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<span>Biography</span> </div> </a> <button aria-controls="toc-Biography-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Biography subsection</span> </button> <ul id="toc-Biography-sublist" class="vector-toc-list"> <li id="toc-Early_years" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Early_years"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Early years</span> </div> </a> <ul id="toc-Early_years-sublist" class="vector-toc-list"> <li id="toc-Variational_calculus" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Variational_calculus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Variational calculus</span> </div> </a> <ul id="toc-Variational_calculus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Miscellanea_Taurinensia" 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href="#Units_of_measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.1</span> <span>Units of measurement</span> </div> </a> <ul id="toc-Units_of_measurement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-École_Normale" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#École_Normale"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.2</span> <span>École Normale</span> </div> </a> <ul id="toc-École_Normale-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-École_Polytechnique" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#École_Polytechnique"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.3</span> <span>École Polytechnique</span> </div> </a> <ul id="toc-École_Polytechnique-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Late_years" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Late_years"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.4</span> <span>Late years</span> </div> </a> <ul id="toc-Late_years-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Work_in_Berlin" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Work_in_Berlin"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Work in Berlin</span> </div> </a> <button aria-controls="toc-Work_in_Berlin-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Work in Berlin subsection</span> </button> <ul id="toc-Work_in_Berlin-sublist" class="vector-toc-list"> <li id="toc-Lagrangian_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lagrangian_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Lagrangian mechanics</span> </div> </a> <ul id="toc-Lagrangian_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Algebra" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Algebra"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Algebra</span> </div> </a> <ul id="toc-Algebra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Number_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Number_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Number theory</span> </div> </a> <ul id="toc-Number_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_mathematical_work" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_mathematical_work"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Other mathematical work</span> </div> </a> <ul id="toc-Other_mathematical_work-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Astronomy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Astronomy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Astronomy</span> </div> </a> <ul id="toc-Astronomy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fundamental_treatise" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fundamental_treatise"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Fundamental treatise</span> </div> </a> <ul id="toc-Fundamental_treatise-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Work_in_France" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Work_in_France"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Work in France</span> </div> </a> <button aria-controls="toc-Work_in_France-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Work in France subsection</span> </button> <ul id="toc-Work_in_France-sublist" class="vector-toc-list"> <li id="toc-Differential_calculus_and_calculus_of_variations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Differential_calculus_and_calculus_of_variations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Differential calculus and calculus of variations</span> </div> </a> <ul id="toc-Differential_calculus_and_calculus_of_variations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Infinitesimals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Infinitesimals"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Infinitesimals</span> </div> </a> <ul id="toc-Infinitesimals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Number_theory_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Number_theory_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Number theory</span> </div> </a> <ul id="toc-Number_theory_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Celestial_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Celestial_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Celestial mechanics</span> </div> </a> <ul id="toc-Celestial_mechanics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Prizes_and_distinctions" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Prizes_and_distinctions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Prizes and distinctions</span> </div> </a> <ul id="toc-Prizes_and_distinctions-sublist" class="vector-toc-list"> </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"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Joseph-Louis Lagrange</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 88 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-88" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">88 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AC%D9%88%D8%B2%D9%8A%D9%81_%D9%84%D9%88%D9%8A_%D9%84%D8%A7%D8%BA%D8%B1%D8%A7%D9%86%D8%AC" title="جوزيف لوي لاغرانج – Arabic" lang="ar" hreflang="ar" data-title="جوزيف لوي لاغرانج" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Asturian" lang="ast" hreflang="ast" data-title="Joseph-Louis Lagrange" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Jozef_Lui_Laqranj" title="Jozef Lui Laqranj – Azerbaijani" lang="az" hreflang="az" data-title="Jozef Lui Laqranj" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%98%D9%88%D8%B2%D9%81-%D9%84%D9%88%DB%8C%DB%8C_%D9%84%D8%A7%D9%82%D8%B1%D8%A7%D9%86%DA%98" title="ژوزف-لویی لاقرانژ – South Azerbaijani" lang="azb" hreflang="azb" data-title="ژوزف-لویی لاقرانژ" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Minnan" lang="nan" hreflang="nan" data-title="Joseph-Louis Lagrange" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%96%D0%B0%D0%B7%D1%8D%D1%84_%D0%9B%D1%83%D1%96_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6" title="Жазэф Луі Лагранж – Belarusian" lang="be" hreflang="be" data-title="Жазэф Луі Лагранж" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%96%D0%BE%D0%B7%D0%B5%D1%84-%D0%9B%D1%83%D0%B8_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6" title="Жозеф-Луи Лагранж – Bulgarian" lang="bg" hreflang="bg" data-title="Жозеф-Луи Лагранж" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Bosnian" lang="bs" hreflang="bs" data-title="Joseph Louis Lagrange" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Catalan" lang="ca" hreflang="ca" data-title="Joseph Louis Lagrange" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Czech" lang="cs" hreflang="cs" data-title="Joseph-Louis Lagrange" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Welsh" lang="cy" hreflang="cy" data-title="Joseph-Louis Lagrange" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Danish" lang="da" hreflang="da" data-title="Joseph Louis Lagrange" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – German" lang="de" hreflang="de" data-title="Joseph-Louis Lagrange" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Estonian" lang="et" hreflang="et" data-title="Joseph-Louis Lagrange" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%96%CE%BF%CE%B6%CE%AD%CF%86_%CE%9B%CE%BF%CF%85%CE%AF_%CE%9B%CE%B1%CE%B3%CE%BA%CF%81%CE%AC%CE%BD%CE%B6" title="Ζοζέφ Λουί Λαγκράνζ – Greek" lang="el" hreflang="el" data-title="Ζοζέφ Λουί Λαγκράνζ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Spanish" lang="es" hreflang="es" data-title="Joseph-Louis Lagrange" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Esperanto" lang="eo" hreflang="eo" data-title="Joseph-Louis Lagrange" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Basque" lang="eu" hreflang="eu" data-title="Joseph-Louis Lagrange" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%98%D9%88%D8%B2%D9%81_%D9%84%D9%88%D8%A6%DB%8C_%D9%84%D8%A7%DA%AF%D8%B1%D8%A7%D9%86%DA%98" title="ژوزف لوئی لاگرانژ – Persian" lang="fa" hreflang="fa" data-title="ژوزف لوئی لاگرانژ" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – French" lang="fr" hreflang="fr" data-title="Joseph-Louis Lagrange" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Irish" lang="ga" hreflang="ga" data-title="Joseph Louis Lagrange" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Galician" lang="gl" hreflang="gl" data-title="Joseph Louis Lagrange" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A1%B0%EC%A0%9C%ED%94%84%EB%A3%A8%EC%9D%B4_%EB%9D%BC%EA%B7%B8%EB%9E%91%EC%A3%BC" title="조제프루이 라그랑주 – Korean" lang="ko" hreflang="ko" data-title="조제프루이 라그랑주" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BA%D5%B8%D5%A6%D5%A5%D6%86_%D4%BC%D5%B8%D6%82%D5%AB_%D4%BC%D5%A1%D5%A3%D6%80%D5%A1%D5%B6%D5%AA" title="Ժոզեֆ Լուի Լագրանժ – Armenian" lang="hy" hreflang="hy" data-title="Ժոզեֆ Լուի Լագրանժ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%9C%E0%A5%8B%E0%A4%B8%E0%A5%87%E0%A4%AB_%E0%A4%B2%E0%A5%81%E0%A4%88_%E0%A4%B2%E0%A4%BE%E0%A4%97%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%82%E0%A4%9C" title="जोसेफ लुई लाग्रांज – Hindi" lang="hi" hreflang="hi" data-title="जोसेफ लुई लाग्रांज" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Croatian" lang="hr" hreflang="hr" data-title="Joseph-Louis Lagrange" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Joseph-Louis_de_Lagrange" title="Joseph-Louis de Lagrange – Ido" lang="io" hreflang="io" data-title="Joseph-Louis de Lagrange" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Joseph-Louis_de_Lagrange" title="Joseph-Louis de Lagrange – Indonesian" lang="id" hreflang="id" data-title="Joseph-Louis de Lagrange" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Icelandic" lang="is" hreflang="is" data-title="Joseph-Louis Lagrange" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Italian" lang="it" hreflang="it" data-title="Joseph-Louis Lagrange" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%96%27%D7%95%D7%96%D7%A3-%D7%9C%D7%95%D7%90%D7%99_%D7%9C%D7%92%D7%A8%D7%90%D7%A0%D7%96%27" title="ז'וזף-לואי לגראנז' – Hebrew" lang="he" hreflang="he" data-title="ז'וזף-לואי לגראנז'" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Joseph-Louis_de_Lagrange" title="Joseph-Louis de Lagrange – Javanese" lang="jv" hreflang="jv" data-title="Joseph-Louis de Lagrange" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%9C%E0%B3%8B%E0%B2%B8%E0%B3%86%E0%B2%AB%E0%B3%8D_%E0%B2%B2%E0%B3%82%E0%B2%AF%E0%B2%BF_%E0%B2%B2%E0%B2%97%E0%B3%8D%E0%B2%B0%E0%B2%BE%E0%B2%82%E0%B2%9C%E0%B3%8D" title="ಜೋಸೆಫ್ ಲೂಯಿ ಲಗ್ರಾಂಜ್ – Kannada" lang="kn" hreflang="kn" data-title="ಜೋಸೆಫ್ ಲೂಯಿ ಲಗ್ರಾಂಜ್" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9F%E1%83%9D%E1%83%96%E1%83%94%E1%83%A4_%E1%83%9A%E1%83%A3%E1%83%98_%E1%83%9A%E1%83%90%E1%83%92%E1%83%A0%E1%83%90%E1%83%9C%E1%83%9F%E1%83%98" title="ჟოზეფ ლუი ლაგრანჟი – Georgian" lang="ka" hreflang="ka" data-title="ჟოზეფ ლუი ლაგრანჟი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6" title="Лагранж – Kazakh" lang="kk" hreflang="kk" data-title="Лагранж" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Haitian Creole" lang="ht" hreflang="ht" data-title="Joseph-Louis Lagrange" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Kurdish" lang="ku" hreflang="ku" data-title="Joseph-Louis Lagrange" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%96%D0%BE%D0%B7%D0%B5%D1%84_%D0%9B%D1%83%D0%B8_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6" title="Жозеф Луи Лагранж – Kyrgyz" lang="ky" hreflang="ky" data-title="Жозеф Луи Лагранж" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Iosephus_Ludovicus_Lagrange" title="Iosephus Ludovicus Lagrange – Latin" lang="la" hreflang="la" data-title="Iosephus Ludovicus Lagrange" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C5%BDozefs_Lagran%C5%BEs" title="Žozefs Lagranžs – Latvian" lang="lv" hreflang="lv" data-title="Žozefs Lagranžs" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Luxembourgish" lang="lb" hreflang="lb" data-title="Joseph-Louis Lagrange" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Lithuanian" lang="lt" hreflang="lt" data-title="Joseph Louis Lagrange" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Hungarian" lang="hu" hreflang="hu" data-title="Joseph Louis Lagrange" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%96%D0%BE%D0%B7%D0%B5%D1%84_%D0%9B%D1%83%D1%98_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6" title="Жозеф Луј Лагранж – Macedonian" lang="mk" hreflang="mk" data-title="Жозеф Луј Лагранж" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Malagasy" lang="mg" hreflang="mg" data-title="Joseph-Louis Lagrange" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B2%E0%B4%97%E0%B5%8D%E0%B4%B0%E0%B4%BE%E0%B4%9E%E0%B5%8D%E0%B4%9C%E0%B5%8D" title="ലഗ്രാഞ്ജ് – Malayalam" lang="ml" hreflang="ml" data-title="ലഗ്രാഞ്ജ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%9C%E0%A5%8B%E0%A4%B8%E0%A5%87%E0%A4%AB_%E0%A4%B2%E0%A5%81%E0%A4%88_%E0%A4%B2%E0%A4%BE%E0%A4%97%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%82%E0%A4%9C" title="जोसेफ लुई लाग्रांज – Marathi" lang="mr" hreflang="mr" data-title="जोसेफ लुई लाग्रांज" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%9F%E1%83%9D%E1%83%96%E1%83%94%E1%83%A4-%E1%83%9A%E1%83%A3%E1%83%98_%E1%83%9A%E1%83%90%E1%83%92%E1%83%A0%E1%83%90%E1%83%9C%E1%83%9F%E1%83%98" title="ჟოზეფ-ლუი ლაგრანჟი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ჟოზეფ-ლუი ლაგრანჟი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AC%D9%88%D8%B2%D9%8A%D9%81_%D9%84%D9%88%D9%89_%D9%84%D8%A7%D8%AC%D8%B1%D8%A7%D9%86%D8%AC" title="جوزيف لوى لاجرانج – Egyptian Arabic" lang="arz" hreflang="arz" data-title="جوزيف لوى لاجرانج" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Malay" lang="ms" hreflang="ms" data-title="Joseph-Louis Lagrange" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%82%E1%80%BB%E1%80%AD%E1%80%AF%E1%80%B8%E1%80%87%E1%80%80%E1%80%BA-%E1%80%9C%E1%80%B0%E1%80%9D%E1%80%AE_%E1%80%9C%E1%80%AC%E1%80%82%E1%80%B1%E1%80%AB%E1%80%84%E1%80%B7%E1%80%BA" title="ဂျိုးဇက်-လူဝီ လာဂေါင့် – Burmese" lang="my" hreflang="my" data-title="ဂျိုးဇက်-လူဝီ လာဂေါင့်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Dutch" lang="nl" hreflang="nl" data-title="Joseph-Louis Lagrange" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B8%E3%83%A7%E3%82%BC%E3%83%95%EF%BC%9D%E3%83%AB%E3%82%A4%E3%83%BB%E3%83%A9%E3%82%B0%E3%83%A9%E3%83%B3%E3%82%B8%E3%83%A5" title="ジョゼフ＝ルイ・ラグランジュ – Japanese" lang="ja" hreflang="ja" data-title="ジョゼフ＝ルイ・ラグランジュ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Joseph-Louis Lagrange" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Joseph Louis Lagrange" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Uzbek" lang="uz" hreflang="uz" data-title="Joseph-Louis Lagrange" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Piedmontese" lang="pms" hreflang="pms" data-title="Joseph-Louis Lagrange" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Polish" lang="pl" hreflang="pl" data-title="Joseph Louis Lagrange" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Portuguese" lang="pt" hreflang="pt" data-title="Joseph-Louis Lagrange" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Romanian" lang="ro" hreflang="ro" data-title="Joseph-Louis Lagrange" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6,_%D0%96%D0%BE%D0%B7%D0%B5%D1%84_%D0%9B%D1%83%D0%B8" title="Лагранж, Жозеф Луи – Russian" lang="ru" hreflang="ru" data-title="Лагранж, Жозеф Луи" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%9C%E0%A5%8B%E0%A4%B8%E0%A5%87%E0%A4%AB%E0%A4%BC_%E0%A4%B2%E0%A5%81%E0%A4%AF%E0%A4%BF_%E0%A4%B2%E0%A4%97%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%9E%E0%A5%8D%E0%A4%9C%E0%A5%87" title="जोसेफ़ लुयि लग्राञ्जे – Sanskrit" lang="sa" hreflang="sa" data-title="जोसेफ़ लुयि लग्राञ्जे" data-language-autonym="संस्कृतम्" data-language-local-name="Sanskrit" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Scots" lang="sco" hreflang="sco" data-title="Joseph-Louis Lagrange" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Joseph_Luis_Lagrange" title="Joseph Luis Lagrange – Albanian" lang="sq" hreflang="sq" data-title="Joseph Luis Lagrange" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Sicilian" lang="scn" hreflang="scn" data-title="Joseph-Louis Lagrange" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%A2%E0%B7%9D%E0%B7%83%E0%B7%90%E0%B7%86%E0%B7%8A_%E0%B6%BD%E0%B7%94%E0%B7%80%E0%B7%93_%E0%B6%BD%E0%B6%9C%E0%B7%8A%E0%B6%BB%E0%B7%9A%E0%B6%B1%E0%B7%8A%E0%B6%A2%E0%B7%8A" title="ජෝසැෆ් ලුවී ලග්රේන්ජ් – Sinhala" lang="si" hreflang="si" data-title="ජෝසැෆ් ලුවී ලග්රේන්ජ්" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Simple English" lang="en-simple" hreflang="en-simple" data-title="Joseph-Louis Lagrange" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Slovak" lang="sk" hreflang="sk" data-title="Joseph Louis Lagrange" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Joseph-Louis_de_Lagrange" title="Joseph-Louis de Lagrange – Slovenian" lang="sl" hreflang="sl" data-title="Joseph-Louis de Lagrange" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%DB%86%D8%B2%DB%8E%D9%81_%D9%84%D9%88%DB%8C_%D9%84%D8%A7%DA%AF%D8%B1%D8%A7%D9%86%DA%98" title="ژۆزێف لوی لاگرانژ – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ژۆزێف لوی لاگرانژ" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%96%D0%BE%D0%B7%D0%B5%D1%84_%D0%9B%D1%83%D1%98_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6" title="Жозеф Луј Лагранж – Serbian" lang="sr" hreflang="sr" data-title="Жозеф Луј Лагранж" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Joseph-Louis Lagrange" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Finnish" lang="fi" hreflang="fi" data-title="Joseph-Louis Lagrange" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Swedish" lang="sv" hreflang="sv" data-title="Joseph-Louis Lagrange" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Tagalog" lang="tl" hreflang="tl" data-title="Joseph Louis Lagrange" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9C%E0%AF%8B%E0%AE%9A%E0%AE%AA%E0%AF%8D_%E0%AE%B2%E0%AF%82%E0%AE%AF%E0%AE%BF_%E0%AE%B2%E0%AE%BE%E0%AE%95%E0%AF%8D%E0%AE%B0%E0%AE%BE%E0%AE%9E%E0%AF%8D%E0%AE%9A%E0%AE%BF" title="ஜோசப் லூயி லாக்ராஞ்சி – Tamil" lang="ta" hreflang="ta" data-title="ஜோசப் லூயி லாக்ராஞ்சி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%9C%E0%B1%8B%E0%B0%B8%E0%B1%86%E0%B0%AB%E0%B1%8D_%E0%B0%B2%E0%B1%82%E0%B0%AF%E0%B0%BF%E0%B0%B8%E0%B1%8D_%E0%B0%B2%E0%B1%86%E0%B0%97%E0%B1%8D%E0%B0%B0%E0%B0%BE%E0%B0%82%E0%B0%9C%E0%B1%8D" title="జోసెఫ్ లూయిస్ లెగ్రాంజ్ – Telugu" lang="te" hreflang="te" data-title="జోసెఫ్ లూయిస్ లెగ్రాంజ్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%82%E0%B8%8C%E0%B9%81%E0%B8%8B%E0%B9%87%E0%B8%9F-%E0%B8%AB%E0%B8%A5%E0%B8%B8%E0%B8%A2%E0%B8%AA%E0%B9%8C_%E0%B8%A5%E0%B8%B2%E0%B8%81%E0%B8%A3%E0%B9%87%E0%B8%AD%E0%B8%87%E0%B8%8C%E0%B9%8C" title="โฌแซ็ฟ-หลุยส์ ลากร็องฌ์ – Thai" lang="th" hreflang="th" data-title="โฌแซ็ฟ-หลุยส์ ลากร็องฌ์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D2%B6%D0%BE%D0%B7%D0%B5%D1%84_%D0%9B%D1%83%D0%B8_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6v" title="Ҷозеф Луи Лагранжv – Tajik" lang="tg" hreflang="tg" data-title="Ҷозеф Луи Лагранжv" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange – Turkish" lang="tr" hreflang="tr" data-title="Joseph-Louis Lagrange" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%96%D0%BE%D0%B7%D0%B5%D1%84-%D0%9B%D1%83%D1%97_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6" title="Жозеф-Луї Лагранж – Ukrainian" lang="uk" hreflang="uk" data-title="Жозеф-Луї Лагранж" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AC%D9%88%D8%B2%D9%81_%D9%84%D9%88%D8%A6%DB%8C_%D9%84%D8%A7%DA%AF%D8%B1%D8%A7%D9%86%D8%AC" title="جوزف لوئی لاگرانج – Urdu" lang="ur" hreflang="ur" data-title="جوزف لوئی لاگرانج" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Vietnamese" lang="vi" hreflang="vi" data-title="Joseph Louis Lagrange" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Waray" lang="war" hreflang="war" data-title="Joseph Louis Lagrange" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%BA%A6%E7%91%9F%E5%A4%AB%C2%B7%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5" title="约瑟夫·拉格朗日 – Wu" lang="wuu" hreflang="wuu" data-title="约瑟夫·拉格朗日" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Joseph_Louis_Lagrange" title="Joseph Louis Lagrange – Yoruba" lang="yo" hreflang="yo" data-title="Joseph Louis Lagrange" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5" title="拉格朗日 – Cantonese" lang="yue" hreflang="yue" data-title="拉格朗日" data-language-autonym="粵語" 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Italian-French scientist (1736–1813)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Lagrange" redirects here. For the soldier, see <a href="/wiki/Joseph_Lagrange_(soldier)" title="Joseph Lagrange (soldier)">Joseph Lagrange (soldier)</a>. For other uses, see <a href="/wiki/Lagrange_(disambiguation)" class="mw-disambig" title="Lagrange (disambiguation)">Lagrange (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Joseph-Louis Lagrange</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Lagrange_crop.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Lagrange_crop.jpg/220px-Lagrange_crop.jpg" decoding="async" width="220" height="246" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Lagrange_crop.jpg/330px-Lagrange_crop.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Lagrange_crop.jpg/440px-Lagrange_crop.jpg 2x" data-file-width="1043" data-file-height="1167" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="nickname">Giuseppe Lodovico Lagrangia</div><br /><span style="display:none">(<span class="bday">1736-01-25</span>)</span>25 January 1736<br /><div style="display:inline" class="birthplace"><a href="/wiki/Turin" title="Turin">Turin</a>, <a href="/wiki/Kingdom_of_Sardinia" title="Kingdom of Sardinia">Kingdom of Sardinia</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">10 April 1813<span style="display:none">(1813-04-10)</span> (aged 77)<br /><div style="display:inline" class="deathplace">Paris, <a href="/wiki/First_French_Empire" title="First French Empire">First French Empire</a></div></td></tr><tr><th scope="row" class="infobox-label">Citizenship</th><td class="infobox-data category"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><a href="/wiki/Kingdom_of_Sardinia" title="Kingdom of Sardinia">Sardinia</a></li><li><a href="/wiki/First_French_Empire" title="First French Empire">French Empire</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/University_of_Turin" title="University of Turin">University of Turin</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/List_of_things_named_after_Joseph-Louis_Lagrange" title="List of things named after Joseph-Louis Lagrange"><i>(See list)</i></a></li><li><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical mechanics</a></li><li><a href="/wiki/Calculus_of_variations" title="Calculus of variations">Calculus of variations</a></li><li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial mechanics</a></li><li><a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Mathematical analysis</a></li><li><a href="/wiki/Number_theory" title="Number theory">Number theory</a></li><li><a href="/wiki/Theory_of_equations" title="Theory of equations">Theory of equations</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"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li>Mathematics</li><li><a href="/wiki/Astronomy" title="Astronomy">Astronomy</a></li><li><a href="/wiki/Mechanics" title="Mechanics">Mechanics</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/%C3%89cole_Normale" class="mw-redirect" title="École Normale">École Normale</a></li><li><a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Academic advisors</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> (epistolary correspondent)</li><li><a href="/wiki/Giovanni_Battista_Beccaria" title="Giovanni Battista Beccaria">Giovanni Battista Beccaria</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Notable students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/Joseph_Fourier" title="Joseph Fourier">Joseph Fourier</a></li><li><a href="/wiki/Giovanni_Plana" title="Giovanni Plana">Giovanni Plana</a></li><li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Siméon Poisson</a></li></ul></div></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Joseph-Louis Lagrange</b><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> (born <b>Giuseppe Luigi Lagrangia</b><sup id="cite_ref-britannica_6-0" class="reference"><a href="#cite_note-britannica-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> or <b>Giuseppe Ludovico De la Grange Tournier</b>;<sup id="cite_ref-luilag_8-0" class="reference"><a href="#cite_note-luilag-8"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup> 25 January 1736 – 10 April 1813), also reported as <b>Giuseppe Luigi Lagrange</b><sup id="cite_ref-laei_10-0" class="reference"><a href="#cite_note-laei-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> or <b>Lagrangia</b>,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> was an Italian <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, <a href="/wiki/Physicist" title="Physicist">physicist</a> and <a href="/wiki/Astronomer" title="Astronomer">astronomer</a>, later naturalized French. He made significant contributions to the fields of <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">analysis</a>, <a href="/wiki/Number_theory" title="Number theory">number theory</a>, and both <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical</a> and <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a>. </p><p>In 1766, on the recommendation of <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> and <a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">d'Alembert</a>, Lagrange succeeded Euler as the director of mathematics at the <a href="/wiki/Prussian_Academy_of_Sciences" title="Prussian Academy of Sciences">Prussian Academy of Sciences</a> in Berlin, <a href="/wiki/Prussia" title="Prussia">Prussia</a>, where he stayed for over twenty years, producing many volumes of work and winning several prizes of the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a>. Lagrange's treatise on <a href="/wiki/Analytical_mechanics" title="Analytical mechanics">analytical mechanics</a> (<i><a href="/wiki/M%C3%A9canique_analytique" title="Mécanique analytique">Mécanique analytique</a></i>, 4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1788–89), which was written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> and formed a basis for the development of <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a> in the nineteenth century. </p><p>In 1787, at age 51, he moved from Berlin to Paris and became a member of the French Academy of Sciences. He remained in France until the end of his life. He was instrumental in the <a href="/wiki/History_of_the_metric_system" title="History of the metric system">decimalisation</a> process in <a href="/wiki/French_First_Republic" title="French First Republic">Revolutionary France</a>, became the first professor of analysis at the <a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a> upon its opening in 1794, was a founding member of the <a href="/wiki/Bureau_des_Longitudes" title="Bureau des Longitudes">Bureau des Longitudes</a>, and became <a href="/wiki/S%C3%A9nat_conservateur" title="Sénat conservateur">Senator</a> in 1799. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Scientific_contribution">Scientific contribution</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=1" title="Edit section: Scientific contribution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lagrange was one of the creators of the <a href="/wiki/Calculus_of_variations" title="Calculus of variations">calculus of variations</a>, deriving the <a href="/wiki/Euler%E2%80%93Lagrange_equation" title="Euler–Lagrange equation">Euler–Lagrange equations</a> for extrema of <a href="/wiki/Functional_(mathematics)" title="Functional (mathematics)">functionals</a>. He extended the method to include possible constraints, arriving at the method of <a href="/wiki/Lagrange_multipliers" class="mw-redirect" title="Lagrange multipliers">Lagrange multipliers</a>. Lagrange invented the method of solving <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a> known as <a href="/wiki/Method_of_variation_of_parameters" class="mw-redirect" title="Method of variation of parameters">variation of parameters</a>, applied <a href="/wiki/Differential_calculus" title="Differential calculus">differential calculus</a> to the <a href="/wiki/Probability_theory" title="Probability theory">theory of probabilities</a> and worked on solutions for <a href="/wiki/Algebraic_equations" class="mw-redirect" title="Algebraic equations">algebraic equations</a>. He proved that <a href="/wiki/Lagrange%27s_four-square_theorem" title="Lagrange's four-square theorem">every natural number is a sum of four squares</a>. His treatise <i>Theorie des fonctions analytiques</i> laid some of the foundations of <a href="/wiki/Group_theory" title="Group theory">group theory</a>, anticipating <a href="/wiki/%C3%89variste_Galois" title="Évariste Galois">Galois</a>. In <a href="/wiki/Calculus" title="Calculus">calculus</a>, Lagrange developed a novel approach to <a href="/wiki/Lagrange_interpolation" class="mw-redirect" title="Lagrange interpolation">interpolation</a> and <a href="/wiki/Taylor%27s_theorem" title="Taylor's theorem">Taylor's theorem</a>. He studied the <a href="/wiki/Three-body_problem" title="Three-body problem">three-body problem</a> for the Earth, Sun and Moon (1764) and the movement of Jupiter's satellites (1766), and in 1772 found the special-case solutions to this problem that yield what are now known as <a href="/wiki/Lagrangian_point" class="mw-redirect" title="Lagrangian point">Lagrangian points</a>. Lagrange is best known for transforming <a href="/wiki/Newtonian_mechanics" class="mw-redirect" title="Newtonian mechanics">Newtonian mechanics</a> into a branch of analysis, <a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian mechanics</a>. He presented the mechanical "principles" as simple results of the variational calculus. </p> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=2" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1224211176">.mw-parser-output .quotebox{background-color:#F9F9F9;border:1px solid #aaa;box-sizing:border-box;padding:10px;font-size:88%;max-width:100%}.mw-parser-output .quotebox.floatleft{margin:.5em 1.4em .8em 0}.mw-parser-output .quotebox.floatright{margin:.5em 0 .8em 1.4em}.mw-parser-output .quotebox.centered{overflow:hidden;position:relative;margin:.5em auto .8em auto}.mw-parser-output .quotebox.floatleft span,.mw-parser-output .quotebox.floatright span{font-style:inherit}.mw-parser-output .quotebox>blockquote{margin:0;padding:0;border-left:0;font-family:inherit;font-size:inherit}.mw-parser-output .quotebox-title{text-align:center;font-size:110%;font-weight:bold}.mw-parser-output .quotebox-quote>:first-child{margin-top:0}.mw-parser-output .quotebox-quote:last-child>:last-child{margin-bottom:0}.mw-parser-output .quotebox-quote.quoted:before{font-family:"Times New Roman",serif;font-weight:bold;font-size:large;color:gray;content:" “ ";vertical-align:-45%;line-height:0}.mw-parser-output .quotebox-quote.quoted:after{font-family:"Times New Roman",serif;font-weight:bold;font-size:large;color:gray;content:" ” ";line-height:0}.mw-parser-output .quotebox .left-aligned{text-align:left}.mw-parser-output .quotebox .right-aligned{text-align:right}.mw-parser-output .quotebox .center-aligned{text-align:center}.mw-parser-output .quotebox .quote-title,.mw-parser-output .quotebox .quotebox-quote{display:block}.mw-parser-output .quotebox cite{display:block;font-style:normal}@media screen and (max-width:640px){.mw-parser-output .quotebox{width:100%!important;margin:0 0 .8em!important;float:none!important}}</style><div class="quotebox pullquote floatright" style="width:20%; ;"> <blockquote class="quotebox-quote left-aligned" style=""> <p>In appearance he was of medium height, and slightly formed, with pale blue eyes and a colourless complexion. In character he was nervous and timid, he detested controversy, and to avoid it willingly allowed others to take the credit for what he had himself done. </p><p>He always thought out the subject of his papers before he began to compose them, and usually wrote them straight off without a single erasure or correction. </p><p><a href="/wiki/W.W._Rouse_Ball" class="mw-redirect" title="W.W. Rouse Ball">W.W. Rouse Ball</a><sup id="cite_ref-RouseBall_12-0" class="reference"><a href="#cite_note-RouseBall-12"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> </blockquote> </div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Joseph_Louis_Lagrange2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Joseph_Louis_Lagrange2.jpg/220px-Joseph_Louis_Lagrange2.jpg" decoding="async" width="220" height="305" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Joseph_Louis_Lagrange2.jpg/330px-Joseph_Louis_Lagrange2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Joseph_Louis_Lagrange2.jpg/440px-Joseph_Louis_Lagrange2.jpg 2x" data-file-width="739" data-file-height="1024" /></a><figcaption>Portrait of Joseph-Louis Lagrange (18th-century)</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Early_years">Early years</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=3" title="Edit section: Early years"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Firstborn of eleven children as <i>Giuseppe Lodovico Lagrangia</i>, Lagrange was of Italian and French descent.<sup id="cite_ref-laei_10-1" class="reference"><a href="#cite_note-laei-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> His paternal great-grandfather was a <a href="/wiki/Kingdom_of_France_(1498-1791)" class="mw-redirect" title="Kingdom of France (1498-1791)">French</a> captain of cavalry, whose family originated from the French region of <a href="/wiki/Tours" title="Tours">Tours</a>.<sup id="cite_ref-laei_10-2" class="reference"><a href="#cite_note-laei-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> After serving under <a href="/wiki/Louis_XIV" title="Louis XIV">Louis XIV</a>, he had entered the service of <a href="/wiki/Charles_Emmanuel_II" class="mw-redirect" title="Charles Emmanuel II">Charles Emmanuel II</a>, <a href="/wiki/Duchy_of_Savoy" title="Duchy of Savoy">Duke of Savoy</a>, and married a <a href="/wiki/Conti_di_Segni" class="mw-redirect" title="Conti di Segni">Conti</a> from the noble Roman family.<sup id="cite_ref-laei_10-3" class="reference"><a href="#cite_note-laei-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Lagrange's father, Giuseppe Francesco Lodovico, was a doctor in Law at the <a href="/wiki/University_of_Torino" class="mw-redirect" title="University of Torino">University of Torino</a>, while his mother was the only child of a rich doctor of <a href="/wiki/Cambiano" title="Cambiano">Cambiano</a>, in the countryside of <a href="/wiki/Turin" title="Turin">Turin</a>.<sup id="cite_ref-laei_10-4" class="reference"><a href="#cite_note-laei-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-St_Andrew_13-0" class="reference"><a href="#cite_note-St_Andrew-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> He was raised as a Roman Catholic (but later on became an <a href="/wiki/Agnostic" class="mw-redirect" title="Agnostic">agnostic</a>).<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>His father, who had charge of <a href="/wiki/Charles_Emmanuel_III" title="Charles Emmanuel III">the King</a>'s military chest and was Treasurer of the Office of Public Works and Fortifications in Turin, should have maintained a good social position and wealth, but before his son grew up he had lost most of his property in speculations. A career as a lawyer was planned out for Lagrange by his father,<sup id="cite_ref-laei_10-5" class="reference"><a href="#cite_note-laei-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> and certainly Lagrange seems to have accepted this willingly. He studied at the <a href="/wiki/University_of_Turin" title="University of Turin">University of Turin</a> and his favourite subject was classical Latin. At first, he had no great enthusiasm for mathematics, finding Greek geometry rather dull. </p><p>It was not until he was seventeen that he showed any taste for mathematics – his interest in the subject being first excited by a paper by <a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a> from 1693<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> which he came across by accident. Alone and unaided he threw himself into mathematical studies; at the end of a year's incessant toil he was already an accomplished mathematician. <a href="/wiki/Charles_Emmanuel_III" title="Charles Emmanuel III">Charles Emmanuel III</a> appointed Lagrange to serve as the "Sostituto del Maestro di Matematica" (mathematics assistant professor) at the Royal Military Academy of the Theory and Practice of Artillery in 1755, where he taught courses in calculus and mechanics to support the Piedmontese army's early adoption of the ballistics theories of <a href="/wiki/Benjamin_Robins" title="Benjamin Robins">Benjamin Robins</a> and <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>. In that capacity, Lagrange was the first to teach calculus in an engineering school. According to <a href="https://it.wikipedia.org/wiki/Alessandro_Vittorio_Papacino_D%27Antoni" class="extiw" title="it:Alessandro Vittorio Papacino D'Antoni">Alessandro Papacino D'Antoni</a>, the academy's military commander and famous artillery theorist, Lagrange unfortunately proved to be a problematic professor with his oblivious teaching style, abstract reasoning, and impatience with artillery and fortification-engineering applications.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In this academy one of his students was <a href="/wiki/Fran%C3%A7ois_Daviet_de_Foncenex" title="François Daviet de Foncenex">François Daviet</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Variational_calculus">Variational calculus</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=4" title="Edit section: Variational calculus"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lagrange is one of the founders of the <a href="/wiki/Calculus_of_variations" title="Calculus of variations">calculus of variations</a>. Starting in 1754, he worked on the problem of the <a href="/wiki/Tautochrone" class="mw-redirect" title="Tautochrone">tautochrone</a>, discovering a method of maximizing and minimizing functionals in a way similar to finding extrema of functions. Lagrange wrote several letters to <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> between 1754 and 1756 describing his results. He outlined his "δ-algorithm", leading to the <a href="/wiki/Euler%E2%80%93Lagrange_equation" title="Euler–Lagrange equation">Euler–Lagrange equations</a> of variational calculus and considerably simplifying Euler's earlier analysis.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Lagrange also applied his ideas to problems of classical mechanics, generalising the results of Euler and <a href="/wiki/Pierre_Louis_Maupertuis" title="Pierre Louis Maupertuis">Maupertuis</a>. </p><p>Euler was very impressed with Lagrange's results. It has been stated that "with characteristic courtesy he withheld a paper he had previously written, which covered some of the same ground, in order that the young Italian might have time to complete his work, and claim the undisputed invention of the new calculus"; however, this chivalric view has been disputed.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Lagrange published his method in two memoirs of the Turin Society in 1762 and 1773. </p> <div class="mw-heading mw-heading4"><h4 id="Miscellanea_Taurinensia"><i>Miscellanea Taurinensia</i></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=5" title="Edit section: Miscellanea Taurinensia"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1758, with the aid of his pupils (mainly with Daviet), Lagrange established a society, which was subsequently incorporated as the <a href="/w/index.php?title=Turin_Academy_of_Sciences&action=edit&redlink=1" class="new" title="Turin Academy of Sciences (page does not exist)">Turin Academy of Sciences</a>, and most of his early writings are to be found in the five volumes of its transactions, usually known as the <i>Miscellanea Taurinensia</i>. Many of these are elaborate papers. The first volume contains a paper on the theory of the propagation of sound; in this he indicates a mistake made by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a>, obtains the general <a href="/wiki/Differential_equation" title="Differential equation">differential equation</a> for the motion, and integrates it for motion in a straight line. This volume also contains the complete solution of the problem of a <a href="/wiki/Vibrating_string" class="mw-redirect" title="Vibrating string">string vibrating transversely</a>; in this paper, he points out a lack of generality in the solutions previously given by <a href="/wiki/Brook_Taylor" title="Brook Taylor">Brook Taylor</a>, <a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">D'Alembert</a>, and Euler, and arrives at the conclusion that the form of the curve at any time <i>t</i> is given by the equation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=a\sin(mx)\sin(nt)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>a</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=a\sin(mx)\sin(nt)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/143c20102dc2550f9522938d9565ea869d605e9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.579ex; height:2.843ex;" alt="{\displaystyle y=a\sin(mx)\sin(nt)\,}"></span>. The article concludes with a masterly discussion of <a href="/wiki/Echo_(phenomenon)" class="mw-redirect" title="Echo (phenomenon)">echoes</a>, <a href="/wiki/Beat_(acoustics)" title="Beat (acoustics)">beats</a>, and compound sounds. Other articles in this volume are on <a href="/wiki/Recurrence_relation" title="Recurrence relation">recurring</a> <a href="/wiki/Series_(mathematics)" title="Series (mathematics)">series</a>, <a href="/wiki/Probability" title="Probability">probabilities</a>, and the <a href="/wiki/Calculus_of_variations" title="Calculus of variations">calculus of variations</a>. </p><p>The second volume contains a long paper embodying the results of several papers in the first volume on the theory and notation of the calculus of variations, and he illustrates its use by deducing the <a href="/wiki/Principle_of_least_action" class="mw-redirect" title="Principle of least action">principle of least action</a>, and by solutions of various problems in <a href="/wiki/Dynamics_(mechanics)" class="mw-redirect" title="Dynamics (mechanics)">dynamics</a>. </p><p>The third volume includes the solution of several dynamical problems by means of the calculus of variations; some papers on the <a href="/wiki/Integral_calculus" class="mw-redirect" title="Integral calculus">integral calculus</a>; a solution of a <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Fermat</a>'s problem: given an integer <span class="texhtml"><i>n</i></span> which is not a <a href="/wiki/Square_number" title="Square number">perfect square</a>, to find a number <span class="texhtml"><i>x</i></span> such that <span class="texhtml"><i>nx</i><sup>2</sup> + 1</span><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="Not sure that this is the correct formula (January 2022)">verification needed</span></a></i>]</sup> is a perfect square; and the general differential equations of <a href="/wiki/N-body_problem" title="N-body problem">motion for three bodies</a> moving under their mutual attractions. </p><p>The next work he produced was in 1764 on the <a href="/wiki/Libration" title="Libration">libration</a> of the Moon, and an explanation as to why the same face was always turned to the earth, a problem which he treated by the aid of <a href="/wiki/Virtual_work" title="Virtual work">virtual work</a>. His solution is especially interesting as containing the germ of the idea of generalised equations of motion, equations which he first formally proved in 1780. </p> <div class="mw-heading mw-heading3"><h3 id="Berlin">Berlin</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=6" title="Edit section: Berlin"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Already by 1756, <a href="/wiki/Euler" class="mw-redirect" title="Euler">Euler</a> and <a href="/wiki/Maupertuis" class="mw-redirect" title="Maupertuis">Maupertuis</a>, seeing Lagrange's mathematical talent, tried to persuade Lagrange to come to Berlin, but he shyly refused the offer. In 1765, <a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">d'Alembert</a> interceded on Lagrange's behalf with <a href="/wiki/Frederick_the_Great" title="Frederick the Great">Frederick of Prussia</a> and by letter, asked him to leave Turin for a considerably more prestigious position in Berlin. He again turned down the offer, responding that<sup id="cite_ref-Vinter2000_20-0" class="reference"><a href="#cite_note-Vinter2000-20"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 361">: 361 </span></sup> </p> <dl><dd><i>It seems to me that Berlin would not be at all suitable for me while M.Euler is there</i>.</dd></dl> <p>In 1766, after Euler left Berlin for <a href="/wiki/Saint_Petersburg" title="Saint Petersburg">Saint Petersburg</a>, Frederick himself wrote to Lagrange expressing the wish of "the greatest king in Europe" to have "the greatest mathematician in Europe" resident at his court. Lagrange was finally persuaded. He spent the next twenty years in <a href="/wiki/Prussia" title="Prussia">Prussia</a>, where he produced a long series of papers published in the Berlin and Turin transactions, and composed his monumental work, the <i>Mécanique analytique</i>. In 1767, he married his cousin Vittoria Conti. </p><p>Lagrange was a favourite of the king, who frequently lectured him on the advantages of perfect regularity of life. The lesson was accepted, and Lagrange studied his mind and body as though they were machines, and experimented to find the exact amount of work which he could do before exhaustion. Every night he set himself a definite task for the next day, and on completing any branch of a subject he wrote a short analysis to see what points in the demonstrations or the subject-matter were capable of improvement. He carefully planned his papers before writing them, usually without a single erasure or correction. </p><p>Nonetheless, during his years in Berlin, Lagrange's health was rather poor, and that of his wife Vittoria was even worse. She died in 1783 after years of illness and Lagrange was very depressed. In 1786, Frederick II died, and the climate of Berlin became difficult for Lagrange.<sup id="cite_ref-St_Andrew_13-1" class="reference"><a href="#cite_note-St_Andrew-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Paris">Paris</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=7" title="Edit section: Paris"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1786, following Frederick's death, Lagrange received similar invitations from states including Spain and <a href="/wiki/Naples" title="Naples">Naples</a>, and he accepted the offer of <a href="/wiki/Louis_XVI_of_France" class="mw-redirect" title="Louis XVI of France">Louis XVI</a> to move to Paris. In France he was received with every mark of distinction and special apartments in the Louvre were prepared for his reception, and he became a member of the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a>, which later became part of the <a href="/wiki/French_Institute" class="mw-redirect" title="French Institute">Institut de France</a> (1795). At the beginning of his residence in Paris, he was seized with an attack of melancholy, and even the printed copy of his <i>Mécanique</i> on which he had worked for a quarter of a century lay for more than two years unopened on his desk. Curiosity as to the results of the <a href="/wiki/French_Revolution" title="French Revolution">French Revolution</a> first stirred him out of his lethargy, a curiosity which soon turned to alarm as the revolution developed. </p><p>It was about the same time, 1792, that the unaccountable sadness of his life and his timidity moved the compassion of 24-year-old Renée-Françoise-Adélaïde Le Monnier, daughter of his friend, the astronomer <a href="/wiki/Pierre_Charles_Le_Monnier" title="Pierre Charles Le Monnier">Pierre Charles Le Monnier</a>. She insisted on marrying him and proved a devoted wife to whom he became warmly attached. </p><p>In September 1793, the <a href="/wiki/Reign_of_Terror" title="Reign of Terror">Reign of Terror</a> began. Under the intervention of Antoine <a href="/wiki/Lavoisier" class="mw-redirect" title="Lavoisier">Lavoisier</a>, who himself was by then already thrown out of the academy along with many other scholars, Lagrange was specifically exempted by name in the decree of October 1793 that ordered all foreigners to leave France. On 4 May 1794, Lavoisier and 27 other <a href="/wiki/Tax_farming" class="mw-redirect" title="Tax farming">tax farmers</a> were arrested and sentenced to death and guillotined on the afternoon after the trial. Lagrange said on the death of Lavoisier: </p> <dl><dd><i>It took only a moment to cause this head to fall and a hundred years will not suffice to produce its like.</i><sup id="cite_ref-St_Andrew_13-2" class="reference"><a href="#cite_note-St_Andrew-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Though Lagrange had been preparing to escape from France while there was yet time, he was never in any danger; different revolutionary governments (and at a later time, <a href="/wiki/Napoleon_I_of_France" class="mw-redirect" title="Napoleon I of France">Napoleon</a>) gave him honours and distinctions. This luckiness or safety may to some extent be due to his life attitude he expressed many years before: "<i>I believe that, in general, one of the first principles of every wise man is to conform strictly to the laws of the country in which he is living, even when they are unreasonable</i>".<sup id="cite_ref-St_Andrew_13-3" class="reference"><a href="#cite_note-St_Andrew-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> A striking testimony to the respect in which he was held was shown in 1796 when the French commissary in Italy was ordered to attend in the full state on Lagrange's father and tender the congratulations of the republic on the achievements of his son, who "had done honour to all mankind by his genius, and whom it was the special glory of <a href="/wiki/Piedmont" title="Piedmont">Piedmont</a> to have produced". It may be added that Napoleon, when he attained power, warmly encouraged scientific studies in France, and was a liberal benefactor of them. Appointed <a href="/wiki/S%C3%A9nat_conservateur" title="Sénat conservateur">senator</a> in 1799, he was the first signer of the <a href="/wiki/S%C3%A9natus-consulte" title="Sénatus-consulte">Sénatus-consulte</a> which in 1802 annexed his fatherland Piedmont to France.<sup id="cite_ref-laei_10-6" class="reference"><a href="#cite_note-laei-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> He acquired French citizenship in consequence.<sup id="cite_ref-laei_10-7" class="reference"><a href="#cite_note-laei-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The French claimed he was a French mathematician, but the Italians continued to claim him as Italian.<i><sup id="cite_ref-St_Andrew_13-4" class="reference"><a href="#cite_note-St_Andrew-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></i> </p> <div class="mw-heading mw-heading4"><h4 id="Units_of_measurement">Units of measurement</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=8" title="Edit section: Units of measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lagrange was involved in the development of the <a href="/wiki/Metric_system" title="Metric system">metric system</a> of measurement in the 1790s. He was offered the presidency of the Commission for the reform of weights and measures (<i><a href="/wiki/General_Conference_on_Weights_and_Measures" title="General Conference on Weights and Measures">la Commission des Poids et Mesures</a></i>) when he was preparing to escape. After Lavoisier's death in 1794, it was largely Lagrange who influenced the choice of the <a href="/wiki/Metre" title="Metre">metre</a> and <a href="/wiki/Kilogram" title="Kilogram">kilogram</a> units with <a href="/wiki/Decimal" title="Decimal">decimal</a> subdivision, by the commission of 1799.<sup id="cite_ref-Delambre1816_21-0" class="reference"><a href="#cite_note-Delambre1816-21"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Lagrange was also one of the founding members of the <a href="/wiki/Bureau_des_Longitudes" title="Bureau des Longitudes">Bureau des Longitudes</a> in 1795. </p> <div class="mw-heading mw-heading4"><h4 id="École_Normale"><span id=".C3.89cole_Normale"></span>École Normale</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=9" title="Edit section: École Normale"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1795, Lagrange was appointed to a mathematical chair at the newly established <a href="/wiki/%C3%89cole_Normale_Sup%C3%A9rieure" class="mw-redirect" title="École Normale Supérieure">École Normale</a>, which enjoyed only a short existence of four months. His lectures there were elementary; they contain nothing of any mathematical importance, though they do provide a brief historical insight into his reason for proposing <a href="/wiki/Undecimal#Undecimal_in_the_history_of_measurement" title="Undecimal">undecimal</a> or Base 11 as the base number for the reformed system of weights and measures.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 23">: 23 </span></sup> The lectures were published because the professors had to "pledge themselves to the representatives of the people and to each other neither to read nor to repeat from memory" ["Les professeurs aux Écoles Normales ont pris, avec les Représentants du Peuple, et entr'eux l'engagement de ne point lire ou débiter de mémoire des discours écrits"<sup id="cite_ref-Book1_23-0" class="reference"><a href="#cite_note-Book1-23"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: iii">: iii </span></sup>]. The discourses were ordered and taken down in shorthand to enable the deputies to see how the professors acquitted themselves. It was also thought the published lectures would interest a significant portion of the citizenry ["Quoique des feuilles sténographiques soient essentiellement destinées aux élèves de l'École Normale, on doit prévoir quיelles seront lues par une grande partie de la Nation"<sup id="cite_ref-Book1_23-1" class="reference"><a href="#cite_note-Book1-23"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: v">: v </span></sup>]. </p> <div class="mw-heading mw-heading4"><h4 id="École_Polytechnique"><span id=".C3.89cole_Polytechnique"></span>École Polytechnique</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=10" title="Edit section: École Polytechnique"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1794, Lagrange was appointed professor of the <a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a>; and his lectures there, described by mathematicians who had the good fortune to be able to attend them, were almost perfect both in form and matter.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2008)">citation needed</span></a></i>]</sup> Beginning with the merest elements, he led his hearers on until, almost unknown to themselves, they were themselves extending the bounds of the subject: above all he impressed on his pupils the advantage of always using general methods expressed in a symmetrical notation. </p><p>However, Lagrange does not seem to have been a successful teacher. <a href="/wiki/Joseph_Fourier" title="Joseph Fourier">Fourier</a>, who attended his lectures in 1795, wrote: </p> <dl><dd>his voice is very feeble, at least in that he does not become heated; he has a very marked Italian accent and pronounces the <i>s</i> like <i>z</i> [...] The students, of whom the majority are incapable of appreciating him, give him little welcome, but the <i>professeurs</i> make amends for it.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Late_years">Late years</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=11" title="Edit section: Late years"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Lagrange%27s_tomb_at_the_Pantheon.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Lagrange%27s_tomb_at_the_Pantheon.jpg/250px-Lagrange%27s_tomb_at_the_Pantheon.jpg" decoding="async" width="250" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Lagrange%27s_tomb_at_the_Pantheon.jpg/375px-Lagrange%27s_tomb_at_the_Pantheon.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Lagrange%27s_tomb_at_the_Pantheon.jpg/500px-Lagrange%27s_tomb_at_the_Pantheon.jpg 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption>Lagrange's tomb in the crypt of the <a href="/wiki/Panth%C3%A9on,_Paris" class="mw-redirect" title="Panthéon, Paris">Panthéon</a></figcaption></figure><p> In 1810, Lagrange started a thorough revision of the <i>Mécanique analytique</i>, but he was able to complete only about two-thirds of it before his death in Paris in 1813, in 128 <a href="/wiki/Rue_du_Faubourg_Saint-Honor%C3%A9" title="Rue du Faubourg Saint-Honoré">rue du Faubourg Saint-Honoré</a>. Napoleon honoured him with the Grand Croix of the Ordre Impérial de la Réunion just two days before he died. He was buried that same year in the <a href="/wiki/Panth%C3%A9on" title="Panthéon">Panthéon</a> in Paris. The inscription on his tomb reads in translation:</p><blockquote><p>JOSEPH LOUIS LAGRANGE. Senator. Count of the Empire. Grand Officer of the Legion of Honour. Grand Cross of the Imperial <a href="/wiki/Order_of_the_Reunion" title="Order of the Reunion">Order of the Reunion</a>. Member of the Institute and the Bureau of Longitude. Born in Turin on 25 January 1736. Died in Paris on 10 April 1813.</p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Work_in_Berlin">Work in Berlin</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=12" title="Edit section: Work in Berlin"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lagrange was extremely active scientifically during the twenty years he spent in Berlin. Not only did he produce his <i>Mécanique analytique</i>, but he contributed between one and two hundred papers to the Academy of Turin, the Berlin Academy, and the French Academy. Some of these are really treatises, and all without exception are of a high order of excellence. Except for a short time when he was ill he produced on average about one paper a month. Of these, note the following as amongst the most important. </p><p>First, his contributions to the fourth and fifth volumes, 1766–1773, of the <i>Miscellanea Taurinensia</i>; of which the most important was the one in 1771, in which he discussed how numerous <a href="/wiki/Astronomy" title="Astronomy">astronomical</a> observations should be combined so as to give the most probable result. And later, his contributions to the first two volumes, 1784–1785, of the transactions of the Turin Academy; to the first of which he contributed a paper on the pressure exerted by fluids in motion, and to the second an article on integration by <a href="/wiki/Infinite_series" class="mw-redirect" title="Infinite series">infinite series</a>, and the kind of problems for which it is suitable. </p><p>Most of the papers sent to Paris were on astronomical questions, and among these, including his paper on the <a href="/wiki/Jupiter" title="Jupiter">Jovian</a> system in 1766, his essay on the problem of three bodies in 1772, his work on the <a href="/wiki/Secular_equation" class="mw-redirect" title="Secular equation">secular equation</a> of the Moon in 1773, and his treatise on cometary perturbations in 1778. These were all written on subjects proposed by the <a href="/wiki/Acad%C3%A9mie_fran%C3%A7aise" class="mw-redirect" title="Académie française">Académie française</a>, and in each case, the prize was awarded to him. </p> <div class="mw-heading mw-heading3"><h3 id="Lagrangian_mechanics">Lagrangian mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=13" title="Edit section: Lagrangian mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline 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href="mw-data:TemplateStyles:r1126788409"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle" style="padding-left:0.9em;padding-right:0.9em;"><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">F</mtext> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2ad0a6d6780c3abc5247abd82bd8a2249d56ff3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.318ex; height:5.509ex;" alt="{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}"></span><div class="sidebar-caption" style="font-size:90%;padding:0.6em 0;font-style:italic;"><a href="/wiki/Second_law_of_motion" class="mw-redirect" title="Second law of motion">Second law of motion</a></div></td></tr><tr><th class="sidebar-heading" style="font-weight: bold; display:block;margin-bottom:1.0em;"> <div class="hlist"> <ul><li><a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">History</a></li> <li><a href="/wiki/Timeline_of_classical_mechanics" title="Timeline of classical mechanics">Timeline</a></li> <li><a href="/wiki/List_of_textbooks_on_classical_mechanics_and_quantum_mechanics" title="List of textbooks on classical mechanics and quantum mechanics">Textbooks</a></li></ul> </div></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Branches</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Applied_mechanics" title="Applied mechanics">Applied</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum</a></li> <li><a href="/wiki/Analytical_dynamics" class="mw-redirect" title="Analytical dynamics">Dynamics</a></li> <li><a href="/wiki/Classical_field_theory" title="Classical field theory">Field theory</a></li> <li><a href="/wiki/Kinematics" title="Kinematics">Kinematics</a></li> <li><a href="/wiki/Kinetics_(physics)" title="Kinetics (physics)">Kinetics</a></li> <li><a href="/wiki/Statics" title="Statics">Statics</a></li> <li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical mechanics</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Fundamentals</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Acceleration" title="Acceleration">Acceleration</a></li> <li><a href="/wiki/Angular_momentum" title="Angular momentum">Angular momentum</a></li> <li><a href="/wiki/Couple_(mechanics)" title="Couple (mechanics)">Couple</a></li> <li><a href="/wiki/D%27Alembert%27s_principle" title="D'Alembert's principle">D'Alembert's principle</a></li> <li><a href="/wiki/Energy" title="Energy">Energy</a> <ul><li><a href="/wiki/Kinetic_energy#Newtonian_kinetic_energy" title="Kinetic energy">kinetic</a></li> <li><a href="/wiki/Potential_energy" title="Potential energy">potential</a></li></ul></li> <li><a href="/wiki/Force" title="Force">Force</a></li> <li><a href="/wiki/Frame_of_reference" title="Frame of reference">Frame of reference</a></li> <li><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial frame of reference</a></li> <li><a href="/wiki/Impulse_(physics)" title="Impulse (physics)">Impulse</a></li> <li><span class="nowrap"><a href="/wiki/Inertia" title="Inertia">Inertia</a> / <a href="/wiki/Moment_of_inertia" title="Moment of inertia">Moment of inertia</a></span></li> <li><a href="/wiki/Mass" title="Mass">Mass</a></li> <li><br /><a href="/wiki/Mechanical_power_(physics)" class="mw-redirect" title="Mechanical power (physics)">Mechanical power</a></li> <li><a href="/wiki/Work_(physics)" title="Work (physics)">Mechanical work</a></li> <li><br /><a href="/wiki/Moment_(physics)" title="Moment (physics)">Moment</a></li> <li><a href="/wiki/Momentum" title="Momentum">Momentum</a></li> <li><a href="/wiki/Space" title="Space">Space</a></li> <li><a href="/wiki/Speed" title="Speed">Speed</a></li> <li><a href="/wiki/Time" title="Time">Time</a></li> <li><a href="/wiki/Torque" title="Torque">Torque</a></li> <li><a href="/wiki/Velocity" title="Velocity">Velocity</a></li> <li><a href="/wiki/Virtual_work" title="Virtual work">Virtual work</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Formulations</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"> <ul><li><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><b><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a></b></div></li> <li><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><b><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical mechanics</a></b> <div class="plainlist"><ul><li><a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian mechanics</a></li><li><a href="/wiki/Hamiltonian_mechanics" title="Hamiltonian mechanics">Hamiltonian mechanics</a></li><li><a href="/wiki/Routhian_mechanics" title="Routhian mechanics">Routhian mechanics</a></li><li><a href="/wiki/Hamilton%E2%80%93Jacobi_equation" title="Hamilton–Jacobi equation">Hamilton–Jacobi equation</a></li><li><a href="/wiki/Appell%27s_equation_of_motion" title="Appell's equation of motion">Appell's equation of motion</a></li><li><a href="/wiki/Koopman%E2%80%93von_Neumann_classical_mechanics" title="Koopman–von Neumann classical mechanics">Koopman–von Neumann mechanics</a></li></ul></div></div></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Core topics</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Damping" title="Damping">Damping</a></li> <li><a href="/wiki/Displacement_(geometry)" title="Displacement (geometry)">Displacement</a></li> <li><a href="/wiki/Equations_of_motion" title="Equations of motion">Equations of motion</a></li> <li><a href="/wiki/Euler%27s_laws_of_motion" title="Euler's laws of motion"><span class="wrap">Euler's laws of motion</span></a></li> <li><a href="/wiki/Fictitious_force" title="Fictitious force">Fictitious force</a></li> <li><a href="/wiki/Friction" title="Friction">Friction</a></li> <li><a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">Harmonic oscillator</a></li></ul> </div> <ul><li><span class="nowrap"><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial</a> / <a href="/wiki/Non-inertial_reference_frame" title="Non-inertial reference frame">Non-inertial reference frame</a></span></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Motion" title="Motion">Motion</a> (<a href="/wiki/Linear_motion" title="Linear motion">linear</a>)</li> <li><a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation"><span class="wrap">Newton's law of universal gravitation</span></a></li> <li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a></li> <li><a href="/wiki/Relative_velocity" title="Relative velocity">Relative velocity</a></li> <li><a href="/wiki/Rigid_body" title="Rigid body">Rigid body</a> <ul><li><a href="/wiki/Rigid_body_dynamics" title="Rigid body dynamics">dynamics</a></li> <li><a href="/wiki/Euler%27s_equations_(rigid_body_dynamics)" title="Euler's equations (rigid body dynamics)">Euler's equations</a></li></ul></li> <li><a href="/wiki/Simple_harmonic_motion" title="Simple harmonic motion">Simple harmonic motion</a></li> <li><a href="/wiki/Vibration" title="Vibration">Vibration</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)"><a href="/wiki/Rotation_around_a_fixed_axis" title="Rotation around a fixed axis">Rotation</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Circular_motion" title="Circular motion">Circular motion</a></li> <li><a href="/wiki/Rotating_reference_frame" title="Rotating reference frame">Rotating reference frame</a></li> <li><a href="/wiki/Centripetal_force" title="Centripetal force">Centripetal force</a></li> <li><a href="/wiki/Centrifugal_force" title="Centrifugal force">Centrifugal force</a> <ul><li><a href="/wiki/Reactive_centrifugal_force" title="Reactive centrifugal force">reactive</a></li></ul></li> <li><a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis force</a></li> <li><a href="/wiki/Pendulum_(mechanics)" title="Pendulum (mechanics)">Pendulum</a></li> <li><a href="/wiki/Tangential_speed" title="Tangential speed">Tangential speed</a></li> <li><a href="/wiki/Rotational_frequency" title="Rotational frequency">Rotational frequency</a></li></ul> </div> <ul><li><a href="/wiki/Angular_acceleration" title="Angular acceleration">Angular acceleration</a> / <a href="/wiki/Angular_displacement" title="Angular displacement">displacement</a> / <a href="/wiki/Angular_frequency" title="Angular frequency">frequency</a> / <a href="/wiki/Angular_velocity" title="Angular velocity">velocity</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a></li> <li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Jeremiah_Horrocks" title="Jeremiah Horrocks">Horrocks</a></li> <li><a href="/wiki/Edmond_Halley" title="Edmond Halley">Halley</a></li> <li><a href="/wiki/Pierre_Louis_Maupertuis" title="Pierre Louis Maupertuis">Maupertuis</a></li> <li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a></li> <li><a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann Bernoulli</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">d'Alembert</a></li> <li><a href="/wiki/Alexis_Clairaut" title="Alexis Clairaut">Clairaut</a></li> <li><a class="mw-selflink selflink">Lagrange</a></li> <li><a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Laplace</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/William_Rowan_Hamilton" title="William Rowan Hamilton">Hamilton</a></li> <li><a href="/wiki/Carl_Gustav_Jacob_Jacobi" title="Carl Gustav Jacob Jacobi">Jacobi</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li> <li><a href="/wiki/Edward_Routh" title="Edward Routh">Routh</a></li> <li><a href="/wiki/Joseph_Liouville" title="Joseph Liouville">Liouville</a></li> <li><a href="/wiki/Paul_%C3%89mile_Appell" title="Paul Émile Appell">Appell</a></li> <li><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a></li> <li><a href="/wiki/Bernard_Koopman" title="Bernard Koopman">Koopman</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><span class="nowrap"><span class="nowrap"><span class="noviewer" typeof="mw:File"><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/14px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/21px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/28px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Classical_mechanics" title="Category:Classical mechanics">Category</a></span></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Classical_mechanics" title="Template:Classical mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Classical_mechanics" title="Template talk:Classical mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Classical_mechanics" title="Special:EditPage/Template:Classical mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>Between 1772 and 1788, Lagrange re-formulated Classical/Newtonian mechanics to simplify formulas and ease calculations. These mechanics are called <a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian mechanics</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Algebra">Algebra</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=14" title="Edit section: Algebra"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The greater number of his papers during this time were, however, contributed to the <a href="/wiki/Prussian_Academy_of_Sciences" title="Prussian Academy of Sciences">Prussian Academy of Sciences</a>. Several of them deal with questions in <a href="/wiki/Algebra" title="Algebra">algebra</a>. </p> <ul><li>His discussion of representations of integers by <a href="/wiki/Quadratic_form" title="Quadratic form">quadratic forms</a> (1769) and by more general algebraic forms (1770).</li> <li>His tract on the <a href="/wiki/Elimination_theory" title="Elimination theory">Theory of Elimination</a>, 1770.</li> <li><a href="/wiki/Lagrange%27s_theorem_(group_theory)" title="Lagrange's theorem (group theory)">Lagrange's theorem</a> that the order of a subgroup H of a group G must divide the order of G.</li> <li>His papers of 1770 and 1771 on the general process for solving an <a href="/wiki/Algebraic_equation" title="Algebraic equation">algebraic equation</a> of any degree via the <i><a href="/wiki/Lagrange_resolvents" class="mw-redirect" title="Lagrange resolvents">Lagrange resolvents</a></i>. This method fails to give a general formula for solutions of an equation of degree five and higher because the auxiliary equation involved has a higher degree than the original one. The significance of this method is that it exhibits the already known formulas for solving equations of second, third, and fourth degrees as manifestations of a single principle, and was foundational in <a href="/wiki/Galois_theory" title="Galois theory">Galois theory</a>. The complete solution of a binomial equation (namely an equation of the form <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ax^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ax^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1279250941829edb9b59d769190f7034631f824" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.778ex; height:2.343ex;" alt="{\displaystyle ax^{n}}"></span> ± <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19206e7d4dab695ccb34c502eff0741e98dbdfc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.258ex; height:2.176ex;" alt="{\displaystyle b=0}"></span>) is also treated in these papers.</li> <li>In 1773, Lagrange considered a <a href="/wiki/Functional_determinant" title="Functional determinant">functional determinant</a> of order 3, a special case of a <a href="/wiki/Jacobian_matrix_and_determinant" title="Jacobian matrix and determinant">Jacobian</a>. He also proved the expression for the <a href="/wiki/Volume" title="Volume">volume</a> of a <a href="/wiki/Tetrahedron" title="Tetrahedron">tetrahedron</a> with one of the vertices at the origin as the one-sixth of the <a href="/wiki/Absolute_value" title="Absolute value">absolute value</a> of the <a href="/wiki/Determinant" title="Determinant">determinant</a> formed by the coordinates of the other three vertices.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Number_theory">Number theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=15" title="Edit section: Number theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Several of his early papers also deal with questions of number theory. </p> <ul><li>Lagrange (1766–1769) was the first European to prove that <a href="/wiki/Pell%27s_equation" title="Pell's equation">Pell's equation</a> <span class="texhtml"><i>x</i><sup>2</sup> − <i>ny</i><sup>2</sup> = 1</span> has a nontrivial solution in the integers for any non-square natural number <span class="texhtml mvar" style="font-style:italic;">n</span>.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li>He proved the theorem, stated by <a href="/wiki/Bachet" class="mw-redirect" title="Bachet">Bachet</a> without justification, that <a href="/wiki/Lagrange%27s_four-square_theorem" title="Lagrange's four-square theorem">every positive integer is the sum of four squares</a>, 1770.</li> <li>He proved <a href="/wiki/Wilson%27s_theorem" title="Wilson's theorem">Wilson's theorem</a> that (for any integer <span class="texhtml"><i>n</i> > 1</span>): <span class="texhtml mvar" style="font-style:italic;">n</span> is a prime if and only if <span class="texhtml">(<i>n</i> − 1)! + 1</span> is a multiple of <span class="texhtml mvar" style="font-style:italic;">n</span>, 1771.</li> <li>His papers of 1773, 1775, and 1777 gave demonstrations of several results enunciated by Fermat, and not previously proved.</li> <li>His <a href="/wiki/List_of_important_publications_in_mathematics#Recherches_d'Arithmétique" title="List of important publications in mathematics">Recherches d'Arithmétique</a> of 1775 developed a general theory of binary <a href="/wiki/Quadratic_forms" class="mw-redirect" title="Quadratic forms">quadratic forms</a> to handle the general problem of when an integer is representable by the form <span class="texhtml"><i>ax</i><sup>2</sup> + <i>by</i><sup>2</sup> + <i>cxy</i></span>.</li> <li>He made contributions to the theory of <a href="/wiki/Continued_fraction" title="Continued fraction">continued fractions</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Other_mathematical_work">Other mathematical work</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=16" title="Edit section: Other mathematical work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are also numerous articles on various points of <a href="/wiki/Analytical_geometry" class="mw-redirect" title="Analytical geometry">analytical geometry</a>. In two of them, written rather later, in 1792 and 1793, he reduced the <a href="/wiki/Quadric" title="Quadric">equations of the quadrics</a> (or conicoids) to their <a href="/wiki/Canonical_form" title="Canonical form">canonical forms</a>. </p><p>During the years from 1772 to 1785, he contributed a long series of papers which created the science of <a href="/wiki/Partial_differential_equation" title="Partial differential equation">partial differential equations</a>. A large part of these results was collected in the second edition of Euler's integral calculus which was published in 1794. </p> <div class="mw-heading mw-heading3"><h3 id="Astronomy">Astronomy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=17" title="Edit section: Astronomy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lastly, there are numerous papers on problems in <a href="/wiki/Astronomy" title="Astronomy">astronomy</a>. Of these the most important are the following: </p> <ul><li>Attempting to solve the <a href="/wiki/Three-body_problem" title="Three-body problem">general three-body problem</a>, with the consequent discovery of the two constant-pattern solutions, collinear and equilateral, 1772. Those solutions were later seen to explain what are now known as the <a href="/wiki/Lagrangian_point" class="mw-redirect" title="Lagrangian point">Lagrangian points</a>.</li> <li>On the attraction of ellipsoids, 1773: this is founded on <a href="/wiki/Colin_Maclaurin" title="Colin Maclaurin">Maclaurin</a>'s work.</li> <li>On the secular equation of the Moon, 1773; also noticeable for the earliest introduction of the idea of the potential. The potential of a body at any point is the sum of the mass of every element of the body when divided by its distance from the point. Lagrange showed that if the potential of a body at an external point were known, the attraction in any direction could be at once found. The theory of the potential was elaborated in a paper sent to Berlin in 1777.</li> <li>On the motion of the nodes of a planet's <a href="/wiki/Orbit" title="Orbit">orbit</a>, 1774.</li> <li>On the stability of the planetary orbits, 1776.</li> <li>Two papers in which the method of determining the orbit of a <a href="/wiki/Comet" title="Comet">comet</a> from three observations is completely worked out, 1778 and 1783: this has not indeed proved practically available, but his system of calculating the perturbations by means of mechanical quadratures has formed the basis of most subsequent researches on the subject.</li> <li>His determination of the secular and periodic variations of the <a href="/wiki/Orbital_elements" title="Orbital elements">elements</a> of the planets, 1781–1784: the upper limits assigned for these agree closely with those obtained later by <a href="/wiki/Urbain_Le_Verrier" title="Urbain Le Verrier">Le Verrier</a>, and Lagrange proceeded as far as the knowledge then possessed of the masses of the planets permitted.</li> <li>Three papers on the method of interpolation, 1783, 1792 and 1793: the part of finite differences dealing therewith is now in the same stage as that in which Lagrange left it.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Fundamental_treatise">Fundamental treatise</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=18" title="Edit section: Fundamental treatise"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Over and above these various papers he composed his fundamental treatise, the <i>Mécanique analytique</i>. </p><p>In this book, he lays down the law of virtual work, and from that one fundamental principle, by the aid of the calculus of variations, deduces the whole of <a href="/wiki/Mechanics" title="Mechanics">mechanics</a>, both of solids and fluids. </p><p>The object of the book is to show that the subject is implicitly included in a single principle, and to give general formulae from which any particular result can be obtained. The method of generalised co-ordinates by which he obtained this result is perhaps the most brilliant result of his analysis. Instead of following the motion of each individual part of a material system, as D'Alembert and Euler had done, he showed that, if we determine its configuration by a sufficient number of variables <i>x</i>, called <a href="/wiki/Generalized_coordinates" title="Generalized coordinates">generalized coordinates</a>, whose number is the same as that of the degrees of freedom possessed by the system, then the kinetic and potential energies of the system can be expressed in terms of those variables, and the differential equations of motion thence deduced by simple differentiation. For example, in dynamics of a rigid system he replaces the consideration of the particular problem by the general equation, which is now usually written in the form </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d}{dt}}{\frac {\partial T}{\partial {\dot {x}}}}-{\frac {\partial T}{\partial x}}+{\frac {\partial V}{\partial x}}=0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d}{dt}}{\frac {\partial T}{\partial {\dot {x}}}}-{\frac {\partial T}{\partial x}}+{\frac {\partial V}{\partial x}}=0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08cf0f979a4df013678b5e8088d1cbde0b90f8f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:25.003ex; height:5.509ex;" alt="{\displaystyle {\frac {d}{dt}}{\frac {\partial T}{\partial {\dot {x}}}}-{\frac {\partial T}{\partial x}}+{\frac {\partial V}{\partial x}}=0,}"></span></dd></dl> <p>where <i>T</i> represents the kinetic energy and <i>V</i> represents the potential energy of the system. He then presented what we now know as the method of <a href="/wiki/Lagrange_multipliers" class="mw-redirect" title="Lagrange multipliers">Lagrange multipliers</a>—though this is not the first time that method was published—as a means to solve this equation.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> Amongst other minor theorems here given it may suffice to mention the proposition that the kinetic energy imparted by the given impulses to a material system under given constraints is a maximum, and the <a href="/wiki/Principle_of_least_action" class="mw-redirect" title="Principle of least action">principle of least action</a>. All the analysis is so elegant that Sir <a href="/wiki/William_Rowan_Hamilton" title="William Rowan Hamilton">William Rowan Hamilton</a> said the work could be described only as a scientific poem. Lagrange remarked that mechanics was really a branch of <a href="/wiki/Pure_mathematics" title="Pure mathematics">pure mathematics</a> analogous to a geometry of four dimensions, namely, the time and the three coordinates of the point in space; and it is said that he prided himself that from the beginning to the end of the work there was not a single diagram. At first no printer could be found who would publish the book; but <a href="/wiki/Adrien-Marie_Legendre" title="Adrien-Marie Legendre">Legendre</a> at last persuaded a Paris firm to undertake it, and it was issued under the supervision of Laplace, Cousin, Legendre (editor) and Condorcet in 1788.<sup id="cite_ref-St_Andrew_13-5" class="reference"><a href="#cite_note-St_Andrew-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Work_in_France">Work in France</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=19" title="Edit section: Work in France"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Differential_calculus_and_calculus_of_variations">Differential calculus and calculus of variations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=20" title="Edit section: Differential calculus and calculus of variations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Lagrange_portrait.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Lagrange_portrait.jpg/220px-Lagrange_portrait.jpg" decoding="async" width="220" height="247" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/1/19/Lagrange_portrait.jpg 1.5x" data-file-width="235" data-file-height="264" /></a><figcaption>Joseph-Louis Lagrange</figcaption></figure> <p>Lagrange's lectures on the <a href="/wiki/Differential_calculus" title="Differential calculus">differential calculus</a> at École Polytechnique form the basis of his treatise <i>Théorie des fonctions analytiques</i>, which was published in 1797. This work is the extension of an idea contained in a paper he had sent to the Berlin papers in 1772, and its object is to substitute for the differential calculus a group of theorems based on the development of algebraic functions in series, relying in particular on the principle of the <a href="/wiki/Generality_of_algebra" title="Generality of algebra">generality of algebra</a>. </p><p>A somewhat similar method had been previously used by <a href="/wiki/John_Landen" title="John Landen">John Landen</a> in the <i>Residual Analysis</i>, published in London in 1758. Lagrange believed that he could thus get rid of those difficulties, connected with the use of infinitely large and infinitely small quantities, to which philosophers objected in the usual treatment of the differential calculus. The book is divided into three parts: of these, the first treats of the general theory of functions, and gives an algebraic proof of <a href="/wiki/Taylor%27s_theorem" title="Taylor's theorem">Taylor's theorem</a>, the validity of which is, however, open to question; the second deals with applications to geometry; and the third with applications to mechanics. </p><p> Another treatise on the same lines was his <i>Leçons sur le calcul des fonctions</i>, issued in 1804, with the second edition in 1806. It is in this book that Lagrange formulated his celebrated method of <a href="/wiki/Lagrange_multipliers" class="mw-redirect" title="Lagrange multipliers">Lagrange multipliers</a>, in the context of problems of variational calculus with integral constraints. These works devoted to differential calculus and calculus of variations may be considered as the starting point for the researches of <a href="/wiki/Augustin_Louis_Cauchy" class="mw-redirect" title="Augustin Louis Cauchy">Cauchy</a>, <a href="/wiki/Carl_Gustav_Jakob_Jacobi" class="mw-redirect" title="Carl Gustav Jakob Jacobi">Jacobi</a>, and <a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Weierstrass</a>.</p><ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Lagrange-6.jpg" class="mw-file-description" title="1813 copy of "Theorie des fonctions analytiques""><img alt="1813 copy of "Theorie des fonctions analytiques"" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Lagrange-6.jpg/76px-Lagrange-6.jpg" decoding="async" width="76" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Lagrange-6.jpg/115px-Lagrange-6.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Lagrange-6.jpg/153px-Lagrange-6.jpg 2x" data-file-width="3362" data-file-height="5275" /></a></span></div> <div class="gallerytext">1813 copy of "Theorie des fonctions analytiques"</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Lagrange-7.jpg" class="mw-file-description" title="Title page to "Theorie des fonctions analytiques""><img alt="Title page to "Theorie des fonctions analytiques"" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Lagrange-7.jpg/90px-Lagrange-7.jpg" decoding="async" width="90" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Lagrange-7.jpg/136px-Lagrange-7.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Lagrange-7.jpg/181px-Lagrange-7.jpg 2x" data-file-width="3178" data-file-height="4210" /></a></span></div> <div class="gallerytext">Title page to "Theorie des fonctions analytiques"</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Lagrange-9.jpg" class="mw-file-description" title="Introduction to "Theorie des fonctions analytiques""><img alt="Introduction to "Theorie des fonctions analytiques"" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lagrange-9.jpg/76px-Lagrange-9.jpg" decoding="async" width="76" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lagrange-9.jpg/115px-Lagrange-9.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lagrange-9.jpg/153px-Lagrange-9.jpg 2x" data-file-width="3297" data-file-height="5171" /></a></span></div> <div class="gallerytext">Introduction to "Theorie des fonctions analytiques"</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Lagrange-10.jpg" class="mw-file-description" title="First page of "Theorie des fonctions analytiques""><img alt="First page of "Theorie des fonctions analytiques"" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Lagrange-10.jpg/72px-Lagrange-10.jpg" decoding="async" width="72" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Lagrange-10.jpg/108px-Lagrange-10.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Lagrange-10.jpg/144px-Lagrange-10.jpg 2x" data-file-width="3201" data-file-height="5346" /></a></span></div> <div class="gallerytext">First page of "Theorie des fonctions analytiques"</div> </li> </ul><figure typeof="mw:File/Thumb"><a href="/wiki/File:Lagrange-2.jpg" class="mw-file-description"><img alt="Title page of volume I of Lagrange's "Mécanique Analytique" (1811)" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Lagrange-2.jpg/170px-Lagrange-2.jpg" decoding="async" width="170" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Lagrange-2.jpg/256px-Lagrange-2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Lagrange-2.jpg/340px-Lagrange-2.jpg 2x" data-file-width="3431" data-file-height="4654" /></a><figcaption>Title page of volume I of Lagrange's "Mécanique Analytique" (1811)</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Infinitesimals">Infinitesimals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=21" title="Edit section: Infinitesimals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At a later period Lagrange fully embraced the use of <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimals</a> in preference to founding the differential calculus on the study of algebraic forms; and in the preface to the second edition of the <i>Mécanique Analytique</i>, which was issued in 1811, he justifies the employment of infinitesimals, and concludes by saying that: </p> <dl><dd><i>When we have grasped the spirit of the infinitesimal method, and have verified the exactness of its results either by the geometrical method of prime and ultimate ratios, or by the analytical method of derived functions, we may employ infinitely small quantities as a sure and valuable means of shortening and simplifying our proofs.</i></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Number_theory_2">Number theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=22" title="Edit section: Number theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>His <i>Résolution des équations numériques</i>, published in 1798, was also the fruit of his lectures at École Polytechnique. There he gives the method of approximating the real roots of an equation by means of <a href="/wiki/Continued_fraction" title="Continued fraction">continued fractions</a>, and enunciates several other theorems. In a note at the end, he shows how <a href="/wiki/Fermat%27s_little_theorem" title="Fermat's little theorem">Fermat's little theorem</a>, that is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{p-1}-1\equiv 0{\pmod {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo>≡</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em" /> <mi>p</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{p-1}-1\equiv 0{\pmod {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be97827a21014a57cae45b5465ed46013e9457bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.507ex; height:3.176ex;" alt="{\displaystyle a^{p-1}-1\equiv 0{\pmod {p}}}"></span></dd></dl> <p>where <i>p</i> is a prime and <i>a</i> is prime to <i>p</i>, may be applied to give the complete algebraic solution of any binomial equation. He also here explains how the equation whose roots are the squares of the differences of the roots of the original equation may be used so as to give considerable information as to the position and nature of those roots. </p> <div class="mw-heading mw-heading3"><h3 id="Celestial_mechanics">Celestial mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=23" title="Edit section: Celestial mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A theory of the <a href="/wiki/Planetary_motion" class="mw-redirect" title="Planetary motion">planetary motions</a> had formed the subject of some of the most remarkable of Lagrange's Berlin papers. In 1806 the subject was reopened by <a href="/wiki/Sim%C3%A9on_Poisson" class="mw-redirect" title="Siméon Poisson">Poisson</a>, who, in a paper read before the French Academy, showed that Lagrange's formulae led to certain limits for the stability of the orbits. Lagrange, who was present, now discussed the whole subject afresh, and in a letter communicated to the academy in 1808 explained how, by the variation of arbitrary constants, the periodical and secular inequalities of any system of mutually interacting bodies could be determined. </p> <div class="mw-heading mw-heading2"><h2 id="Prizes_and_distinctions">Prizes and distinctions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=24" title="Edit section: Prizes and distinctions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Euler proposed Lagrange for election to the Berlin Academy and he was elected on 2 September 1756. He was elected a Fellow of the <a href="/wiki/Royal_Society_of_Edinburgh" title="Royal Society of Edinburgh">Royal Society of Edinburgh</a> in 1790, a Fellow of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a> and a foreign member of the <a href="/wiki/Royal_Swedish_Academy_of_Sciences" title="Royal Swedish Academy of Sciences">Royal Swedish Academy of Sciences</a> in 1806. In 1808, <a href="/wiki/Napoleon" title="Napoleon">Napoleon</a> made Lagrange a Grand Officer of the <a href="/wiki/Legion_of_Honour" title="Legion of Honour">Legion of Honour</a> and a <a href="/wiki/Count_of_the_Empire" class="mw-redirect" title="Count of the Empire">Count of the Empire</a>. He was awarded the Grand Croix of the <a href="/wiki/Order_of_the_Reunion" title="Order of the Reunion">Ordre Impérial de la Réunion</a> in 1813, a week before his death in Paris, and was buried in the <a href="/wiki/Panth%C3%A9on" title="Panthéon">Panthéon</a>, a <a href="/wiki/Mausoleum" title="Mausoleum">mausoleum</a> dedicated to the most honoured French people. </p><p>Lagrange was awarded the 1764 prize of the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a> for his memoir on the <a href="/wiki/Libration" title="Libration">libration</a> of the Moon. In 1766 the academy proposed a problem of the motion of the <a href="/wiki/Satellites_of_Jupiter" class="mw-redirect" title="Satellites of Jupiter">satellites of Jupiter</a>, and the prize again was awarded to Lagrange. He also shared or won the prizes of 1772, 1774, and 1778. </p><p>Lagrange is one of the <a href="/wiki/List_of_the_72_names_on_the_Eiffel_Tower" title="List of the 72 names on the Eiffel Tower">72 prominent French scientists</a> who were commemorated on plaques at the first stage of the <a href="/wiki/Eiffel_Tower" title="Eiffel Tower">Eiffel Tower</a> when it first opened. <i>Rue Lagrange</i> in the 5th Arrondissement in Paris is named after him. In Turin, the street where the house of his birth still stands is named <i>via Lagrange</i>. The <a href="/wiki/Lunar_crater" class="mw-redirect" title="Lunar crater">lunar crater</a> <a href="/wiki/Lagrange_(crater)" title="Lagrange (crater)">Lagrange</a> and the asteroid <a href="/wiki/1006_Lagrangea" title="1006 Lagrangea">1006 Lagrangea</a> also bear his name. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=25" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/List_of_things_named_after_Joseph-Louis_Lagrange" title="List of things named after Joseph-Louis Lagrange">List of things named after Joseph-Louis Lagrange</a></li> <li><a href="/wiki/Four-dimensional_space" title="Four-dimensional space">Four-dimensional space</a></li> <li><a href="/wiki/Gauss%27s_law" title="Gauss's law">Gauss's law</a></li> <li><a href="/wiki/History_of_the_metre" title="History of the metre">History of the metre</a></li> <li><a href="/wiki/Undecimal#Undecimal_in_the_history_of_measurement" title="Undecimal">Lagrange's role in measurement reform</a></li> <li><a href="/wiki/Seconds_pendulum" title="Seconds pendulum">Seconds pendulum</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=26" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output 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href="/wiki/American_English" title="American English">US</a>: </span><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="'l' in 'lie'">l</span><span title="/ə/: 'a' in 'about'">ə</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="/ɡ/: 'g' in 'guy'">ɡ</span><span title="'r' in 'rye'">r</span><span title="/eɪ/: 'a' in 'face'">eɪ</span><span title="'n' in 'nigh'">n</span><span title="/dʒ/: 'j' in 'jam'">dʒ</span></span>,<span class="wrap"> </span><span style="border-bottom:1px dotted"><span title="'l' in 'lie'">l</span><span title="/ə/: 'a' in 'about'">ə</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="/ɡ/: 'g' in 'guy'">ɡ</span><span title="'r' in 'rye'">r</span><span title="/ɑː/: 'a' in 'father'">ɑː</span><span title="'n' in 'nigh'">n</span><span title="/dʒ/: 'j' in 'jam'">dʒ</span></span>,<span class="wrap"> </span><span style="border-bottom:1px dotted"><span title="'l' in 'lie'">l</span><span title="/ə/: 'a' in 'about'">ə</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="/ɡ/: 'g' in 'guy'">ɡ</span><span title="'r' in 'rye'">r</span><span title="/ɒ̃/: nasal 'an' in 'vin blanc'">ɒ̃</span><span title="/ʒ/: 's' in 'pleasure'">ʒ</span></span>/</a></span></span>;<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1177148991"><span class="IPA-label IPA-label-small">French:</span> <span class="IPA nowrap" lang="fr-Latn-fonipa"><a href="/wiki/Help:IPA/French" title="Help:IPA/French">[ʒozɛf<span class="wrap"> </span>lwi<span class="wrap"> </span>laɡʁɑ̃ʒ]</a></span>.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1177148991"><span class="IPA-label IPA-label-small">Italian:</span> <span class="IPA nowrap" lang="it-Latn-fonipa"><a href="/wiki/Help:IPA/Italian" title="Help:IPA/Italian">[dʒuˈzɛppe<span class="wrap"> </span>luˈiːdʒi<span class="wrap"> </span>laˈɡrandʒa]</a></span>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1177148991"><span class="IPA-label IPA-label-small">Italian:</span> <span class="IPA nowrap" lang="it-Latn-fonipa"><a href="/wiki/Help:IPA/Italian" title="Help:IPA/Italian">[dʒuˈzɛppe<span class="wrap"> </span>ludoˈviːko<span class="wrap"> </span>de<span class="wrap"> </span>la<span class="wrap"> </span>ˈɡranʒ<span class="wrap"> </span>turˈnje]</a></span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1177148991"><span class="IPA-label IPA-label-small">French:</span> <span class="IPA nowrap" lang="fr-Latn-fonipa"><a href="/wiki/Help:IPA/French" title="Help:IPA/French">[də<span class="wrap"> </span>la<span class="wrap"> </span>ɡʁɑ̃ʒ<span class="wrap"> </span>tuʁnje]</a></span>.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=27" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=28" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output 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0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20210423180914/https://www.lexico.com/definition/lagrange,_joseph_louis?s=t">"Lagrange, Joseph Louis"</a>. <i><a href="/wiki/Lexico" title="Lexico">Lexico</a> UK English Dictionary</i>. <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. Archived from <a rel="nofollow" class="external text" href="http://www.lexico.com/definition/Lagrange,+Joseph+Louis">the original</a> on 23 April 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Lagrange%2C+Joseph+Louis&rft.btitle=Lexico+UK+English+Dictionary&rft.pub=Oxford+University+Press&rft_id=http%3A%2F%2Fwww.lexico.com%2Fdefinition%2FLagrange%2C%2BJoseph%2BLouis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://dictionary.reference.com/browse/lagrange">"Lagrange"</a>. <i><a href="/wiki/Random_House_Webster%27s_Unabridged_Dictionary" title="Random House Webster's Unabridged Dictionary">Random House Webster's Unabridged Dictionary</a></i>.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="Reference-AHD-Lagrange" class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ahdictionary.com/word/search.html?q=Lagrange">"Lagrange"</a>. <i><a href="/wiki/The_American_Heritage_Dictionary_of_the_English_Language" title="The American Heritage Dictionary of the English Language">The American Heritage Dictionary of the English Language</a></i> (5th ed.). HarperCollins<span class="reference-accessdate">. Retrieved <span class="nowrap">6 August</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+American+Heritage+Dictionary+of+the+English+Language&rft.atitle=Lagrange&rft_id=https%3A%2F%2Fwww.ahdictionary.com%2Fword%2Fsearch.html%3Fq%3DLagrange&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.merriam-webster.com/dictionary/Lagrange">"Lagrange"</a>. <i><a href="/wiki/Merriam-Webster" title="Merriam-Webster">Merriam-Webster.com Dictionary</a></i>. Merriam-Webster<span class="reference-accessdate">. Retrieved <span class="nowrap">6 August</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Merriam-Webster.com+Dictionary&rft.atitle=Lagrange&rft_id=https%3A%2F%2Fwww.merriam-webster.com%2Fdictionary%2FLagrange&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-britannica-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-britannica_6-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.britannica.com/biography/Joseph-Louis-Lagrange-comte-de-lEmpire">Joseph-Louis Lagrange, comte de l’Empire</a>, <i>Encyclopædia Britannica</i></span> </li> <li id="cite_note-luilag-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-luilag_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAngelo_Genocchi1883" class="citation web cs1 cs1-prop-foreign-lang-source">Angelo Genocchi (1883). <a rel="nofollow" class="external text" href="https://archive.org/details/ilprimosecolodel00acca">"Luigi Lagrange"</a>. <i>Il primo secolo della R. Accademia delle Scienze di Torino</i> (in Italian). Accademia delle Scienze di Torino. pp. 86–95<span class="reference-accessdate">. Retrieved <span class="nowrap">2 January</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Il+primo+secolo+della+R.+Accademia+delle+Scienze+di+Torino&rft.atitle=Luigi+Lagrange&rft.pages=86-95&rft.date=1883&rft.au=Angelo+Genocchi&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Filprimosecolodel00acca&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-laei-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-laei_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-laei_10-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-laei_10-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-laei_10-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-laei_10-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-laei_10-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-laei_10-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-laei_10-7"><sup><i><b>h</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLuigi_Pepe" class="citation web cs1 cs1-prop-foreign-lang-source">Luigi Pepe. <a rel="nofollow" class="external text" href="http://www.treccani.it/enciclopedia/giuseppe-luigi-lagrange/">"Giuseppe Luigi Lagrange"</a>. <i>Dizionario Biografico degli Italiani</i> (in Italian). Enciclopedia Italiana<span class="reference-accessdate">. Retrieved <span class="nowrap">8 July</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Dizionario+Biografico+degli+Italiani&rft.atitle=Giuseppe+Luigi+Lagrange&rft.au=Luigi+Pepe&rft_id=http%3A%2F%2Fwww.treccani.it%2Fenciclopedia%2Fgiuseppe-luigi-lagrange%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="https://books.google.com/books?id=VUWno1sOwnUC&pg=PA342">[1]</a> <i>Encyclopedia of Space and Astronomy.</i></span> </li> <li id="cite_note-RouseBall-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-RouseBall_12-0">^</a></b></span> <span class="reference-text"><a href="/wiki/W._W._Rouse_Ball" title="W. W. Rouse Ball">W. W. Rouse Ball</a>, 1908, <a rel="nofollow" class="external text" href="http://www.maths.tcd.ie/pub/HistMath/People/Lagrange/RouseBall/RB_Lagrange.html">Joseph Louis Lagrange (1736–1813)</a>," <i><a href="/wiki/Rouse_History_of_Mathematics" class="mw-redirect" title="Rouse History of Mathematics">A Short Account of the History of Mathematics</a></i>, 4th ed. pp. 401–412. Complete article online, p.338 and 333: <a rel="nofollow" class="external autonumber" href="http://www.gutenberg.org/files/31246/31246-pdf.pdf">[2]</a></span> </li> <li id="cite_note-St_Andrew-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-St_Andrew_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-St_Andrew_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-St_Andrew_13-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-St_Andrew_13-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-St_Andrew_13-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-St_Andrew_13-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Lagrange.html">Lagrange</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070325121637/http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Lagrange.html">Archived</a> 25 March 2007 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> St. Andrew University</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorris_Kline1986" class="citation book cs1">Morris Kline (1986). <i>Mathematics and the Search for Knowledge</i>. Oxford University Press. p. 214. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-504230-6" title="Special:BookSources/978-0-19-504230-6"><bdi>978-0-19-504230-6</bdi></a>. <q>Lagrange and Laplace, though of Catholic parentage, were agnostics.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+and+the+Search+for+Knowledge&rft.pages=214&rft.pub=Oxford+University+Press&rft.date=1986&rft.isbn=978-0-19-504230-6&rft.au=Morris+Kline&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHalley,_E.1693" class="citation journal cs1">Halley, E. (1693). <a rel="nofollow" class="external text" href="https://doi.org/10.1098/rstl.1693.0074">"IV. An Instance of the Excellence of the Modern ALGEBRA, in the Resolution of the Problem of finding the Foci of Optick Glasses universally"</a>. <i><a href="/wiki/Philosophical_Transactions_of_the_Royal_Society_of_London" class="mw-redirect" title="Philosophical Transactions of the Royal Society of London">Philosophical Transactions of the Royal Society of London</a></i>. <b>17</b> (205): 960–969. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1693.0074">10.1098/rstl.1693.0074</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:186212029">186212029</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+of+London&rft.atitle=IV.+An+Instance+of+the+Excellence+of+the+Modern+ALGEBRA%2C+in+the+Resolution+of+the+Problem+of+finding+the+Foci+of+Optick+Glasses+universally&rft.volume=17&rft.issue=205&rft.pages=960-969&rft.date=1693&rft_id=info%3Adoi%2F10.1098%2Frstl.1693.0074&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A186212029%23id-name%3DS2CID&rft.au=Halley%2C+E.&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%2Frstl.1693.0074&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSteele2005" class="citation book cs1"><a href="/w/index.php?title=Military_%27Progress%27_and_Newtonian_Science&action=edit&redlink=1" class="new" title="Military 'Progress' and Newtonian Science (page does not exist)">Steele, Brett</a> (2005). "13". In Brett Steele; Tamera Dorland (eds.). <i>The Heirs of Archimedes: Science and the Art of War through the Age of Enlightenment</i>. Cambridge: MIT Press. pp. 368, 375. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-19516-X" title="Special:BookSources/0-262-19516-X"><bdi>0-262-19516-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=13&rft.btitle=The+Heirs+of+Archimedes%3A+Science+and+the+Art+of+War+through+the+Age+of+Enlightenment&rft.place=Cambridge&rft.pages=368%2C+375&rft.pub=MIT+Press&rft.date=2005&rft.isbn=0-262-19516-X&rft.aulast=Steele&rft.aufirst=Brett&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFde_Andrade_Martins2008" class="citation book cs1 cs1-prop-foreign-lang-source">de Andrade Martins, Roberto (2008). "A busca da Ciência <i>a priori</i> no final do Seculo XVIII e a origem da Análise dimensional". In Roberto de Andrade Martins; Lilian Al-Chueyr Pereira Martins; Cibelle Celestino Silva; Juliana Mesquita Hidalgo Ferreira (eds.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=yiuwanC2NlYC"><i>Filosofia E Historia Da Ciência No Cone Sul. 3 Encontro</i></a> (in Portuguese). AFHIC. p. 406. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4357-1633-9" title="Special:BookSources/978-1-4357-1633-9"><bdi>978-1-4357-1633-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=A+busca+da+Ci%C3%AAncia+a+priori+no+final+do+Seculo+XVIII+e+a+origem+da+An%C3%A1lise+dimensional&rft.btitle=Filosofia+E+Historia+Da+Ci%C3%AAncia+No+Cone+Sul.+3+Encontro&rft.pages=406&rft.pub=AFHIC&rft.date=2008&rft.isbn=978-1-4357-1633-9&rft.aulast=de+Andrade+Martins&rft.aufirst=Roberto&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DyiuwanC2NlYC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">Although some authors speak of a general method of solving "<a href="/wiki/Isoperimetric" class="mw-redirect" title="Isoperimetric">isoperimetric</a> problems", the eighteenth-century meaning of this expression amounts to "problems in variational calculus", reserving the adjective "relative" for problems with isoperimetric-type constraints. The celebrated method of <a href="/wiki/Lagrange_multipliers" class="mw-redirect" title="Lagrange multipliers">Lagrange multipliers</a>, which applies to the optimization of functions of several variables subject to constraints, did not appear until much later. See <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFraser1992" class="citation journal cs1">Fraser, Craig (1992). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0315-0860%2892%2990052-D">"Isoperimetric Problems in the Variational Calculus of Euler and Lagrange"</a>. <i>Historia Mathematica</i>. <b>19</b>: 4–23. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0315-0860%2892%2990052-D">10.1016/0315-0860(92)90052-D</a></span>.</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=Isoperimetric+Problems+in+the+Variational+Calculus+of+Euler+and+Lagrange&rft.volume=19&rft.pages=4-23&rft.date=1992&rft_id=info%3Adoi%2F10.1016%2F0315-0860%2892%2990052-D&rft.aulast=Fraser&rft.aufirst=Craig&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252F0315-0860%252892%252990052-D&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">Galletto, D., <i>The genesis of Mécanique analytique</i>, La Mécanique analytique de Lagrange et son héritage, II (Turin, 1989). Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 126 (1992), suppl. 2, 277–370, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1264671">1264671</a>.</span> </li> <li id="cite_note-Vinter2000-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Vinter2000_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRichard_B._Vinter2000" class="citation book cs1">Richard B. Vinter (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PY9xscfbfiYC"><i>Optimal Control</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8176-4075-0" title="Special:BookSources/978-0-8176-4075-0"><bdi>978-0-8176-4075-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optimal+Control&rft.pub=Springer&rft.date=2000&rft.isbn=978-0-8176-4075-0&rft.au=Richard+B.+Vinter&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPY9xscfbfiYC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-Delambre1816-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Delambre1816_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDelambre1816" class="citation book cs1">Delambre, Jean Baptiste Joseph (1816). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=BbxeAAAAcAAJ&pg=PR1">"Notice sur la vie et les ouvrages de M. Malus, et de M. le Comte Lagrange"</a>. <i>Mémoires de la classe des Sciences mathématiques et physiques de l'Institut de France, Année 1812, Seconde Partie</i>. Paris: Firmin Didot. pp. xxvii–lxxx.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Notice+sur+la+vie+et+les+ouvrages+de+M.+Malus%2C+et+de+M.+le+Comte+Lagrange&rft.btitle=M%C3%A9moires+de+la+classe+des+Sciences+math%C3%A9matiques+et+physiques+de+l%27Institut+de+France%2C+Ann%C3%A9e+1812%2C+Seconde+Partie&rft.place=Paris&rft.pages=xxvii-lxxx&rft.pub=Firmin+Didot&rft.date=1816&rft.aulast=Delambre&rft.aufirst=Jean+Baptiste+Joseph&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DBbxeAAAAcAAJ%26pg%3DPR1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLagrangeLaplace1795" class="citation book cs1">Lagrange, Joseph-Louis; Laplace, Pierre-Simon (1795). "Mathématiques". <i>Séances des écoles normales, recueillies par des sténographes, et revues par les professeurs. Seconde partie. Débats. Tome premier</i>. Paris: L. Reynier. pp. 3–23. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/780161317">780161317</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Math%C3%A9matiques&rft.btitle=S%C3%A9ances+des+%C3%A9coles+normales%2C+recueillies+par+des+st%C3%A9nographes%2C+et+revues+par+les+professeurs.+Seconde+partie.+D%C3%A9bats.+Tome+premier&rft.place=Paris&rft.pages=3-23&rft.pub=L.+Reynier&rft.date=1795&rft_id=info%3Aoclcnum%2F780161317&rft.aulast=Lagrange&rft.aufirst=Joseph-Louis&rft.au=Laplace%2C+Pierre-Simon&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-Book1-23"><span class="mw-cite-backlink">^ <a href="#cite_ref-Book1_23-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Book1_23-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">"Avertissement". <i>Séances des Écoles normales, recueillies par des sténographes, et revues par les professeurs. Nouvelle édition. Leçons. Tome premier</i>. Paris: Cercle-Social. 1795. pp. iii–viii. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/490193660">490193660</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Avertissement&rft.btitle=S%C3%A9ances+des+%C3%89coles+normales%2C+recueillies+par+des+st%C3%A9nographes%2C+et+revues+par+les+professeurs.+Nouvelle+%C3%A9dition.+Le%C3%A7ons.+Tome+premier&rft.place=Paris&rft.pages=iii-viii&rft.pub=Cercle-Social&rft.date=1795&rft_id=info%3Aoclcnum%2F490193660&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text">Ivor Grattan-Guinness. Convolutions in French Mathematics, 1800–1840. Birkhäuser 1990. Vol. I, p.108. <a rel="nofollow" class="external autonumber" href="https://books.google.com/books?id=dHe00X4MDKMC&q=%22His+voice+is+very+feeble%22&pg=PA108">[3]</a></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=41029"><i>Œuvres</i>, t.1, 671–732</a></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">Marco Panza, "The Origins of Analytic Mechanics in the 18th Century", in Hans Niels Jahnke (editor), <i>A History of Analysis</i>, 2003, p. 149</span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=29" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <p>The initial version of this article was taken from the <a href="/wiki/Public_domain" title="Public domain">public domain</a> resource <i><a href="/wiki/Rouse_History_of_Mathematics" class="mw-redirect" title="Rouse History of Mathematics">A Short Account of the History of Mathematics</a></i> (4th edition, 1908) by <a href="/wiki/W._W._Rouse_Ball" title="W. W. Rouse Ball">W. W. Rouse Ball</a>. </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaria_Teresa_BorgatoLuigi_Pepe1990" class="citation cs2 cs1-prop-foreign-lang-source">Maria Teresa Borgato; Luigi Pepe (1990), <i>Lagrange, appunti per una biografia scientifica</i> (in Italian), Torino: La Rosa</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lagrange%2C+appunti+per+una+biografia+scientifica&rft.place=Torino&rft.pub=La+Rosa&rft.date=1990&rft.au=Maria+Teresa+Borgato&rft.au=Luigi+Pepe&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></li> <li><i>Columbia Encyclopedia</i>, 6th ed., 2005, "<a rel="nofollow" class="external text" href="http://www.encyclopedia.com/html/L/Lagrange.asp">Lagrange, Joseph Louis.</a>"</li> <li><a href="/wiki/W._W._Rouse_Ball" title="W. W. Rouse Ball">W. W. Rouse Ball</a>, 1908, "<a rel="nofollow" class="external text" href="http://www.maths.tcd.ie/pub/HistMath/People/Lagrange/RouseBall/RB_Lagrange.html">Joseph Louis Lagrange (1736–1813)</a>" <i>A Short Account of the History of Mathematics</i>, 4th ed. <a rel="nofollow" class="external text" href="http://www.gutenberg.org/ebooks/31246">also on Gutenberg</a></li> <li>Chanson, Hubert, 2007, "<a rel="nofollow" class="external text" href="http://espace.library.uq.edu.au/eserv.php?pid=UQ:119883&dsID=hb07_5.pdf">Velocity Potential in Real Fluid Flows: Joseph-Louis Lagrange's Contribution</a>," <i>La Houille Blanche</i> 5: 127–31.</li> <li>Fraser, Craig G., 2005, "Théorie des fonctions analytiques" in <a href="/wiki/Ivor_Grattan-Guinness" title="Ivor Grattan-Guinness">Grattan-Guinness, I.</a>, ed., <i>Landmark Writings in Western Mathematics</i>. Elsevier: 258–76.</li> <li>Lagrange, Joseph-Louis. (1811). <i>Mécanique Analytique</i>. Courcier (reissued by <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, 2009; <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/978-1-108-00174-8" title="Special:BookSources/978-1-108-00174-8">978-1-108-00174-8</a>)</li> <li>Lagrange, J.L. (1781) "Mémoire sur la Théorie du Mouvement des Fluides"(Memoir on the Theory of Fluid Motion) in Serret, J.A., ed., 1867. <i>Oeuvres de Lagrange, Vol. 4</i>. Paris" Gauthier-Villars: 695–748.</li> <li>Pulte, Helmut, 2005, "Méchanique Analytique" in Grattan-Guinness, I., ed., <i>Landmark Writings in Western Mathematics</i>. Elsevier: 208–24.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFA._ConteC._MancinelliE._Borgi.L._Pepe2013" class="citation cs2 cs1-prop-foreign-lang-source">A. Conte; C. Mancinelli; E. Borgi.; L. Pepe, eds. (2013), <i>Lagrange. Un europeo a Torino</i> (in Italian), Torino: Hapax Editore, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-88-88000-57-2" title="Special:BookSources/978-88-88000-57-2"><bdi>978-88-88000-57-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lagrange.+Un+europeo+a+Torino&rft.place=Torino&rft.pub=Hapax+Editore&rft.date=2013&rft.isbn=978-88-88000-57-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Joseph-Louis_Lagrange&action=edit&section=30" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Joseph-Louis_Lagrange" class="extiw" title="commons:Category:Joseph-Louis Lagrange">Joseph-Louis Lagrange</a></span>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Joseph-Louis_Lagrange" class="extiw" title="q:Special:Search/Joseph-Louis Lagrange">Joseph-Louis Lagrange</a></b></i>.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Lagrange.html">"Joseph-Louis Lagrange"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Joseph-Louis+Lagrange&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FLagrange.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_Wolfgang_Weisstein" class="mw-redirect" title="Eric Wolfgang Weisstein">Weisstein, Eric Wolfgang</a> (ed.). <a rel="nofollow" class="external text" href="http://scienceworld.wolfram.com/biography/Lagrange.html">"Lagrange, Joseph (1736–1813)"</a>. <i><a href="/wiki/ScienceWorld" class="mw-redirect" title="ScienceWorld">ScienceWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ScienceWorld&rft.atitle=Lagrange%2C+Joseph+%281736%E2%80%931813%29&rft_id=http%3A%2F%2Fscienceworld.wolfram.com%2Fbiography%2FLagrange.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.daviddarling.info/encyclopedia/L/Lagrange.html">Lagrange, Joseph Louis de: The Encyclopedia of Astrobiology, Astronomy and Space Flight</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClerke1911" class="citation encyclopaedia cs1"><a href="/wiki/Agnes_Mary_Clerke" title="Agnes Mary Clerke">Clerke, Agnes Mary</a> (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Lagrange, Joseph Louis"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Lagrange,_Joseph_Louis">"Lagrange, Joseph Louis" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 16 (11th ed.). pp. 75–78.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Lagrange%2C+Joseph+Louis&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=75-78&rft.edition=11th&rft.date=1911&rft.aulast=Clerke&rft.aufirst=Agnes+Mary&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJoseph-Louis+Lagrange" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=17864">Joseph-Louis Lagrange</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060613024154/http://about-physicists.org/lagrange.html">The Founders of Classical Mechanics: Joseph Louis Lagrange</a></li> <li><a rel="nofollow" class="external text" href="https://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html">The Lagrange Points</a></li> <li><a rel="nofollow" class="external text" href="https://map.gsfc.nasa.gov/media/ContentMedia/lagrange.pdf">Derivation of Lagrange's result (not Lagrange's method)</a></li> <li>Lagrange's works (in French) <a rel="nofollow" class="external text" href="http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN308899466">Oeuvres de Lagrange, edited by Joseph Alfred Serret, Paris 1867, digitized by Göttinger Digitalisierungszentrum</a> (Mécanique analytique is in volumes 11 and 12.)</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130513140933/http://portail.mathdoc.fr/cgi-bin/oetoc?id=OE_LAGRANGE__1">Joseph Louis de Lagrange – Œuvres complètes</a> Gallica-Math</li> <li><a rel="nofollow" class="external text" href="http://www.persee.fr/web/revues/home/prescript/article/rhs_0151-4105_1974_num_27_1_1044">Inventaire chronologique de l'œuvre de Lagrange</a> Persee</li> <li><a rel="nofollow" class="external text" href="https://www.gutenberg.org/ebooks/author/38388">Works by Joseph-Louis Lagrange</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%22Lagrange%2C%20Joseph-Louis%22%20OR%20subject%3A%22Joseph-Louis%20Lagrange%22%20OR%20creator%3A%22Lagrange%2C%20Joseph-Louis%22%20OR%20creator%3A%22Joseph-Louis%20Lagrange%22%20OR%20creator%3A%22Lagrange%2C%20J%2E%22%20OR%20title%3A%22Joseph-Louis%20Lagrange%22%20OR%20description%3A%22Lagrange%2C%20Joseph-Louis%22%20OR%20description%3A%22Joseph-Louis%20Lagrange%22%29%20OR%20%28%221736-1813%22%20AND%20Lagrange%29%29%20AND%20%28-mediatype:software%29">Works by or about Joseph-Louis Lagrange</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.loc.gov/item/04007770/"><i>Mécanique analytique</i> (Paris, 1811-15)</a></li></ul> <div class="navbox-styles"><link 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.navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Joseph-Louis_Lagrange" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Joseph-Louis_Lagrange" title="Template:Joseph-Louis Lagrange"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Joseph-Louis_Lagrange" title="Template talk:Joseph-Louis Lagrange"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Joseph-Louis_Lagrange" title="Special:EditPage/Template:Joseph-Louis Lagrange"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Joseph-Louis_Lagrange" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Joseph-Louis Lagrange</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lagrange_multiplier" title="Lagrange multiplier">Lagrange multiplier</a></li> <li><a href="/wiki/Lagrange_polynomial" title="Lagrange polynomial">Lagrange polynomial</a></li> <li><a href="/wiki/Lagrange%27s_four-square_theorem" title="Lagrange's four-square theorem">Lagrange's four-square theorem</a></li> <li><a href="/wiki/Lagrange%27s_theorem_(group_theory)" title="Lagrange's theorem (group theory)">Lagrange's theorem (group theory)</a></li> <li><a href="/wiki/Lagrange%27s_identity" title="Lagrange's identity">Lagrange's identity</a></li> <li><a href="/wiki/Lagrange%27s_identity_(boundary_value_problem)" title="Lagrange's identity (boundary value problem)">Lagrange's identity (boundary value problem)</a></li> <li><a href="/wiki/Lagrange%27s_trigonometric_identities" class="mw-redirect" title="Lagrange's trigonometric identities">Lagrange's trigonometric identities</a></li> <li><a href="/wiki/Lagrange_multiplier" title="Lagrange multiplier">Lagrange multiplier</a></li> <li><a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian mechanics</a></li> <li><a href="/wiki/Mean_value_theorem" title="Mean value theorem">Lagrange's mean value theorem</a></li> <li><a href="/wiki/Lagrange_stability" title="Lagrange stability">Lagrange stability</a></li> <li><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrange point</a></li></ul> </div></td></tr></tbody></table></div> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 0}.mw-parser-output .portal-bar-related{font-size:100%;justify-content:flex-start}.mw-parser-output .portal-bar-unbordered{padding:0 1.7em;margin-left:0}.mw-parser-output .portal-bar-header{margin:0 1em 0 0.5em;flex:0 0 auto;min-height:24px}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;flex:0 1 auto;padding:0.15em 0;column-gap:1em;align-items:baseline;margin:0;list-style:none}.mw-parser-output .portal-bar-content-related{margin:0;list-style:none}.mw-parser-output .portal-bar-item{display:inline-block;margin:0.15em 0.2em;min-height:24px;line-height:24px}@media screen and (max-width:768px){.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;flex-flow:column wrap;align-items:baseline}.mw-parser-output .portal-bar-header{text-align:center;flex:0;padding-left:0.5em;margin:0 auto}.mw-parser-output .portal-bar-related{font-size:100%;align-items:flex-start}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;align-items:center;flex:0;column-gap:1em;border-top:1px solid #a2a9b1;margin:0 auto;list-style:none}.mw-parser-output .portal-bar-content-related{border-top:none;margin:0;list-style:none}}.mw-parser-output .navbox+link+.portal-bar,.mw-parser-output .navbox+style+.portal-bar,.mw-parser-output .navbox+link+.portal-bar-bordered,.mw-parser-output .navbox+style+.portal-bar-bordered,.mw-parser-output .sister-bar+link+.portal-bar,.mw-parser-output .sister-bar+style+.portal-bar,.mw-parser-output .portal-bar+.navbox-styles+.navbox,.mw-parser-output .portal-bar+.navbox-styles+.sister-bar{margin-top:-1px}</style><div class="portal-bar noprint metadata noviewer portal-bar-bordered" role="navigation" aria-label="Portals"><span class="portal-bar-header"><a href="/wiki/Wikipedia:Contents/Portals" title="Wikipedia:Contents/Portals">Portals</a>:</span><ul class="portal-bar-content"><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/19px-P_vip.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/28px-P_vip.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/37px-P_vip.svg.png 2x" data-file-width="1911" data-file-height="1944" /></span></span> </span><a href="/wiki/Portal:Biography" title="Portal:Biography">Biography</a></li><li class="portal-bar-item"><span class="nowrap"><span class="mw-image-border" typeof="mw:File"><span><img alt="flag" src="//upload.wikimedia.org/wikipedia/en/thumb/0/03/Flag_of_Italy.svg/21px-Flag_of_Italy.svg.png" decoding="async" width="21" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/0/03/Flag_of_Italy.svg/32px-Flag_of_Italy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/0/03/Flag_of_Italy.svg/42px-Flag_of_Italy.svg.png 2x" data-file-width="1500" data-file-height="1000" /></span></span> </span><a href="/wiki/Portal:Italy" title="Portal:Italy">Italy</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/19px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/29px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/38px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/19px-Crab_Nebula.jpg" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/29px-Crab_Nebula.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/38px-Crab_Nebula.jpg 2x" data-file-width="3864" data-file-height="3864" /></span></span> </span><a href="/wiki/Portal:Astronomy" title="Portal:Astronomy">Astronomy</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:He1523a.jpg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/16px-He1523a.jpg" decoding="async" width="16" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/25px-He1523a.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/33px-He1523a.jpg 2x" data-file-width="180" data-file-height="207" /></a></span> </span><a href="/wiki/Portal:Stars" title="Portal:Stars">Stars</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/19px-RocketSunIcon.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/29px-RocketSunIcon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/38px-RocketSunIcon.svg.png 2x" data-file-width="128" data-file-height="128" /></span></span> </span><a href="/wiki/Portal:Spaceflight" title="Portal:Spaceflight">Spaceflight</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/21px-Earth-moon.jpg" decoding="async" width="21" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/32px-Earth-moon.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/42px-Earth-moon.jpg 2x" data-file-width="3000" data-file-height="2400" /></span></span> </span><a href="/wiki/Portal:Outer_space" title="Portal:Outer space">Outer space</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Solar_system.jpg/15px-Solar_system.jpg" decoding="async" width="15" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Solar_system.jpg/23px-Solar_system.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Solar_system.jpg/30px-Solar_system.jpg 2x" data-file-width="4500" data-file-height="5600" /></span></span> </span><a href="/wiki/Portal:Solar_System" title="Portal:Solar System">Solar System</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_kalzium.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/19px-Nuvola_apps_kalzium.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/29px-Nuvola_apps_kalzium.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/38px-Nuvola_apps_kalzium.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Science" title="Portal:Science">Science</a></li></ul></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q80222#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q80222#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q80222#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, 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href="http://id.worldcat.org/fast/165884/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJrKT6pjK86ghGdDcRJMT3">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/118568698">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n86803071">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12125247f">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb12125247f">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00518414">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Lagrange, Joseph Louis"><a rel="nofollow" class="external text" href="https://opac.sbn.it/nome/CFIV092910">Italy</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35856215">Australia</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35730577">2</a></span></li></ul></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=nlk20010100967&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX1335885">Spain</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX1675297">2</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX1511034">3</a></span></li></ul></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.bnportugal.gov.pt/aut/catbnp/1644906">Portugal</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p069356157">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/99064156">Norway</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90271571">2</a></span></li></ul></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://katalog.nsk.hr/F/?func=direct&doc_number=000506618&local_base=nsk10">Croatia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://www.bncatalogo.cl/F?func=direct&local_base=red10&doc_number=000174679">Chile</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.nlg.gr/cgi-bin/koha/opac-authoritiesdetail.pl?authid=139580">Greece</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/vs68b59d4g2mdf4">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810539600105606">Poland</a></span></li><li><span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8034&url_prefix=https://opac.vatlib.it/auth/detail/&id=495/137017">Vatican</a></span><ul><li><span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8034&url_prefix=https://opac.vatlib.it/auth/detail/&id=495/369117">2</a></span></li><li><span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8034&url_prefix=https://opac.vatlib.it/auth/detail/&id=495/128327">3</a></span></li></ul></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007264013905171">Israel</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058515628106706">Catalonia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://opac.kbr.be/LIBRARY/doc/AUTHORITY/14444198">Belgium</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA01352513?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=17864">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:lagrange.joseph-louis">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/109270">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/1061634">Trove</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/1117882">2</a></span></li></ul></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="LAGRANGE, Giuseppe Luigi"><a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/giuseppe-luigi-lagrange_(Dizionario-Biografico)">Italian People</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd118568698.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/118568698">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/029680271">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6gh9nsx">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Joseph-Louis_Lagrange&oldid=1259095801">https://en.wikipedia.org/w/index.php?title=Joseph-Louis_Lagrange&oldid=1259095801</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Lagrangian_mechanics" title="Category:Lagrangian mechanics">Lagrangian mechanics</a></li><li><a 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