lang="lt" hreflang="lt" data-title="Archimedas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Archimedde" title="Archimedde – Ligurian" lang="lij" hreflang="lij" data-title="Archimedde" data-language-autonym="Ligure" data-language-local-name="Ligurian" class="interlanguage-link-target">Ligure</a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Archimedes" title="Archimedes – Limburgish" lang="li" hreflang="li" data-title="Archimedes" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target">Limburgs</a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Arcimede" title="Arcimede – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Arcimede" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target">Lingua Franca Nova</a></li><li class="interlanguage-link interwiki-olo mw-list-item"><a href="https://olo.wikipedia.org/wiki/Arkhimedes" title="Arkhimedes – Livvi-Karelian" lang="olo" hreflang="olo" data-title="Arkhimedes" data-language-autonym="Livvinkarjala" data-language-local-name="Livvi-Karelian" class="interlanguage-link-target">Livvinkarjala</a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Archimede" title="Archimede – Lombard" lang="lmo" hreflang="lmo" data-title="Archimede" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target">Lombard</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Arkhim%C3%A9d%C3%A9sz" title="Arkhimédész – Hungarian" lang="hu" hreflang="hu" data-title="Arkhimédész" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mad mw-list-item"><a href="https://mad.wikipedia.org/wiki/Archimedes" title="Archimedes – Madurese" lang="mad" hreflang="mad" data-title="Archimedes" data-language-autonym="Madhurâ" data-language-local-name="Madurese" class="interlanguage-link-target">Madhurâ</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Macedonian" lang="mk" hreflang="mk" data-title="Архимед" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Arsimeda" title="Arsimeda – Malagasy" lang="mg" hreflang="mg" data-title="Arsimeda" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target">Malagasy</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%86%E0%B5%BC%E0%B4%95%E0%B5%8D%E0%B4%95%E0%B4%BF%E0%B4%AE%E0%B4%BF%E0%B4%A1%E0%B5%80%E0%B4%B8%E0%B5%8D%E2%80%8C" title="ആർക്കിമിഡീസ്‌ – Malayalam" lang="ml" hreflang="ml" data-title="ആർക്കിമിഡീസ്‌" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Arkimede" title="Arkimede – Maltese" lang="mt" hreflang="mt" data-title="Arkimede" data-language-autonym="Malti" data-language-local-name="Maltese" class="interlanguage-link-target">Malti</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A4%BF%E0%A4%AE%E0%A4%BF%E0%A4%A1%E0%A5%80%E0%A4%9C" title="आर्किमिडीज – Marathi" lang="mr" hreflang="mr" data-title="आर्किमिडीज" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%90%E1%83%A0%E1%83%A5%E1%83%98%E1%83%9B%E1%83%94%E1%83%93%E1%83%94" title="არქიმედე – Mingrelian" lang="xmf" hreflang="xmf" data-title="არქიმედე" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target">მარგალური</a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D8%B1%D8%B4%D9%85%D9%8A%D8%AF%D8%B3" title="ارشميدس – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ارشميدس" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target">مصرى</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Archimedes" title="Archimedes – Malay" lang="ms" hreflang="ms" data-title="Archimedes" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Archimedes" title="Archimedes – Minangkabau" lang="min" hreflang="min" data-title="Archimedes" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" class="interlanguage-link-target">Minangkabau</a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Arquimedes" title="Arquimedes – Mirandese" lang="mwl" hreflang="mwl" data-title="Arquimedes" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target">Mirandés</a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Mongolian" lang="mn" hreflang="mn" data-title="Архимед" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target">Монгол</a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%AC%E1%80%81%E1%80%AE%E1%80%99%E1%80%AE%E1%80%B8%E1%80%92%E1%80%AE%E1%80%B8%E1%80%85%E1%80%BA" title="အာခီမီးဒီးစ် – Burmese" lang="my" hreflang="my" data-title="အာခီမီးဒီးစ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Archimedes" title="Archimedes – Dutch" lang="nl" hreflang="nl" data-title="Archimedes" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-nds-nl mw-list-item"><a href="https://nds-nl.wikipedia.org/wiki/Archimedes" title="Archimedes – Low Saxon" lang="nds-NL" hreflang="nds-NL" data-title="Archimedes" data-language-autonym="Nedersaksies" data-language-local-name="Low Saxon" class="interlanguage-link-target">Nedersaksies</a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A4%BF%E0%A4%AE%E0%A4%BF%E0%A4%A1%E0%A4%BF%E0%A4%9C" title="आर्किमिडिज – Nepali" lang="ne" hreflang="ne" data-title="आर्किमिडिज" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target">नेपाली</a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A4%BF%E0%A4%AE%E0%A4%BF%E0%A4%A1%E0%A4%BF%E0%A4%9C" title="आर्किमिडिज – Newari" lang="new" hreflang="new" data-title="आर्किमिडिज" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target">नेपाल भाषा</a></li><li class="interlanguage-link interwiki-ja badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ja.wikipedia.org/wiki/%E3%82%A2%E3%83%AB%E3%82%AD%E3%83%A1%E3%83%87%E3%82%B9" title="アルキメデス – Japanese" lang="ja" hreflang="ja" data-title="アルキメデス" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-nap mw-list-item"><a href="https://nap.wikipedia.org/wiki/Archem%C3%A8de" title="Archemède – Neapolitan" lang="nap" hreflang="nap" data-title="Archemède" data-language-autonym="Napulitano" data-language-local-name="Neapolitan" class="interlanguage-link-target">Napulitano</a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Chechen" lang="ce" hreflang="ce" data-title="Архимед" data-language-autonym="Нохчийн" data-language-local-name="Chechen" class="interlanguage-link-target">Нохчийн</a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Archimedes" title="Archimedes – Northern Frisian" lang="frr" hreflang="frr" data-title="Archimedes" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target">Nordfriisk</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Arkimedes" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Arkimedes" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Arquim%C3%A8des" title="Arquimèdes – Occitan" lang="oc" hreflang="oc" data-title="Arquimèdes" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%86%E0%AC%B0%E0%AD%8D%E0%AC%95%E0%AC%AE%E0%AC%BF%E0%AC%A1%E0%AC%BC%E0%AC%BF%E0%AC%B8" title="ଆର୍କମିଡ଼ିସ – Odia" lang="or" hreflang="or" data-title="ଆର୍କମିଡ଼ିସ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target">ଓଡ଼ିଆ</a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Arkimeedis" title="Arkimeedis – Oromo" lang="om" hreflang="om" data-title="Arkimeedis" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target">Oromoo</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Arximed" title="Arximed – Uzbek" lang="uz" hreflang="uz" data-title="Arximed" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%86%E0%A8%B0%E0%A8%95%E0%A9%80%E0%A8%AE%E0%A8%BF%E0%A8%A1%E0%A9%80%E0%A8%9C%E0%A8%BC" title="ਆਰਕੀਮਿਡੀਜ਼ – Punjabi" lang="pa" hreflang="pa" data-title="ਆਰਕੀਮਿਡੀਜ਼" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D8%B1%D8%B4%D9%85%DB%8C%D8%AF%D8%B3" title="ارشمیدس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ارشمیدس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A7%D8%B1%D8%B4%D9%85%D9%8A%D8%AF%D8%B3" title="ارشميدس – Pashto" lang="ps" hreflang="ps" data-title="ارشميدس" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Archimedes" title="Archimedes – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Archimedes" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target">Patois</a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Archimede" title="Archimede – Piedmontese" lang="pms" hreflang="pms" data-title="Archimede" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target">Piemontèis</a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Archimedes" title="Archimedes – Low German" lang="nds" hreflang="nds" data-title="Archimedes" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target">Plattdüütsch</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Archimedes" title="Archimedes – Polish" lang="pl" hreflang="pl" data-title="Archimedes" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Arquimedes" title="Arquimedes – Portuguese" lang="pt" hreflang="pt" data-title="Arquimedes" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Arximed" title="Arximed – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Arximed" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target">Qaraqalpaqsha</a></li><li class="interlanguage-link interwiki-crh mw-list-item"><a href="https://crh.wikipedia.org/wiki/Arhimed" title="Arhimed – Crimean Tatar" lang="crh" hreflang="crh" data-title="Arhimed" data-language-autonym="Qırımtatarca" data-language-local-name="Crimean Tatar" class="interlanguage-link-target">Qırımtatarca</a></li><li class="interlanguage-link interwiki-ro badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ro.wikipedia.org/wiki/Arhimede" title="Arhimede – Romanian" lang="ro" hreflang="ro" data-title="Arhimede" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Arkhimidis" title="Arkhimidis – Quechua" lang="qu" hreflang="qu" data-title="Arkhimidis" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target">Runa Simi</a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D1%96%D0%BC%D0%B5%D0%B4" title="Архімед – Rusyn" lang="rue" hreflang="rue" data-title="Архімед" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target">Русиньскый</a></li><li class="interlanguage-link interwiki-ru badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://ru.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Russian" lang="ru" hreflang="ru" data-title="Архимед" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Yakut" lang="sah" hreflang="sah" data-title="Архимед" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target">Саха тыла</a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A4%BF%E0%A4%AE%E0%A4%BF%E0%A4%A1%E0%A5%80%E0%A4%B8%E0%A5%8D" title="आर्किमिडीस् – Sanskrit" lang="sa" hreflang="sa" data-title="आर्किमिडीस्" data-language-autonym="संस्कृतम्" data-language-local-name="Sanskrit" class="interlanguage-link-target">संस्कृतम्</a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%9F%E1%B1%A8%E1%B1%A0%E1%B1%A2%E1%B1%AE%E1%B1%B0%E1%B1%A4%E1%B1%A5" title="ᱟᱨᱠᱢᱮᱰᱤᱥ – Santali" lang="sat" hreflang="sat" data-title="ᱟᱨᱠᱢᱮᱰᱤᱥ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="Santali" class="interlanguage-link-target">ᱥᱟᱱᱛᱟᱲᱤ</a></li><li class="interlanguage-link interwiki-skr mw-list-item"><a href="https://skr.wikipedia.org/wiki/%D8%A7%D8%B1%D8%B4%DB%8C%D9%85%DB%8C%D8%AF%D8%B3" title="ارشیمیدس – Saraiki" lang="skr" hreflang="skr" data-title="ارشیمیدس" data-language-autonym="سرائیکی" data-language-local-name="Saraiki" class="interlanguage-link-target">سرائیکی</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Archimedes" title="Archimedes – Scots" lang="sco" hreflang="sco" data-title="Archimedes" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Arkimedi" title="Arkimedi – Albanian" lang="sq" hreflang="sq" data-title="Arkimedi" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Archimedi" title="Archimedi – Sicilian" lang="scn" hreflang="scn" data-title="Archimedi" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target">Sicilianu</a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%86%E0%B6%9A%E0%B7%92%E0%B6%B8%E0%B7%92%E0%B6%A9%E0%B7%93%E0%B7%83%E0%B7%8A" title="ආකිමිඩීස් – Sinhala" lang="si" hreflang="si" data-title="ආකිමිඩීස්" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target">සිංහල</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Archimedes" title="Archimedes – Simple English" lang="en-simple" hreflang="en-simple" data-title="Archimedes" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A7%D8%B1%D8%B4%D9%85%D9%8A%D8%AF%D8%B3" title="ارشميدس – Sindhi" lang="sd" hreflang="sd" data-title="ارشميدس" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target">سنڌي</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Archimedes_zo_Syrak%C3%BAz" title="Archimedes zo Syrakúz – Slovak" lang="sk" hreflang="sk" data-title="Archimedes zo Syrakúz" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</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/Arhimed" title="Arhimed – Slovenian" lang="sl" hreflang="sl" data-title="Arhimed" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%D8%A7%D8%B1%DA%A9%DB%8C%D9%85%DB%8C%D8%AF%D8%B2" title="ئارکیمیدز – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ئارکیمیدز" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Serbian" lang="sr" hreflang="sr" data-title="Архимед" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Arhimed" title="Arhimed – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Arhimed" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Archimedes" title="Archimedes – Sundanese" lang="su" hreflang="su" data-title="Archimedes" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target">Sunda</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Arkhimedes" title="Arkhimedes – Finnish" lang="fi" hreflang="fi" data-title="Arkhimedes" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Swedish" lang="sv" hreflang="sv" data-title="Arkimedes" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Tagalog" lang="tl" hreflang="tl" data-title="Arkimedes" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%B0%E0%AF%8D%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%BF%E0%AE%AE%E0%AF%86%E0%AE%9F%E0%AF%86%E0%AE%9A%E0%AF%81" title="அர்க்கிமெடெசு – Tamil" lang="ta" hreflang="ta" data-title="அர்க்கிமெடெசு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Arxmides" title="Arxmides – Kabyle" lang="kab" hreflang="kab" data-title="Arxmides" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target">Taqbaylit</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Tatar" lang="tt" hreflang="tt" data-title="Архимед" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%86%E0%B0%B0%E0%B1%8D%E0%B0%95%E0%B0%BF%E0%B0%AE%E0%B1%86%E0%B0%A1%E0%B0%BF%E0%B0%B8%E0%B1%8D" title="ఆర్కిమెడిస్ – Telugu" lang="te" hreflang="te" data-title="ఆర్కిమెడిస్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-th badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B2%E0%B8%A3%E0%B9%8C%E0%B8%84%E0%B8%B4%E0%B8%A1%E0%B8%B4%E0%B8%94%E0%B8%B5%E0%B8%AA" title="อาร์คิมิดีส – Thai" lang="th" hreflang="th" data-title="อาร์คิมิดีส" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Tajik" lang="tg" hreflang="tg" data-title="Архимед" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target">Тоҷикӣ</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Ar%C5%9Fimet" title="Arşimet – Turkish" lang="tr" hreflang="tr" data-title="Arşimet" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Arhimed" title="Arhimed – Turkmen" lang="tk" hreflang="tk" data-title="Arhimed" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target">Türkmençe</a></li><li class="interlanguage-link interwiki-tyv mw-list-item"><a href="https://tyv.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Tuvinian" lang="tyv" hreflang="tyv" data-title="Архимед" data-language-autonym="Тыва дыл" data-language-local-name="Tuvinian" class="interlanguage-link-target">Тыва дыл</a></li><li class="interlanguage-link interwiki-udm mw-list-item"><a href="https://udm.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Архимед – Udmurt" lang="udm" hreflang="udm" data-title="Архимед" data-language-autonym="Удмурт" data-language-local-name="Udmurt" class="interlanguage-link-target">Удмурт</a></li><li class="interlanguage-link interwiki-uk badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://uk.wikipedia.org/wiki/%D0%90%D1%80%D1%85%D1%96%D0%BC%D0%B5%D0%B4" title="Архімед – Ukrainian" lang="uk" hreflang="uk" data-title="Архімед" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%B1%D8%B4%D9%85%DB%8C%D8%AF%D8%B3" title="ارشمیدس – Urdu" lang="ur" hreflang="ur" data-title="ارشمیدس" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Archimede" title="Archimede – Venetian" lang="vec" hreflang="vec" data-title="Archimede" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target">Vèneto</a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Arhimed" title="Arhimed – Veps" lang="vep" hreflang="vep" data-title="Arhimed" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target">Vepsän kel’</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Archimedes" title="Archimedes – Vietnamese" lang="vi" hreflang="vi" data-title="Archimedes" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-vo mw-list-item"><a href="https://vo.wikipedia.org/wiki/Arkimedes" title="Arkimedes – Volapük" lang="vo" hreflang="vo" data-title="Arkimedes" data-language-autonym="Volapük" data-language-local-name="Volapük" class="interlanguage-link-target">Volapük</a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Archimedes" title="Archimedes – Võro" lang="vro" hreflang="vro" data-title="Archimedes" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target">Võro</a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/%C3%85rtchimede" title="Årtchimede – Walloon" lang="wa" hreflang="wa" data-title="Årtchimede" data-language-autonym="Walon" data-language-local-name="Walloon" class="interlanguage-link-target">Walon</a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E4%BA%9E%E5%9F%BA%E7%B1%B3%E5%BE%B7" title="亞基米德 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="亞基米德" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target">文言</a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Archimedes" title="Archimedes – Waray" lang="war" hreflang="war" data-title="Archimedes" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target">Winaray</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7" title="阿基米德 – Wu" lang="wuu" hreflang="wuu" data-title="阿基米德" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%A8%D7%9B%D7%99%D7%9E%D7%A2%D7%93" title="ארכימעד – Yiddish" lang="yi" hreflang="yi" data-title="ארכימעד" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target">ייִדיש</a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Archimedes" title="Archimedes – Yoruba" lang="yo" hreflang="yo" data-title="Archimedes" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target">Yorùbá</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7" title="阿基米德 – Cantonese" lang="yue" hreflang="yue" data-title="阿基米德" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Ar%C5%9Fimed" title="Arşimed – Dimli" lang="diq" hreflang="diq" data-title="Arşimed" data-language-autonym="Zazaki" data-language-local-name="Dimli" class="interlanguage-link-target">Zazaki</a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Archimeds" title="Archimeds – Samogitian" lang="sgs" hreflang="sgs" data-title="Archimeds" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target">Žemaitėška</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7" title="阿基米德 – Chinese" lang="zh" hreflang="zh" data-title="阿基米德" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li><li class="interlanguage-link interwiki-ann mw-list-item"><a href="https://ann.wikipedia.org/wiki/Achimedis" title="Achimedis – Obolo" lang="ann" hreflang="ann" data-title="Achimedis" data-language-autonym="Obolo" data-language-local-name="Obolo" class="interlanguage-link-target">Obolo</a></li><li class="interlanguage-link interwiki-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/Arkim%C3%A8d%C3%A8s" title="Arkimèdès – Betawi" lang="bew" hreflang="bew" data-title="Arkimèdès" data-language-autonym="Betawi" data-language-local-name="Betawi" class="interlanguage-link-target">Betawi</a></li><li class="interlanguage-link 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title="Archimedes (disambiguation)">Archimedes (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Archimedes of Syracuse</div></th></tr><tr><td colspan="2" class="infobox-subheader" style="font-size:125%;"><div class="nickname" lang="grc">Ἀρχιμήδης</div></td></tr><tr><td colspan="2" class="infobox-image"><a href="/wiki/File:Domenico-Fetti_Archimedes_1620.jpg" class="mw-file-description"><img alt="A painting of an older man puzzling over geometric problems" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Domenico-Fetti_Archimedes_1620.jpg/220px-Domenico-Fetti_Archimedes_1620.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Domenico-Fetti_Archimedes_1620.jpg/330px-Domenico-Fetti_Archimedes_1620.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Domenico-Fetti_Archimedes_1620.jpg/440px-Domenico-Fetti_Archimedes_1620.jpg 2x" data-file-width="1364" data-file-height="1818" /></a><div class="infobox-caption">Archimedes Thoughtful by <a href="/wiki/Domenico_Fetti" title="Domenico Fetti">Fetti</a> (1620)</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><abbr title="circa">c.</abbr> 287 BC <div style="display:inline" class="birthplace"><a href="/wiki/Syracuse,_Sicily" title="Syracuse, Sicily">Syracuse</a>, <a href="/wiki/Sicily" title="Sicily">Sicily</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">c. 212 BC (aged approximately 75) <div style="display:inline" class="deathplace">Syracuse, Sicily</div></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><div class="collapsible-list mw-collapsible mw-collapsed" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold;"><div>List</div></div> <ul class="mw-collapsible-content" style="margin-top: 0; margin-bottom: 0; line-height: inherit; list-style: none; margin-left: 0;"><li style="line-height: inherit; margin: 0"><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a> <a href="/wiki/Archimedes%27_screw" title="Archimedes' screw">Archimedes' screw</a> <a href="/wiki/Center_of_mass#History" title="Center of mass">Center of gravity</a> <a href="/wiki/Statics" title="Statics">Statics</a> <a href="/wiki/Fluid_statics" class="mw-redirect" title="Fluid statics">Hydrostatics</a> <a href="/wiki/Lever" title="Lever">Law of the lever</a> <a href="/wiki/Archimedes%27_use_of_infinitesimals" class="mw-redirect" title="Archimedes' use of infinitesimals">Indivisibles</a> <a href="/wiki/Neusis_construction" title="Neusis construction">Neuseis constructions</a><a href="#cite_note-1">[1]</a> <a href="/wiki/List_of_things_named_after_Archimedes" title="List of things named after Archimedes">List of other things named after him</a></li></ul> </div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546" />Scientific career</td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a> <a href="/wiki/Physics" title="Physics">Physics</a> <a href="/wiki/Astronomy" title="Astronomy">Astronomy</a> <a href="/wiki/Mechanics" title="Mechanics">Mechanics</a> <a href="/wiki/Engineering" title="Engineering">Engineering</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> Archimedes of Syracuse<a href="#cite_note-2">[a]</a> (<a href="/wiki/Help:IPA/English" title="Help:IPA/English">/ˌɑːrkɪˈmiːdiːz/</a> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key">AR-kim-EE-deez</a>;<a href="#cite_note-Collins-3">[2]</a> <abbr title="circa">c.</abbr> 287 – c. 212 BC) was an <a href="/wiki/Ancient_Greece" title="Ancient Greece">Ancient Greek</a> <a href="/wiki/Greek_mathematics" title="Greek mathematics">mathematician</a>, <a href="/wiki/Physicist" title="Physicist">physicist</a>, <a href="/wiki/Engineer" title="Engineer">engineer</a>, <a href="/wiki/Astronomer" title="Astronomer">astronomer</a>, and <a href="/wiki/Invention" title="Invention">inventor</a> from the ancient city of <a href="/wiki/Syracuse,_Sicily" title="Syracuse, Sicily">Syracuse</a> in <a href="/wiki/History_of_Greek_and_Hellenistic_Sicily" class="mw-redirect" title="History of Greek and Hellenistic Sicily">Sicily</a>.<a href="#cite_note-4">[3]</a> Although few details of his life are known, he is considered one of the leading scientists in <a href="/wiki/Classical_antiquity" title="Classical antiquity">classical antiquity</a>. Regarded as the greatest mathematician of <a href="/wiki/Ancient_history" title="Ancient history">ancient history</a>, and one of the greatest of all time,<a href="#cite_note-LitList-5">[4]</a> Archimedes anticipated modern <a href="/wiki/Calculus" title="Calculus">calculus</a> and <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">analysis</a> by applying the concept of the <a href="/wiki/Cavalieri%27s_principle" title="Cavalieri's principle">infinitely small</a> and the <a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">method of exhaustion</a> to derive and rigorously prove many <a href="/wiki/Geometry" title="Geometry">geometrical</a> <a href="/wiki/Theorem" title="Theorem">theorems</a>.<a href="#cite_note-:2-6">[5]</a><a href="#cite_note-:9-7">[6]</a> These include the <a href="/wiki/Area_of_a_circle" title="Area of a circle">area of a circle</a>, the <a href="/wiki/Surface_area" title="Surface area">surface area</a> and <a href="/wiki/Volume" title="Volume">volume</a> of a <a href="/wiki/Sphere" title="Sphere">sphere</a>, the area of an <a href="/wiki/Ellipse" title="Ellipse">ellipse</a>, the area under a <a href="/wiki/Parabola" title="Parabola">parabola</a>, the volume of a segment of a <a href="/wiki/Paraboloid_of_revolution" class="mw-redirect" title="Paraboloid of revolution">paraboloid of revolution</a>, the volume of a segment of a <a href="/wiki/Hyperboloid_of_revolution" class="mw-redirect" title="Hyperboloid of revolution">hyperboloid of revolution</a>, and the area of a <a href="/wiki/Spiral" title="Spiral">spiral</a>.<a href="#cite_note-8">[7]</a><a href="#cite_note-:0-9">[8]</a><a href="#cite_note-10">[9]</a> Archimedes' other mathematical achievements include deriving an <a href="/wiki/Approximations_of_%CF%80" title="Approximations of π">approximation of pi (π)</a>, defining and investigating the <a href="/wiki/Archimedean_spiral" title="Archimedean spiral">Archimedean spiral</a>, and devising a system using <a href="/wiki/Exponentiation" title="Exponentiation">exponentiation</a> for expressing <a href="/wiki/Large_numbers" title="Large numbers">very large numbers</a>. He was also one of the first to <a href="/wiki/Applied_mathematics" title="Applied mathematics">apply mathematics</a> to <a href="/wiki/Physics" title="Physics">physical phenomena</a>, working on <a href="/wiki/Statics" title="Statics">statics</a> and <a href="/wiki/Hydrostatics" title="Hydrostatics">hydrostatics</a>. Archimedes' achievements in this area include a proof of the law of the <a href="/wiki/Lever" title="Lever">lever</a>,<a href="#cite_note-11">[10]</a> the widespread use of the concept of <a href="/wiki/Center_of_mass#History" title="Center of mass">center of gravity</a>,<a href="#cite_note-12">[11]</a> and the enunciation of the law of <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> known as <a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a>.<a href="#cite_note-graf-13">[12]</a> In astronomy, he made measurements of the apparent diameter of the <a href="/wiki/Sun" title="Sun">Sun</a> and the size of the <a href="/wiki/Universe" title="Universe">universe</a>.<a href="#cite_note-14">[13]</a><a href="#cite_note-:7-15">[14]</a> He is also said to have built a <a href="/wiki/Planetarium" title="Planetarium">planetarium</a> device that demonstrated the movements of the known celestial bodies, and may have been a precursor to the <a href="/wiki/Antikythera_mechanism" title="Antikythera mechanism">Antikythera mechanism</a>.<a href="#cite_note-:11-16">[15]</a> He is also credited with designing innovative <a href="/wiki/Machine" title="Machine">machines</a>, such as his <a href="/wiki/Archimedes%27_screw" title="Archimedes' screw">screw pump</a>, <a href="/wiki/Block_and_tackle" title="Block and tackle">compound pulleys</a>, and defensive war machines to protect his native <a href="/wiki/Syracuse,_Sicily" title="Syracuse, Sicily">Syracuse</a> from invasion. Archimedes died during the <a href="/wiki/Siege_of_Syracuse_(213%E2%80%93212_BC)" title="Siege of Syracuse (213–212 BC)">siege of Syracuse</a>, when he was killed by a Roman soldier despite orders that he should not be harmed. <a href="/wiki/Cicero" title="Cicero">Cicero</a> describes visiting Archimedes' tomb, which was surmounted by a <a href="/wiki/Sphere" title="Sphere">sphere</a> and a <a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">cylinder</a> that Archimedes requested be placed there to represent his most valued mathematical discovery. Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. <a href="/wiki/Alexandria" title="Alexandria">Alexandrian</a> mathematicians read and quoted him, but the first comprehensive compilation was not made until <abbr title="circa">c.</abbr> 530 AD by <a href="/wiki/Isidore_of_Miletus" title="Isidore of Miletus">Isidore of Miletus</a> in <a href="/wiki/Byzantine" class="mw-redirect" title="Byzantine">Byzantine</a> <a href="/wiki/Constantinople" title="Constantinople">Constantinople</a>, while <a href="/wiki/Eutocius_of_Ascalon" title="Eutocius of Ascalon">Eutocius</a>' commentaries on Archimedes' works in the same century opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the <a href="/wiki/Middle_Ages" title="Middle Ages">Middle Ages</a> were an influential source of ideas for scientists during the <a href="/wiki/History_of_science_in_the_Renaissance" class="mw-redirect" title="History of science in the Renaissance">Renaissance</a> and again <a href="/wiki/Scientific_Revolution" title="Scientific Revolution">in the 17th century</a>,<a href="#cite_note-17">[16]</a><a href="#cite_note-18">[17]</a> while the discovery in 1906 of previously lost works by Archimedes in the <a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a> has provided new insights into how he obtained mathematical results.<a href="#cite_note-19">[18]</a><a href="#cite_note-20">[19]</a><a href="#cite_note-21">[20]</a><a href="#cite_note-22">[21]</a> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2></div> <div class="mw-heading mw-heading3"><h3 id="Early_life">Early life</h3></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Cicero_Discovering_the_Tomb_of_Archimedes_by_Benjamin_West.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Cicero_Discovering_the_Tomb_of_Archimedes_by_Benjamin_West.jpeg/250px-Cicero_Discovering_the_Tomb_of_Archimedes_by_Benjamin_West.jpeg" decoding="async" width="220" height="151" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Cicero_Discovering_the_Tomb_of_Archimedes_by_Benjamin_West.jpeg/330px-Cicero_Discovering_the_Tomb_of_Archimedes_by_Benjamin_West.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Cicero_Discovering_the_Tomb_of_Archimedes_by_Benjamin_West.jpeg/500px-Cicero_Discovering_the_Tomb_of_Archimedes_by_Benjamin_West.jpeg 2x" data-file-width="5937" data-file-height="4081" /></a><figcaption><a href="/wiki/Cicero" title="Cicero">Cicero</a> Discovering the Tomb of Archimedes (1805) by <a href="/wiki/Benjamin_West" title="Benjamin West">Benjamin West</a></figcaption></figure> Archimedes was born c. 287 BC in the seaport city of <a href="/wiki/Syracuse,_Sicily" title="Syracuse, Sicily">Syracuse</a>, <a href="/wiki/Sicily" title="Sicily">Sicily</a>, at that time a self-governing colony in <a href="/wiki/Magna_Graecia" title="Magna Graecia">Magna Graecia</a>. The date of birth is based on a statement by the Byzantine Greek scholar <a href="/wiki/John_Tzetzes" title="John Tzetzes">John Tzetzes</a> that Archimedes lived for 75 years before his death in 212 BC.<a href="#cite_note-:0-9">[8]</a> <a href="/wiki/Plutarch" title="Plutarch">Plutarch</a> wrote in his <a href="/wiki/Parallel_Lives" title="Parallel Lives">Parallel Lives</a> that Archimedes was related to King <a href="/wiki/Hiero_II_of_Syracuse" title="Hiero II of Syracuse">Hiero II</a>, the ruler of Syracuse, although <a href="/wiki/Cicero" title="Cicero">Cicero</a> suggests he was of humble origin.<a href="#cite_note-23">[22]</a><a href="#cite_note-dijksterhuis-24">[23]</a> In the <a href="/wiki/The_Sand_Reckoner" title="The Sand Reckoner">Sand-Reckoner</a>, Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known.<a href="#cite_note-dijksterhuis-24">[23]</a><a href="#cite_note-:3-25">[24]</a> A biography of Archimedes was written by his friend Heracleides, but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children, or if he ever visited <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a>, Egypt, during his youth.<a href="#cite_note-:4-26">[25]</a> From his surviving written works, it is clear that he maintained collegial relations with scholars based there, including his friend <a href="/wiki/Conon_of_Samos" title="Conon of Samos">Conon of Samos</a> and the head librarian <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes of Cyrene</a>.<a href="#cite_note-27">[b]</a> <div class="mw-heading mw-heading3"><h3 id="Career">Career</h3></div> The standard versions of Archimedes' life were written long after his death by Greek and Roman historians. The earliest reference to Archimedes occurs in the <a href="/wiki/Histories_(Polybius)" title="Histories (Polybius)">Histories</a> by <a href="/wiki/Polybius" title="Polybius">Polybius</a> (<abbr title="circa">c.</abbr> 200–118 BC), written about 70 years after his death.<a href="#cite_note-dijksterhuis-24">[23]</a> It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in order to defend the city from the Romans.<a href="#cite_note-death-28">[26]</a> Polybius remarks how, during the <a href="/wiki/Second_Punic_War" title="Second Punic War">Second Punic War</a>, Syracuse switched allegiances from <a href="/wiki/Roman_Republic" title="Roman Republic">Rome</a> to <a href="/wiki/Carthage" title="Carthage">Carthage</a>, resulting in a military campaign under the command of <a href="/wiki/Marcus_Claudius_Marcellus" title="Marcus Claudius Marcellus">Marcus Claudius Marcellus</a> and <a href="/wiki/Appius_Claudius_Pulcher_(consul_212_BC)" title="Appius Claudius Pulcher (consul 212 BC)">Appius Claudius Pulcher</a>, who besieged the city from 213 to 212 BC. He notes that the Romans underestimated Syracuse's defenses, and mentions several machines Archimedes designed, including improved <a href="/wiki/Catapult" title="Catapult">catapults</a>, crane-like machines that could be swung around in an arc, and other <a href="/wiki/Lithobolos" title="Lithobolos">stone-throwers</a>. Although the Romans ultimately captured the city, they suffered considerable losses due to Archimedes' inventiveness.<a href="#cite_note-29">[27]</a> Cicero (106–43 BC) mentions Archimedes in some of his works.<a href="#cite_note-dijksterhuis-24">[23]</a> While serving as a <a href="/wiki/Quaestor" title="Quaestor">quaestor</a> in Sicily, Cicero found what was presumed to be Archimedes' tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes.<a href="#cite_note-:0-9">[8]</a><a href="#cite_note-30">[28]</a> Cicero had the tomb cleaned up and was able to see the carving and read some of the verses that had been added as an inscription. The tomb carried a sculpture illustrating Archimedes' <a href="/wiki/On_the_Sphere_and_Cylinder" title="On the Sphere and Cylinder">favorite mathematical proof</a>, that the volume and surface area of the sphere are two-thirds that of an enclosing cylinder including its bases.<a href="#cite_note-31">[29]</a><a href="#cite_note-32">[30]</a> He also mentions that Marcellus brought to Rome two planetariums Archimedes built.<a href="#cite_note-:5-33">[31]</a> The Roman historian <a href="/wiki/Livy" title="Livy">Livy</a> (59 BC–17 AD) retells Polybius' story of the capture of Syracuse and Archimedes' role in it.<a href="#cite_note-death-28">[26]</a> <div class="mw-heading mw-heading3"><h3 id="Death">Death</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Death_of_Archimedes_(1815)_by_Thomas_Degeorge.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Death_of_Archimedes_%281815%29_by_Thomas_Degeorge.png/250px-Death_of_Archimedes_%281815%29_by_Thomas_Degeorge.png" decoding="async" width="220" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Death_of_Archimedes_%281815%29_by_Thomas_Degeorge.png/330px-Death_of_Archimedes_%281815%29_by_Thomas_Degeorge.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Death_of_Archimedes_%281815%29_by_Thomas_Degeorge.png/500px-Death_of_Archimedes_%281815%29_by_Thomas_Degeorge.png 2x" data-file-width="1200" data-file-height="1084" /></a><figcaption>The Death of Archimedes (1815) by <a href="/wiki/Thomas_Degeorge" title="Thomas Degeorge">Thomas Degeorge</a><a href="#cite_note-34">[32]</a></figcaption></figure> Plutarch (45–119 AD) provides at least two accounts on how Archimedes died after Syracuse was taken.<a href="#cite_note-dijksterhuis-24">[23]</a> According to the most popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. This enraged the soldier, who killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by Archimedes' death, as he considered him a valuable scientific asset (he called Archimedes "a geometrical <a href="/wiki/Hecatoncheires" title="Hecatoncheires">Briareus</a>") and had ordered that he should not be harmed.<a href="#cite_note-:6-35">[33]</a><a href="#cite_note-36">[34]</a> The last words attributed to Archimedes are "<a href="/wiki/Do_not_disturb_my_circles" class="mw-redirect" title="Do not disturb my circles">Do not disturb my circles</a>" (<a href="/wiki/Latin_language" class="mw-redirect" title="Latin language">Latin</a>: Noli turbare circulos meos; <a href="/wiki/Greek_language" title="Greek language">Greek</a>: μὴ μου τοὺς κύκλους τάραττε), a reference to the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier.<a href="#cite_note-dijksterhuis-24">[23]</a> There is no reliable evidence that Archimedes uttered these words and they do not appear in Plutarch's account. A similar quotation is found in the work of <a href="/wiki/Valerius_Maximus" title="Valerius Maximus">Valerius Maximus</a> (fl. 30 AD), who wrote in Memorable Doings and Sayings, "... sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare'" ("... but protecting the dust with his hands, said 'I beg of you, do not disturb this'").<a href="#cite_note-death-28">[26]</a> <div class="mw-heading mw-heading2"><h2 id="Discoveries_and_inventions">Discoveries and inventions</h2></div> <div class="mw-heading mw-heading3"><h3 id="Archimedes'_principle">Archimedes' principle</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Displacement-measurement.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Displacement-measurement.svg/250px-Displacement-measurement.svg.png" decoding="async" width="220" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Displacement-measurement.svg/330px-Displacement-measurement.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Displacement-measurement.svg/500px-Displacement-measurement.svg.png 2x" data-file-width="960" data-file-height="694" /></a><figcaption>Measurement of volume by displacement, (a) before and (b) after an object has been submerged; the amount by which the liquid rises in the cylinder (∆V) is equal to the volume of the object</figcaption></figure> The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to <a href="/wiki/Vitruvius" title="Vitruvius">Vitruvius</a>, a crown for a temple had been made for <a href="/wiki/Hiero_II_of_Syracuse" title="Hiero II of Syracuse">King Hiero II of Syracuse</a>, who supplied the pure gold to be used. The crown was likely made in the shape of a <a href="/wiki/Wreaths_and_crowns_in_antiquity" title="Wreaths and crowns in antiquity">votive wreath</a>.<a href="#cite_note-crown-37">[35]</a> Archimedes was asked to determine whether some silver had been substituted by the goldsmith without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its <a href="/wiki/Density" title="Density">density</a>.<a href="#cite_note-vitruvius-38">[36]</a> In this account, Archimedes noticed while taking a bath that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the golden crown's <a href="/wiki/Volume" title="Volume">volume</a>. Archimedes was so excited by this discovery that he took to the streets naked, having forgotten to dress, crying "<a href="/wiki/Eureka_(word)" title="Eureka (word)">Eureka</a>!" (<a href="/wiki/Greek_language" title="Greek language">Greek</a>: "εὕρηκα, heúrēka!, <abbr style="font-size:85%" title="literal translation">lit.</abbr> 'I have found [it]!'). For practical purposes water is incompressible,<a href="#cite_note-39">[37]</a> so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, its density could be obtained; if cheaper and less dense metals had been added, the density would be lower than that of gold. Archimedes found that this is what had happened, proving that silver had been mixed in.<a href="#cite_note-crown-37">[35]</a><a href="#cite_note-vitruvius-38">[36]</a> The story of the golden crown does not appear anywhere in Archimedes' known works. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure <a href="/wiki/Displacement_(fluid)" title="Displacement (fluid)">water displacement</a>.<a href="#cite_note-inaccuracy-40">[38]</a> Archimedes may have instead sought a solution that applied the <a href="/wiki/Hydrostatics" title="Hydrostatics">hydrostatics</a> principle known as <a href="/wiki/Archimedes%27s_principle" class="mw-redirect" title="Archimedes's principle">Archimedes' principle</a>, found in his treatise <a href="/wiki/On_Floating_Bodies" title="On Floating Bodies">On Floating Bodies</a>: a body immersed in a fluid experiences a <a href="/wiki/Buoyancy" title="Buoyancy">buoyant force</a> equal to the weight of the fluid it displaces.<a href="#cite_note-41">[39]</a> Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing it on a scale with a pure gold reference sample of the same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly.<a href="#cite_note-graf-13">[12]</a> <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a>, who invented a <a href="/wiki/Hydrostatic_equilibrium" title="Hydrostatic equilibrium">hydrostatic balance</a> in 1586 inspired by Archimedes' work, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself."<a href="#cite_note-42">[40]</a><a href="#cite_note-galileo-43">[41]</a> <div class="mw-heading mw-heading3"><h3 id="Law_of_the_lever">Law of the lever</h3></div> While Archimedes did not invent the <a href="/wiki/Lever" title="Lever">lever</a>, he gave a mathematical proof of the principle involved in his work <a href="/wiki/On_the_Equilibrium_of_Planes" title="On the Equilibrium of Planes">On the Equilibrium of Planes</a>.<a href="#cite_note-44">[42]</a> Earlier descriptions of the principle of the lever are found in a work by <a href="/wiki/Euclid" title="Euclid">Euclid</a> and in the <a href="/wiki/Mechanics_(Aristotle)" title="Mechanics (Aristotle)">Mechanical Problems</a>, belonging to the <a href="/wiki/Peripatetic_school" title="Peripatetic school">Peripatetic school</a> of the followers of <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a>, the authorship of which has been attributed by some to <a href="/wiki/Archytas" title="Archytas">Archytas</a>.<a href="#cite_note-lever_rorres-45">[43]</a><a href="#cite_note-lever_clagett-46">[44]</a> There are several, often conflicting, reports regarding Archimedes' feats using the lever to lift very heavy objects. Plutarch describes how Archimedes designed <a href="/wiki/Block_and_tackle" title="Block and tackle">block-and-tackle</a> <a href="/wiki/Pulley" title="Pulley">pulley</a> systems, allowing sailors to use the principle of <a href="/wiki/Lever" title="Lever">leverage</a> to lift objects that would otherwise have been too heavy to move.<a href="#cite_note-47">[45]</a> According to <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus of Alexandria</a>, Archimedes' work on levers and his understanding of <a href="/wiki/Mechanical_advantage" title="Mechanical advantage">mechanical advantage</a> caused him to remark: "Give me a place to stand on, and I will move the Earth" (<a href="/wiki/Greek_language" title="Greek language">Greek</a>: δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω).<a href="#cite_note-48">[46]</a> <a href="/wiki/Olympiodorus_the_Younger" title="Olympiodorus the Younger">Olympiodorus</a> later attributed the same boast to Archimedes' invention of the baroulkos, a kind of <a href="/wiki/Windlass" title="Windlass">windlass</a>, rather than the lever.<a href="#cite_note-:10-49">[47]</a> <div class="mw-heading mw-heading3"><h3 id="Archimedes'_screw">Archimedes' screw</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Archimedes%27_screw" title="Archimedes' screw">Archimedes' screw</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Archimedes-screw_one-screw-threads_with-ball_3D-view_animated_small.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Archimedes-screw_one-screw-threads_with-ball_3D-view_animated_small.gif/220px-Archimedes-screw_one-screw-threads_with-ball_3D-view_animated_small.gif" decoding="async" width="220" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Archimedes-screw_one-screw-threads_with-ball_3D-view_animated_small.gif/330px-Archimedes-screw_one-screw-threads_with-ball_3D-view_animated_small.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Archimedes-screw_one-screw-threads_with-ball_3D-view_animated_small.gif/440px-Archimedes-screw_one-screw-threads_with-ball_3D-view_animated_small.gif 2x" data-file-width="505" data-file-height="365" /></a><figcaption>The <a href="/wiki/Archimedes%27_screw" title="Archimedes' screw">Archimedes' screw</a> can raise water efficiently</figcaption></figure> A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of <a href="/wiki/Syracuse,_Sicily" title="Syracuse, Sicily">Syracuse</a>. <a href="/wiki/Athenaeus" title="Athenaeus">Athenaeus of Naucratis</a> quotes a certain Moschion in a description on how King Hiero II commissioned the design of a huge ship, the <a href="/wiki/Syracusia" title="Syracusia">Syracusia</a>, which could be used for luxury travel, carrying supplies, and as a display of <a href="/wiki/Navy" title="Navy">naval power</a>.<a href="#cite_note-50">[48]</a> The Syracusia is said to have been the largest ship built in <a href="/wiki/Classical_antiquity" title="Classical antiquity">classical antiquity</a> and, according to Moschion's account, it was launched by Archimedes.<a href="#cite_note-:10-49">[47]</a> The ship presumably was capable of carrying 600 people and included garden decorations, a <a href="/wiki/Gymnasium_(ancient_Greece)" title="Gymnasium (ancient Greece)">gymnasium</a>, and a temple dedicated to the goddess <a href="/wiki/Aphrodite" title="Aphrodite">Aphrodite</a> among its facilities.<a href="#cite_note-51">[49]</a> The account also mentions that, in order to remove any potential water leaking through the hull, a device with a revolving screw-shaped blade inside a cylinder was designed by Archimedes. Archimedes' screw was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. The screw is still in use today for pumping liquids and granulated solids such as coal and grain. Described by <a href="/wiki/Vitruvius" title="Vitruvius">Vitruvius</a>, Archimedes' device may have been an improvement on a screw pump that was used to irrigate the <a href="/wiki/Hanging_Gardens_of_Babylon" title="Hanging Gardens of Babylon">Hanging Gardens of Babylon</a>.<a href="#cite_note-52">[50]</a><a href="#cite_note-53">[51]</a> The world's first seagoing <a href="/wiki/Steamboat" title="Steamboat">steamship</a> with a <a href="/wiki/Propeller" title="Propeller">screw propeller</a> was the <a href="/wiki/SS_Archimedes" title="SS Archimedes">SS Archimedes</a>, which was launched in 1839 and named in honor of Archimedes and his work on the screw.<a href="#cite_note-54">[52]</a> <div class="mw-heading mw-heading3"><h3 id="Archimedes'_claw">Archimedes' claw</h3></div> Archimedes is said to have designed a <a href="/wiki/Claw_of_Archimedes" title="Claw of Archimedes">claw</a> as a weapon to defend the city of Syracuse. Also known as "<style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style>the ship shaker", the claw consisted of a crane-like arm from which a large metal <a href="/wiki/Grappling_hook" title="Grappling hook">grappling hook</a> was suspended. When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it.<a href="#cite_note-55">[53]</a> There have been modern experiments to test the feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device.<a href="#cite_note-56">[54]</a> Archimedes has also been credited with improving the power and accuracy of the <a href="/wiki/Catapult" title="Catapult">catapult</a>, and with inventing the <a href="/wiki/Odometer" title="Odometer">odometer</a> during the <a href="/wiki/First_Punic_War" title="First Punic War">First Punic War</a>. The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled.<a href="#cite_note-57">[55]</a><a href="#cite_note-58">[56]</a> <div class="mw-heading mw-heading3"><h3 id="Heat_ray">Heat ray</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Archimedes%27_heat_ray" title="Archimedes' heat ray">Archimedes' heat ray</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Archimedes_Heat_Ray_conceptual_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Archimedes_Heat_Ray_conceptual_diagram.svg/250px-Archimedes_Heat_Ray_conceptual_diagram.svg.png" decoding="async" width="220" height="263" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Archimedes_Heat_Ray_conceptual_diagram.svg/330px-Archimedes_Heat_Ray_conceptual_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Archimedes_Heat_Ray_conceptual_diagram.svg/440px-Archimedes_Heat_Ray_conceptual_diagram.svg.png 2x" data-file-width="300" data-file-height="358" /></a><figcaption>Mirrors placed as a <a href="/wiki/Parabolic_reflector" title="Parabolic reflector">parabolic reflector</a> to attack upcoming ships</figcaption></figure> As legend has it, Archimedes arranged mirrors as a <a href="/wiki/Parabolic_reflector" title="Parabolic reflector">parabolic reflector</a> to burn ships attacking Syracuse using focused sunlight. While there is no extant contemporary evidence of this feat and modern scholars believe it did not happen, Archimedes may have written a work on mirrors entitled Catoptrica,<a href="#cite_note-:0-59">[c]</a> and <a href="/wiki/Lucian" title="Lucian">Lucian</a> and <a href="/wiki/Galen" title="Galen">Galen</a>, writing in the second century AD, mentioned that during the <a href="/wiki/Siege_of_Syracuse_(213%E2%80%93212_BC)" title="Siege of Syracuse (213–212 BC)">siege of Syracuse</a> Archimedes had burned enemy ships. Nearly four hundred years later, <a href="/wiki/Anthemius_of_Tralles" title="Anthemius of Tralles">Anthemius</a>, despite skepticism, tried to reconstruct Archimedes' hypothetical reflector geometry.<a href="#cite_note-60">[57]</a> The purported device, sometimes called "<a href="/wiki/Archimedes%27_heat_ray" title="Archimedes' heat ray">Archimedes' heat ray</a>", has been the subject of an ongoing debate about its credibility since the <a href="/wiki/Renaissance" title="Renaissance">Renaissance</a>.<a href="#cite_note-61">[58]</a> <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> rejected it as false, while modern researchers have attempted to recreate the effect using only the means that would have been available to Archimedes, mostly with negative results.<a href="#cite_note-death_ray-62">[59]</a><a href="#cite_note-63">[60]</a> It has been suggested that a large array of highly polished <a href="/wiki/Bronze" title="Bronze">bronze</a> or <a href="/wiki/Copper" title="Copper">copper</a> shields acting as mirrors could have been employed to focus sunlight onto a ship, but the overall effect would have been blinding, <a href="/wiki/Glare_(vision)" title="Glare (vision)">dazzling</a>, or distracting the crew of the ship rather than fire.<a href="#cite_note-death_ray2-64">[61]</a> Using modern materials and larger scale, sunlight-concentrating <a href="/wiki/Solar_furnace" title="Solar furnace">solar furnaces</a> can reach very high temperatures, and are sometimes <a href="/wiki/Concentrated_solar_power" title="Concentrated solar power">used for generating electricity</a>.<a href="#cite_note-65">[62]</a> <div class="mw-heading mw-heading3"><h3 id="Astronomical_instruments">Astronomical instruments</h3></div> Archimedes discusses astronomical measurements of the Earth, Sun, and Moon, as well as <a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus</a>' heliocentric model of the universe, in the Sand-Reckoner. Without the use of either trigonometry or a table of chords, Archimedes determines the Sun's apparent diameter by first describing the procedure and instrument used to make observations (a straight rod with pegs or grooves),<a href="#cite_note-66">[63]</a><a href="#cite_note-67">[64]</a> applying correction factors to these measurements, and finally giving the result in the form of upper and lower bounds to account for observational error.<a href="#cite_note-:3-25">[24]</a> <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>, quoting Hipparchus, also references Archimedes' <a href="/wiki/Solstice" title="Solstice">solstice</a> observations in the Almagest. This would make Archimedes the first known Greek to have recorded multiple solstice dates and times in successive years.<a href="#cite_note-:4-26">[25]</a> Cicero's <a href="/wiki/De_re_publica" title="De re publica">De re publica</a> portrays a fictional conversation taking place in 129 BC. After the capture of Syracuse in the <a href="/wiki/Second_Punic_War" title="Second Punic War">Second Punic War</a>, <a href="/wiki/Marcus_Claudius_Marcellus" title="Marcus Claudius Marcellus">Marcellus</a> is said to have taken back to Rome two mechanisms which were constructed by Archimedes and which showed the motion of the Sun, Moon and five planets. Cicero also mentions similar mechanisms designed by <a href="/wiki/Thales" class="mw-redirect" title="Thales">Thales of Miletus</a> and <a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus of Cnidus</a>. The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the <a href="/wiki/Temple_of_Honor_and_Virtue" title="Temple of Honor and Virtue">Temple of Virtue</a> in Rome. Marcellus's mechanism was demonstrated, according to Cicero, by <a href="/wiki/Gaius_Sulpicius_Gallus" title="Gaius Sulpicius Gallus">Gaius Sulpicius Gallus</a> to <a href="/wiki/Lucius_Furius_Philus" title="Lucius Furius Philus">Lucius Furius Philus</a>, who described it thus:<a href="#cite_note-68">[65]</a><a href="#cite_note-69">[66]</a> <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">Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. <div class="paragraphbreak" style="margin-top:0.5em"></div> When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth when the Sun was in line.</blockquote> This is a description of a small <a href="/wiki/Planetarium" title="Planetarium">planetarium</a>. <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus of Alexandria</a> reports on a now lost treatise by Archimedes dealing with the construction of these mechanisms entitled On Sphere-Making.<a href="#cite_note-:5-33">[31]</a><a href="#cite_note-70">[67]</a> Modern research in this area has been focused on the <a href="/wiki/Antikythera_mechanism" title="Antikythera mechanism">Antikythera mechanism</a>, another device built <abbr title="circa">c.</abbr> 100 BC designed with a similar purpose, with some scholars regarding Archimedes' device as a precursor.<a href="#cite_note-:11-16">[15]</a><a href="#cite_note-71">[68]</a> Constructing mechanisms of this kind would have required a sophisticated knowledge of <a href="/wiki/Differential_(mechanical_device)" title="Differential (mechanical device)">differential gearing</a>.<a href="#cite_note-72">[69]</a> This was once thought to have been beyond the range of the technology available in ancient times, but the discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks.<a href="#cite_note-73">[70]</a><a href="#cite_note-74">[71]</a> <div class="mw-heading mw-heading2"><h2 id="Mathematics">Mathematics</h2></div> While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of <a href="/wiki/Greek_mathematics" title="Greek mathematics">mathematics</a>. <a href="/wiki/Plutarch" title="Plutarch">Plutarch</a> wrote that Archimedes "placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life",<a href="#cite_note-:6-35">[33]</a> though some scholars believe this may be a mischaracterization.<a href="#cite_note-75">[72]</a><a href="#cite_note-76">[73]</a><a href="#cite_note-77">[74]</a> <div class="mw-heading mw-heading3"><h3 id="Method_of_exhaustion">Method of exhaustion</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:PiArchimede4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/PiArchimede4.svg/250px-PiArchimede4.svg.png" decoding="async" width="220" height="131" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/PiArchimede4.svg/330px-PiArchimede4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/be/PiArchimede4.svg/440px-PiArchimede4.svg.png 2x" data-file-width="420" data-file-height="251" /></a><figcaption>Archimedes calculates the side of the 12-gon from that of the <a href="/wiki/Hexagon" title="Hexagon">hexagon</a> and for each subsequent doubling of the sides of the regular polygon</figcaption></figure> Archimedes was able to use <a href="/wiki/Cavalieri%27s_principle" title="Cavalieri's principle">indivisibles</a> (a precursor to <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimals</a>) in a way that is similar to modern <a href="/wiki/Integral" title="Integral">integral calculus</a>.<a href="#cite_note-:2-6">[5]</a> Through proof by contradiction (<a href="/wiki/Reductio_ad_absurdum" title="Reductio ad absurdum">reductio ad absurdum</a>), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the <a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">method of exhaustion</a>, and he employed it to approximate the areas of figures and the value of <a href="/wiki/Pi" title="Pi">π</a>. In <a href="/wiki/Measurement_of_a_Circle" title="Measurement of a Circle">Measurement of a Circle</a>, he did this by drawing a larger <a href="/wiki/Regular_hexagon" class="mw-redirect" title="Regular hexagon">regular hexagon</a> outside a <a href="/wiki/Circle" title="Circle">circle</a> then a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each <a href="/wiki/Regular_polygon" title="Regular polygon">regular polygon</a>, calculating the length of a side of each polygon at each step. As the number of sides increases, it becomes a more accurate approximation of a circle. After four such steps, when the polygons had 96 sides each, he was able to determine that the value of π lay between 3<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>⁠1/7⁠ (approx. 3.1429) and 3<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" />⁠10/71⁠ (approx. 3.1408), consistent with its actual value of approximately 3.1416.<a href="#cite_note-78">[75]</a> He also proved that the <a href="/wiki/Area_of_a_circle" title="Area of a circle">area of a circle</a> was equal to π multiplied by the <a href="/wiki/Square" title="Square">square</a> of the <a href="/wiki/Radius" title="Radius">radius</a> of the circle (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi r^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd37db3982ad4e1157dcf8ddbfb280e7bae3b192" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.435ex; height:2.676ex;" alt="{\displaystyle \pi r^{2}}" />). <div class="mw-heading mw-heading3"><h3 id="Archimedean_property">Archimedean property</h3></div> In <a href="/wiki/On_the_Sphere_and_Cylinder" title="On the Sphere and Cylinder">On the Sphere and Cylinder</a>, Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. Today this is known as the <a href="/wiki/Archimedean_property" title="Archimedean property">Archimedean property</a> of real numbers.<a href="#cite_note-79">[76]</a> Archimedes gives the value of the <a href="/wiki/Square_root" title="Square root">square root</a> of 3 as lying between <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" />⁠265/153⁠ (approximately 1.7320261) and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" />⁠1351/780⁠ (approximately 1.7320512) in Measurement of a Circle. The actual value is approximately 1.7320508, making this a very accurate estimate. He introduced this result without offering any explanation of how he had obtained it. This aspect of the work of Archimedes caused <a href="/wiki/John_Wallis" title="John Wallis">John Wallis</a> to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results."<a href="#cite_note-80">[77]</a> It is possible that he used an <a href="/wiki/Iteration" title="Iteration">iterative</a> procedure to calculate these values.<a href="#cite_note-81">[78]</a><a href="#cite_note-82">[79]</a> <div class="mw-heading mw-heading3"><h3 id="The_infinite_series">The infinite series</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Parabolic_segment_and_inscribed_triangle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Parabolic_segment_and_inscribed_triangle.svg/180px-Parabolic_segment_and_inscribed_triangle.svg.png" decoding="async" width="180" height="296" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Parabolic_segment_and_inscribed_triangle.svg/270px-Parabolic_segment_and_inscribed_triangle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/Parabolic_segment_and_inscribed_triangle.svg/360px-Parabolic_segment_and_inscribed_triangle.svg.png 2x" data-file-width="243" data-file-height="400" /></a><figcaption>A proof that the area of the <a href="/wiki/Parabola" title="Parabola">parabolic</a> segment in the upper figure is equal to 4/3 that of the inscribed triangle in the lower figure from <a href="/wiki/Quadrature_of_the_Parabola" title="Quadrature of the Parabola">Quadrature of the Parabola</a></figcaption></figure> In <a href="/wiki/Quadrature_of_the_Parabola" title="Quadrature of the Parabola">Quadrature of the Parabola</a>, Archimedes proved that the area enclosed by a <a href="/wiki/Parabola" title="Parabola">parabola</a> and a straight line is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" />⁠4/3⁠ times the area of a corresponding inscribed <a href="/wiki/Triangle" title="Triangle">triangle</a> as shown in the figure at right. He expressed the solution to the problem as an <a href="/wiki/Series_(mathematics)#History_of_the_theory_of_infinite_series" title="Series (mathematics)">infinite</a> <a href="/wiki/Geometric_series" title="Geometric series">geometric series</a> with the <a href="/wiki/Geometric_series#Common_ratio_r" title="Geometric series">common ratio</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" />⁠1/4⁠: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{n=0}^{\infty }4^{-n}=1+4^{-1}+4^{-2}+4^{-3}+\cdots ={4 \over 3}.\;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>n</mi> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mo>+</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> <mo>.</mo> <mspace width="thickmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{n=0}^{\infty }4^{-n}=1+4^{-1}+4^{-2}+4^{-3}+\cdots ={4 \over 3}.\;}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a27b8944909dc6de31998c85104a4dfca51187cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:42.622ex; height:6.843ex;" alt="{\displaystyle \sum _{n=0}^{\infty }4^{-n}=1+4^{-1}+4^{-2}+4^{-3}+\cdots ={4 \over 3}.\;}" /></dd></dl> If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller <a href="/wiki/Secant_line" title="Secant line">secant lines</a>, and whose third vertex is where the line that is parallel to the parabola's axis and that passes through the midpoint of the base intersects the parabola, and so on. This proof uses a variation of the series <a href="/wiki/1/4_%2B_1/16_%2B_1/64_%2B_1/256_%2B_%C2%B7_%C2%B7_%C2%B7" class="mw-redirect" title="1/4 + 1/16 + 1/64 + 1/256 + · · ·">1/4 + 1/16 + 1/64 + 1/256 + · · ·</a> which sums to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" />⁠1/3⁠. <div class="mw-heading mw-heading3"><h3 id="Myriad_of_myriads">Myriad of myriads</h3></div> In <a href="/wiki/The_Sand_Reckoner" title="The Sand Reckoner">The Sand Reckoner</a>, Archimedes set out to calculate a number that was greater than the grains of sand needed to fill the universe. In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote:<blockquote>There are some, King <a href="/wiki/Gelo,_son_of_Hiero_II" title="Gelo, son of Hiero II">Gelo</a>, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited.</blockquote>To solve the problem, Archimedes devised a system of counting based on the <a href="/wiki/Myriad" title="Myriad">myriad</a>. The word itself derives from the Greek μυριάς, murias, for the number 10,000. He proposed a number system using powers of a myriad of myriads (100 million, i.e., 10,000 x 10,000) and concluded that the number of grains of sand required to fill the universe would be 8 <a href="/wiki/Names_of_large_numbers" title="Names of large numbers">vigintillion</a>, or 8×1063.<a href="#cite_note-83">[80]</a> <div class="mw-heading mw-heading2"><h2 id="Writings">Writings</h2></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Archimedes_%E2%80%93_Opere,_1615_%E2%80%93_BEIC_9741168.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Archimedes_%E2%80%93_Opere%2C_1615_%E2%80%93_BEIC_9741168.jpg/180px-Archimedes_%E2%80%93_Opere%2C_1615_%E2%80%93_BEIC_9741168.jpg" decoding="async" width="180" height="287" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Archimedes_%E2%80%93_Opere%2C_1615_%E2%80%93_BEIC_9741168.jpg/270px-Archimedes_%E2%80%93_Opere%2C_1615_%E2%80%93_BEIC_9741168.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Archimedes_%E2%80%93_Opere%2C_1615_%E2%80%93_BEIC_9741168.jpg/360px-Archimedes_%E2%80%93_Opere%2C_1615_%E2%80%93_BEIC_9741168.jpg 2x" data-file-width="1323" data-file-height="2112" /></a><figcaption>Front page of Archimedes' Opera, in Greek and Latin, edited by <a href="/wiki/David_Rivault_de_Flurence" class="mw-redirect" title="David Rivault de Flurence">David Rivault</a> (1615)</figcaption></figure> The works of Archimedes were written in <a href="/wiki/Doric_Greek" title="Doric Greek">Doric Greek</a>, the dialect of ancient Syracuse.<a href="#cite_note-84">[81]</a> Many written works by Archimedes have not survived or are only extant in heavily edited fragments; at least seven of his treatises are known to have existed due to references made by other authors.<a href="#cite_note-:0-9">[8]</a> <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus of Alexandria</a> mentions On Sphere-Making and another work on <a href="/wiki/Polyhedron" title="Polyhedron">polyhedra</a>, while <a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a> quotes a remark about <a href="/wiki/Refraction" title="Refraction">refraction</a> from the now-lost Catoptrica.<a href="#cite_note-:0-59">[c]</a> Archimedes made his work known through correspondence with mathematicians in <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a>. The writings of Archimedes were first collected by the <a href="/wiki/Byzantine_Empire" title="Byzantine Empire">Byzantine</a> Greek architect <a href="/wiki/Isidore_of_Miletus" title="Isidore of Miletus">Isidore of Miletus</a> (<abbr title="circa">c.</abbr> 530 AD), while commentaries on the works of Archimedes written by <a href="/wiki/Eutocius_of_Ascalon" title="Eutocius of Ascalon">Eutocius</a> in the same century helped bring his work to a wider audience. Archimedes' work was translated into Arabic by <a href="/wiki/Th%C4%81bit_ibn_Qurra" title="Thābit ibn Qurra">Thābit ibn Qurra</a> (836–901 AD), and into Latin via Arabic by <a href="/wiki/Gerard_of_Cremona" title="Gerard of Cremona">Gerard of Cremona</a> (c. 1114–1187). Direct Greek to Latin translations were later done by <a href="/wiki/William_of_Moerbeke" title="William of Moerbeke">William of Moerbeke</a> (c. 1215–1286) and <a href="/wiki/Iacopo_da_San_Cassiano" title="Iacopo da San Cassiano">Iacobus Cremonensis</a> (c. 1400–1453).<a href="#cite_note-85">[82]</a><a href="#cite_note-86">[83]</a> During the <a href="/wiki/History_of_science_in_the_Renaissance" class="mw-redirect" title="History of science in the Renaissance">Renaissance</a>, the <a href="/wiki/Editio_princeps" title="Editio princeps">Editio princeps</a> (First Edition) was published in <a href="/wiki/Basel" title="Basel">Basel</a> in 1544 by <a href="/wiki/Johann_Herwagen" title="Johann Herwagen">Johann Herwagen</a> with the works of Archimedes in Greek and Latin.<a href="#cite_note-87">[84]</a> <div class="mw-heading mw-heading3"><h3 id="Surviving_works">Surviving works</h3></div> The following are ordered chronologically based on new terminological and historical criteria set by Knorr (1978) and Sato (1986).<a href="#cite_note-88">[85]</a><a href="#cite_note-89">[86]</a> <div class="mw-heading mw-heading4"><h4 id="Measurement_of_a_Circle">Measurement of a Circle</h4></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/Measurement_of_a_Circle" title="Measurement of a Circle">Measurement of a Circle</a></div> This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who was a student of <a href="/wiki/Conon_of_Samos" title="Conon of Samos">Conon of Samos</a>. In Proposition II, Archimedes gives an approximation of the value of pi (π), showing that it is greater than <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" />⁠223/71⁠ (3.1408...) and less than <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" />⁠22/7⁠ (3.1428...). <div class="mw-heading mw-heading4"><h4 id="The_Sand_Reckoner">The Sand Reckoner</h4></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/The_Sand_Reckoner" title="The Sand Reckoner">The Sand Reckoner</a></div> In this treatise, also known as Psammites, Archimedes finds a number that is greater than the <a href="/wiki/Sand" title="Sand">grains of sand</a> needed to fill the universe. This book mentions the <a href="/wiki/Heliocentrism" title="Heliocentrism">heliocentric</a> theory of the <a href="/wiki/Solar_System" title="Solar System">Solar System</a> proposed by <a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus of Samos</a>, as well as contemporary ideas about the size of the Earth and the distance between various <a href="/wiki/Celestial_bodies" class="mw-redirect" title="Celestial bodies">celestial bodies</a>, and attempts to measure the apparent diameter of the <a href="/wiki/Sun" title="Sun">Sun</a>.<a href="#cite_note-:7-15">[14]</a> By using a system of numbers based on powers of the <a href="/wiki/Myriad" title="Myriad">myriad</a>, Archimedes concludes that the number of grains of sand required to fill the universe is 8×1063 in modern notation. The introductory letter states that Archimedes' father was an astronomer named Phidias. The Sand Reckoner is the only surviving work in which Archimedes discusses his views on astronomy.<a href="#cite_note-90">[87]</a> <div class="mw-heading mw-heading4"><h4 id="On_the_Equilibrium_of_Planes">On the Equilibrium of Planes</h4></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_the_Equilibrium_of_Planes" title="On the Equilibrium of Planes">On the Equilibrium of Planes</a></div> There are two books to On the Equilibrium of Planes: the first contains seven <a href="/wiki/Axiom" title="Axiom">postulates</a> and fifteen <a href="/wiki/Proposition" title="Proposition">propositions</a>, while the second book contains ten propositions. In the first book, Archimedes proves the law of the <a href="/wiki/Lever" title="Lever">lever</a>, which states that: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712" /><blockquote class="templatequote"><a href="/wiki/Magnitude_(mathematics)" title="Magnitude (mathematics)">Magnitudes</a> are in equilibrium at distances reciprocally proportional to their weights.</blockquote> Archimedes uses the principles derived to calculate the areas and <a href="/wiki/Center_of_mass" title="Center of mass">centers of gravity</a> of various geometric figures including <a href="/wiki/Triangle" title="Triangle">triangles</a>, <a href="/wiki/Parallelogram" title="Parallelogram">parallelograms</a> and <a href="/wiki/Parabola" title="Parabola">parabolas</a>.<a href="#cite_note-works-91">[88]</a> <div class="mw-heading mw-heading4"><h4 id="Quadrature_of_the_Parabola">Quadrature of the Parabola</h4></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/Quadrature_of_the_Parabola" title="Quadrature of the Parabola">Quadrature of the Parabola</a></div> In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a <a href="/wiki/Parabola" title="Parabola">parabola</a> and a straight line is 4/3 the area of a <a href="/wiki/Triangle" title="Triangle">triangle</a> with equal base and height. He achieves this in one of his proofs by calculating the value of a <a href="/wiki/Geometric_series" title="Geometric series">geometric series</a> that sums to infinity with the <a href="/wiki/Ratio" title="Ratio">ratio</a> 1/4. <div class="mw-heading mw-heading4"><h4 id="On_the_Sphere_and_Cylinder">On the Sphere and Cylinder</h4></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_the_Sphere_and_Cylinder" title="On the Sphere and Cylinder">On the Sphere and Cylinder</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Esfera_Arqu%C3%ADmedes.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Esfera_Arqu%C3%ADmedes.svg/250px-Esfera_Arqu%C3%ADmedes.svg.png" decoding="async" width="200" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Esfera_Arqu%C3%ADmedes.svg/330px-Esfera_Arqu%C3%ADmedes.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Esfera_Arqu%C3%ADmedes.svg/500px-Esfera_Arqu%C3%ADmedes.svg.png 2x" data-file-width="1019" data-file-height="1067" /></a><figcaption>A sphere has 2/3 the volume and surface area of its circumscribing cylinder including its bases</figcaption></figure> In this two-volume treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a <a href="/wiki/Sphere" title="Sphere">sphere</a> and a <a href="/wiki/Circumscribe" class="mw-redirect" title="Circumscribe">circumscribed</a> <a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">cylinder</a> of the same height and <a href="/wiki/Diameter" title="Diameter">diameter</a>. The volume is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" />⁠4/3⁠πr3 for the sphere, and 2πr3 for the cylinder. The surface area is 4πr2 for the sphere, and 6πr2 for the cylinder (including its two bases), where r is the radius of the sphere and cylinder. <div class="mw-heading mw-heading4"><h4 id="On_Spirals">On Spirals</h4></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_Spirals" title="On Spirals">On Spirals</a></div> This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the <a href="/wiki/Archimedean_spiral" title="Archimedean spiral">Archimedean spiral</a>. It is the <a href="/wiki/Locus_(mathematics)" title="Locus (mathematics)">locus</a> of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant <a href="/wiki/Angular_velocity" title="Angular velocity">angular velocity</a>. Equivalently, in modern <a href="/wiki/Polar_coordinate_system" title="Polar coordinate system">polar coordinates</a> (r, θ), it can be described by the equation <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,r=a+b\theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mi>r</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,r=a+b\theta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9168c1d8cb658b99ff96f53fae23efcb2a60a6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.692ex; height:2.343ex;" alt="{\displaystyle \,r=a+b\theta }" /> with <a href="/wiki/Real_number" title="Real number">real numbers</a> a and b. This is an early example of a <a href="/wiki/Curve" title="Curve">mechanical curve</a> (a curve traced by a moving <a href="/wiki/Point_(geometry)" title="Point (geometry)">point</a>) considered by a Greek mathematician. <div class="mw-heading mw-heading4"><h4 id="On_Conoids_and_Spheroids">On Conoids and Spheroids</h4></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_Conoids_and_Spheroids" title="On Conoids and Spheroids">On Conoids and Spheroids</a></div> This is a work in 32 propositions addressed to Dositheus. In this treatise Archimedes calculates the areas and volumes of <a href="/wiki/Cross_section_(geometry)" title="Cross section (geometry)">sections</a> of <a href="/wiki/Cone_(geometry)" class="mw-redirect" title="Cone (geometry)">cones</a>, spheres, and paraboloids. <div class="mw-heading mw-heading4"><h4 id="On_Floating_Bodies">On Floating Bodies</h4></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_Floating_Bodies" title="On Floating Bodies">On Floating Bodies</a></div> There are two books of On Floating Bodies. In the first book, Archimedes spells out the law of <a href="https://en.wiktionary.org/wiki/equilibrium" class="extiw" title="wikt:equilibrium">equilibrium</a> of fluids and proves that water will adopt a spherical form around a center of gravity. This may have been an attempt at explaining the theory of contemporary Greek astronomers such as <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a> that the Earth is round. The fluids described by Archimedes are not self-gravitating since he assumes the existence of a point towards which all things fall in order to derive the spherical shape. <a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a> of buoyancy is given in this work, stated as follows:<a href="#cite_note-graf-13">[12]</a><a href="#cite_note-92">[89]</a> <blockquote>Any body wholly or partially immersed in fluid experiences an upthrust equal to, but opposite in direction to, the weight of the fluid displaced.</blockquote> In the second part, he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, similar to the way that icebergs float.<a href="#cite_note-93">[90]</a> <div class="mw-heading mw-heading4"><h4 id="Ostomachion">Ostomachion</h4></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/Ostomachion" title="Ostomachion">Ostomachion</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Stomachion.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Stomachion.JPG/200px-Stomachion.JPG" decoding="async" width="200" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/21/Stomachion.JPG 1.5x" data-file-width="270" data-file-height="263" /></a><figcaption><a href="/wiki/Ostomachion" title="Ostomachion">Ostomachion</a> is a <a href="/wiki/Dissection_puzzle" title="Dissection puzzle">dissection puzzle</a> found in the <a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a></figcaption></figure> Also known as Loculus of Archimedes or Archimedes' Box,<a href="#cite_note-:1-94">[91]</a> this is a <a href="/wiki/Dissection_puzzle" title="Dissection puzzle">dissection puzzle</a> similar to a <a href="/wiki/Tangram" title="Tangram">Tangram</a>, and the treatise describing it was found in more complete form in the <a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a>. Archimedes calculates the areas of the 14 pieces which can be assembled to form a <a href="/wiki/Square" title="Square">square</a>. <a href="/wiki/Reviel_Netz" title="Reviel Netz">Reviel Netz</a> of <a href="/wiki/Stanford_University" title="Stanford University">Stanford University</a> argued in 2003 that Archimedes was attempting to determine how many ways the pieces could be assembled into the shape of a square. Netz calculates that the pieces can be made into a square 17,152 ways.<a href="#cite_note-95">[92]</a> The number of arrangements is 536 when solutions that are equivalent by rotation and reflection are excluded.<a href="#cite_note-96">[93]</a> The puzzle represents an example of an early problem in <a href="/wiki/Combinatorics" title="Combinatorics">combinatorics</a>. The origin of the puzzle's name is unclear, and it has been suggested that it is taken from the <a href="/wiki/Ancient_Greek" title="Ancient Greek">Ancient Greek</a> word for "throat" or "gullet", stomachos (στόμαχος).<a href="#cite_note-97">[94]</a> <a href="/wiki/Ausonius" title="Ausonius">Ausonius</a> calls the puzzle Ostomachion, a Greek compound word formed from the roots of osteon (ὀστέον, 'bone') and machē (μάχη, 'fight').<a href="#cite_note-:1-94">[91]</a> <div class="mw-heading mw-heading4"><h4 id="The_cattle_problem">The cattle problem</h4></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/Archimedes%27s_cattle_problem" title="Archimedes's cattle problem">Archimedes' cattle problem</a></div> <a href="/wiki/Gotthold_Ephraim_Lessing" title="Gotthold Ephraim Lessing">Gotthold Ephraim Lessing</a> discovered this work in a Greek manuscript consisting of a 44-line poem in the <a href="/wiki/Herzog_August_Library" title="Herzog August Library">Herzog August Library</a> in <a href="/wiki/Wolfenb%C3%BCttel" title="Wolfenbüttel">Wolfenbüttel</a>, Germany in 1773. It is addressed to Eratosthenes and the mathematicians in Alexandria. Archimedes challenges them to count the numbers of cattle in the <a href="/wiki/The_Cattle_of_Helios" class="mw-redirect" title="The Cattle of Helios">Herd of the Sun</a> by solving a number of simultaneous <a href="/wiki/Diophantine_equation" title="Diophantine equation">Diophantine equations</a>. There is a more difficult version of the problem in which some of the answers are required to be <a href="/wiki/Square_number" title="Square number">square numbers</a>. A. Amthor first solved this version of the problem<a href="#cite_note-98">[95]</a> in 1880, and the answer is a <a href="/wiki/Very_large_number" class="mw-redirect" title="Very large number">very large number</a>, approximately 7.760271×10206544.<a href="#cite_note-99">[96]</a> <div class="mw-heading mw-heading4"><h4 id="The_Method_of_Mechanical_Theorems">The Method of Mechanical Theorems</h4></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/The_Method_of_Mechanical_Theorems" title="The Method of Mechanical Theorems">The Method of Mechanical Theorems</a></div> This treatise was thought lost until the discovery of the <a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a> in 1906. In this work Archimedes uses <a href="/wiki/Cavalieri%27s_principle" title="Cavalieri's principle">indivisibles</a>,<a href="#cite_note-:2-6">[5]</a><a href="#cite_note-:9-7">[6]</a> and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume. He may have considered this method lacking in formal rigor, so he also used the <a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">method of exhaustion</a> to derive the results. As with <a href="/wiki/Archimedes%27s_cattle_problem" title="Archimedes's cattle problem">The Cattle Problem</a>, The Method of Mechanical Theorems was written in the form of a letter to <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a> in <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a>. <div class="mw-heading mw-heading3"><h3 id="Apocryphal_works">Apocryphal works</h3></div> Archimedes' <a href="/wiki/Book_of_Lemmas" title="Book of Lemmas">Book of Lemmas</a> or Liber Assumptorum is a treatise with 15 propositions on the nature of circles. The earliest known copy of the text is in <a href="/wiki/Arabic_language" class="mw-redirect" title="Arabic language">Arabic</a>. <a href="/wiki/T._L._Heath" class="mw-redirect" title="T. L. Heath">T. L. Heath</a> and <a href="/wiki/Marshall_Clagett" title="Marshall Clagett">Marshall Clagett</a> argued that it cannot have been written by Archimedes in its current form, since it quotes Archimedes, suggesting modification by another author. The Lemmas may be based on an earlier work by Archimedes that is now lost.<a href="#cite_note-100">[97]</a> It has also been claimed that the <a href="/wiki/Heron%27s_formula" title="Heron's formula">formula</a> for calculating the area of a triangle from the length of its sides was known to Archimedes,<a href="#cite_note-101">[d]</a> though its first appearance is in the work of <a href="/wiki/Hero_of_Alexandria" title="Hero of Alexandria">Heron of Alexandria</a> in the 1st century AD.<a href="#cite_note-102">[98]</a> Other questionable attributions to Archimedes' work include the Latin poem <a href="/wiki/Carmen_de_ponderibus_et_mensuris" class="mw-redirect" title="Carmen de ponderibus et mensuris">Carmen de ponderibus et mensuris</a> (4th or 5th century), which describes the use of a <a href="/wiki/Hydrostatic_equilibrium" title="Hydrostatic equilibrium">hydrostatic balance</a>, to solve the problem of the crown, and the 12th-century text <a href="/wiki/Mappae_clavicula" title="Mappae clavicula">Mappae clavicula</a>, which contains instructions on how to perform <a href="/wiki/Assay" title="Assay">assaying</a> of metals by calculating their specific gravities.<a href="#cite_note-kingcrown-103">[99]</a><a href="#cite_note-104">[100]</a> <div class="mw-heading mw-heading3"><h3 id="Archimedes_Palimpsest">Archimedes Palimpsest</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Archimedes_Palimpsest.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Archimedes_Palimpsest.jpg/250px-Archimedes_Palimpsest.jpg" decoding="async" width="220" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Archimedes_Palimpsest.jpg/330px-Archimedes_Palimpsest.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Archimedes_Palimpsest.jpg/500px-Archimedes_Palimpsest.jpg 2x" data-file-width="665" data-file-height="448" /></a><figcaption>In 1906, the Archimedes Palimpsest revealed works by Archimedes thought to have been lost</figcaption></figure> The foremost document containing Archimedes' work is the Archimedes Palimpsest. In 1906, the Danish professor <a href="/wiki/Johan_Ludvig_Heiberg_(historian)" title="Johan Ludvig Heiberg (historian)">Johan Ludvig Heiberg</a> visited <a href="/wiki/Constantinople" title="Constantinople">Constantinople</a> to examine a 174-page <a href="/wiki/Goatskin_(material)" title="Goatskin (material)">goatskin</a> <a href="/wiki/Parchment" title="Parchment">parchment</a> of prayers, written in the 13th century, after reading a short transcription published seven years earlier by <a href="/wiki/Athanasios_Papadopoulos-Kerameus" title="Athanasios Papadopoulos-Kerameus">Papadopoulos-Kerameus</a>.<a href="#cite_note-:8-105">[101]</a><a href="#cite_note-106">[102]</a> He confirmed that it was indeed a <a href="/wiki/Palimpsest" title="Palimpsest">palimpsest</a>, a document with text that had been written over an erased older work. Palimpsests were created by scraping the ink from existing works and reusing them, a common practice in the Middle Ages, as <a href="/wiki/Vellum" title="Vellum">vellum</a> was expensive. The older works in the palimpsest were identified by scholars as 10th-century copies of previously lost treatises by Archimedes.<a href="#cite_note-:8-105">[101]</a><a href="#cite_note-107">[103]</a> The parchment spent hundreds of years in a monastery library in Constantinople before being sold to a private collector in the 1920s. On 29 October 1998, it was sold at auction to an anonymous buyer for a total of $2.2 million.<a href="#cite_note-108">[104]</a><a href="#cite_note-109">[105]</a> The palimpsest holds seven treatises, including the only surviving copy of On Floating Bodies in the original Greek. It is the only known source of The Method of Mechanical Theorems, referred to by <a href="/wiki/Suda" title="Suda">Suidas</a> and thought to have been lost forever. Stomachion was also discovered in the palimpsest, with a more complete analysis of the puzzle than had been found in previous texts. The palimpsest was stored at the <a href="/wiki/Walters_Art_Museum" title="Walters Art Museum">Walters Art Museum</a> in <a href="/wiki/Baltimore" title="Baltimore">Baltimore</a>, <a href="/wiki/Maryland" title="Maryland">Maryland</a>, where it was subjected to a range of modern tests including the use of <a href="/wiki/Ultraviolet" title="Ultraviolet">ultraviolet</a> and <a href="/wiki/X-ray" title="X-ray">X-ray</a> <a href="/wiki/Light" title="Light">light</a> to read the overwritten text.<a href="#cite_note-110">[106]</a> It has since returned to its anonymous owner.<a href="#cite_note-111">[107]</a><a href="#cite_note-112">[108]</a> The treatises in the Archimedes Palimpsest include: <ul><li><a href="/wiki/On_the_Equilibrium_of_Planes" title="On the Equilibrium of Planes">On the Equilibrium of Planes</a></li> <li><a href="/wiki/On_Spirals" title="On Spirals">On Spirals</a></li> <li><a href="/wiki/Measurement_of_a_Circle" title="Measurement of a Circle">Measurement of a Circle</a></li> <li><a href="/wiki/On_the_Sphere_and_Cylinder" title="On the Sphere and Cylinder">On the Sphere and Cylinder</a></li> <li><a href="/wiki/On_Floating_Bodies" title="On Floating Bodies">On Floating Bodies</a></li> <li><a href="/wiki/The_Method_of_Mechanical_Theorems" title="The Method of Mechanical Theorems">The Method of Mechanical Theorems</a></li> <li><a href="/wiki/Stomachion" class="mw-redirect" title="Stomachion">Stomachion</a></li> <li>Speeches by the 4th century BC politician <a href="/wiki/Hypereides" title="Hypereides">Hypereides</a></li> <li>A commentary on <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a>'s <a href="/wiki/Categories_(Aristotle)" title="Categories (Aristotle)">Categories</a></li> <li>Other works</li></ul> <div class="mw-heading mw-heading2"><h2 id="Legacy">Legacy</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/List_of_things_named_after_Archimedes" title="List of things named after Archimedes">List of things named after Archimedes</a> and <a href="/wiki/Eureka_(disambiguation)" class="mw-redirect mw-disambig" title="Eureka (disambiguation)">Eureka</a></div> Sometimes called the father of mathematics and <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a>, Archimedes had a wide influence on mathematics and science.<a href="#cite_note-LitList2-113">[109]</a> <div class="mw-heading mw-heading3"><h3 id="Mathematics_and_physics">Mathematics and physics</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Gerhard_Thieme_Archimedes.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Gerhard_Thieme_Archimedes.jpg/220px-Gerhard_Thieme_Archimedes.jpg" decoding="async" width="220" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Gerhard_Thieme_Archimedes.jpg/330px-Gerhard_Thieme_Archimedes.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Gerhard_Thieme_Archimedes.jpg/440px-Gerhard_Thieme_Archimedes.jpg 2x" data-file-width="717" data-file-height="540" /></a><figcaption> Bronze statue of Archimedes in <a href="/wiki/Berlin" title="Berlin">Berlin</a></figcaption></figure> Historians of science and mathematics almost universally agree that Archimedes was the finest mathematician from antiquity. <a href="/wiki/Eric_Temple_Bell" title="Eric Temple Bell">Eric Temple Bell</a>, for instance, wrote: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712" /><blockquote class="templatequote">Any list of the three "greatest" mathematicians of all history would include the name of Archimedes. The other two usually associated with him are <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> and <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a>. Some, considering the relative wealth—or poverty—of mathematics and physical science in the respective ages in which these giants lived, and estimating their achievements against the background of their times, would put Archimedes first.<a href="#cite_note-114">[110]</a></blockquote> Likewise, <a href="/wiki/Alfred_North_Whitehead" title="Alfred North Whitehead">Alfred North Whitehead</a> and <a href="/wiki/George_F._Simmons" title="George F. Simmons">George F. Simmons</a> said of Archimedes: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712" /><blockquote class="templatequote">... in the year 1500 Europe knew less than Archimedes who died in the year 212 BC ...<a href="#cite_note-115">[111]</a></blockquote><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712" /><blockquote class="templatequote">If we consider what all other men accomplished in mathematics and physics, on every continent and in every civilization, from the beginning of time down to the seventeenth century in Western Europe, the achievements of Archimedes outweighs it all. He was a great civilization all by himself.<a href="#cite_note-116">[112]</a></blockquote> <a href="/wiki/Reviel_Netz" title="Reviel Netz">Reviel Netz</a>, Suppes Professor in Greek Mathematics and Astronomy at <a href="/wiki/Stanford_University" title="Stanford University">Stanford University</a> and an expert in Archimedes notes: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712" /><blockquote class="templatequote">And so, since Archimedes led more than anyone else to the formation of the calculus and since he was the pioneer of the application of mathematics to the physical world, it turns out that Western science is but a series of footnotes to Archimedes. Thus, it turns out that Archimedes is the most important scientist who ever lived.<a href="#cite_note-117">[113]</a></blockquote> <a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a> repeatedly expressed admiration for Archimedes, and attributed his invention <a href="/wiki/Architonnerre" title="Architonnerre">Architonnerre</a> to Archimedes.<a href="#cite_note-Nelson_Examiner-118">[114]</a><a href="#cite_note-PennyM-119">[115]</a><a href="#cite_note-Thurston1996-120">[116]</a> <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a> called him "superhuman" and "my master",<a href="#cite_note-121">[117]</a><a href="#cite_note-122">[118]</a> while <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a> said, "I think Archimedes is comparable to no one", consciously emulating him in his early work.<a href="#cite_note-123">[119]</a> <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a> said, "He who understands Archimedes and <a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius</a> will admire less the achievements of the foremost men of later times".<a href="#cite_note-124">[120]</a> Gauss's heroes were Archimedes and Newton,<a href="#cite_note-125">[121]</a> and <a href="/wiki/Moritz_Cantor" title="Moritz Cantor">Moritz Cantor</a>, who studied under Gauss in the <a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a>, reported that he once remarked in conversation that "there had been only three epoch-making mathematicians: Archimedes, Newton, and <a href="/wiki/Gotthold_Eisenstein" title="Gotthold Eisenstein">Eisenstein</a>".<a href="#cite_note-126">[122]</a> The inventor <a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Nikola Tesla</a> praised him, saying: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712" /><blockquote class="templatequote">Archimedes was my ideal. I admired the works of artists, but to my mind, they were only shadows and semblances. The inventor, I thought, gives to the world creations which are palpable, which live and work.<a href="#cite_note-127">[123]</a></blockquote> <div class="mw-heading mw-heading3"><h3 id="Honors_and_commemorations">Honors and commemorations</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Archimedes_bronze_coin.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Archimedes_bronze_coin.jpg/250px-Archimedes_bronze_coin.jpg" decoding="async" width="220" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Archimedes_bronze_coin.jpg/330px-Archimedes_bronze_coin.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Archimedes_bronze_coin.jpg/500px-Archimedes_bronze_coin.jpg 2x" data-file-width="1188" data-file-height="561" /></a><figcaption>1612 drawing of a now-lost bronze coin depicting Archimedes</figcaption></figure> Italian numismatist and archaeologist Filippo Paruta (1552–1629) and <a href="/wiki/Leonardo_Agostini" title="Leonardo Agostini">Leonardo Agostini</a> (1593–1676) reported on a bronze coin in Sicily with the portrait of Archimedes on the obverse and a cylinder and sphere with the monogram ARMD in Latin on the reverse.<a href="#cite_note-128">[124]</a> Although the coin is now lost and its date is not precisely known, <a href="/wiki/Ivo_Schneider" title="Ivo Schneider">Ivo Schneider</a> described the reverse as "a sphere resting on a base – probably a rough image of one of the planetaria created by Archimedes," and suggested it might have been minted in Rome for Marcellus who "according to ancient reports, brought two spheres of Archimedes with him to Rome".<a href="#cite_note-129">[125]</a> There is a <a href="/wiki/Impact_crater" title="Impact crater">crater</a> on the <a href="/wiki/Moon" title="Moon">Moon</a> named <a href="/wiki/Archimedes_(crater)" title="Archimedes (crater)">Archimedes</a> (<style data-mw-deduplicate="TemplateStyles:r1156832818">.mw-parser-output .geo-default,.mw-parser-output .geo-dms,.mw-parser-output .geo-dec{display:inline}.mw-parser-output .geo-nondefault,.mw-parser-output .geo-multi-punct,.mw-parser-output .geo-inline-hidden{display:none}.mw-parser-output .longitude,.mw-parser-output .latitude{white-space:nowrap}</style><a class="external text" href="https://geohack.toolforge.org/geohack.php?pagename=Archimedes&params=29.7_N_4_W_">29°42′N 4°00′W / 29.7°N 4.0°W / 29.7; -4.0</a>) in his honor, as well as a lunar <a href="/wiki/Mountain_range" title="Mountain range">mountain range</a>, the <a href="/wiki/Montes_Archimedes" title="Montes Archimedes">Montes Archimedes</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1156832818" /><a class="external text" href="https://geohack.toolforge.org/geohack.php?pagename=Archimedes&params=25.3_N_4.6_W_">25°18′N 4°36′W / 25.3°N 4.6°W / 25.3; -4.6</a>).<a href="#cite_note-130">[126]</a> <figure typeof="mw:File/Thumb"><a href="/wiki/File:FieldsMedalFront.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/FieldsMedalFront.jpg/250px-FieldsMedalFront.jpg" decoding="async" width="190" height="183" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/FieldsMedalFront.jpg/330px-FieldsMedalFront.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/FieldsMedalFront.jpg/500px-FieldsMedalFront.jpg 2x" data-file-width="2493" data-file-height="2398" /></a><figcaption>The <a href="/wiki/Fields_Medal" title="Fields Medal">Fields Medal</a> carries a portrait of Archimedes</figcaption></figure> The <a href="/wiki/Fields_Medal" title="Fields Medal">Fields Medal</a> for outstanding achievement in mathematics carries a portrait of Archimedes, along with a carving illustrating his proof on the sphere and the cylinder. The inscription around the head of Archimedes is a quote attributed to 1st century AD poet <a href="/wiki/Marcus_Manilius" title="Marcus Manilius">Manilius</a>, which reads in Latin: Transire suum pectus mundoque potiri ("Rise above oneself and grasp the world").<a href="#cite_note-131">[127]</a><a href="#cite_note-132">[128]</a><a href="#cite_note-133">[129]</a> Archimedes has appeared on postage stamps issued by <a href="/wiki/East_Germany" title="East Germany">East Germany</a> (1973), <a href="/wiki/Greece" title="Greece">Greece</a> (1983), <a href="/wiki/Italy" title="Italy">Italy</a> (1983), <a href="/wiki/Nicaragua" title="Nicaragua">Nicaragua</a> (1971), <a href="/wiki/San_Marino" title="San Marino">San Marino</a> (1982), and <a href="/wiki/Spain" title="Spain">Spain</a> (1963).<a href="#cite_note-134">[130]</a> The exclamation of <a href="/wiki/Eureka_(word)" title="Eureka (word)">Eureka!</a> attributed to Archimedes is the state motto of <a href="/wiki/California" title="California">California</a>. In this instance, the word refers to the discovery of gold near <a href="/wiki/Sutter%27s_Mill" title="Sutter's Mill">Sutter's Mill</a> in 1848 which sparked the <a href="/wiki/California_gold_rush" title="California gold rush">California gold rush</a>.<a href="#cite_note-135">[131]</a> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/28px-P_vip.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/41px-P_vip.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/55px-P_vip.svg.png 2x" data-file-width="1911" data-file-height="1944" /><a href="/wiki/Portal:Biography" title="Portal:Biography">Biography portal</a></li><li class="portalbox-entry"><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/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-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/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></li><li class="portalbox-entry"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/40px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="25" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/60px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Concepts">Concepts</h3></div> <ul><li><a href="/wiki/Arbelos" title="Arbelos">Arbelos</a></li> <li><a href="/wiki/Archimedean_point" title="Archimedean point">Archimedean point</a></li> <li><a href="/wiki/Axiom_of_Archimedes" class="mw-redirect" title="Axiom of Archimedes">Archimedes' axiom</a></li> <li><a href="/wiki/Archimedes_number" title="Archimedes number">Archimedes number</a></li> <li><a href="/wiki/Archimedes_paradox" class="mw-redirect" title="Archimedes paradox">Archimedes paradox</a></li> <li><a href="/wiki/Archimedean_solid" title="Archimedean solid">Archimedean solid</a></li> <li><a href="/wiki/Archimedes%27_circles" class="mw-redirect" title="Archimedes' circles">Archimedes' twin circles</a></li> <li><a href="/wiki/Methods_of_computing_square_roots" title="Methods of computing square roots">Methods of computing square roots</a></li> <li><a href="/wiki/Salinon" title="Salinon">Salinon</a></li> <li><a href="/wiki/Steam_cannon" title="Steam cannon">Steam cannon</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="People">People</h3></div> <ul><li><a href="/wiki/Diocles_(mathematician)" title="Diocles (mathematician)">Diocles</a></li> <li><a href="/wiki/Pseudo-Archimedes" title="Pseudo-Archimedes">Pseudo-Archimedes</a></li> <li><a href="/wiki/Zhang_Heng" title="Zhang Heng">Zhang Heng</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-lower-alpha" style="column-width: 35em;"> <ol class="references"> <li id="cite_note-2"><a href="#cite_ref-2">^</a> <a href="/wiki/Doric_Greek_language" class="mw-redirect" title="Doric Greek language">Doric Greek</a>: <a href="https://en.wiktionary.org/wiki/%E1%BC%88%CF%81%CF%87%CE%B9%CE%BC%CE%AE%CE%B4%CE%B7%CF%82#Ancient_Greek" class="extiw" title="wikt:Ἀρχιμήδης">Ἀρχιμήδης</a>, <style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style>pronounced <a href="/wiki/Help:IPA" title="Help:IPA">[arkʰimɛːdɛ̂ːs]</a>. </li> <li id="cite_note-27"><a href="#cite_ref-27">^</a> In the preface to On Spirals addressed to Dositheus of Pelusium, Archimedes says that "many years have elapsed since Conon's death." <a href="/wiki/Conon_of_Samos" title="Conon of Samos">Conon of Samos</a> lived c. 280–220 BC, suggesting that Archimedes may have been an older man when writing some of his works. </li> <li id="cite_note-:0-59">^ <a href="#cite_ref-:0_59-0">a</a> <a href="#cite_ref-:0_59-1">b</a> The treatises by Archimedes known to exist only through references in the works of other authors are: On Sphere-Making and a work on <a href="/wiki/Polyhedron" title="Polyhedron">polyhedra</a> mentioned by <a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus of Alexandria</a>; Catoptrica, a work on optics mentioned by <a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a>; Principles, addressed to Zeuxippus and explaining the number system used in <a href="/wiki/The_Sand_Reckoner" title="The Sand Reckoner">The Sand Reckoner</a>; On Balances or On Levers; On Centers of Gravity; On the Calendar. </li> <li id="cite_note-101"><a href="#cite_ref-101">^</a> <a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer">Boyer, Carl Benjamin</a>. 1991. A History of Mathematics. <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><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-54397-8" title="Special:BookSources/978-0-471-54397-8">978-0-471-54397-8</a>: "Arabic scholars inform us that the familiar area formula for a triangle in terms of its three sides, usually known as Heron's formula – <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle k={\sqrt {s(s-a)(s-b)(s-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>s</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle k={\sqrt {s(s-a)(s-b)(s-c)}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4d237714d5c5cb144a7a407a5a9ea63e72b9bbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:28.179ex; height:3.343ex;" alt="{\displaystyle \textstyle k={\sqrt {s(s-a)(s-b)(s-c)}}}" />, where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}" /> is the semiperimeter – was known to Archimedes several centuries before Heron lived. Arabic scholars also attribute to Archimedes the 'theorem on the broken <a href="/wiki/Chord_(geometry)" title="Chord (geometry)">chord</a>' ... Archimedes is reported by the Arabs to have given several proofs of the theorem." </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626" /><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKnorr1978" class="citation journal cs1">Knorr, Wilbur R. (1978). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0315-0860%2878%2990134-9">"Archimedes and the spirals: The heuristic background"</a>. <a href="/wiki/Historia_Mathematica" title="Historia Mathematica">Historia Mathematica</a>. 5 (1): 43–75. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0315-0860%2878%2990134-9">10.1016/0315-0860(78)90134-9</a>. <q>"To be sure, Pappus does twice mention the theorem on the tangent to the spiral [IV, 36, 54]. But in both instances the issue is Archimedes' inappropriate use of a 'solid neusis,' that is, of a construction involving the sections of solids, in the solution of a plane problem. Yet Pappus' own resolution of the difficulty [IV, 54] is by his own classification a 'solid' method, as it makes use of conic sections." (p. 48)</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Historia+Mathematica&rft.atitle=Archimedes+and+the+spirals%3A+The+heuristic+background&rft.volume=5&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E43-%3C%2Fspan%3E75&rft.date=1978&rft_id=info%3Adoi%2F10.1016%2F0315-0860%2878%2990134-9&rft.aulast=Knorr&rft.aufirst=Wilbur+R.&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252F0315-0860%252878%252990134-9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-Collins-3"><a href="#cite_ref-Collins_3-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.collinsdictionary.com/dictionary/english/archimedes?showCookiePolicy=true">"Archimedes"</a>. Collins Dictionary. n.d. Retrieved 25 September 2014.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archimedes&rft.pub=Collins+Dictionary&rft_id=http%3A%2F%2Fwww.collinsdictionary.com%2Fdictionary%2Fenglish%2Farchimedes%3FshowCookiePolicy%3Dtrue&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.bbc.co.uk/history/historic_figures/archimedes.shtml">"Archimedes (c. 287 – c. 212 BC)"</a>. BBC History. Retrieved 7 June 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archimedes+%28c.+287+%E2%80%93+c.+212+BC%29&rft.pub=BBC+History&rft_id=https%3A%2F%2Fwww.bbc.co.uk%2Fhistory%2Fhistoric_figures%2Farchimedes.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-LitList-5"><a href="#cite_ref-LitList_5-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJohn_M._Henshaw2014" class="citation book cs1">John M. Henshaw (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-0ljBAAAQBAJ&pg=PA68">An Equation for Every Occasion: Fifty-Two Formulas and Why They Matter</a>. JHU Press. p. 68. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4214-1492-8" title="Special:BookSources/978-1-4214-1492-8"><bdi>978-1-4214-1492-8</bdi></a>. <q>Archimedes is on most lists of the greatest mathematicians of all time and is considered the greatest mathematician of antiquity.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Equation+for+Every+Occasion%3A+Fifty-Two+Formulas+and+Why+They+Matter&rft.pages=68&rft.pub=JHU+Press&rft.date=2014&rft.isbn=978-1-4214-1492-8&rft.au=John+M.+Henshaw&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-0ljBAAAQBAJ%26pg%3DPA68&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCalinger1999" class="citation book cs1">Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall. p. 150. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-02-318285-3" title="Special:BookSources/978-0-02-318285-3"><bdi>978-0-02-318285-3</bdi></a>. <q>Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (ca. 287 212 BC), the most original and profound mathematician of antiquity.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Contextual+History+of+Mathematics&rft.pages=150&rft.pub=Prentice-Hall&rft.date=1999&rft.isbn=978-0-02-318285-3&rft.aulast=Calinger&rft.aufirst=Ronald&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www-history.mcs.st-and.ac.uk/Biographies/Archimedes.html">"Archimedes of Syracuse"</a>. The MacTutor History of Mathematics archive. January 1999. Retrieved 9 June 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archimedes+of+Syracuse&rft.pub=The+MacTutor+History+of+Mathematics+archive&rft.date=1999-01&rft_id=http%3A%2F%2Fwww-history.mcs.st-and.ac.uk%2FBiographies%2FArchimedes.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSadri_Hassani2013" class="citation book cs1">Sadri Hassani (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=GWPgBwAAQBAJ&pg=PA81">Mathematical Methods: For Students of Physics and Related Fields</a>. Springer Science & Business Media. p. 81. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-21562-4" title="Special:BookSources/978-0-387-21562-4"><bdi>978-0-387-21562-4</bdi></a>. <q>Archimedes is arguably believed to be the greatest mathematician of antiquity.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Methods%3A+For+Students+of+Physics+and+Related+Fields&rft.pages=81&rft.pub=Springer+Science+%26+Business+Media&rft.date=2013&rft.isbn=978-0-387-21562-4&rft.au=Sadri+Hassani&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DGWPgBwAAQBAJ%26pg%3DPA81&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHans_Niels_Jahnke" class="citation book cs1">Hans Niels Jahnke. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=CVRZEXFVsZkC&pg=PA21">A History of Analysis</a>. American Mathematical Soc. p. 21. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-9050-9" title="Special:BookSources/978-0-8218-9050-9"><bdi>978-0-8218-9050-9</bdi></a>. <q>Archimedes was the greatest mathematician of antiquity and one of the greatest of all times</q></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+Analysis&rft.pages=21&rft.pub=American+Mathematical+Soc.&rft.isbn=978-0-8218-9050-9&rft.au=Hans+Niels+Jahnke&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DCVRZEXFVsZkC%26pg%3DPA21&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFStephen_Hawking2007" class="citation book cs1">Stephen Hawking (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=eU_RzM7OoI4C&pg=PT12">God Created The Integers: The Mathematical Breakthroughs that Changed History</a>. Running Press. p. 12. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7624-3272-1" title="Special:BookSources/978-0-7624-3272-1"><bdi>978-0-7624-3272-1</bdi></a>. <q>Archimedes, the greatest mathematician of antiquity</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=God+Created+The+Integers%3A+The+Mathematical+Breakthroughs+that+Changed+History&rft.pages=12&rft.pub=Running+Press&rft.date=2007&rft.isbn=978-0-7624-3272-1&rft.au=Stephen+Hawking&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DeU_RzM7OoI4C%26pg%3DPT12&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHirshfeld2009" class="citation book cs1">Hirshfeld, Alan (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=zbcfLoZKDl8C&pg=PA206">Eureka Man: The Life and Legacy of Archimedes</a>. Bloomsbury Publishing. p. 206. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8027-1979-9" title="Special:BookSources/978-0-8027-1979-9"><bdi>978-0-8027-1979-9</bdi></a>. <q>the Archimedes Palimpsest has ridden the roiling waves of circumstance to become the most celebrated link to antiquity's greatest mathematician-inventor</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Eureka+Man%3A+The+Life+and+Legacy+of+Archimedes&rft.pages=206&rft.pub=Bloomsbury+Publishing&rft.date=2009&rft.isbn=978-0-8027-1979-9&rft.aulast=Hirshfeld&rft.aufirst=Alan&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DzbcfLoZKDl8C%26pg%3DPA206&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"><div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFVallianatos2014" class="citation news cs1">Vallianatos, Evaggelos (27 July 2014). <a rel="nofollow" class="external text" href="https://www.huffpost.com/entry/archimedes-the-greatest-scientist-who-ever-lived_b_5390263">"Archimedes: The Greatest Scientist Who Ever Lived"</a>. 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Retrieved 3 May 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archimedes&rft_id=https%3A%2F%2Fwww.math.wichita.edu%2Fhistory%2FMen%2Farchimedes.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFLivio2017" class="citation news cs1">Livio, Mario (6 December 2017). <a rel="nofollow" class="external text" href="https://www.huffpost.com/entry/whos-the-greatest-mathematician-of-them-all_b_5526648">"Who's the Greatest Mathematician of Them All?"</a>. HuffPost. Retrieved 7 May 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=HuffPost&rft.atitle=Who%27s+the+Greatest+Mathematician+of+Them+All%3F&rft.date=2017-12-06&rft.aulast=Livio&rft.aufirst=Mario&rft_id=https%3A%2F%2Fwww.huffpost.com%2Fentry%2Fwhos-the-greatest-mathematician-of-them-all_b_5526648&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-:2-6">^ <a href="#cite_ref-:2_6-0">a</a> <a href="#cite_ref-:2_6-1">b</a> <a href="#cite_ref-:2_6-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPowers2020" class="citation web cs1">Powers, J. (2020). <a rel="nofollow" class="external text" href="https://old.maa.org/sites/default/files/images/upload_library/46/HOMSIGMAA/2020-Jeffery%20Powers.pdf">"Did Archimedes do calculus?"</a> (PDF). maa.org. 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(February 1996). <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/HistTopics/The_rise_of_calculus/">"A history of calculus"</a>. <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a>. Retrieved 7 August 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+history+of+calculus&rft.pub=University+of+St+Andrews&rft.date=1996-02&rft.au=O%27Connor%2C+J.J.&rft.au=Robertson%2C+E.F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FHistTopics%2FThe_rise_of_calculus%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-:0-9">^ <a href="#cite_ref-:0_9-0">a</a> <a href="#cite_ref-:0_9-1">b</a> <a href="#cite_ref-:0_9-2">c</a> <a href="#cite_ref-:0_9-3">d</a> <a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Heath, Thomas L.</a> 1897. 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Retrieved 12 August 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archimedes%27+Claw%3A+watch+an+animation&rft.pub=Weber+State+University&rft.aulast=Carroll&rft.aufirst=Bradley+W&rft_id=http%3A%2F%2Fphysics.weber.edu%2Fcarroll%2FArchimedes%2Fclaw.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-57"><a href="#cite_ref-57">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSleeswyk1981" class="citation journal cs1">Sleeswyk, André Wegener (1981). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/24964584">"Vitruvius' Odometer"</a>. Scientific American. 245 (4): 188–201. <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/1981SciAm.245d.188S">1981SciAm.245d.188S</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%2Fscientificamerican1081-188">10.1038/scientificamerican1081-188</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/0036-8733">0036-8733</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/24964584">24964584</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Vitruvius%27+Odometer&rft.volume=245&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E188-%3C%2Fspan%3E201&rft.date=1981&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican1081-188&rft.issn=0036-8733&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F24964584%23id-name%3DJSTOR&rft_id=info%3Abibcode%2F1981SciAm.245d.188S&rft.aulast=Sleeswyk&rft.aufirst=Andr%C3%A9+Wegener&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F24964584&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-58"><a href="#cite_ref-58">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://archive.today/20070905125400/http://www.tmth.edu.gr/en/aet/5/55.html">"Ancient Greek Scientists: Hero of Alexandria"</a>. Technology Museum of Thessaloniki. Archived from <a rel="nofollow" class="external text" href="http://www.tmth.edu.gr/en/aet/5/55.html">the original</a> on 5 September 2007. Retrieved 14 September 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Ancient+Greek+Scientists%3A+Hero+of+Alexandria&rft.pub=Technology+Museum+of+Thessaloniki&rft_id=http%3A%2F%2Fwww.tmth.edu.gr%2Fen%2Faet%2F5%2F55.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-60"><a href="#cite_ref-60">^</a> Archimedes's contemporary <a href="/wiki/Diocles_(mathematician)" title="Diocles (mathematician)">Diocles</a> made no mention of Archimedes or burning ships in his treatise about focusing reflectors. Diocles, On Burning Mirors, ed. G. J. Toomer, Berlin: Springer, 1976. <div class="paragraphbreak" style="margin-top:0.5em"></div> Lucian, Hippias, <a rel="nofollow" class="external text" href="https://archive.org/details/lucianha01luciuoft/lucianha01luciuoft/page/36/">¶ 2</a>, in Lucian, vol. 1, ed. A. M. Harmon, Harvard, 1913, pp. 36–37, says Archimedes burned ships with his <a href="/wiki/Techne" title="Techne">techne</a>, "skill". <div class="paragraphbreak" style="margin-top:0.5em"></div> <a href="/wiki/Galen" title="Galen">Galen</a>, On temperaments 3.2, mentions pyreia, "torches". <div class="paragraphbreak" style="margin-top:0.5em"></div> <a href="/wiki/Anthemius_of_Tralles" title="Anthemius of Tralles">Anthemius of Tralles</a>, On miraculous engines 153 [Westerman]. <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKnorr1983" class="citation journal cs1">Knorr, Wilbur (1983). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1086/353176">"The Geometry of Burning-Mirrors in Antiquity"</a>. Isis. 74 (1): 53–73. <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%2F353176">10.1086/353176</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>.</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+Geometry+of+Burning-Mirrors+in+Antiquity&rft.volume=74&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E53-%3C%2Fspan%3E73&rft.date=1983&rft_id=info%3Adoi%2F10.1086%2F353176&rft.issn=0021-1753&rft.aulast=Knorr&rft.aufirst=Wilbur&rft_id=http%3A%2F%2Fdx.doi.org%2F10.1086%2F353176&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-61"><a href="#cite_ref-61">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSimms1977" class="citation journal cs1">Simms, D. 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Journal for the History of Astronomy. 30 (3): 238–307. <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/1999JHA....30..237E">1999JHA....30..237E</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%2F002182869903000305">10.1177/002182869903000305</a>. <q>But even before Hipparchus, Archimedes had described a similar instrument in his Sand-Reckoner. A fuller description of the same sort of instrument is given by Pappus of Alexandria ... Figure 30 is based on Archimedes and Pappus. Rod R has a groove that runs its whole length ... A cylinder or prism C is fixed to a small block that slides freely in the groove (p. 281).</q></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+Material+Culture+of+Greek+Astronomy&rft.volume=30&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E238-%3C%2Fspan%3E307&rft.date=1999-08-01&rft_id=info%3Adoi%2F10.1177%2F002182869903000305&rft_id=info%3Abibcode%2F1999JHA....30..237E&rft.aulast=Evans&rft.aufirst=James&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-67"><a href="#cite_ref-67">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFToomerJones2016" class="citation encyclopaedia cs1">Toomer, G. J.; Jones, Alexander (7 March 2016). "Astronomical Instruments". Oxford Research Encyclopedia of Classics. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Facrefore%2F9780199381135.013.886">10.1093/acrefore/9780199381135.013.886</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780199381135" title="Special:BookSources/9780199381135"><bdi>9780199381135</bdi></a>. <q>Perhaps the earliest instrument, apart from sundials, of which we have a detailed description is the device constructed by Archimedes (Sand-Reckoner 11-15) for measuring the sun's apparent diameter; this was a rod along which different coloured pegs could be moved.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Astronomical+Instruments&rft.btitle=Oxford+Research+Encyclopedia+of+Classics&rft.date=2016-03-07&rft_id=info%3Adoi%2F10.1093%2Facrefore%2F9780199381135.013.886&rft.isbn=9780199381135&rft.aulast=Toomer&rft.aufirst=G.+J.&rft.au=Jones%2C+Alexander&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-68"><a href="#cite_ref-68">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCicero" class="citation web cs1"><a href="/wiki/Cicero" title="Cicero">Cicero</a>. <a rel="nofollow" class="external text" href="http://www.thelatinlibrary.com/cicero/repub1.shtml#21">"De re publica 1.xiv §21"</a>. thelatinlibrary.com. Retrieved 23 July 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=De+re+publica+1.xiv+%C2%A721&rft.pub=thelatinlibrary.com&rft.au=Cicero&rft_id=http%3A%2F%2Fwww.thelatinlibrary.com%2Fcicero%2Frepub1.shtml%2321&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-69"><a href="#cite_ref-69">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCicero2005" class="citation book cs1"><a href="/wiki/Cicero" title="Cicero">Cicero</a> (9 February 2005). <a rel="nofollow" class="external text" href="https://www.gutenberg.org/ebooks/14988">De re publica Complete e-text in English from Gutenberg.org</a>. Retrieved 18 September 2007 – via <a href="/wiki/Project_Gutenberg" title="Project Gutenberg">Project Gutenberg</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=De+re+publica+Complete+e-text+in+English+from+Gutenberg.org&rft.date=2005-02-09&rft.au=Cicero&rft_id=https%3A%2F%2Fwww.gutenberg.org%2Febooks%2F14988&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-70"><a href="#cite_ref-70">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWright2017" class="citation book cs1">Wright, Michael T. (2017). "Archimedes, Astronomy, and the Planetarium". In Rorres, Chris (ed.). Archimedes in the 21st Century: Proceedings of a World Conference at the Courant Institute of Mathematical Sciences. Trends in the History of Science. Cham: Springer. pp. 125–141. <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%2F978-3-319-58059-3_7">10.1007/978-3-319-58059-3_7</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-58059-3" title="Special:BookSources/978-3-319-58059-3"><bdi>978-3-319-58059-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Archimedes%2C+Astronomy%2C+and+the+Planetarium&rft.btitle=Archimedes+in+the+21st+Century%3A+Proceedings+of+a+World+Conference+at+the+Courant+Institute+of+Mathematical+Sciences&rft.place=Cham&rft.series=Trends+in+the+History+of+Science&rft.pages=%3Cspan+class%3D%22nowrap%22%3E125-%3C%2Fspan%3E141&rft.pub=Springer&rft.date=2017&rft_id=info%3Adoi%2F10.1007%2F978-3-319-58059-3_7&rft.isbn=978-3-319-58059-3&rft.aulast=Wright&rft.aufirst=Michael+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-71"><a href="#cite_ref-71">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20131212212956/http://www.math.sunysb.edu/~tony/whatsnew/column/antikytheraII-0500/diff4.html">"The Antikythera Mechanism II"</a>. <a href="/wiki/Stony_Brook_University" title="Stony Brook University">Stony Brook University</a>. Archived from <a rel="nofollow" class="external text" href="http://www.math.sunysb.edu/~tony/whatsnew/column/antikytheraII-0500/diff4.html">the original</a> on 12 December 2013. Retrieved 25 December 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Antikythera+Mechanism+II&rft.pub=Stony+Brook+University&rft_id=http%3A%2F%2Fwww.math.sunysb.edu%2F~tony%2Fwhatsnew%2Fcolumn%2FantikytheraII-0500%2Fdiff4.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-72"><a href="#cite_ref-72">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFNoble_Wilford2008" class="citation news cs1">Noble Wilford, John (31 July 2008). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2008/07/31/science/31computer.html?_r=0">"Discovering How Greeks Computed in 100 B.C."</a> <a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a>. Retrieved 25 December 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Discovering+How+Greeks+Computed+in+100+B.C.&rft.date=2008-07-31&rft.aulast=Noble+Wilford&rft.aufirst=John&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2008%2F07%2F31%2Fscience%2F31computer.html%3F_r%3D0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-73"><a href="#cite_ref-73">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://news.bbc.co.uk/1/hi/sci/tech/6191462.stm">"Ancient Moon 'computer' revisited"</a>. BBC News. 29 November 2006. Retrieved 23 July 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Ancient+Moon+%27computer%27+revisited&rft.date=2006-11-29&rft_id=http%3A%2F%2Fnews.bbc.co.uk%2F1%2Fhi%2Fsci%2Ftech%2F6191462.stm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-74"><a href="#cite_ref-74">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRorres" class="citation web cs1">Rorres, Chris. <a rel="nofollow" class="external text" href="http://www.math.nyu.edu/~crorres/Archimedes/Sphere/SphereIntro.html">"Spheres and Planetaria"</a>. Courant Institute of Mathematical Sciences. Retrieved 23 July 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Spheres+and+Planetaria&rft.pub=Courant+Institute+of+Mathematical+Sciences&rft.aulast=Rorres&rft.aufirst=Chris&rft_id=http%3A%2F%2Fwww.math.nyu.edu%2F~crorres%2FArchimedes%2FSphere%2FSphereIntro.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-75"><a href="#cite_ref-75">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRusso2013" class="citation journal cs1">Russo, L. (2013). <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs40329-013-0016-y">"Archimedes between legend and fact"</a>. Lettera Matematica. 1 (3): 91–95. <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%2Fs40329-013-0016-y">10.1007/s40329-013-0016-y</a>. <q>It is amazing that for a long time Archimedes's attitude towards the applications of science was deduced from the acritical acceptance of the opinion of Plutarch: a polygraph who lived centuries later, in a cultural climate that was completely different, certainly could not have known the intimate thoughts of the scientist. On the other hand, the dedication with which Archimedes developed applications of all kinds is well documented: of catoptrica, as Apuleius tells in the passage already cited (Apologia, 16), of hydrostatics (from the design of clocks to naval engineering: we know from Athenaeus (Deipnosophistae, V, 206d) that the largest ship in Antiquity, the Syracusia, was constructed under his supervision), and of mechanics (from machines to hoist weights to those for raising water and devices of war).</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Lettera+Matematica&rft.atitle=Archimedes+between+legend+and+fact.&rft.volume=1&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E91-%3C%2Fspan%3E95&rft.date=2013&rft_id=info%3Adoi%2F10.1007%2Fs40329-013-0016-y&rft.aulast=Russo&rft.aufirst=L.&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%252Fs40329-013-0016-y&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-76"><a href="#cite_ref-76">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFDrachmann1968" class="citation journal cs1"><a href="/wiki/A._G._Drachmann" title="A. G. Drachmann">Drachmann, A. G.</a> (1968). "Archimedes and the Science of Physics". Centaurus. 12 (1): 1–11. <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....1D">1968Cent...12....1D</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.tb00074.x">10.1111/j.1600-0498.1968.tb00074.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=Archimedes+and+the+Science+of+Physics&rft.volume=12&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1-%3C%2Fspan%3E11&rft.date=1968&rft_id=info%3Adoi%2F10.1111%2Fj.1600-0498.1968.tb00074.x&rft_id=info%3Abibcode%2F1968Cent...12....1D&rft.aulast=Drachmann&rft.aufirst=A.+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-77"><a href="#cite_ref-77">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCarrier2008" class="citation thesis cs1">Carrier, Richard (2008). <a rel="nofollow" class="external text" href="https://clio.columbia.edu/catalog/8602980">Attitudes toward the natural philosopher in the early Roman empire (100 B.C. to 313 A.D.)</a> (Thesis). Retrieved 6 April 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Attitudes+toward+the+natural+philosopher+in+the+early+Roman+empire+%28100+B.C.+to+313+A.D.%29&rft.date=2008&rft.aulast=Carrier&rft.aufirst=Richard&rft_id=https%3A%2F%2Fclio.columbia.edu%2Fcatalog%2F8602980&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> "Hence Plutarch's conclusion that Archimedes disdained all mechanics, shop work, or anything useful as low and vulgar, and only directed himself to geometric theory, is obviously untrue. Thus, as several scholars have now concluded, his account of Archimedes appears to be a complete fabrication, invented to promote the Platonic values it glorifies by attaching them to a much-revered hero." (p.444) </li> <li id="cite_note-78"><a href="#cite_ref-78">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHeath,_T.L." class="citation web cs1">Heath, T.L. <a rel="nofollow" class="external text" href="http://www.math.ubc.ca/~cass/archimedes/circle.html">"Archimedes on measuring the circle"</a>. math.ubc.ca. Retrieved 30 October 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archimedes+on+measuring+the+circle&rft.pub=math.ubc.ca&rft.au=Heath%2C+T.L.&rft_id=http%3A%2F%2Fwww.math.ubc.ca%2F~cass%2Farchimedes%2Fcircle.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-79"><a href="#cite_ref-79">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKaye,_R.W." class="citation web cs1">Kaye, R.W. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090316065753/http://web.mat.bham.ac.uk/R.W.Kaye/seqser/archfields">"Archimedean ordered fields"</a>. web.mat.bham.ac.uk. Archived from <a rel="nofollow" class="external text" href="http://web.mat.bham.ac.uk/R.W.Kaye/seqser/archfields">the original</a> on 16 March 2009. Retrieved 7 November 2009.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archimedean+ordered+fields&rft.pub=web.mat.bham.ac.uk&rft.au=Kaye%2C+R.W.&rft_id=http%3A%2F%2Fweb.mat.bham.ac.uk%2FR.W.Kaye%2Fseqser%2Farchfields&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-80"><a href="#cite_ref-80">^</a> Quoted in Heath, T.L. Works of Archimedes, Dover Publications, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-42084-4" title="Special:BookSources/978-0-486-42084-4">978-0-486-42084-4</a>. </li> <li id="cite_note-81"><a href="#cite_ref-81">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.maa.org/programs/maa-awards/writing-awards/of-calculations-past-and-present-the-archimedean-algorithm">"Of Calculations Past and Present: The Archimedean Algorithm"</a>. maa.org. Mathematical Association of America. Retrieved 14 April 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=maa.org&rft.atitle=Of+Calculations+Past+and+Present%3A+The+Archimedean+Algorithm&rft_id=https%3A%2F%2Fwww.maa.org%2Fprograms%2Fmaa-awards%2Fwriting-awards%2Fof-calculations-past-and-present-the-archimedean-algorithm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-82"><a href="#cite_ref-82">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMcKeeman,_Bill" class="citation web cs1"><a href="/w/index.php?title=William_M._McKeeman&action=edit&redlink=1" class="new" title="William M. McKeeman (page does not exist)">McKeeman, Bill</a>. <a rel="nofollow" class="external text" href="http://www.mathworks.com/matlabcentral/fileexchange/29504-the-computation-of-pi-by-archimedes/content/html/ComputationOfPiByArchimedes.html#37">"The Computation of Pi by Archimedes"</a>. Matlab Central. Retrieved 30 October 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Matlab+Central&rft.atitle=The+Computation+of+Pi+by+Archimedes&rft.au=McKeeman%2C+Bill&rft_id=http%3A%2F%2Fwww.mathworks.com%2Fmatlabcentral%2Ffileexchange%2F29504-the-computation-of-pi-by-archimedes%2Fcontent%2Fhtml%2FComputationOfPiByArchimedes.html%2337&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-83"><a href="#cite_ref-83">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCarroll" class="citation web cs1">Carroll, Bradley W. <a rel="nofollow" class="external text" href="http://physics.weber.edu/carroll/Archimedes/sand.htm">"The Sand Reckoner"</a>. Weber State University. Retrieved 23 July 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Sand+Reckoner&rft.pub=Weber+State+University&rft.aulast=Carroll&rft.aufirst=Bradley+W&rft_id=http%3A%2F%2Fphysics.weber.edu%2Fcarroll%2FArchimedes%2Fsand.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-84"><a href="#cite_ref-84">^</a> Encyclopedia of ancient Greece By Wilson, Nigel Guy <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-aFtPdh6-2QC&pg=PA77">p. 77</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160508081544/https://books.google.com/books?id=-aFtPdh6-2QC&pg=PA77">Archived</a> 8 May 2016 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7945-0225-6" title="Special:BookSources/978-0-7945-0225-6">978-0-7945-0225-6</a> (2006) </li> <li id="cite_note-85"><a href="#cite_ref-85">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFClagett1982" class="citation journal cs1">Clagett, Marshall (1982). 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Bell, Men of Mathematics, p 237 </li> <li id="cite_note-127"><a href="#cite_ref-127">^</a> W. Bernard Carlson, Tesla: Inventor of the Electrical Age, p 57 </li> <li id="cite_note-128"><a href="#cite_ref-128">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFParutaAgostini1697" class="citation book cs1 cs1-prop-foreign-lang-source">Paruta, Filippo; Agostini, Leonardo (1697). <a rel="nofollow" class="external text" href="https://dn720400.ca.archive.org/0/items/lasiciliadifilip00paru/lasiciliadifilip00paru.pdf">La Sicilia descritta con medaglie</a> [Sicily described by medals] (PDF) (in Italian). Marco Maier. pp. 73, 326. Retrieved 20 January 2025.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=La+Sicilia+descritta+con+medaglie&rft.pages=73%2C+326&rft.pub=Marco+Maier&rft.date=1697&rft.aulast=Paruta&rft.aufirst=Filippo&rft.au=Agostini%2C+Leonardo&rft_id=https%3A%2F%2Fdn720400.ca.archive.org%2F0%2Fitems%2Flasiciliadifilip00paru%2Flasiciliadifilip00paru.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-129"><a href="#cite_ref-129">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSchneider1979" class="citation book cs1 cs1-prop-foreign-lang-source">Schneider, Ivo (1979). Archimedes. Ingenieur, Naturwissenschaftler und Mathematiker [Archimedes. Engineer, natural scientist and mathematician] (in German). Darmstadt: Wissenschaftliche Buchgesellschaft. pp. 19, 23. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-534-06844-0" title="Special:BookSources/3-534-06844-0"><bdi>3-534-06844-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Archimedes.+Ingenieur%2C+Naturwissenschaftler+und+Mathematiker&rft.place=Darmstadt&rft.pages=19%2C+23&rft.pub=Wissenschaftliche+Buchgesellschaft&rft.date=1979&rft.isbn=3-534-06844-0&rft.aulast=Schneider&rft.aufirst=Ivo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-130"><a href="#cite_ref-130">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFriedlander,_JayWilliams,_Dave" class="citation web cs1">Friedlander, Jay; Williams, Dave. <a rel="nofollow" class="external text" href="https://nssdc.gsfc.nasa.gov/imgcat/html/object_page/a15_m_1541.html">"Oblique view of Archimedes crater on the Moon"</a>. <a href="/wiki/NASA" title="NASA">NASA</a>. Retrieved 13 September 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Oblique+view+of+Archimedes+crater+on+the+Moon&rft.pub=NASA&rft.au=Friedlander%2C+Jay&rft.au=Williams%2C+Dave&rft_id=http%3A%2F%2Fnssdc.gsfc.nasa.gov%2Fimgcat%2Fhtml%2Fobject_page%2Fa15_m_1541.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-131"><a href="#cite_ref-131">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRiehm2002" class="citation journal cs1">Riehm, C. (2002). <a rel="nofollow" class="external text" href="https://www.ams.org/notices/200207/comm-riehm.pdf">"The early history of the Fields Medal"</a> (PDF). Notices of the AMS. 49 (7): 778–782. <q>The Latin inscription from the Roman poet Manilius surrounding the image may be translated 'To pass beyond your understanding and make yourself master of the universe.' The phrase comes from Manilius's Astronomica 4.392 from the first century A.D. (p. 782).</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notices+of+the+AMS&rft.atitle=The+early+history+of+the+Fields+Medal&rft.volume=49&rft.issue=7&rft.pages=%3Cspan+class%3D%22nowrap%22%3E778-%3C%2Fspan%3E782&rft.date=2002&rft.aulast=Riehm&rft.aufirst=C.&rft_id=https%3A%2F%2Fwww.ams.org%2Fnotices%2F200207%2Fcomm-riehm.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-132"><a href="#cite_ref-132">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.fields.utoronto.ca/about/fields-medal">"The Fields Medal"</a>. Fields Institute for Research in Mathematical Sciences. 5 February 2015. Retrieved 23 April 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Fields+Institute+for+Research+in+Mathematical+Sciences&rft.atitle=The+Fields+Medal&rft.date=2015-02-05&rft_id=http%3A%2F%2Fwww.fields.utoronto.ca%2Fabout%2Ffields-medal&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-133"><a href="#cite_ref-133">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mathunion.org/imu-awards/fields-medal">"Fields Medal"</a>. <a href="/wiki/International_Mathematical_Union" title="International Mathematical Union">International Mathematical Union</a>. Retrieved 23 April 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Fields+Medal&rft.pub=International+Mathematical+Union&rft_id=https%3A%2F%2Fwww.mathunion.org%2Fimu-awards%2Ffields-medal&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-134"><a href="#cite_ref-134">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRorres" class="citation web cs1">Rorres, Chris. <a rel="nofollow" class="external text" href="http://math.nyu.edu/~crorres/Archimedes/Stamps/stamps.html">"Stamps of Archimedes"</a>. Courant Institute of Mathematical Sciences. Retrieved 25 August 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Stamps+of+Archimedes&rft.pub=Courant+Institute+of+Mathematical+Sciences&rft.aulast=Rorres&rft.aufirst=Chris&rft_id=http%3A%2F%2Fmath.nyu.edu%2F~crorres%2FArchimedes%2FStamps%2Fstamps.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> <li id="cite_note-135"><a href="#cite_ref-135">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20071012123245/http://capitolmuseum.ca.gov/VirtualTour.aspx?content1=1278&Content2=1374&Content3=1294">"California Symbols"</a>. California State Capitol Museum. Archived from <a rel="nofollow" class="external text" href="http://www.capitolmuseum.ca.gov/VirtualTour.aspx?content1=1278&Content2=1374&Content3=1294">the original</a> on 12 October 2007. Retrieved 14 September 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=California+Symbols&rft.pub=California+State+Capitol+Museum&rft_id=http%3A%2F%2Fwww.capitolmuseum.ca.gov%2FVirtualTour.aspx%3Fcontent1%3D1278%26Content2%3D1374%26Content3%3D1294&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></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 .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><a href="/wiki/File:Wikisource-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/40px-Wikisource-logo.svg.png" decoding="async" width="38" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/60px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/120px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></a></div> <div class="side-box-text plainlist"><a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> has the text of the <a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">1911 Encyclopædia Britannica</a> article "<a href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Archimedes" class="extiw" title="wikisource:1911 Encyclopædia Britannica/Archimedes">Archimedes</a>".</div></div> </div> <ul><li><a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer">Boyer, Carl Benjamin</a>. 1991. <a href="//archive.org/details/historyofmathema00boye" class="extiw" title="iarchive:historyofmathema00boye">A History of Mathematics</a>. New York: Wiley. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-54397-8" title="Special:BookSources/978-0-471-54397-8">978-0-471-54397-8</a>.</li> <li><a href="/wiki/Marshall_Clagett" title="Marshall Clagett">Clagett, Marshall</a>. 1964–1984. Archimedes in the Middle Ages 1–5. Madison, WI: <a href="/wiki/University_of_Wisconsin_Press" title="University of Wisconsin Press">University of Wisconsin Press</a>.</li> <li>Clagett, Marshall. 1970. <a href="//archive.org/details/dictionaryofscie0001unse/page/213/mode/1up" class="extiw" title="iarchive:dictionaryofscie0001unse/page/213/mode/1up">"Archimedes"</a>. In <a href="/wiki/Charles_Coulston_Gillispie" title="Charles Coulston Gillispie">Charles Coulston Gillispie</a>, ed. <a href="/wiki/Dictionary_of_Scientific_Biography" title="Dictionary of Scientific Biography">Dictionary of Scientific Biography</a>. Vol. 1 (Abailard–Berg). New York: Charles Scribner's Sons. pp. 213–231.</li> <li><a href="/wiki/Eduard_Jan_Dijksterhuis" title="Eduard Jan Dijksterhuis">Dijksterhuis, Eduard J.</a> 1956. Archimedes. Translated by C. Dikshoorn. Copenhagen: Ejnar Munksgaard. Chapters 1–5 were translated from Archimedes (in Dutch). Groningen: Noordhoff. 1938. Later chapters appeared in Euclides Vols. 15–17, 20. 1938–1944. Reprinted 1987 by Princeton University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-08421-1" title="Special:BookSources/0-691-08421-1">0-691-08421-1</a></li> <li><a href="/wiki/Mary_Gow" title="Mary Gow">Gow, Mary</a>. 2005. <a href="//archive.org/details/archimedesmathem0000gowm" class="extiw" title="iarchive:archimedesmathem0000gowm">Archimedes: Mathematical Genius of the Ancient World</a>. <a href="/wiki/Enslow_Publishing" title="Enslow Publishing">Enslow Publishing</a>. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7660-2502-8" title="Special:BookSources/978-0-7660-2502-8">978-0-7660-2502-8</a>.</li> <li>Hasan, Heather. 2005. <a href="//archive.org/details/archimedesfather00hasa" class="extiw" title="iarchive:archimedesfather00hasa">Archimedes: The Father of Mathematics</a>. Rosen Central. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4042-0774-5" title="Special:BookSources/978-1-4042-0774-5">978-1-4042-0774-5</a>.</li> <li><a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Heath, Thomas L.</a> 1897. <a href="//archive.org/details/worksofarchimede029517mbp" class="extiw" title="iarchive:worksofarchimede029517mbp">Works of Archimedes</a>. <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-42084-4" title="Special:BookSources/978-0-486-42084-4">978-0-486-42084-4</a>. Complete works of Archimedes in English.</li> <li><a href="/wiki/Reviel_Netz" title="Reviel Netz">Netz, Reviel</a>. 2004–2017. The Works of Archimedes: Translation and Commentary. 1–2. Cambridge University Press. Vol. 1: "The Two Books on the Sphere and the Cylinder". <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-66160-7" title="Special:BookSources/978-0-521-66160-7">978-0-521-66160-7</a>. Vol. 2: "On Spirals". <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-66145-4" title="Special:BookSources/978-0-521-66145-4">978-0-521-66145-4</a>.</li> <li>Netz, Reviel, and William Noel. 2007. The Archimedes Codex. <a href="/wiki/Orion_Publishing_Group" title="Orion Publishing Group">Orion Publishing Group</a>. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-297-64547-4" title="Special:BookSources/978-0-297-64547-4">978-0-297-64547-4</a>.</li> <li><a href="/wiki/Clifford_A._Pickover" title="Clifford A. Pickover">Pickover, Clifford A.</a> 2008. Archimedes to Hawking: Laws of Science and the Great Minds Behind Them. <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-533611-5" title="Special:BookSources/978-0-19-533611-5">978-0-19-533611-5</a>.</li> <li>Simms, Dennis L. 1995. Archimedes the Engineer. <a href="/wiki/Continuum_International_Publishing_Group" title="Continuum International Publishing Group">Continuum International Publishing Group</a>. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7201-2284-8" title="Special:BookSources/978-0-7201-2284-8">978-0-7201-2284-8</a>.</li> <li><a href="/wiki/Sherman_K._Stein" title="Sherman K. Stein">Stein, Sherman</a>. 1999. <a href="//archive.org/details/archimedeswhatdi00stei" class="extiw" title="iarchive:archimedeswhatdi00stei">Archimedes: What Did He Do Besides Cry Eureka?</a>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-718-2" title="Special:BookSources/978-0-88385-718-2">978-0-88385-718-2</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985" /><style data-mw-deduplicate="TemplateStyles:r1250146164">.mw-parser-output .sister-box .side-box-abovebelow{padding:0.75em 0;text-align:center}.mw-parser-output .sister-box 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-abovebelow"> Archimedes at Wikipedia's <a href="/wiki/Wikipedia:Wikimedia_sister_projects" title="Wikipedia:Wikimedia sister projects">sister projects</a></div> <div class="side-box-flex"> <div class="side-box-text plainlist"><ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/0/06/Wiktionary-logo-v2.svg/40px-Wiktionary-logo-v2.svg.png" decoding="async" width="27" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/0/06/Wiktionary-logo-v2.svg/60px-Wiktionary-logo-v2.svg.png 1.5x" data-file-width="391" data-file-height="391" /><a href="https://en.wiktionary.org/wiki/Special:Search/Archimedes" class="extiw" title="wikt:Special:Search/Archimedes">Definitions</a> from Wiktionary</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="20" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 1.5x" data-file-width="1024" data-file-height="1376" /><a href="https://commons.wikimedia.org/wiki/Category:Archimedes" class="extiw" title="c:Category:Archimedes">Media</a> from Commons</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/27px-Wikinews-logo.svg.png" decoding="async" width="27" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/41px-Wikinews-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/54px-Wikinews-logo.svg.png 2x" data-file-width="759" data-file-height="415" /><a href="https://en.wikinews.org/wiki/Particle_accelerator_reveals_long-lost_writings_of_Archimedes" class="extiw" title="n:Particle accelerator reveals long-lost writings of Archimedes">News</a> from Wikinews</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/23px-Wikiquote-logo.svg.png" decoding="async" width="23" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/35px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/46px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /><a href="https://en.wikiquote.org/wiki/Archimedes" class="extiw" title="q:Archimedes">Quotations</a> from Wikiquote</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/40px-Wikisource-logo.svg.png" decoding="async" width="26" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/60px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /><a href="https://en.wikisource.org/wiki/Author:Archimedes" class="extiw" title="s:Author:Archimedes">Texts</a> from Wikisource</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/27px-Wikibooks-logo.svg.png" decoding="async" width="27" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/41px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/54px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /><a href="https://en.wikibooks.org/wiki/FHSST_Physics/Forces/Definition" class="extiw" title="b:FHSST Physics/Forces/Definition">Textbooks</a> from Wikibooks</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/27px-Wikiversity_logo_2017.svg.png" decoding="async" width="27" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/41px-Wikiversity_logo_2017.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/54px-Wikiversity_logo_2017.svg.png 2x" data-file-width="626" data-file-height="512" /><a href="https://en.wikiversity.org/wiki/Ancient_Innovations" class="extiw" title="v:Ancient Innovations">Resources</a> from Wikiversity</li></ul></div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://www.wilbourhall.org/index.html#archimedes">Heiberg's Edition of Archimedes</a>. Texts in Classical Greek, with some in English.</li> <li><a rel="nofollow" class="external text" href="https://www.bbc.co.uk/programmes/b00773bv">Archimedes</a> on <a href="/wiki/In_Our_Time_(radio_series)" title="In Our Time (radio series)">In Our Time</a> at the <a href="/wiki/BBC" title="BBC">BBC</a></li> <li><a rel="nofollow" class="external text" href="https://www.gutenberg.org/ebooks/author/2545">Works by Archimedes</a> at <a href="/wiki/Project_Gutenberg" title="Project Gutenberg">Project Gutenberg</a></li> <li><a rel="nofollow" class="external text" href="https://archive.org/search.php?query=%28%28subject%3A%22Archimedes%22%20OR%20creator%3A%22Archimedes%22%20OR%20description%3A%22Archimedes%22%20OR%20title%3A%22Archimedes%22%29%20OR%20%28%22287-212%22%20AND%20Archimedes%29%29%20AND%20%28-mediatype:software%29">Works by or about Archimedes</a> at the <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a></li> <li><a rel="nofollow" class="external text" href="https://www.inphoproject.org/thinker/2546">Archimedes</a> at the <a href="/wiki/Indiana_Philosophy_Ontology_Project" class="mw-redirect" title="Indiana Philosophy Ontology Project">Indiana Philosophy Ontology Project</a></li> <li><a rel="nofollow" class="external text" href="https://philpapers.org/s/archimedes">Archimedes</a> at <a href="/wiki/PhilPapers" title="PhilPapers">PhilPapers</a></li> <li><a rel="nofollow" class="external text" href="http://www.archimedespalimpsest.org/">The Archimedes Palimpsest project at The Walters Art Museum in Baltimore, Maryland</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.mathpages.com/home/kmath038/kmath038.htm">"Archimedes and the Square Root of 3"</a>. MathPages.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathPages.com&rft.atitle=Archimedes+and+the+Square+Root+of+3&rft_id=http%3A%2F%2Fwww.mathpages.com%2Fhome%2Fkmath038%2Fkmath038.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.mathpages.com/home/kmath343/kmath343.htm">"Archimedes on Spheres and Cylinders"</a>. MathPages.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathPages.com&rft.atitle=Archimedes+on+Spheres+and+Cylinders&rft_id=http%3A%2F%2Fwww.mathpages.com%2Fhome%2Fkmath343%2Fkmath343.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArchimedes" class="Z3988"></li> <li><a rel="nofollow" class="external text" href="http://web.mit.edu/2.009/www/experiments/steamCannon/ArchimedesSteamCannon.html">Testing the Archimedes steam cannon</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100329220142/http://web.mit.edu/2.009/www/experiments/steamCannon/ArchimedesSteamCannon.html">Archived</a> 29 March 2010 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist 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.navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Archimedes" title="Template:Archimedes"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Archimedes" title="Template talk:Archimedes"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Archimedes" title="Special:EditPage/Template:Archimedes"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Archimedes193" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Archimedes</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Written works</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Measurement_of_a_Circle" title="Measurement of a Circle">Measurement of a Circle</a></li> <li><a href="/wiki/The_Sand_Reckoner" title="The Sand Reckoner">The Sand Reckoner</a></li> <li><a href="/wiki/On_the_Equilibrium_of_Planes" title="On the Equilibrium of Planes">On the Equilibrium of Planes</a></li> <li><a href="/wiki/Quadrature_of_the_Parabola" title="Quadrature of the Parabola">Quadrature of the Parabola</a></li> <li><a href="/wiki/On_the_Sphere_and_Cylinder" title="On the Sphere and Cylinder">On the Sphere and Cylinder</a></li> <li><a href="/wiki/On_Spirals" title="On Spirals">On Spirals</a></li> <li><a href="/wiki/On_Conoids_and_Spheroids" title="On Conoids and Spheroids">On Conoids and Spheroids</a></li> <li><a href="/wiki/On_Floating_Bodies" title="On Floating Bodies">On Floating Bodies</a></li> <li><a href="/wiki/Ostomachion" title="Ostomachion">Ostomachion</a></li> <li><a href="/wiki/The_Method_of_Mechanical_Theorems" title="The Method of Mechanical Theorems">The Method of Mechanical Theorems</a></li> <li><a href="/wiki/Book_of_Lemmas" title="Book of Lemmas">Book of Lemmas</a> (apocryphal)</li></ul> </div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><a href="/wiki/File:Domenico-Fetti_Archimedes_1620.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Domenico-Fetti_Archimedes_1620.jpg/90px-Domenico-Fetti_Archimedes_1620.jpg" decoding="async" width="90" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Domenico-Fetti_Archimedes_1620.jpg/135px-Domenico-Fetti_Archimedes_1620.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Domenico-Fetti_Archimedes_1620.jpg/180px-Domenico-Fetti_Archimedes_1620.jpg 2x" data-file-width="1364" data-file-height="1818" /></a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Discoveries and inventions</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/Archimedean_solid" title="Archimedean solid">Archimedean solid</a></li> <li><a href="/wiki/Archimedes%27s_cattle_problem" title="Archimedes's cattle problem">Archimedes's cattle problem</a></li> <li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a></li> <li><a href="/wiki/Archimedes%27s_screw" class="mw-redirect" title="Archimedes's screw">Archimedes's screw</a></li> <li><a href="/wiki/Claw_of_Archimedes" title="Claw of Archimedes">Claw of Archimedes</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous</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/Archimedes%27_heat_ray" title="Archimedes' heat ray">Archimedes' heat ray</a></li> <li><a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a></li> <li><a href="/wiki/List_of_things_named_after_Archimedes" title="List of things named after Archimedes">List of things named after Archimedes</a></li> <li><a href="/wiki/Pseudo-Archimedes" title="Pseudo-Archimedes">Pseudo-Archimedes</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related 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><a href="/wiki/Euclid" title="Euclid">Euclid</a></li> <li><a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus of Cnidus</a></li> <li><a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius of Perga</a></li> <li><a href="/wiki/Hero_of_Alexandria" title="Hero of Alexandria">Hero of Alexandria</a></li> <li><a href="/wiki/Eutocius_of_Ascalon" title="Eutocius of Ascalon">Eutocius of Ascalon</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div> <ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:Archimedes" title="Category:Archimedes">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Ancient_Greek_mathematics550" style="padding:3px"><table class="nowraplinks mw-collapsible 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_mathematics" title="Template:Ancient Greek mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Ancient_Greek_mathematics" title="Template talk:Ancient Greek mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Ancient_Greek_mathematics" title="Special:EditPage/Template:Ancient Greek mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Ancient_Greek_mathematics550" style="font-size:114%;margin:0 4em"><a href="/wiki/Greek_mathematics" title="Greek mathematics">Ancient Greek mathematics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_Greek_mathematicians" title="List of Greek mathematicians">Mathematicians</a> <a href="/wiki/Timeline_of_ancient_Greek_mathematicians" title="Timeline of ancient Greek mathematicians">(timeline)</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anaxagoras" title="Anaxagoras">Anaxagoras</a></li> <li><a href="/wiki/Anthemius_of_Tralles" title="Anthemius of Tralles">Anthemius</a></li> <li><a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius</a></li> <li><a class="mw-selflink selflink">Archimedes</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/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/Dinostratus" title="Dinostratus">Dinostratus</a></li> <li><a href="/wiki/Diocles_(mathematician)" title="Diocles (mathematician)">Diocles</a></li> <li><a href="/wiki/Dionysodorus" title="Dionysodorus">Dionysodorus</a></li> <li><a href="/wiki/Diophantus" title="Diophantus">Diophantus</a></li> <li><a href="/wiki/Domninus_of_Larissa" title="Domninus of Larissa">Domninus</a></li> <li><a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a></li> <li><a href="/wiki/Eudemus_of_Rhodes" title="Eudemus of Rhodes">Eudemus</a></li> <li><a href="/wiki/Euclid" title="Euclid">Euclid</a></li> <li><a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus</a></li> <li><a href="/wiki/Eutocius_of_Ascalon" title="Eutocius of Ascalon">Eutocius</a></li> <li><a href="/wiki/Geminus" title="Geminus">Geminus</a></li> <li><a href="/wiki/Heliodorus_of_Larissa" title="Heliodorus of Larissa">Heliodorus</a></li> <li><a href="/wiki/Hero_of_Alexandria" title="Hero of Alexandria">Heron</a></li> <li><a href="/wiki/Hipparchus" title="Hipparchus">Hipparchus</a></li> <li><a href="/wiki/Hippasus" title="Hippasus">Hippasus</a></li> <li><a href="/wiki/Hippias" title="Hippias">Hippias</a></li> <li><a href="/wiki/Hippocrates_of_Chios" title="Hippocrates of Chios">Hippocrates</a></li> <li><a href="/wiki/Hypatia" title="Hypatia">Hypatia</a></li> <li><a href="/wiki/Hypsicles" title="Hypsicles">Hypsicles</a></li> <li><a href="/wiki/Isidore_of_Miletus" title="Isidore of Miletus">Isidore of Miletus</a></li> <li><a href="/wiki/Leon_(mathematician)" title="Leon (mathematician)">Leon</a></li> <li><a href="/wiki/Marinus_of_Neapolis" title="Marinus of Neapolis">Marinus</a></li> <li><a href="/wiki/Menaechmus" title="Menaechmus">Menaechmus</a></li> <li><a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria">Menelaus</a></li> <li><a href="/wiki/Metrodorus_(grammarian)" title="Metrodorus (grammarian)">Metrodorus</a></li> <li><a href="/wiki/Nicomachus" title="Nicomachus">Nicomachus</a></li> <li><a href="/wiki/Nicomedes_(mathematician)" title="Nicomedes (mathematician)">Nicomedes</a></li> <li><a href="/wiki/Nicoteles_of_Cyrene" title="Nicoteles of Cyrene">Nicoteles</a></li> <li><a href="/wiki/Oenopides" title="Oenopides">Oenopides</a></li> <li><a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus</a></li> <li><a href="/wiki/Perseus_(geometer)" title="Perseus (geometer)">Perseus</a></li> <li><a href="/wiki/Philolaus" title="Philolaus">Philolaus</a></li> <li><a href="/wiki/Philon" title="Philon">Philon</a></li> <li><a href="/wiki/Philonides_of_Laodicea" title="Philonides of Laodicea">Philonides</a></li> <li><a href="/wiki/Plato" title="Plato">Plato</a></li> <li><a href="/wiki/Porphyry_of_Tyre" title="Porphyry of Tyre">Porphyry of Tyre</a></li> <li><a href="/wiki/Posidonius" title="Posidonius">Posidonius</a></li> <li><a href="/wiki/Proclus" title="Proclus">Proclus</a></li> <li><a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a></li> <li><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li> <li><a href="/wiki/Serenus_of_Antino%C3%B6polis" title="Serenus of Antinoöpolis">Serenus </a></li> <li><a href="/wiki/Simplicius_of_Cilicia" title="Simplicius of Cilicia">Simplicius</a></li> <li><a href="/wiki/Sosigenes_of_Alexandria" class="mw-redirect" title="Sosigenes of Alexandria">Sosigenes</a></li> <li><a href="/wiki/Sporus_of_Nicaea" title="Sporus of Nicaea">Sporus</a></li> <li><a href="/wiki/Thales_of_Miletus" title="Thales of Miletus">Thales</a></li> <li><a href="/wiki/Theaetetus_(mathematician)" title="Theaetetus (mathematician)">Theaetetus</a></li> <li><a href="/wiki/Theano_(philosopher)" title="Theano (philosopher)">Theano</a></li> <li><a href="/wiki/Theodorus_of_Cyrene" title="Theodorus of Cyrene">Theodorus</a></li> <li><a href="/wiki/Theodosius_of_Bithynia" title="Theodosius of Bithynia">Theodosius</a></li> <li><a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a></li> <li><a href="/wiki/Theon_of_Smyrna" title="Theon of Smyrna">Theon of Smyrna</a></li> <li><a href="/wiki/Thymaridas" title="Thymaridas">Thymaridas</a></li> <li><a href="/wiki/Xenocrates" title="Xenocrates">Xenocrates</a></li> <li><a href="/wiki/Zeno_of_Elea" title="Zeno of Elea">Zeno of Elea</a></li> <li><a href="/wiki/Zeno_of_Sidon" title="Zeno of Sidon">Zeno of Sidon</a></li> <li><a href="/wiki/Zenodorus_(mathematician)" title="Zenodorus (mathematician)">Zenodorus</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Treatises</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Almagest" title="Almagest">Almagest</a></li> <li><a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a></li> <li><a href="/wiki/Arithmetica" title="Arithmetica">Arithmetica</a></li> <li><a href="/wiki/Apollonius_of_Perga#Conics" title="Apollonius of Perga">Conics (Apollonius)</a></li> <li><a href="/wiki/Catoptrics" title="Catoptrics">Catoptrics</a></li> <li><a href="/wiki/Data_(Euclid)" class="mw-redirect" title="Data (Euclid)">Data (Euclid)</a></li> <li><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Elements (Euclid)</a></li> <li><a href="/wiki/Measurement_of_a_Circle" title="Measurement of a Circle">Measurement of a Circle</a></li> <li><a href="/wiki/On_Conoids_and_Spheroids" title="On Conoids and Spheroids">On Conoids and Spheroids</a></li> <li><a href="/wiki/On_the_Sizes_and_Distances_(Aristarchus)" title="On the Sizes and Distances (Aristarchus)">On the Sizes and Distances (Aristarchus)</a></li> <li><a href="/wiki/On_Sizes_and_Distances_(Hipparchus)" title="On Sizes and Distances (Hipparchus)">On Sizes and Distances (Hipparchus)</a></li> <li><a href="/wiki/Autolycus_of_Pitane" title="Autolycus of Pitane">On the Moving Sphere (Autolycus)</a></li> <li><a href="/wiki/Euclid%27s_Optics" title="Euclid's Optics">Optics (Euclid)</a></li> <li><a href="/wiki/On_Spirals" title="On Spirals">On Spirals</a></li> <li><a href="/wiki/On_the_Sphere_and_Cylinder" title="On the Sphere and Cylinder">On the Sphere and Cylinder</a></li> <li><a href="/wiki/Ostomachion" title="Ostomachion">Ostomachion</a></li> <li><a href="/wiki/Planisphaerium" title="Planisphaerium">Planisphaerium</a></li> <li><a href="/wiki/Theodosius%27_Spherics" title="Theodosius' Spherics">Spherics (Theodosius)</a></li> <li><a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria">Spherics (Menelaus)</a></li> <li><a href="/wiki/The_Quadrature_of_the_Parabola" class="mw-redirect" title="The Quadrature of the Parabola">The Quadrature of the Parabola</a></li> <li><a href="/wiki/The_Sand_Reckoner" title="The Sand Reckoner">The Sand Reckoner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Problems</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Constructible_number" title="Constructible number">Constructible numbers</a> <ul><li><a href="/wiki/Angle_trisection" title="Angle trisection">Angle trisection</a></li> <li><a href="/wiki/Doubling_the_cube" title="Doubling the cube">Doubling the cube</a></li> <li><a href="/wiki/Squaring_the_circle" title="Squaring the circle">Squaring the circle</a></li></ul></li> <li><a href="/wiki/Problem_of_Apollonius" title="Problem of Apollonius">Problem of Apollonius</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts and definitions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Angle" title="Angle">Angle</a> <ul><li><a href="/wiki/Central_angle" title="Central angle">Central</a></li> <li><a href="/wiki/Inscribed_angle" title="Inscribed angle">Inscribed</a></li></ul></li> <li><a href="/wiki/Axiomatic_system" title="Axiomatic system">Axiomatic system</a> <ul><li><a href="/wiki/Axiom" title="Axiom">Axiom</a></li></ul></li> <li><a href="/wiki/Chord_(geometry)" title="Chord (geometry)">Chord</a></li> <li><a href="/wiki/Circles_of_Apollonius" title="Circles of Apollonius">Circles of Apollonius</a> <ul><li><a href="/wiki/Apollonian_circles" title="Apollonian circles">Apollonian circles</a></li> <li><a href="/wiki/Apollonian_gasket" title="Apollonian gasket">Apollonian gasket</a></li></ul></li> <li><a href="/wiki/Circumscribed_circle" title="Circumscribed circle">Circumscribed circle</a></li> <li><a href="/wiki/Commensurability_(mathematics)" title="Commensurability (mathematics)">Commensurability</a></li> <li><a href="/wiki/Diophantine_equation" title="Diophantine equation">Diophantine equation</a></li> <li><a href="https://en.wikiquote.org/wiki/Doctrine_of_proportion_(mathematics)" class="extiw" title="wikiquote:Doctrine of proportion (mathematics)">Doctrine of proportionality</a></li> <li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a></li> <li><a href="/wiki/Golden_ratio" title="Golden ratio">Golden ratio</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a></li> <li><a href="/wiki/Incircle_and_excircles_of_a_triangle" class="mw-redirect" title="Incircle and excircles of a triangle">Incircle and excircles of a triangle</a></li> <li><a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">Method of exhaustion</a></li> <li><a href="/wiki/Parallel_postulate" title="Parallel postulate">Parallel postulate</a></li> <li><a href="/wiki/Platonic_solid" title="Platonic solid">Platonic solid</a></li> <li><a href="/wiki/Lune_of_Hippocrates" title="Lune of Hippocrates">Lune of Hippocrates</a></li> <li><a href="/wiki/Quadratrix_of_Hippias" title="Quadratrix of Hippias">Quadratrix of Hippias</a></li> <li><a href="/wiki/Regular_polygon" title="Regular polygon">Regular polygon</a></li> <li><a href="/wiki/Straightedge_and_compass_construction" title="Straightedge and compass construction">Straightedge and compass construction</a></li> <li><a href="/wiki/Triangle_center" title="Triangle center">Triangle center</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Results</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">In <a href="/wiki/Euclid%27s_elements" class="mw-redirect" title="Euclid's elements">Elements</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Angle_bisector_theorem" title="Angle bisector theorem">Angle bisector theorem</a></li> <li><a href="/wiki/Exterior_angle_theorem" title="Exterior angle theorem">Exterior angle theorem</a></li> <li><a href="/wiki/Euclidean_algorithm" title="Euclidean algorithm">Euclidean algorithm</a></li> <li><a href="/wiki/Euclid%27s_theorem" title="Euclid's theorem">Euclid's theorem</a></li> <li><a href="/wiki/Geometric_mean_theorem" title="Geometric mean theorem">Geometric mean theorem</a></li> <li><a href="/wiki/Greek_geometric_algebra" class="mw-redirect" title="Greek geometric algebra">Greek geometric algebra</a></li> <li><a href="/wiki/Hinge_theorem" title="Hinge theorem">Hinge theorem</a></li> <li><a href="/wiki/Inscribed_angle_theorem" class="mw-redirect" title="Inscribed angle theorem">Inscribed angle theorem</a></li> <li><a href="/wiki/Intercept_theorem" title="Intercept theorem">Intercept theorem</a></li> <li><a href="/wiki/Intersecting_chords_theorem" title="Intersecting chords theorem">Intersecting chords theorem</a></li> <li><a href="/wiki/Intersecting_secants_theorem" title="Intersecting secants theorem">Intersecting secants theorem</a></li> <li><a href="/wiki/Law_of_cosines" title="Law of cosines">Law of cosines</a></li> <li><a href="/wiki/Pons_asinorum" title="Pons asinorum">Pons asinorum</a></li> <li><a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a></li> <li><a href="/wiki/Tangent-secant_theorem" class="mw-redirect" title="Tangent-secant theorem">Tangent-secant theorem</a></li> <li><a href="/wiki/Thales%27s_theorem" title="Thales's theorem">Thales's theorem</a></li> <li><a href="/wiki/Theorem_of_the_gnomon" title="Theorem of the gnomon">Theorem of the gnomon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Apollonius_of_Tyana" title="Apollonius of Tyana">Apollonius</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Apollonius%27s_theorem" title="Apollonius's theorem">Apollonius's theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aristarchus%27s_inequality" title="Aristarchus's inequality">Aristarchus's inequality</a></li> <li><a href="/wiki/Crossbar_theorem" title="Crossbar theorem">Crossbar theorem</a></li> <li><a href="/wiki/Heron%27s_formula" title="Heron's formula">Heron's formula</a></li> <li><a href="/wiki/Irrational_number" title="Irrational number">Irrational numbers</a></li> <li><a href="/wiki/Law_of_sines" title="Law of sines">Law of sines</a></li> <li><a href="/wiki/Menelaus%27s_theorem" title="Menelaus's theorem">Menelaus's theorem</a></li> <li><a href="/wiki/Pappus%27s_area_theorem" title="Pappus's area theorem">Pappus's area theorem</a></li> <li><a href="/wiki/Diophantus_II.VIII" title="Diophantus II.VIII">Problem II.8 of Arithmetica</a></li> <li><a href="/wiki/Ptolemy%27s_inequality" title="Ptolemy's inequality">Ptolemy's inequality</a></li> <li><a href="/wiki/Ptolemy%27s_table_of_chords" title="Ptolemy's table of chords">Ptolemy's table of chords</a></li> <li><a href="/wiki/Ptolemy%27s_theorem" title="Ptolemy's theorem">Ptolemy's theorem</a></li> <li><a href="/wiki/Spiral_of_Theodorus" title="Spiral of Theodorus">Spiral of Theodorus</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Centers</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cyrene,_Libya" title="Cyrene, Libya">Cyrene</a></li> <li><a href="/wiki/Musaeum" class="mw-redirect" title="Musaeum">Mouseion of Alexandria</a></li> <li><a href="/wiki/Platonic_Academy" title="Platonic Academy">Platonic Academy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ancient_Greek_astronomy" title="Ancient Greek astronomy">Ancient Greek astronomy</a></li> <li><a href="/wiki/Attic_numerals" title="Attic numerals">Attic numerals</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a></li> <li><a href="/wiki/Latin_translations_of_the_12th_century" title="Latin translations of the 12th century">Latin translations of the 12th century</a></li> <li><a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">Non-Euclidean geometry</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy of mathematics</a></li> <li><a href="/wiki/Neusis_construction" title="Neusis construction">Neusis construction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">History of</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/A_History_of_Greek_Mathematics" title="A History of Greek Mathematics">A History of Greek Mathematics</a> <ul><li>by <a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Thomas Heath</a></li></ul></li> <li><a href="/wiki/History_of_algebra" title="History of algebra">algebra</a> <ul><li><a href="/wiki/Timeline_of_algebra" title="Timeline of algebra">timeline</a></li></ul></li> <li><a href="/wiki/History_of_arithmetic" class="mw-redirect" title="History of arithmetic">arithmetic</a> <ul><li><a href="/wiki/Timeline_of_numerals_and_arithmetic" title="Timeline of numerals and arithmetic">timeline</a></li></ul></li> <li><a href="/wiki/History_of_calculus" title="History of calculus">calculus</a> <ul><li><a href="/wiki/Timeline_of_calculus_and_mathematical_analysis" title="Timeline of calculus and mathematical analysis">timeline</a></li></ul></li> <li><a href="/wiki/History_of_geometry" title="History of geometry">geometry</a> <ul><li><a href="/wiki/Timeline_of_geometry" title="Timeline of geometry">timeline</a></li></ul></li> <li><a href="/wiki/History_of_logic" title="History of logic">logic</a> <ul><li><a href="/wiki/Timeline_of_mathematical_logic" title="Timeline of mathematical logic">timeline</a></li></ul></li> <li><a href="/wiki/History_of_mathematics" title="History of mathematics">mathematics</a> <ul><li><a href="/wiki/Timeline_of_mathematics" title="Timeline of mathematics">timeline</a></li></ul></li> <li><a href="/wiki/History_of_numbers" class="mw-redirect" title="History of numbers">numbers</a> <ul><li><a href="/wiki/Prehistoric_counting" class="mw-redirect" title="Prehistoric counting">prehistoric counting</a></li></ul></li> <li><a href="/wiki/History_of_ancient_numeral_systems" title="History of ancient numeral systems">numeral systems</a> <ul><li><a href="/wiki/List_of_numeral_systems" title="List of numeral systems">list</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other cultures</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Arabian/Islamic</a></li> <li><a href="/wiki/Babylonian_mathematics" title="Babylonian mathematics">Babylonian</a></li> <li><a href="/wiki/Chinese_mathematics" title="Chinese mathematics">Chinese</a></li> <li><a href="/wiki/Ancient_Egyptian_mathematics" title="Ancient Egyptian mathematics">Egyptian</a></li> <li><a href="/wiki/Mathematics_of_the_Incas" title="Mathematics of the Incas">Incan</a></li> <li><a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian</a></li> <li><a href="/wiki/Japanese_mathematics" title="Japanese mathematics">Japanese</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/20px-Parthenon_from_west.jpg" decoding="async" width="17" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/40px-Parthenon_from_west.jpg 1.5x" data-file-width="2048" data-file-height="1536" /> <a href="/wiki/Portal:Ancient_Greece" title="Portal:Ancient Greece">Ancient Greece portal</a> • <a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" 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