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class="vector-toc-list"> <li id="toc-Youth_and_education" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Youth_and_education"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Youth and education</span> </div> </a> <ul id="toc-Youth_and_education-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Engineering_days" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Engineering_days"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Engineering days</span> </div> </a> <ul id="toc-Engineering_days-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Professor_at_École_Polytechnique" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Professor_at_École_Polytechnique"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Professor at École Polytechnique</span> </div> </a> <ul id="toc-Professor_at_École_Polytechnique-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_exile" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_exile"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>In exile</span> </div> </a> <ul id="toc-In_exile-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Last_years" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Last_years"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Last years</span> </div> </a> <ul id="toc-Last_years-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Work" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Work"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Work</span> </div> </a> <button aria-controls="toc-Work-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 subsection</span> </button> <ul id="toc-Work-sublist" class="vector-toc-list"> <li id="toc-Early_work" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Early_work"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Early work</span> </div> </a> <ul id="toc-Early_work-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wave_theory,_mechanics,_elasticity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Wave_theory,_mechanics,_elasticity"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Wave theory, mechanics, elasticity</span> </div> </a> <ul id="toc-Wave_theory,_mechanics,_elasticity-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">2.3</span> <span>Number theory</span> </div> </a> <ul id="toc-Number_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complex_functions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complex_functions"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Complex functions</span> </div> </a> <ul id="toc-Complex_functions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cours_d'Analyse" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cours_d'Analyse"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Cours d'Analyse</span> </div> </a> <ul id="toc-Cours_d'Analyse-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Taylor's_theorem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Taylor's_theorem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Taylor's theorem</span> </div> </a> <ul id="toc-Taylor's_theorem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Argument_principle,_stability" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Argument_principle,_stability"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Argument principle, stability</span> </div> </a> <ul id="toc-Argument_principle,_stability-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Published_works" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Published_works"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Published works</span> </div> </a> <ul id="toc-Published_works-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Politics_and_religious_beliefs" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Politics_and_religious_beliefs"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Politics and religious beliefs</span> </div> </a> <ul id="toc-Politics_and_religious_beliefs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</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-Notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</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">6.3</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</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" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><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">Augustin-Louis Cauchy</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 75 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-75" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">75 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Afrikaans" lang="af" hreflang="af" data-title="Augustin Louis Cauchy" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A3%D9%88%D8%BA%D8%B3%D8%AA%D8%A7%D9%86_%D9%84%D9%88%D9%8A_%D9%83%D9%88%D8%B4%D9%8A" title="أوغستان لوي كوشي – Arabic" lang="ar" hreflang="ar" data-title="أوغستان لوي كوشي" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Asturian" lang="ast" hreflang="ast" data-title="Augustin Louis Cauchy" 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/Og%C3%BCsten_Lui_Ko%C5%9Fi" title="Ogüsten Lui Koşi – Azerbaijani" lang="az" hreflang="az" data-title="Ogüsten Lui Koşi" 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/%D8%A2%D9%82%D9%88%D8%B3%D8%AA%DB%8C%D9%86_%D9%84%D9%88%DB%8C%DB%8C_%DA%A9%D9%88%D8%B4%DB%8C" title="آقوستین لویی کوشی – South Azerbaijani" lang="azb" hreflang="azb" data-title="آقوستین لویی کوشی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%93%E0%A6%97%E0%A7%8D%E0%A6%AF%E0%A7%81%E0%A6%B8%E0%A7%8D%E0%A6%A4%E0%A6%BE%E0%A6%81-%E0%A6%B2%E0%A7%81%E0%A6%87_%E0%A6%95%E0%A7%8B%E0%A6%B6%E0%A6%BF" title="ওগ্যুস্তাঁ-লুই কোশি – Bangla" lang="bn" hreflang="bn" data-title="ওগ্যুস্তাঁ-লুই কোশি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%B3%D1%8E%D1%81%D1%82%D1%8D%D0%BD_%D0%9B%D1%83%D1%96_%D0%9A%D0%B0%D1%88%D1%8B" title="Агюстэн Луі Кашы – Belarusian" lang="be" hreflang="be" data-title="Агюстэн Луі Кашы" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D0%B3%D1%8E%D1%81%D1%82%D1%8D%D0%BD-%D0%9B%D1%8E%D1%96_%D0%9A%D0%B0%D1%88%D1%8B" title="Агюстэн-Люі Кашы – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Агюстэн-Люі Кашы" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D0%B3%D1%8E%D1%81%D1%82%D0%B5%D0%BD_%D0%9B%D1%83%D0%B8_%D0%9A%D0%BE%D1%88%D0%B8" title="Огюстен Луи Коши – Bulgarian" lang="bg" hreflang="bg" data-title="Огюстен Луи Коши" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Bosnian" lang="bs" hreflang="bs" data-title="Augustin Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Catalan" lang="ca" hreflang="ca" data-title="Augustin Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Czech" lang="cs" hreflang="cs" data-title="Augustin Louis Cauchy" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Danish" lang="da" hreflang="da" data-title="Augustin Louis Cauchy" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://de.wikipedia.org/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – German" lang="de" hreflang="de" data-title="Augustin-Louis Cauchy" 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/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Estonian" lang="et" hreflang="et" data-title="Augustin-Louis Cauchy" 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%A9%CE%B3%CE%BA%CF%85%CF%83%CF%84%CE%AD%CE%BD-%CE%9B%CE%BF%CF%85%CE%AF_%CE%9A%CF%89%CF%83%CF%8D" title="Ωγκυστέν-Λουί Κωσύ – Greek" lang="el" hreflang="el" data-title="Ωγκυστέν-Λουί Κωσύ" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Spanish" lang="es" hreflang="es" data-title="Augustin Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Esperanto" lang="eo" hreflang="eo" data-title="Augustin Louis Cauchy" 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/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Basque" lang="eu" hreflang="eu" data-title="Augustin-Louis Cauchy" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%DA%AF%D9%88%D8%B3%D8%AA%DB%8C%D9%86_%D9%84%D9%88%DB%8C%DB%8C_%DA%A9%D9%88%D8%B4%DB%8C" title="آگوستین لویی کوشی – Persian" lang="fa" hreflang="fa" data-title="آگوستین لویی کوشی" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – French" lang="fr" hreflang="fr" data-title="Augustin Louis Cauchy" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Galician" lang="gl" hreflang="gl" data-title="Augustin Louis Cauchy" 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%98%A4%EA%B7%80%EC%8A%A4%ED%83%B1_%EB%A3%A8%EC%9D%B4_%EC%BD%94%EC%8B%9C" title="오귀스탱 루이 코시 – Korean" lang="ko" hreflang="ko" data-title="오귀스탱 루이 코시" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%95%D5%A3%D5%B5%D5%B8%D6%82%D5%BD%D5%BF%D5%A5%D5%B6_%D4%BC%D5%B8%D6%82%D5%AB_%D4%BF%D5%B8%D5%B7%D5%AB" title="Օգյուստեն Լուի Կոշի – Armenian" lang="hy" hreflang="hy" data-title="Օգյուստեն Լուի Կոշի" 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%91%E0%A4%97%E0%A4%B8%E0%A5%8D%E0%A4%9F%E0%A4%BF%E0%A4%A8_%E0%A4%B2%E0%A5%81%E0%A4%88_%E0%A4%95%E0%A5%8C%E0%A4%B6%E0%A5%80" title="ऑगस्टिन लुई कौशी – Hindi" lang="hi" hreflang="hi" data-title="ऑगस्टिन लुई कौशी" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Croatian" lang="hr" hreflang="hr" data-title="Augustin Louis Cauchy" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Indonesian" lang="id" hreflang="id" data-title="Augustin Louis Cauchy" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Interlingua" lang="ia" hreflang="ia" data-title="Augustin-Louis Cauchy" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Icelandic" lang="is" hreflang="is" data-title="Augustin Louis Cauchy" 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/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Italian" lang="it" hreflang="it" data-title="Augustin-Louis Cauchy" 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%90%D7%95%D7%92%D7%95%D7%A1%D7%98%D7%9F_%D7%9C%D7%95%D7%90%D7%99_%D7%A7%D7%95%D7%A9%D7%99" title="אוגוסטן לואי קושי – Hebrew" lang="he" hreflang="he" data-title="אוגוסטן לואי קושי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%86%E0%B2%97%E0%B2%B8%E0%B3%8D%E0%B2%9F%E0%B2%BF%E0%B2%A8%E0%B3%8D-%E0%B2%B2%E0%B3%82%E0%B2%AF%E0%B2%BF_%E0%B2%95%E0%B3%8C%E0%B2%9A%E0%B2%BF" title="ಆಗಸ್ಟಿನ್-ಲೂಯಿ ಕೌಚಿ – Kannada" lang="kn" hreflang="kn" data-title="ಆಗಸ್ಟಿನ್-ಲೂಯಿ ಕೌಚಿ" 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%9D%E1%83%92%E1%83%98%E1%83%A3%E1%83%A1%E1%83%A2%E1%83%94%E1%83%9C_%E1%83%9A%E1%83%A3%E1%83%98_%E1%83%99%E1%83%9D%E1%83%A8%E1%83%98" title="ოგიუსტენ ლუი კოში – Georgian" lang="ka" hreflang="ka" data-title="ოგიუსტენ ლუი კოში" 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%9E%D0%B3%D1%8E%D1%81%D1%82%D0%B5%D0%BD_%D0%9B%D1%83%D0%B8_%D0%9A%D0%BE%D1%88%D0%B8" title="Огюстен Луи Коши – Kazakh" lang="kk" hreflang="kk" data-title="Огюстен Луи Коши" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Haitian Creole" lang="ht" hreflang="ht" data-title="Augustin Louis Cauchy" 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-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Augustinus_Ludovicus_Cauchy" title="Augustinus Ludovicus Cauchy – Latin" lang="la" hreflang="la" data-title="Augustinus Ludovicus Cauchy" 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/Ogist%C4%93ns_Ko%C5%A1%C4%AB" title="Ogistēns Košī – Latvian" lang="lv" hreflang="lv" data-title="Ogistēns Košī" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Lithuanian" lang="lt" hreflang="lt" data-title="Augustin-Louis Cauchy" 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/Augustin_Cauchy" title="Augustin Cauchy – Hungarian" lang="hu" hreflang="hu" data-title="Augustin Cauchy" 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%9E%D0%B3%D0%B8%D1%81%D1%82%D0%B5%D0%BD_%D0%9B%D1%83%D1%98_%D0%9A%D0%BE%D1%88%D0%B8" title="Огистен Луј Коши – Macedonian" lang="mk" hreflang="mk" data-title="Огистен Луј Коши" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Malagasy" lang="mg" hreflang="mg" data-title="Augustin Louis Cauchy" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%93%E0%A4%97%E0%A5%81%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A4%81_%E0%A4%B2%E0%A5%81%E0%A4%88_%E0%A4%95%E0%A5%89%E0%A4%B6%E0%A5%80" title="ओगुस्तँ लुई कॉशी – Marathi" lang="mr" hreflang="mr" data-title="ओगुस्तँ लुई कॉशी" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%88%D8%AC%D8%B3%D8%AA%D9%8A%D9%86_%D9%84%D9%88%D9%89_%D9%83%D9%88%D8%B4%D9%89" title="اوجستين لوى كوشى – Egyptian Arabic" lang="arz" hreflang="arz" data-title="اوجستين لوى كوشى" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Dutch" lang="nl" hreflang="nl" data-title="Augustin Louis Cauchy" 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%AA%E3%83%BC%E3%82%AE%E3%83%A5%E3%82%B9%E3%82%BF%E3%83%B3%EF%BC%9D%E3%83%AB%E3%82%A4%E3%83%BB%E3%82%B3%E3%83%BC%E3%82%B7%E3%83%BC" title="オーギュスタン＝ルイ・コーシー – Japanese" lang="ja" hreflang="ja" data-title="オーギュスタン＝ルイ・コーシー" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Augustin Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Augustin Louis Cauchy" 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-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Occitan" lang="oc" hreflang="oc" data-title="Augustin Louis Cauchy" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Uzbek" lang="uz" hreflang="uz" data-title="Augustin-Louis Cauchy" 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/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Piedmontese" lang="pms" hreflang="pms" data-title="Augustin-Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Polish" lang="pl" hreflang="pl" data-title="Augustin Louis Cauchy" 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/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Portuguese" lang="pt" hreflang="pt" data-title="Augustin-Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Romanian" lang="ro" hreflang="ro" data-title="Augustin Louis Cauchy" 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%9A%D0%BE%D1%88%D0%B8,_%D0%9E%D0%B3%D1%8E%D1%81%D1%82%D0%B5%D0%BD_%D0%9B%D1%83%D0%B8" title="Коши, Огюстен Луи – Russian" lang="ru" hreflang="ru" data-title="Коши, Огюстен 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%95%E0%A5%8B%E0%A4%B7%E0%A4%BF_%E0%A4%85%E0%A4%97%E0%A4%B8%E0%A5%8D%E0%A4%9F%E0%A5%80%E0%A4%A8%E0%A5%8D_%E0%A4%B2%E0%A5%82%E0%A4%AF%E0%A5%80" title="कोषि अगस्टीन् लूयी – Sanskrit" lang="sa" hreflang="sa" data-title="कोषि अगस्टीन् लूयी" 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/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Scots" lang="sco" hreflang="sco" data-title="Augustin-Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Albanian" lang="sq" hreflang="sq" data-title="Augustin Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Sicilian" lang="scn" hreflang="scn" data-title="Augustin Louis Cauchy" 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/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Sinhala" lang="si" hreflang="si" data-title="Augustin-Louis Cauchy" 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/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Augustin-Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Slovak" lang="sk" hreflang="sk" data-title="Augustin Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Slovenian" lang="sl" hreflang="sl" data-title="Augustin Louis Cauchy" 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/%D8%A6%DB%86%DA%AF%D9%88%D8%B3%D8%AA%DB%8C%D9%86-%D9%84%D9%88%DB%8C_%DA%A9%DB%86%D8%B4%DB%8C" title="ئۆگوستین-لوی کۆشی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ئۆگوستین-لوی کۆشی" 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%9E%D0%B3%D0%B8%D1%81%D1%82%D0%B5%D0%BD_%D0%9B%D1%83%D1%98_%D0%9A%D0%BE%D1%88%D0%B8" title="Огистен Луј Коши – Serbian" lang="sr" hreflang="sr" data-title="Огистен Луј Коши" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Augustin Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Finnish" lang="fi" hreflang="fi" data-title="Augustin Louis Cauchy" 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/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Swedish" lang="sv" hreflang="sv" data-title="Augustin Louis Cauchy" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%95%E0%AF%81%E0%AE%B8%E0%AF%8D%E0%AE%9F%E0%AE%BF%E0%AE%A9%E0%AF%8D-%E0%AE%B2%E0%AF%82%E0%AE%AF%E0%AE%BF_%E0%AE%95%E0%AF%8B%E0%AE%9A%E0%AE%BF" title="அகுஸ்டின்-லூயி கோசி – Tamil" lang="ta" hreflang="ta" data-title="அகுஸ்டின்-லூயி கோசி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Ugu%E1%B9%A3tin-Luwis_Kucy" title="Uguṣtin-Luwis Kucy – Tachelhit" lang="shi" hreflang="shi" data-title="Uguṣtin-Luwis Kucy" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Augustin_Louis_Cauchy" title="Augustin Louis Cauchy – Turkish" lang="tr" hreflang="tr" data-title="Augustin Louis Cauchy" 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%9E%D0%B3%D1%8E%D1%81%D1%82%D0%B5%D0%BD-%D0%9B%D1%83%D1%97_%D0%9A%D0%BE%D1%88%D1%96" title="Огюстен-Луї Коші – Ukrainian" lang="uk" hreflang="uk" data-title="Огюстен-Луї Коші" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy – Vietnamese" lang="vi" hreflang="vi" data-title="Augustin-Louis Cauchy" 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-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%A5%A5%E5%8F%A4%E6%96%AF%E4%B8%81%C2%B7%E8%B7%AF%E6%98%93%C2%B7%E6%9F%AF%E8%A5%BF" title="奥古斯丁·路易·柯西 – Wu" lang="wuu" hreflang="wuu" data-title="奥古斯丁·路易·柯西" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%A5%A7%E5%8F%A4%E6%96%AF%E4%B8%81-%E8%B7%AF%E6%98%93%C2%B7%E6%9F%AF%E8%A5%BF" title="奧古斯丁-路易·柯西 – Cantonese" lang="yue" hreflang="yue" data-title="奧古斯丁-路易·柯西" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A5%A7%E5%8F%A4%E6%96%AF%E4%B8%81-%E8%B7%AF%E6%98%93%C2%B7%E6%9F%AF%E8%A5%BF" title="奧古斯丁-路易·柯西 – Chinese" lang="zh" hreflang="zh" data-title="奧古斯丁-路易·柯西" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Cauchy&redirect=no" class="mw-redirect" title="Cauchy">Cauchy</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">French mathematician (1789–1857)</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">"Cauchy" redirects here. For other uses, see <a href="/wiki/Cauchy_(disambiguation)" class="mw-disambig" title="Cauchy (disambiguation)">Cauchy (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Augustin-Louis Cauchy</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Augustin-Louis_Cauchy_1901.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Augustin-Louis_Cauchy_1901.jpg/220px-Augustin-Louis_Cauchy_1901.jpg" decoding="async" width="220" height="305" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/d/d3/Augustin-Louis_Cauchy_1901.jpg 1.5x" data-file-width="280" data-file-height="388" /></a></span><div class="infobox-caption">Cauchy around 1840. Lithography by Zéphirin Belliard after a painting by Jean Roller.</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1789-08-21</span>)</span>21 August 1789<br /><div style="display:inline" class="birthplace"><a href="/wiki/Paris" title="Paris">Paris</a>, <a href="/wiki/Kingdom_of_France" title="Kingdom of France">France</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">23 May 1857<span style="display:none">(1857-05-23)</span> (aged 67)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Sceaux,_Hauts-de-Seine" title="Sceaux, Hauts-de-Seine">Sceaux</a>, <a href="/wiki/Second_French_Empire" title="Second French Empire">France</a></div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><a href="/wiki/France" title="France">French</a></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/%C3%89cole_Nationale_des_Ponts_et_Chauss%C3%A9es" class="mw-redirect" title="École Nationale des Ponts et Chaussées">École Nationale des Ponts et Chaussées</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Civil_engineering" title="Civil engineering">Civil engineering</a> <br /><a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Mathematical analysis</a><br /><a href="/wiki/Gradient_descent" title="Gradient descent">Gradient descent</a><br /><a href="/wiki/Implicit_function_theorem" title="Implicit function theorem">Implicit function theorem</a><br /><a href="/wiki/Intermediate_value_theorem" title="Intermediate value theorem">Intermediate value theorem</a><br /><a href="/wiki/Spectral_theorem" title="Spectral theorem">Spectral theorem</a><br /><a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">Limit (mathematics)</a><br /><a href="/wiki/List_of_topics_named_after_Augustin-Louis_Cauchy" class="mw-redirect" title="List of topics named after Augustin-Louis Cauchy">See full list</a></td></tr><tr><th scope="row" class="infobox-label">Spouse</th><td class="infobox-data">Aloise de Bure</td></tr><tr><th scope="row" class="infobox-label">Children</th><td class="infobox-data">Marie Françoise Alicia, Marie Mathilde</td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data">Grand Prize of L'Académie Royale des Sciences</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"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a>, <a href="/wiki/Physics" title="Physics">physics</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/%C3%89cole_Centrale_du_Panth%C3%A9on" class="mw-redirect" title="École Centrale du Panthéon">École Centrale du Panthéon</a> <br /><a href="/wiki/%C3%89cole_Nationale_des_Ponts_et_Chauss%C3%A9es" class="mw-redirect" title="École Nationale des Ponts et Chaussées">École Nationale des Ponts et Chaussées</a> <br /> <a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><a href="/wiki/Francesco_Fa%C3%A0_di_Bruno" title="Francesco Faà di Bruno">Francesco Faà di Bruno</a><br /><a href="/wiki/Viktor_Bunyakovsky" title="Viktor Bunyakovsky">Viktor Bunyakovsky</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><a href="/wiki/Baron" title="Baron">Baron</a> <b>Augustin-Louis Cauchy</b> <span class="nobold noexcerpt nowraplinks" style="font-size:;"><span style="font-size: 85%;"><a href="/wiki/Fellow_of_the_Royal_Society" title="Fellow of the Royal Society">FRS</a></span> <span style="font-size: 85%;"><a href="/wiki/Fellow_of_the_Royal_Society_of_Edinburgh" class="mw-redirect" title="Fellow of the Royal Society of Edinburgh">FRSE</a></span></span> (<span class="rt-commentedText nowrap"><style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style><span class="IPA-label IPA-label-small"><a href="/wiki/British_English" title="British English">UK</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="/ˈ/: primary stress follows">ˈ</span><span title="'k' in 'kind'">k</span><span title="/oʊ/: 'o' in 'code'">oʊ</span><span title="/ʃ/: 'sh' in 'shy'">ʃ</span><span title="/i/: 'y' in 'happy'">i</span></span>/</a></span></span> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key"><i title="English pronunciation respelling"><span style="font-size:90%">KOH</span>-shee</i></a>, <span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'k' in 'kind'">k</span><span title="/aʊ/: 'ou' in 'mouth'">aʊ</span><span title="/ʃ/: 'sh' in 'shy'">ʃ</span><span title="/i/: 'y' in 'happy'">i</span></span><span class="wrap"> </span>/</a></span></span> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key"><i title="English pronunciation respelling"><span style="font-size:90%">KOW</span>-shee</i></a>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-collins_2-0" class="reference"><a href="#cite_note-collins-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <span class="nowrap"><span class="rt-commentedText nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1177148991" /><span class="IPA-label IPA-label-small"><a 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="'k' in 'kind'">k</span><span title="/oʊ/: 'o' in 'code'">oʊ</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="/ʃ/: 'sh' in 'shy'">ʃ</span><span title="/iː/: 'ee' in 'fleece'">iː</span></span><span class="wrap"> </span>/</a></span></span></span> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key"><i title="English pronunciation respelling">koh-<span style="font-size:90%">SHEE</span></i></a>;<sup id="cite_ref-collins_2-1" class="reference"><a href="#cite_note-collins-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> <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">[oɡystɛ̃<span class="wrap"> </span>lwi<span class="wrap"> </span>koʃi]</a></span>; 21 August 1789 – 23 May 1857) was a French <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, engineer, and <a href="/wiki/Physicist" title="Physicist">physicist</a>. He was one of the first to rigorously state and prove the key theorems of <a href="/wiki/Calculus" title="Calculus">calculus</a> (thereby creating <a href="/wiki/Real_analysis" title="Real analysis">real analysis</a>), pioneered the field <a href="/wiki/Complex_analysis" title="Complex analysis">complex analysis</a>, and the study of <a href="/wiki/Permutation_group" title="Permutation group">permutation groups</a> in <a href="/wiki/Abstract_algebra" title="Abstract algebra">abstract algebra</a>. Cauchy also contributed to a number of topics in mathematical physics, notably <a href="/wiki/Continuum_mechanics" title="Continuum mechanics">continuum mechanics</a>. </p><p>A profound mathematician, Cauchy had a great influence over his contemporaries and successors;<sup id="cite_ref-FOOTNOTEChisholm1911_4-0" class="reference"><a href="#cite_note-FOOTNOTEChisholm1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Hans_Freudenthal" title="Hans Freudenthal">Hans Freudenthal</a> stated: </p> <dl><dd>"More concepts and theorems have been named for Cauchy than for any other mathematician (in <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elasticity</a> alone there are sixteen concepts and theorems named for Cauchy)."<sup id="cite_ref-FOOTNOTEFreudenthal2008_5-0" class="reference"><a href="#cite_note-FOOTNOTEFreudenthal2008-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Cauchy was a prolific worker; he wrote approximately eight hundred research articles and five complete textbooks on a variety of topics in the fields of mathematics and <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a>. </p> <meta property="mw:PageProp/toc" /> <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=Augustin-Louis_Cauchy&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Youth_and_education">Youth and education</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=2" title="Edit section: Youth and education"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cauchy was the son of <a href="/wiki/Louis_Fran%C3%A7ois_Cauchy" title="Louis François Cauchy">Louis François Cauchy</a> (1760–1848) and Marie-Madeleine Desestre. Cauchy had two brothers: Alexandre Laurent Cauchy (1792–1857), who became a president of a division of the court of appeal in 1847 and a judge of the court of cassation in 1849, and Eugene François Cauchy (1802–1877), a publicist who also wrote several mathematical works. From his childhood he was good at math. </p><p>Cauchy married Aloise de Bure in 1818. She was a close relative of the publisher who published most of Cauchy's works. They had two daughters, Marie Françoise Alicia (1819) and Marie Mathilde (1823). </p><p>Cauchy's father was a highly ranked official in the Parisian police of the <a href="/wiki/Ancien_R%C3%A9gime" class="mw-redirect" title="Ancien Régime">Ancien Régime</a>, but lost this position due to the <a href="/wiki/French_Revolution" title="French Revolution">French Revolution</a> (14 July 1789), which broke out one month before Augustin-Louis was born.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> The Cauchy family survived the revolution and the following <a href="/wiki/Reign_of_Terror" title="Reign of Terror">Reign of Terror</a> during 1793–94 by escaping to <a href="/wiki/Arcueil" title="Arcueil">Arcueil</a>, where Cauchy received his first education, from his father.<sup id="cite_ref-FOOTNOTEBrunoBaker200366_7-0" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200366-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> After the execution of <a href="/wiki/Robespierre" class="mw-redirect" title="Robespierre">Robespierre</a> in 1794, it was safe for the family to return to Paris. There, Louis-François Cauchy found a bureaucratic job in 1800,<sup id="cite_ref-FOOTNOTEBrunoBaker200365–66_8-0" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200365–66-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> and quickly advanced his career. When <a href="/wiki/Napoleon" title="Napoleon">Napoleon</a> came to power in 1799, Louis-François Cauchy was further promoted, and became Secretary-General of the Senate, working directly under <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Laplace</a> (who is now better known for his work on mathematical physics). The mathematician <a href="/wiki/Joseph_Louis_Lagrange" class="mw-redirect" title="Joseph Louis Lagrange">Lagrange</a> was also a friend of the Cauchy family.<sup id="cite_ref-FOOTNOTEChisholm1911_4-1" class="reference"><a href="#cite_note-FOOTNOTEChisholm1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>On Lagrange's advice, Augustin-Louis was enrolled in the <a href="/wiki/%C3%89cole_Centrale_du_Panth%C3%A9on" class="mw-redirect" title="École Centrale du Panthéon">École Centrale du Panthéon</a>, the best secondary school of Paris at that time, in the fall of 1802.<sup id="cite_ref-FOOTNOTEBrunoBaker200366_7-1" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200366-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Most of the curriculum consisted of classical languages; the ambitious Cauchy, being a brilliant student, won many prizes in Latin and the humanities. In spite of these successes, Cauchy chose an engineering career, and prepared himself for the entrance examination to the <a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a>. </p><p>In 1805, he placed second of 293 applicants on this exam and was admitted.<sup id="cite_ref-FOOTNOTEBrunoBaker200366_7-2" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200366-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> One of the main purposes of this school was to give future civil and military engineers a high-level scientific and mathematical education. The school functioned under military discipline, which caused Cauchy some problems in adapting. Nevertheless, he completed the course in 1807, at age 18, and went on to the <a href="/wiki/%C3%89cole_des_Ponts_et_Chauss%C3%A9es" class="mw-redirect" title="École des Ponts et Chaussées">École des Ponts et Chaussées</a> (School for Bridges and Roads). He graduated in civil engineering, with the highest honors. </p> <div class="mw-heading mw-heading3"><h3 id="Engineering_days">Engineering days</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=3" title="Edit section: Engineering days"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>After finishing school in 1810, Cauchy accepted a job as a junior engineer in Cherbourg, where Napoleon intended to build a naval base. Here Cauchy stayed for three years, and was assigned the <a href="/wiki/Canal_de_l%27Ourcq" class="mw-redirect" title="Canal de l'Ourcq">Ourcq Canal</a> project and the <a href="/wiki/Pont_de_Saint-Cloud" title="Pont de Saint-Cloud">Saint-Cloud Bridge</a> project, and worked at the Harbor of Cherbourg.<sup id="cite_ref-FOOTNOTEBrunoBaker200366_7-3" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200366-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Although he had an extremely busy managerial job, he still found time to prepare three mathematical manuscripts, which he submitted to the <i>Première Classe</i> (First Class) of the <a href="/wiki/Institut_de_France" title="Institut de France">Institut de France</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> Cauchy's first two manuscripts (on <a href="/wiki/Regular_polyhedron" title="Regular polyhedron">polyhedra</a>) were accepted; the third one (on directrices of <a href="/wiki/Conic_sections" class="mw-redirect" title="Conic sections">conic sections</a>) was rejected. </p><p>In September 1812, at 23 years old, Cauchy returned to Paris after becoming ill from overwork.<sup id="cite_ref-FOOTNOTEBrunoBaker200366_7-4" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200366-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Another reason for his return to the capital was that he was losing interest in his engineering job, being more and more attracted to the abstract beauty of mathematics; in Paris, he would have a much better chance to find a mathematics related position. When his health improved in 1813, Cauchy chose not to return to Cherbourg.<sup id="cite_ref-FOOTNOTEBrunoBaker200366_7-5" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200366-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Although he formally kept his engineering position, he was transferred from the payroll of the Ministry of the Marine to the Ministry of the Interior. The next three years Cauchy was mainly on unpaid sick leave; he spent his time fruitfully, working on mathematics (on the related topics of <a href="/wiki/Symmetric_functions" class="mw-redirect" title="Symmetric functions">symmetric functions</a>, the <a href="/wiki/Symmetric_group" title="Symmetric group">symmetric group</a> and the theory of higher-order algebraic equations). He attempted admission to the First Class of the Institut de France but failed on three different occasions between 1813 and 1815. In 1815 Napoleon was defeated at Waterloo, and the newly installed king <a href="/wiki/Louis_XVIII" title="Louis XVIII">Louis XVIII</a> took the restoration in hand. The <a href="/wiki/Acad%C3%A9mie_des_Sciences" class="mw-redirect" title="Académie des Sciences">Académie des Sciences</a> was re-established in March 1816; <a href="/wiki/Lazare_Carnot" title="Lazare Carnot">Lazare Carnot</a> and <a href="/wiki/Gaspard_Monge" title="Gaspard Monge">Gaspard Monge</a> were removed from this academy for political reasons, and the king appointed Cauchy to take the place of one of them. The reaction of Cauchy's peers was harsh; they considered the acceptance of his membership in the academy an outrage, and Cauchy created many enemies in scientific circles. </p> <div class="mw-heading mw-heading3"><h3 id="Professor_at_École_Polytechnique"><span id="Professor_at_.C3.89cole_Polytechnique"></span>Professor at École Polytechnique</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=4" title="Edit section: Professor at École Polytechnique"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In November 1815, <a href="/wiki/Louis_Poinsot" title="Louis Poinsot">Louis Poinsot</a>, who was an associate professor at the École Polytechnique, asked to be exempted from his teaching duties for health reasons. Cauchy was by then a rising mathematical star. One of his great successes at that time was the proof of <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Fermat</a>'s <a href="/wiki/Polygonal_number_theorem" class="mw-redirect" title="Polygonal number theorem">polygonal number theorem</a>. He quit his engineering job, and received a one-year contract for teaching mathematics to second-year students of the École Polytechnique. In 1816, this Bonapartist, non-religious school was reorganized, and several liberal professors were fired; Cauchy was promoted to full professor. </p><p>When Cauchy was 28 years old, he was still living with his parents. His father found it time for his son to marry; he found him a suitable bride, Aloïse de Bure, five years his junior. The de Bure family were printers and booksellers, and published most of Cauchy's works.<sup id="cite_ref-FOOTNOTEBradleySandifer20109_10-0" class="reference"><a href="#cite_note-FOOTNOTEBradleySandifer20109-10"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Aloïse and Augustin were married on April 4, 1818, with great Roman Catholic ceremony, in the Church of Saint-Sulpice. In 1819 the couple's first daughter, Marie Françoise Alicia, was born, and in 1823 the second and last daughter, Marie Mathilde.<sup id="cite_ref-FOOTNOTEBelhoste1991134_11-0" class="reference"><a href="#cite_note-FOOTNOTEBelhoste1991134-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>The conservative political climate that lasted until 1830 suited Cauchy perfectly. In 1824 Louis XVIII died, and was succeeded by his even more conservative brother <a href="/wiki/Charles_X_of_France" title="Charles X of France">Charles X</a>. During these years Cauchy was highly productive, and published one important mathematical treatise after another. He received cross-appointments at the <a href="/wiki/Coll%C3%A8ge_de_France" title="Collège de France">Collège de France</a>, and the <a href="/w/index.php?title=Facult%C3%A9_des_sciences_de_Paris&action=edit&redlink=1" class="new" title="Faculté des sciences de Paris (page does not exist)">Faculté des sciences de Paris</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://fr.wikipedia.org/wiki/Facult%C3%A9_des_sciences_de_Paris" class="extiw" title="fr:Faculté des sciences de Paris">fr</a>]</span>. </p> <div class="mw-heading mw-heading3"><h3 id="In_exile">In exile</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=5" title="Edit section: In exile"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In July 1830, the <a href="/wiki/July_Revolution" title="July Revolution">July Revolution</a> occurred in France. Charles X fled the country, and was succeeded by <a href="/wiki/Louis-Philippe" class="mw-redirect" title="Louis-Philippe">Louis-Philippe</a>. Riots, in which uniformed students of the École Polytechnique took an active part, raged close to Cauchy's home in Paris. </p><p>These events marked a turning point in Cauchy's life, and a break in his mathematical productivity. Shaken by the fall of the government and moved by a deep hatred of the liberals who were taking power, Cauchy left France to go abroad, leaving his family behind.<sup id="cite_ref-FOOTNOTEBrunoBaker200367_12-0" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200367-12"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> He spent a short time at <a href="/wiki/Fribourg" title="Fribourg">Fribourg</a> in Switzerland, where he had to decide whether he would swear a required oath of allegiance to the new regime. He refused to do this, and consequently lost all his positions in Paris, except his membership of the academy, for which an oath was not required. In 1831 Cauchy went to the Italian city of <a href="/wiki/Turin" title="Turin">Turin</a>, and after some time there, he accepted an offer from the <a href="/wiki/King_of_Sardinia" class="mw-redirect" title="King of Sardinia">King of Sardinia</a> (who ruled Turin and the surrounding Piedmont region) for a chair of theoretical physics, which was created especially for him. He taught in Turin during 1832–1833. In 1831, he was elected 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>, and the following year a Foreign Honorary Member of the <a href="/wiki/American_Academy_of_Arts_and_Sciences" title="American Academy of Arts and Sciences">American Academy of Arts and Sciences</a>.<sup id="cite_ref-AAAS_13-0" class="reference"><a href="#cite_note-AAAS-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>In August 1833 Cauchy left Turin for <a href="/wiki/Prague" title="Prague">Prague</a> to become the science tutor of the thirteen-year-old Duke of Bordeaux, <a href="/wiki/Henri_d%27Artois" class="mw-redirect" title="Henri d'Artois">Henri d'Artois</a> (1820–1883), the exiled Crown Prince and grandson of Charles X.<sup id="cite_ref-FOOTNOTEBrunoBaker200368_14-0" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200368-14"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> As a professor of the École Polytechnique, Cauchy had been a notoriously bad lecturer, assuming levels of understanding that only a few of his best students could reach, and cramming his allotted time with too much material. Henri d'Artois had neither taste nor talent for either mathematics or science. Although Cauchy took his mission very seriously, he did this with great clumsiness, and with surprising lack of authority over Henri d'Artois. During his civil engineering days, Cauchy once had been briefly in charge of repairing a few of the Parisian sewers, and he made the mistake of mentioning this to his pupil; with great malice, Henri d'Artois went about saying Cauchy started his career in the sewers of Paris. Cauchy's role as tutor lasted until Henri d'Artois became eighteen years old, in September 1838.<sup id="cite_ref-FOOTNOTEBrunoBaker200367_12-1" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200367-12"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Cauchy did hardly any research during those five years, while Henri d'Artois acquired a lifelong dislike of mathematics. Cauchy was named a <a href="/wiki/Baron" title="Baron">baron</a>, a title by which Cauchy set great store. </p><p>In 1834, his wife and two daughters moved to Prague, and Cauchy was reunited with his family after four years in exile. </p> <div class="mw-heading mw-heading3"><h3 id="Last_years">Last years</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=6" title="Edit section: Last years"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cauchy returned to Paris and his position at the Academy of Sciences late in 1838.<sup id="cite_ref-FOOTNOTEBrunoBaker200367_12-2" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200367-12"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> He could not regain his teaching positions, because he still refused to swear an oath of allegiance. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Augustin-Louis_Cauchy.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Augustin-Louis_Cauchy.jpg/220px-Augustin-Louis_Cauchy.jpg" decoding="async" width="220" height="279" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/e3/Augustin-Louis_Cauchy.jpg 1.5x" data-file-width="270" data-file-height="343" /></a><figcaption>Cauchy in later life</figcaption></figure> <p>In August 1839 a vacancy appeared in the <a href="/wiki/Bureau_des_Longitudes" title="Bureau des Longitudes">Bureau des Longitudes</a>. This Bureau bore some resemblance to the academy; for instance, it had the right to co-opt its members. Further, it was believed that members of the Bureau could "forget about" the oath of allegiance, although formally, unlike the Academicians, they were obliged to take it. The Bureau des Longitudes was an organization founded in 1795 to solve the problem of determining position at sea — mainly the <a href="/wiki/Longitude" title="Longitude">longitudinal</a> coordinate, since <a href="/wiki/Latitude" title="Latitude">latitude</a> is easily determined from the position of the sun. Since it was thought that position at sea was best determined by astronomical observations, the Bureau had developed into an organization resembling an academy of astronomical sciences. </p><p>In November 1839 Cauchy was elected to the Bureau, and discovered that the matter of the oath was not so easily dispensed with. Without his oath, the king refused to approve his election. For four years Cauchy was in the position of being elected but not approved; accordingly, he was not a formal member of the Bureau, did not receive payment, could not participate in meetings, and could not submit papers. Still Cauchy refused to take any oaths; however, he did feel loyal enough to direct his research to <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a>. In 1840, he presented a dozen papers on this topic to the academy. He described and illustrated the <a href="/wiki/Signed-digit_representation" title="Signed-digit representation">signed-digit representation</a> of numbers, an innovation presented in England in 1727 by <a href="/wiki/John_Colson" title="John Colson">John Colson</a>. The confounded membership of the Bureau lasted until the end of 1843, when Cauchy was replaced by Poinsot. </p><p>Throughout the nineteenth century the French educational system struggled over the separation of church and state. After losing control of the public education system, the Catholic Church sought to establish its own branch of education and found in Cauchy a staunch and illustrious ally. He lent his prestige and knowledge to the <a href="/w/index.php?title=%C3%89cole_Normale_%C3%89ccl%C3%A9siastique&action=edit&redlink=1" class="new" title="École Normale Écclésiastique (page does not exist)">École Normale Écclésiastique</a>, a school in Paris run by Jesuits, for training teachers for their colleges. He took part in the founding of the <a href="/wiki/Institut_Catholique_de_Paris" class="mw-redirect" title="Institut Catholique de Paris">Institut Catholique</a>. The purpose of this institute was to counter the effects of the absence of Catholic university education in France. These activities did not make Cauchy popular with his colleagues, who, on the whole, supported <a href="/wiki/The_Enlightenment" class="mw-redirect" title="The Enlightenment">the Enlightenment</a> ideals of the French Revolution. When a chair of mathematics became vacant at the Collège de France in 1843, Cauchy applied for it, but received just three of 45 votes. </p><p>In 1848 King Louis-Philippe fled to England. The oath of allegiance was abolished, and the road to an academic appointment was clear for Cauchy. On March 1, 1849, he was reinstated at the Faculté de Sciences, as a professor of mathematical astronomy. After political turmoil all through 1848, France chose to become a Republic, under the Presidency of <a href="/wiki/Napoleon_III_of_France" class="mw-redirect" title="Napoleon III of France">Napoleon III of France</a>. Early 1852 the President made himself Emperor of France, and took the name <a href="/wiki/Napoleon_III" title="Napoleon III">Napoleon III</a>. </p><p>The idea came up in bureaucratic circles that it would be useful to again require a loyalty oath from all state functionaries, including university professors. This time a cabinet minister was able to convince the Emperor to exempt Cauchy from the oath. In 1853, Cauchy was elected an International Member of the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Cauchy remained a professor at the university until his death at the age of 67. He received the <a href="/wiki/Last_Rites" class="mw-redirect" title="Last Rites">Last Rites</a> and died of a bronchial condition at 4 a.m. on 23 May 1857.<sup id="cite_ref-FOOTNOTEBrunoBaker200367_12-3" class="reference"><a href="#cite_note-FOOTNOTEBrunoBaker200367-12"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>His name 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 names inscribed on the Eiffel Tower</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Work">Work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=7" title="Edit section: Work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Early_work">Early work</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=8" title="Edit section: Early work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The genius of Cauchy was illustrated in his simple solution of the <a href="/wiki/Problem_of_Apollonius" title="Problem of Apollonius">problem of Apollonius</a>—describing a <a href="/wiki/Circle" title="Circle">circle</a> touching three given circles—which he discovered in 1805, his generalization of <a href="/wiki/Euler_characteristic" title="Euler characteristic">Euler's formula</a> on <a href="/wiki/Polyhedra" class="mw-redirect" title="Polyhedra">polyhedra</a> in 1811, and in several other elegant problems. More important is his memoir on <a href="/wiki/Wave" title="Wave">wave</a> propagation, which obtained the Grand Prix of the French Academy of Sciences in 1816. Cauchy's writings covered notable topics. In the theory of series he developed the notion of <a href="/wiki/Limit_of_a_sequence" title="Limit of a sequence">convergence</a> and discovered many of the basic formulas for <a href="/wiki/Q-series" class="mw-redirect" title="Q-series">q-series</a>. In the theory of numbers and complex quantities, he was the first to define <a href="/wiki/Complex_number" title="Complex number">complex numbers</a> as pairs of real numbers. He also wrote on the theory of groups and substitutions, the theory of functions, differential equations and determinants.<sup id="cite_ref-FOOTNOTEChisholm1911_4-2" class="reference"><a href="#cite_note-FOOTNOTEChisholm1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Wave_theory,_mechanics,_elasticity"><span id="Wave_theory.2C_mechanics.2C_elasticity"></span>Wave theory, mechanics, elasticity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=9" title="Edit section: Wave theory, mechanics, elasticity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the theory of light he worked on <a href="/wiki/Augustin-Jean_Fresnel" title="Augustin-Jean Fresnel">Fresnel's</a> wave theory and on the <a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">dispersion</a> and <a href="/wiki/Polarization_(waves)" title="Polarization (waves)">polarization</a> of light. He also contributed research in <a href="/wiki/Mechanics" title="Mechanics">mechanics</a>, substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> He wrote on the equilibrium of rods and elastic membranes and on waves in elastic media. He introduced a 3 × 3 symmetric <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrix</a> of numbers that is now known as the <a href="/wiki/Cauchy_stress_tensor" title="Cauchy stress tensor">Cauchy stress tensor</a>.<sup id="cite_ref-FOOTNOTECauchy182742"''De_la_pression_ou_tension_dans_un_corps_solide''"_[On_pressure_or_tension_in_a_solid_body]_17-0" class="reference"><a href="#cite_note-FOOTNOTECauchy182742"''De_la_pression_ou_tension_dans_un_corps_solide''"_[On_pressure_or_tension_in_a_solid_body]-17"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elasticity</a>, he originated the theory of <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stress</a>, and his results are nearly as valuable as those of <a href="/wiki/Sim%C3%A9on_Poisson" class="mw-redirect" title="Siméon Poisson">Siméon Poisson</a>.<sup id="cite_ref-FOOTNOTEChisholm1911_4-3" class="reference"><a href="#cite_note-FOOTNOTEChisholm1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <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=Augustin-Louis_Cauchy&action=edit&section=10" title="Edit section: Number theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Other significant contributions include being the first to prove the <a href="/wiki/Fermat_polygonal_number_theorem" title="Fermat polygonal number theorem">Fermat polygonal number theorem</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Complex_functions">Complex functions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=11" title="Edit section: Complex functions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cauchy is most famous for his single-handed development of <a href="/wiki/Complex_function_theory" class="mw-redirect" title="Complex function theory">complex function theory</a>. The first pivotal theorem proved by Cauchy, now known as <i><a href="/wiki/Cauchy%27s_integral_theorem" title="Cauchy's integral theorem">Cauchy's integral theorem</a></i>, was the following: </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 \oint _{C}f(z)dz=0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{C}f(z)dz=0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/196a30b82502e7e2f3f88b13f0386d81f5703655" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.549ex; height:5.676ex;" alt="{\displaystyle \oint _{C}f(z)dz=0,}" /></span></dd></dl> <p>where <i>f</i>(<i>z</i>) is a complex-valued function <a href="/wiki/Holomorphic_function" title="Holomorphic function">holomorphic</a> on and within the non-self-intersecting closed curve <i>C</i> (contour) lying in the <a href="/wiki/Complex_plane" title="Complex plane">complex plane</a>. The <i>contour integral</i> is taken along the contour <i>C</i>. The rudiments of this theorem can already be found in a paper that the 24-year-old Cauchy presented to the Académie des Sciences (then still called "First Class of the Institute") on August 11, 1814. In full form the theorem was given in 1825.<sup id="cite_ref-FOOTNOTECauchy1825_18-0" class="reference"><a href="#cite_note-FOOTNOTECauchy1825-18"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>In 1826 Cauchy gave a formal definition of a <a href="/wiki/Residue_(mathematics)" class="mw-redirect" title="Residue (mathematics)">residue</a> of a function.<sup id="cite_ref-FOOTNOTECauchy182611"''Sur_un_nouveau_genre_de_calcul_analogue_au_calcul_infinitésimal''"_[On_a_new_type_of_calculus_analogous_to_the_infinitesimal_calculus]_19-0" class="reference"><a href="#cite_note-FOOTNOTECauchy182611"''Sur_un_nouveau_genre_de_calcul_analogue_au_calcul_infinitésimal''"_[On_a_new_type_of_calculus_analogous_to_the_infinitesimal_calculus]-19"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> This concept concerns functions that have <a href="/wiki/Pole_(complex_analysis)" class="mw-redirect" title="Pole (complex analysis)">poles</a>—isolated singularities, i.e., points where a function goes to positive or negative infinity. If the complex-valued function <i>f</i>(<i>z</i>) can be expanded in the <a href="/wiki/Neighborhood" class="mw-redirect" title="Neighborhood">neighborhood</a> of a singularity <i>a</i> as </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 f(z)=\varphi (z)+{\frac {B_{1}}{z-a}}+{\frac {B_{2}}{(z-a)^{2}}}+\cdots +{\frac {B_{n}}{(z-a)^{n}}},\quad B_{i},z,a\in \mathbb {C} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>φ</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mi>z</mi> <mo>−</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>−</mo> <mi>a</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>−</mo> <mi>a</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em"></mspace> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mi>z</mi> <mo>,</mo> <mi>a</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(z)=\varphi (z)+{\frac {B_{1}}{z-a}}+{\frac {B_{2}}{(z-a)^{2}}}+\cdots +{\frac {B_{n}}{(z-a)^{n}}},\quad B_{i},z,a\in \mathbb {C} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e2b181373cc875a86f908f1696a3829e8c2099d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:65.123ex; height:6.009ex;" alt="{\displaystyle f(z)=\varphi (z)+{\frac {B_{1}}{z-a}}+{\frac {B_{2}}{(z-a)^{2}}}+\cdots +{\frac {B_{n}}{(z-a)^{n}}},\quad B_{i},z,a\in \mathbb {C} ,}" /></span></dd></dl> <p>where φ(<i>z</i>) is analytic (i.e., well-behaved without singularities), then <i>f</i> is said to have a pole of order <i>n</i> in the point <i>a</i>. If <i>n</i> = 1, the pole is called simple. The coefficient <i>B</i><sub>1</sub> is called by Cauchy the residue of function <i>f</i> at <i>a</i>. If <i>f</i> is non-singular at <i>a</i> then the residue of <i>f</i> is zero at <i>a</i>. Clearly, the residue is in the case of a simple pole equal to </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 {\underset {z=a}{\mathrm {Res} }}f(z)=\lim _{z\rightarrow a}(z-a)f(z),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <munder> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">s</mi> </mrow> <mrow> <mi>z</mi> <mo>=</mo> <mi>a</mi> </mrow> </munder> </mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mo stretchy="false">→</mo> <mi>a</mi> </mrow> </munder> <mo stretchy="false">(</mo> <mi>z</mi> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\underset {z=a}{\mathrm {Res} }}f(z)=\lim _{z\rightarrow a}(z-a)f(z),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8543ea469e94ad59e2a69b9897adb6b9b69de1be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.006ex; height:4.009ex;" alt="{\displaystyle {\underset {z=a}{\mathrm {Res} }}f(z)=\lim _{z\rightarrow a}(z-a)f(z),}" /></span></dd></dl> <p>where we replaced <i>B</i><sub>1</sub> by the modern notation of the residue. </p><p>In 1831, while in Turin, Cauchy submitted two papers to the Academy of Sciences of Turin. In the first<sup id="cite_ref-FOOTNOTECauchy1831_20-0" class="reference"><a href="#cite_note-FOOTNOTECauchy1831-20"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> he proposed the formula now known as <a href="/wiki/Cauchy%27s_integral_formula" title="Cauchy's integral formula">Cauchy's integral formula</a>, </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 f(a)={\frac {1}{2\pi i}}\oint _{C}{\frac {f(z)}{z-a}}dz,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>π</mi> <mi>i</mi> </mrow> </mfrac> </mrow> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>z</mi> <mo>−</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <mi>d</mi> <mi>z</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(a)={\frac {1}{2\pi i}}\oint _{C}{\frac {f(z)}{z-a}}dz,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/271bef3393ca6e11767a066e10d217e44cd09132" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.042ex; height:6.176ex;" alt="{\displaystyle f(a)={\frac {1}{2\pi i}}\oint _{C}{\frac {f(z)}{z-a}}dz,}" /></span></dd></dl> <p>where <i>f</i>(<i>z</i>) is analytic on <i>C</i> and within the region bounded by the contour <i>C</i> and the complex number <i>a</i> is somewhere in this region. The contour integral is taken counter-clockwise. Clearly, the integrand has a simple pole at <i>z</i> = <i>a</i>. In the second paper<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> he presented the <a href="/wiki/Residue_theorem" title="Residue theorem">residue theorem</a>, </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 {1}{2\pi i}}\oint _{C}f(z)dz=\sum _{k=1}^{n}{\underset {z=a_{k}}{\mathrm {Res} }}f(z),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>π</mi> <mi>i</mi> </mrow> </mfrac> </mrow> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>z</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <munder> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">s</mi> </mrow> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </munder> </mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2\pi i}}\oint _{C}f(z)dz=\sum _{k=1}^{n}{\underset {z=a_{k}}{\mathrm {Res} }}f(z),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6039dddcad4ccf80dbbde660d885104775ee9552" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:29.602ex; height:6.843ex;" alt="{\displaystyle {\frac {1}{2\pi i}}\oint _{C}f(z)dz=\sum _{k=1}^{n}{\underset {z=a_{k}}{\mathrm {Res} }}f(z),}" /></span></dd></dl> <p>where the sum is over all the <i>n</i> poles of <i>f</i>(<i>z</i>) on and within the contour <i>C</i>. These results of Cauchy's still form the core of complex function theory as it is taught today to physicists and electrical engineers. For quite some time, contemporaries of Cauchy ignored his theory, believing it to be too complicated. Only in the 1840s the theory started to get response, with <a href="/wiki/Pierre_Alphonse_Laurent" title="Pierre Alphonse Laurent">Pierre Alphonse Laurent</a> being the first mathematician besides Cauchy to make a substantial contribution (his work on what are now known as <a href="/wiki/Laurent_series" title="Laurent series">Laurent series</a>, published in 1843). </p> <div class="mw-heading mw-heading3"><h3 id="Cours_d'Analyse"><span id="Cours_d.27Analyse"></span>Cours d'Analyse</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=12" title="Edit section: Cours d'Analyse"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cours_d%27Analyse" title="Cours d'Analyse">Cours d'Analyse</a></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Cauchy.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Cauchy.jpg/220px-Cauchy.jpg" decoding="async" width="220" height="319" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/22/Cauchy.jpg 1.5x" data-file-width="283" data-file-height="410" /></a><figcaption>The title page of a textbook by Cauchy.</figcaption></figure><p> In his book <i>Cours d'Analyse</i> Cauchy stressed the importance of rigor in analysis. <i>Rigor</i> in this case meant the rejection of the principle of <i><a href="/wiki/Generality_of_algebra" title="Generality of algebra">Generality of algebra</a></i> (of earlier authors such as Euler and Lagrange) and its replacement by geometry and <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimals</a>.<sup id="cite_ref-FOOTNOTEBorovikKatz2012245–276_22-0" class="reference"><a href="#cite_note-FOOTNOTEBorovikKatz2012245–276-22"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Judith Grabiner wrote Cauchy was "the man who taught rigorous analysis to all of Europe".<sup id="cite_ref-FOOTNOTEGrabiner1981_23-0" class="reference"><a href="#cite_note-FOOTNOTEGrabiner1981-23"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> The book is frequently noted as being the first place that inequalities, and <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 \delta -\varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>−</mo> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta -\varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b969e5a5151f09930debdf61cccd6f7700a8967f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.973ex; height:2.509ex;" alt="{\displaystyle \delta -\varepsilon }" /></span> arguments were introduced into calculus. Here Cauchy defined continuity as follows: <i>The function f(x) is continuous with respect to x between the given limits if, between these limits, an infinitely small increment in the variable always produces an infinitely small increment in the function itself.</i> </p><p>M. Barany claims that the École mandated the inclusion of infinitesimal methods against Cauchy's better judgement.<sup id="cite_ref-FOOTNOTEBarany2011_24-0" class="reference"><a href="#cite_note-FOOTNOTEBarany2011-24"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Gilain notes that when the portion of the curriculum devoted to <i>Analyse Algébrique</i> was reduced in 1825, Cauchy insisted on placing the topic of continuous functions (and therefore also infinitesimals) at the beginning of the Differential Calculus.<sup id="cite_ref-FOOTNOTEGilain1989_25-0" class="reference"><a href="#cite_note-FOOTNOTEGilain1989-25"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> Laugwitz (1989) and Benis-Sinaceur (1973) point out that Cauchy continued to use infinitesimals in his own research as late as 1853. </p><p>Cauchy gave an explicit definition of an infinitesimal in terms of a sequence tending to zero. There has been a vast body of literature written about Cauchy's notion of "infinitesimally small quantities", arguing that they lead from everything from the usual "epsilontic" definitions or to the notions of <a href="/wiki/Non-standard_analysis" class="mw-redirect" title="Non-standard analysis">non-standard analysis</a>. The consensus is that Cauchy omitted or left implicit the important ideas to make clear the precise meaning of the infinitely small quantities he used.<sup id="cite_ref-FOOTNOTEBarany2013_26-0" class="reference"><a href="#cite_note-FOOTNOTEBarany2013-26"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Taylor's_theorem"><span id="Taylor.27s_theorem"></span>Taylor's theorem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=13" title="Edit section: Taylor's theorem"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>He was the first to prove <a href="/wiki/Taylor%27s_theorem" title="Taylor's theorem">Taylor's theorem</a> rigorously, establishing his well-known form of the remainder.<sup id="cite_ref-FOOTNOTEChisholm1911_4-4" class="reference"><a href="#cite_note-FOOTNOTEChisholm1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> He wrote a textbook<sup id="cite_ref-FOOTNOTECauchy1821_27-0" class="reference"><a href="#cite_note-FOOTNOTECauchy1821-27"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> (see the illustration) for his students at the École Polytechnique in which he developed the basic theorems of mathematical analysis as rigorously as possible. In this book he gave the necessary and sufficient condition for the existence of a <a href="/wiki/Limit_of_a_function" title="Limit of a function">limit</a> in the form that is still taught. Also Cauchy's well-known test for <a href="/wiki/Absolute_convergence" title="Absolute convergence">absolute convergence</a> stems from this book: <a href="/wiki/Cauchy_condensation_test" title="Cauchy condensation test">Cauchy condensation test</a>. In 1829 he defined for the first time a complex function of a complex variable in another textbook.<sup id="cite_ref-FOOTNOTECauchy1829_28-0" class="reference"><a href="#cite_note-FOOTNOTECauchy1829-28"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> In spite of these, Cauchy's own research papers often used intuitive, not rigorous, methods;<sup id="cite_ref-FOOTNOTEKline1982176_29-0" class="reference"><a href="#cite_note-FOOTNOTEKline1982176-29"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> thus one of his theorems was exposed to a "counter-example" by <a href="/wiki/Niels_Henrik_Abel" title="Niels Henrik Abel">Abel</a>, later fixed by the introduction of the notion of <a href="/wiki/Uniform_continuity" title="Uniform continuity">uniform continuity</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Argument_principle,_stability"><span id="Argument_principle.2C_stability"></span>Argument principle, stability</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=14" title="Edit section: Argument principle, stability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a paper published in 1855, two years before Cauchy's death, he discussed some theorems, one of which is similar to the "<a href="/wiki/Argument_principle" title="Argument principle">Principle of the argument</a>" in many modern textbooks on complex analysis. In modern control theory textbooks, the <a href="/wiki/Cauchy_argument_principle" class="mw-redirect" title="Cauchy argument principle">Cauchy argument principle</a> is quite frequently used to derive the <a href="/wiki/Nyquist_stability_criterion" title="Nyquist stability criterion">Nyquist stability criterion</a>, which can be used to predict the stability of negative <a href="/wiki/Feedback_amplifier" class="mw-redirect" title="Feedback amplifier">feedback amplifier</a> and negative <a href="/wiki/Feedback" title="Feedback">feedback</a> control systems. Thus Cauchy's work has a strong impact on both pure mathematics and practical engineering. </p> <div class="mw-heading mw-heading2"><h2 id="Published_works">Published works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=15" title="Edit section: Published works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cauchy_-_Le%C3%A7ons_sur_le_calcul_diff%C3%A9rentiel,_1829_-_576181_F.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Cauchy_-_Le%C3%A7ons_sur_le_calcul_diff%C3%A9rentiel%2C_1829_-_576181_F.jpg/220px-Cauchy_-_Le%C3%A7ons_sur_le_calcul_diff%C3%A9rentiel%2C_1829_-_576181_F.jpg" decoding="async" width="220" height="294" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Cauchy_-_Le%C3%A7ons_sur_le_calcul_diff%C3%A9rentiel%2C_1829_-_576181_F.jpg/330px-Cauchy_-_Le%C3%A7ons_sur_le_calcul_diff%C3%A9rentiel%2C_1829_-_576181_F.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Cauchy_-_Le%C3%A7ons_sur_le_calcul_diff%C3%A9rentiel%2C_1829_-_576181_F.jpg/440px-Cauchy_-_Le%C3%A7ons_sur_le_calcul_diff%C3%A9rentiel%2C_1829_-_576181_F.jpg 2x" data-file-width="736" data-file-height="984" /></a><figcaption><i>Leçons sur le calcul différentiel</i>, 1829</figcaption></figure> <p>Cauchy was very productive, in number of papers second only to <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>. It took almost a century to collect all his writings into 27 large volumes: </p> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070724003603/http://portail.mathdoc.fr/cgi-bin/oetoc?id=OE_CAUCHY_1_2">Oeuvres complètes d'Augustin Cauchy publiées sous la direction scientifique de l'Académie des sciences et sous les auspices de M. le ministre de l'Instruction publique (27 volumes)</a> at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (archived July 24, 2007)(Paris : Gauthier-Villars et fils, 1882–1974)</li> <li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://archive.org/details/oeuvresdaugusti01caucrich"><i>Œuvres complètes d'Augustin Cauchy</i></a>. Académie des sciences (France). 1882–1938 – via Ministère de l'éducation nationale.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%C5%92uvres+compl%C3%A8tes+d%27Augustin+Cauchy&rft.pub=Acad%C3%A9mie+des+sciences+%28France%29&rft.date=1882%2F1938&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Foeuvresdaugusti01caucrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li></ul> <p>His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced; these are mainly embodied in his three great treatises: </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCauchy1821" class="citation book cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=UrT0KsbDmDwC&pg=PA11">"Analyse Algébrique"</a>. <a href="/wiki/Cours_d%27Analyse" title="Cours d'Analyse"><i>Cours d'analyse de l'École royale polytechnique</i></a>. Paris: L'Imprimerie Royale, Debure frères, Libraires du Roi et de la <a href="/wiki/Biblioth%C3%A8que_du_Roi" class="mw-redirect" title="Bibliothèque du Roi">Bibliothèque du Roi</a>. 1821. <a rel="nofollow" class="external text" href="https://archive.org/details/coursdanalysede00caucgoog">online</a> at the <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Analyse+Alg%C3%A9brique&rft.btitle=Cours+d%27analyse+de+l%27%C3%89cole+royale+polytechnique&rft.place=Paris&rft.pub=L%27Imprimerie+Royale%2C+Debure+fr%C3%A8res%2C+Libraires+du+Roi+et+de+la+Biblioth%C3%A8que+du+Roi&rft.date=1821&rft.aulast=Cauchy&rft.aufirst=Augustin+Louis&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUrT0KsbDmDwC%26pg%3DPA11&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://gallica.bnf.fr/ark:/12148/bpt6k62404287"><i>Le Calcul infinitésimal</i></a> (1823)</li> <li><i>Leçons sur les applications de calcul infinitésimal</i>; <i>La géométrie</i> (1826–1828)<sup id="cite_ref-FOOTNOTEChisholm1911_4-5" class="reference"><a href="#cite_note-FOOTNOTEChisholm1911-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ul> <p>His other works include: </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCauchy1825" class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://archive.org/details/mmoiresurlesin00cauc/page/n4"><i>Mémoire sur les intégrales définies, prises entre des limites imaginaires</i></a> [<i>A Memorandum on definite integrals taken between imaginary limits</i>] (in French). submitted to the Académie des Sciences on February 28: Paris, De Bure frères. 1825.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=M%C3%A9moire+sur+les+int%C3%A9grales+d%C3%A9finies%2C+prises+entre+des+limites+imaginaires&rft.place=submitted+to+the+Acad%C3%A9mie+des+Sciences+on+February+28&rft.pub=Paris%2C+De+Bure+fr%C3%A8res&rft.date=1825&rft.aulast=Cauchy&rft.aufirst=Augustin+Louis&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmmoiresurlesin00cauc%2Fpage%2Fn4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location (<a href="/wiki/Category:CS1_maint:_location" title="Category:CS1 maint: location">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCauchy1826" class="citation book cs1"><a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_BmOo00FGCuAC/page/n3"><i>Exercices de mathematiques</i></a>. Paris. 1826.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Exercices+de+mathematiques&rft.place=Paris&rft.date=1826&rft.aulast=Cauchy&rft.aufirst=Augustin+Louis&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_BmOo00FGCuAC%2Fpage%2Fn3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCauchy1827" class="citation book cs1 cs1-prop-long-vol"><a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_o6hCzbAYX7cC/page/n3"><i>Exercices de mathematiques</i></a>. Vol. Seconde Année. Paris. 1827.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Exercices+de+mathematiques&rft.place=Paris&rft.date=1827&rft.aulast=Cauchy&rft.aufirst=Augustin+Louis&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_o6hCzbAYX7cC%2Fpage%2Fn3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCauchy1829" class="citation book cs1"><a rel="nofollow" class="external text" href="https://archive.org/details/BRIE000598_TO0324_PNI-2034_000000"><i>Leçons sur le calcul différentiel</i></a>. Paris: De Bure frères. 1829.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Le%C3%A7ons+sur+le+calcul+diff%C3%A9rentiel&rft.place=Paris&rft.pub=De+Bure+fr%C3%A8res&rft.date=1829&rft.aulast=Cauchy&rft.aufirst=Augustin+Louis+Baron&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2FBRIE000598_TO0324_PNI-2034_000000&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCauchy1831" class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=iSVVAAAAcAAJ&pg=PA3"><i>Sur la mecanique celeste et sur un nouveau calcul qui s'applique a un grand nombre de questions diverses etc</i></a> [<i>On Celestial Mechanics and on a new calculation which is applicable to a large number of diverse questions</i>] (in French). presented to the Academy of Sciences of Turin, October 11. 1831.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sur+la+mecanique+celeste+et+sur+un+nouveau+calcul+qui+s%27applique+a+un+grand+nombre+de+questions+diverses+etc&rft.place=presented+to+the+Academy+of+Sciences+of+Turin%2C+October+11&rft.date=1831&rft.aulast=Cauchy&rft.aufirst=Augustin-Louis&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DiSVVAAAAcAAJ%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location (<a href="/wiki/Category:CS1_maint:_location" title="Category:CS1 maint: location">link</a>)</span></li> <li><i><a rel="nofollow" class="external text" href="https://archive.org/details/exercicedanaly01caucrich">Exercices d'analyse et de physique mathematique (Volume 1)</a></i></li> <li><i><a rel="nofollow" class="external text" href="https://archive.org/details/exercicedanaly02caucrich">Exercices d'analyse et de physique mathematique (Volume 2)</a></i></li> <li><i><a rel="nofollow" class="external text" href="https://archive.org/details/exercicedanaly03caucrich">Exercices d'analyse et de physique mathematique (Volume 3)</a></i></li> <li><i><a rel="nofollow" class="external text" href="https://archive.org/details/117770570_004">Exercices d'analyse et de physique mathematique (Volume 4)</a></i> (Paris: Bachelier, 1840–1847)</li> <li><i><a rel="nofollow" class="external text" href="https://gallica.bnf.fr/ark:/12148/btv1b8626657t">Analyse algèbrique</a></i> (Imprimerie Royale, 1821)</li> <li><i><a rel="nofollow" class="external text" href="https://gallica.bnf.fr/ark:/12148/bpt6k78986c">Nouveaux exercices de mathématiques</a></i> (Paris : Gauthier-Villars, 1895)</li> <li><i>Courses of mechanics</i> (for the École Polytechnique)</li> <li><i>Higher algebra</i> (for the <a href="/w/index.php?title=Facult%C3%A9_des_sciences_de_Paris&action=edit&redlink=1" class="new" title="Faculté des sciences de Paris (page does not exist)">Faculté des sciences de Paris</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://fr.wikipedia.org/wiki/Facult%C3%A9_des_sciences_de_Paris" class="extiw" title="fr:Faculté des sciences de Paris">fr</a>]</span>)</li> <li><i>Mathematical physics</i> (for the Collège de France).</li> <li><i><a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k90188b/f34">Mémoire sur l'emploi des equations symboliques dans le calcul infinitésimal et dans le calcul aux différences finis</a></i> CR Ac ad. Sci. Paris, t. XVII, 449–458 (1843) credited as originating the <a href="/wiki/Operational_calculus" title="Operational calculus">operational calculus</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Politics_and_religious_beliefs">Politics and religious beliefs</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=16" title="Edit section: Politics and religious beliefs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Augustin-Louis Cauchy grew up in the house of a staunch royalist. This made his father flee with the family to <a href="/wiki/Arcueil" title="Arcueil">Arcueil</a> during the <a href="/wiki/French_Revolution" title="French Revolution">French Revolution</a>. Their life there during that time was apparently hard; Augustin-Louis's father, Louis François, spoke of living on rice, bread, and crackers during the period. A paragraph from an undated letter from Louis François to his mother in <a href="/wiki/Rouen" title="Rouen">Rouen</a> says:<sup id="cite_ref-FOOTNOTEValson186813Vol._1_30-0" class="reference"><a href="#cite_note-FOOTNOTEValson186813Vol._1-30"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>We never had more than a one-half pound (230 g) of bread — and sometimes not even that. This we supplement with little supply of hard crackers and rice that we are allotted. Otherwise, we are getting along quite well, which is the important thing and goes to show that human beings can get by with little. I should tell you that for my children's pap I still have a bit of fine flour, made from wheat that I grew on my own land. I had three bushels, and I also have a few pounds of <a href="/wiki/Potato_starch" title="Potato starch">potato starch</a>. It is as white as snow and very good, too, especially for very young children. It, too, was grown on my own land.<sup id="cite_ref-FOOTNOTEBelhoste19913_31-0" class="reference"><a href="#cite_note-FOOTNOTEBelhoste19913-31"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p></blockquote><p> In any event, he inherited his father's staunch royalism and hence refused to take oaths to any government after the overthrow of Charles X. </p><p>He was an equally staunch Catholic and a member of the <a href="/wiki/Society_of_Saint_Vincent_de_Paul" title="Society of Saint Vincent de Paul">Society of Saint Vincent de Paul</a>.<sup id="cite_ref-FOOTNOTEBrock1908_32-0" class="reference"><a href="#cite_note-FOOTNOTEBrock1908-32"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> He also had links to the <a href="/wiki/Society_of_Jesus" class="mw-redirect" title="Society of Jesus">Society of Jesus</a> and defended them at the academy when it was politically unwise to do so. His zeal for his faith may have led to his caring for <a href="/wiki/Charles_Hermite" title="Charles Hermite">Charles Hermite</a> during his illness and leading Hermite to become a faithful Catholic. It also inspired Cauchy to plead on behalf of the Irish during the <a href="/wiki/Great_Famine_(Ireland)" title="Great Famine (Ireland)">Great Famine of Ireland</a>. </p><p>His royalism and religious zeal made him contentious, which caused difficulties with his colleagues. He felt that he was mistreated for his beliefs, but his opponents felt he intentionally provoked people by berating them over religious matters or by defending the Jesuits after they had been suppressed. <a href="/wiki/Niels_Henrik_Abel" title="Niels Henrik Abel">Niels Henrik Abel</a> called him a "bigoted Catholic"<sup id="cite_ref-FOOTNOTEBell1986273_33-0" class="reference"><a href="#cite_note-FOOTNOTEBell1986273-33"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> and added he was "mad and there is nothing that can be done about him", but at the same time praised him as a mathematician. Cauchy's views were widely unpopular among mathematicians and when <a href="/wiki/Guglielmo_Libri_Carucci_dalla_Sommaja" title="Guglielmo Libri Carucci dalla Sommaja">Guglielmo Libri Carucci dalla Sommaja</a> was made chair in mathematics before him he, and many others, felt his views were the cause. When Libri was accused of stealing books he was replaced by <a href="/wiki/Joseph_Liouville" title="Joseph Liouville">Joseph Liouville</a> rather than Cauchy, which caused a rift between Liouville and Cauchy. Another dispute with political overtones concerned <a href="/wiki/Jean-Marie_Duhamel" title="Jean-Marie Duhamel">Jean-Marie Constant Duhamel</a> and a claim on inelastic shocks. Cauchy was later shown, by <a href="/wiki/Jean-Victor_Poncelet" title="Jean-Victor Poncelet">Jean-Victor Poncelet</a>, to be wrong. </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=Augustin-Louis_Cauchy&action=edit&section=17" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/List_of_topics_named_after_Augustin-Louis_Cauchy" class="mw-redirect" title="List of topics named after Augustin-Louis Cauchy">List of topics named after Augustin-Louis Cauchy</a></li> <li><a href="/wiki/Cauchy%E2%80%93Binet_formula" title="Cauchy–Binet formula">Cauchy–Binet formula</a></li> <li><a href="/wiki/Cauchy_boundary_condition" title="Cauchy boundary condition">Cauchy boundary condition</a></li> <li><a href="/wiki/Cauchy%27s_convergence_test" title="Cauchy's convergence test">Cauchy's convergence test</a></li> <li><a href="/wiki/Cauchy_(crater)" title="Cauchy (crater)">Cauchy (crater)</a></li> <li><a href="/wiki/Cauchy_determinant" class="mw-redirect" title="Cauchy determinant">Cauchy determinant</a></li> <li><a href="/wiki/Cauchy_distribution" title="Cauchy distribution">Cauchy distribution</a></li> <li><a href="/wiki/Cauchy%27s_equation" title="Cauchy's equation">Cauchy's equation</a></li> <li><a href="/wiki/Cauchy%E2%80%93Euler_equation" title="Cauchy–Euler equation">Cauchy–Euler equation</a></li> <li><a href="/wiki/Cauchy%27s_functional_equation" title="Cauchy's functional equation">Cauchy's functional equation</a></li> <li><a href="/wiki/Cauchy_horizon" title="Cauchy horizon">Cauchy horizon</a></li> <li><a href="/wiki/Cauchy_formula_for_repeated_integration" title="Cauchy formula for repeated integration">Cauchy formula for repeated integration</a></li> <li><a href="/wiki/Cauchy%E2%80%93Frobenius_lemma" class="mw-redirect" title="Cauchy–Frobenius lemma">Cauchy–Frobenius lemma</a></li> <li><a href="/wiki/Cauchy%E2%80%93Hadamard_theorem" title="Cauchy–Hadamard theorem">Cauchy–Hadamard theorem</a></li> <li><a href="/wiki/Cauchy%E2%80%93Kovalevskaya_theorem" title="Cauchy–Kovalevskaya theorem">Cauchy–Kovalevskaya theorem</a></li> <li><a href="/wiki/Cauchy_momentum_equation" title="Cauchy momentum equation">Cauchy momentum equation</a></li> <li><a href="/wiki/Cauchy%E2%80%93Peano_theorem" class="mw-redirect" title="Cauchy–Peano theorem">Cauchy–Peano theorem</a></li> <li><a href="/wiki/Cauchy_principal_value" title="Cauchy principal value">Cauchy principal value</a></li> <li><a href="/wiki/Cauchy_problem" title="Cauchy problem">Cauchy problem</a></li> <li><a href="/wiki/Cauchy_product" title="Cauchy product">Cauchy product</a></li> <li><a href="/wiki/Cauchy%27s_radical_test" class="mw-redirect" title="Cauchy's radical test">Cauchy's radical test</a></li> <li><a href="/wiki/Cauchy%E2%80%93Rassias_stability" title="Cauchy–Rassias stability">Cauchy–Rassias stability</a></li> <li><a href="/wiki/Cauchy%E2%80%93Riemann_equations" title="Cauchy–Riemann equations">Cauchy–Riemann equations</a></li> <li><a href="/wiki/Cauchy%E2%80%93Schwarz_inequality" title="Cauchy–Schwarz inequality">Cauchy–Schwarz inequality</a></li> <li><a href="/wiki/Cauchy_sequence" title="Cauchy sequence">Cauchy sequence</a></li> <li><a href="/wiki/Cauchy_surface" title="Cauchy surface">Cauchy surface</a></li> <li><a href="/wiki/Cauchy%27s_theorem_(geometry)" title="Cauchy's theorem (geometry)">Cauchy's theorem (geometry)</a></li> <li><a href="/wiki/Cauchy%27s_theorem_(group_theory)" title="Cauchy's theorem (group theory)">Cauchy's theorem (group theory)</a></li> <li><a href="/wiki/Maclaurin%E2%80%93Cauchy_test" class="mw-redirect" title="Maclaurin–Cauchy test">Maclaurin–Cauchy test</a></li></ul> </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=Augustin-Louis_Cauchy&action=edit&section=18" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=19" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">His father's dismissal is sometimes seen as the cause of the deep hatred of the French Revolution that Cauchy felt all through his life.</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">In the revolutionary years the French Académie des Sciences was known as the "First Class" of the Institut de France.</span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=20" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJones2003" class="citation cs1"><a href="/wiki/Daniel_Jones_(phonetician)" title="Daniel Jones (phonetician)">Jones, Daniel</a> (2003). <a href="/wiki/Peter_Roach_(phonetician)" title="Peter Roach (phonetician)">Roach, Peter</a>; Hartman, James; <a href="/wiki/Jane_Setter" title="Jane Setter">Setter, Jane</a> (eds.). "Cauchy". <i><a href="/wiki/English_Pronouncing_Dictionary" title="English Pronouncing Dictionary">Cambridge English Pronouncing Dictionary</a></i> (16th ed.). Cambridge University Press. p. 59. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-81693-9" title="Special:BookSources/0-521-81693-9"><bdi>0-521-81693-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Cambridge+English+Pronouncing+Dictionary&rft.atitle=Cauchy&rft.pages=59&rft.date=2003&rft.isbn=0-521-81693-9&rft.aulast=Jones&rft.aufirst=Daniel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></span> </li> <li id="cite_note-collins-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-collins_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-collins_2-1"><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 web cs1"><a rel="nofollow" class="external text" href="https://www.collinsdictionary.com/dictionary/english/cauchy">"Cauchy"</a>. <i><a href="/wiki/Collins_English_Dictionary" title="Collins English Dictionary">Collins English Dictionary</a></i>. <a href="/wiki/HarperCollins" title="HarperCollins">HarperCollins</a><span class="reference-accessdate">. Retrieved <span class="nowrap">3 August</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Collins+English+Dictionary&rft.atitle=Cauchy&rft_id=https%3A%2F%2Fwww.collinsdictionary.com%2Fdictionary%2Fenglish%2Fcauchy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="http://www.dictionary.com/browse/cauchy">"Cauchy"</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> – via dictionary.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Cauchy&rft.btitle=Random+House+Webster%27s+Unabridged+Dictionary&rft_id=http%3A%2F%2Fwww.dictionary.com%2Fbrowse%2Fcauchy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEChisholm1911-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEChisholm1911_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChisholm1911_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChisholm1911_4-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChisholm1911_4-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChisholm1911_4-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChisholm1911_4-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFChisholm1911">Chisholm 1911</a>.</span> </li> <li id="cite_note-FOOTNOTEFreudenthal2008-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEFreudenthal2008_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFFreudenthal2008">Freudenthal 2008</a>.</span> </li> <li id="cite_note-FOOTNOTEBrunoBaker200366-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEBrunoBaker200366_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEBrunoBaker200366_7-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEBrunoBaker200366_7-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTEBrunoBaker200366_7-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-FOOTNOTEBrunoBaker200366_7-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-FOOTNOTEBrunoBaker200366_7-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFBrunoBaker2003">Bruno & Baker 2003</a>, p. 66.</span> </li> <li id="cite_note-FOOTNOTEBrunoBaker200365–66-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBrunoBaker200365–66_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBrunoBaker2003">Bruno & Baker 2003</a>, pp. 65–66.</span> </li> <li id="cite_note-FOOTNOTEBradleySandifer20109-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBradleySandifer20109_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBradleySandifer2010">Bradley & Sandifer 2010</a>, p. 9.</span> </li> <li id="cite_note-FOOTNOTEBelhoste1991134-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBelhoste1991134_11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBelhoste1991">Belhoste 1991</a>, p. 134.</span> </li> <li id="cite_note-FOOTNOTEBrunoBaker200367-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEBrunoBaker200367_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEBrunoBaker200367_12-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEBrunoBaker200367_12-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTEBrunoBaker200367_12-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFBrunoBaker2003">Bruno & Baker 2003</a>, p. 67.</span> </li> <li id="cite_note-AAAS-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-AAAS_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.amacad.org/publications/BookofMembers/ChapterC.pdf">"Book of Members, 1780–2010: Chapter C"</a> <span class="cs1-format">(PDF)</span>. American Academy of Arts and Sciences. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://www.amacad.org/publications/BookofMembers/ChapterC.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2022-10-09<span class="reference-accessdate">. Retrieved <span class="nowrap">13 September</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Book+of+Members%2C+1780%E2%80%932010%3A+Chapter+C&rft.pub=American+Academy+of+Arts+and+Sciences&rft_id=http%3A%2F%2Fwww.amacad.org%2Fpublications%2FBookofMembers%2FChapterC.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEBrunoBaker200368-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBrunoBaker200368_14-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBrunoBaker2003">Bruno & Baker 2003</a>, p. 68.</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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://search.amphilsoc.org/memhist/search?creator=Cauchy&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced">"APS Member History"</a>. <i>search.amphilsoc.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-04-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=search.amphilsoc.org&rft.atitle=APS+Member+History&rft_id=https%3A%2F%2Fsearch.amphilsoc.org%2Fmemhist%2Fsearch%3Fcreator%3DCauchy%26title%3D%26subject%3D%26subdiv%3D%26mem%3D%26year%3D%26year-max%3D%26dead%3D%26keyword%3D%26smode%3Dadvanced&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" 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="CITEREFKurrer2018" class="citation book cs1"><a href="/wiki/Karl-Eugen_Kurrer" title="Karl-Eugen Kurrer">Kurrer, K.-E.</a> (2018). <i>The History of the Theory of Structures. Searching for Equilibrium</i>. Berlin: <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">Wiley</a>. pp. <span class="nowrap">978–</span>979. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-433-03229-9" title="Special:BookSources/978-3-433-03229-9"><bdi>978-3-433-03229-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+History+of+the+Theory+of+Structures.+Searching+for+Equilibrium&rft.place=Berlin&rft.pages=%3Cspan+class%3D%22nowrap%22%3E978-%3C%2Fspan%3E979&rft.pub=Wiley&rft.date=2018&rft.isbn=978-3-433-03229-9&rft.aulast=Kurrer&rft.aufirst=K.-E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTECauchy182742"''De_la_pression_ou_tension_dans_un_corps_solide''"_[On_pressure_or_tension_in_a_solid_body]-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECauchy182742"''De_la_pression_ou_tension_dans_un_corps_solide''"_[On_pressure_or_tension_in_a_solid_body]_17-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCauchy1827">Cauchy 1827</a>, p. 42, "<i>De la pression ou tension dans un corps solide</i>" [On pressure or tension in a solid body].</span> </li> <li id="cite_note-FOOTNOTECauchy1825-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECauchy1825_18-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCauchy1825">Cauchy 1825</a>.</span> </li> <li id="cite_note-FOOTNOTECauchy182611"''Sur_un_nouveau_genre_de_calcul_analogue_au_calcul_infinitésimal''"_[On_a_new_type_of_calculus_analogous_to_the_infinitesimal_calculus]-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECauchy182611"''Sur_un_nouveau_genre_de_calcul_analogue_au_calcul_infinitésimal''"_[On_a_new_type_of_calculus_analogous_to_the_infinitesimal_calculus]_19-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCauchy1826">Cauchy 1826</a>, p. 11, "<i>Sur un nouveau genre de calcul analogue au calcul infinitésimal</i>" [On a new type of calculus analogous to the infinitesimal calculus].</span> </li> <li id="cite_note-FOOTNOTECauchy1831-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECauchy1831_20-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCauchy1831">Cauchy 1831</a>.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text">Cauchy, <i>Mémoire sur les rapports qui existent entre le calcul des Résidus et le calcul des Limites, et sur les avantages qu'offrent ces deux calculs dans la résolution des équations algébriques ou transcendantes</i> (Memorandum on the connections that exist between the residue calculus and the limit calculus, and on the advantages that these two calculi offer in solving algebraic and transcendental equations], presented to the Academy of Sciences of Turin, November 27, 1831.</span> </li> <li id="cite_note-FOOTNOTEBorovikKatz2012245–276-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBorovikKatz2012245–276_22-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBorovikKatz2012">Borovik & Katz 2012</a>, pp. 245–276.</span> </li> <li id="cite_note-FOOTNOTEGrabiner1981-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGrabiner1981_23-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGrabiner1981">Grabiner 1981</a>.</span> </li> <li id="cite_note-FOOTNOTEBarany2011-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBarany2011_24-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBarany2011">Barany 2011</a>.</span> </li> <li id="cite_note-FOOTNOTEGilain1989-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGilain1989_25-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGilain1989">Gilain 1989</a>.</span> </li> <li id="cite_note-FOOTNOTEBarany2013-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBarany2013_26-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBarany2013">Barany 2013</a>.</span> </li> <li id="cite_note-FOOTNOTECauchy1821-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECauchy1821_27-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCauchy1821">Cauchy 1821</a>.</span> </li> <li id="cite_note-FOOTNOTECauchy1829-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECauchy1829_28-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCauchy1829">Cauchy 1829</a>.</span> </li> <li id="cite_note-FOOTNOTEKline1982176-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKline1982176_29-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKline1982">Kline 1982</a>, p. 176.</span> </li> <li id="cite_note-FOOTNOTEValson186813Vol._1-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEValson186813Vol._1_30-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFValson1868">Valson 1868</a>, p. 13, Vol. 1.</span> </li> <li id="cite_note-FOOTNOTEBelhoste19913-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBelhoste19913_31-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBelhoste1991">Belhoste 1991</a>, p. 3.</span> </li> <li id="cite_note-FOOTNOTEBrock1908-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBrock1908_32-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBrock1908">Brock 1908</a>.</span> </li> <li id="cite_note-FOOTNOTEBell1986273-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBell1986273_33-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBell1986">Bell 1986</a>, p. 273.</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=Augustin-Louis_Cauchy&action=edit&section=21" 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 refbegin-hanging-indents refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBelhoste1991" class="citation book cs1">Belhoste, Bruno (1991). <i>Augustin-Louis Cauchy: A Biography</i>. Translated by Frank Ragland. Ann Arbor, Michigan: Springer. p. 134. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-540-97220-X" title="Special:BookSources/3-540-97220-X"><bdi>3-540-97220-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Augustin-Louis+Cauchy%3A+A+Biography&rft.place=Ann+Arbor%2C+Michigan&rft.pages=134&rft.pub=Springer&rft.date=1991&rft.isbn=3-540-97220-X&rft.aulast=Belhoste&rft.aufirst=Bruno&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBell1986" class="citation book cs1"><a href="/wiki/Eric_Temple_Bell" title="Eric Temple Bell">Bell, E. T.</a> (1986). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=BLFL3coT5i4C&pg=PA273"><i>Men of Mathematics</i></a>. Simon and Schuster. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780671628185" title="Special:BookSources/9780671628185"><bdi>9780671628185</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Men+of+Mathematics&rft.pub=Simon+and+Schuster&rft.date=1986&rft.isbn=9780671628185&rft.aulast=Bell&rft.aufirst=E.+T.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DBLFL3coT5i4C%26pg%3DPA273&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBorovikKatz2012" class="citation journal cs1"><a href="/wiki/Alexandre_Borovik" title="Alexandre Borovik">Borovik, Alexandre</a>; <a href="/wiki/Mikhail_Katz" title="Mikhail Katz">Katz, Mikhail G.</a> (2012). "Who gave you the Cauchy--Weierstrass tale? The dual history of rigorous calculus". <i><a href="/wiki/Foundations_of_Science" title="Foundations of Science">Foundations of Science</a></i>. <b>17</b> (3): <span class="nowrap">245–</span>276. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1108.2885">1108.2885</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10699-011-9235-x">10.1007/s10699-011-9235-x</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:119320059">119320059</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Foundations+of+Science&rft.atitle=Who+gave+you+the+Cauchy--Weierstrass+tale%3F+The+dual+history+of+rigorous+calculus&rft.volume=17&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E245-%3C%2Fspan%3E276&rft.date=2012&rft_id=info%3Aarxiv%2F1108.2885&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119320059%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fs10699-011-9235-x&rft.aulast=Borovik&rft.aufirst=Alexandre&rft.au=Katz%2C+Mikhail+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBradleySandifer2010" class="citation book cs1">Bradley, Robert E.; Sandifer, Charles Edward (2010). Buchwald, J. Z. (ed.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=M0or-HGe7D0C"><i>Cauchy's Cours d'analyse: An Annotated Translation</i></a>. Sources and Studies in the History of Mathematics and Physical Sciences. Cauchy, Augustin-Louis. Springer. pp. 10, 285. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4419-0549-9">10.1007/978-1-4419-0549-9</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4419-0548-2" title="Special:BookSources/978-1-4419-0548-2"><bdi>978-1-4419-0548-2</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/2009932254">2009932254</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cauchy%27s+Cours+d%27analyse%3A+An+Annotated+Translation&rft.series=Sources+and+Studies+in+the+History+of+Mathematics+and+Physical+Sciences&rft.pages=10%2C+285&rft.pub=Springer&rft.date=2010&rft_id=info%3Alccn%2F2009932254&rft_id=info%3Adoi%2F10.1007%2F978-1-4419-0549-9&rft.isbn=978-1-4419-0548-2&rft.aulast=Bradley&rft.aufirst=Robert+E.&rft.au=Sandifer%2C+Charles+Edward&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DM0or-HGe7D0C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBrock1908" class="citation encyclopaedia cs1">Brock, Henry Matthias (1908). <span class="cs1-ws-icon" title="s:Catholic Encyclopedia (1913)/Augustin-Louis Cauchy"><a class="external text" href="https://en.wikisource.org/wiki/Catholic_Encyclopedia_(1913)/Augustin-Louis_Cauchy">"Augustin-Louis Cauchy" </a></span>. In Herbermann, Charles (ed.). <i><a href="/wiki/Catholic_Encyclopedia" title="Catholic Encyclopedia">Catholic Encyclopedia</a></i>. Vol. 3. New York: Robert Appleton Company.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Augustin-Louis+Cauchy&rft.btitle=Catholic+Encyclopedia&rft.place=New+York&rft.pub=Robert+Appleton+Company&rft.date=1908&rft.aulast=Brock&rft.aufirst=Henry+Matthias&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBrunoBaker2003" class="citation book cs1">Bruno, Leonard C.; Baker, Lawrence W. (2003) [1999]. <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/mathmathematicia00brun"><i>Math and mathematicians : the history of math discoveries around the world</i></a></span>. Detroit, Mich.: U X L. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0787638137" title="Special:BookSources/0787638137"><bdi>0787638137</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/41497065">41497065</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Math+and+mathematicians+%3A+the+history+of+math+discoveries+around+the+world&rft.place=Detroit%2C+Mich.&rft.pub=U+X+L&rft.date=2003&rft_id=info%3Aoclcnum%2F41497065&rft.isbn=0787638137&rft.aulast=Bruno&rft.aufirst=Leonard+C.&rft.au=Baker%2C+Lawrence+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmathmathematicia00brun&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFChisholm1911" class="citation encyclopaedia cs1"><a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm, Hugh</a>, ed. (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Cauchy, Augustin Louis"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Cauchy,_Augustin_Louis">"Cauchy, Augustin Louis" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 5 (11th ed.). Cambridge University Press. pp. <span class="nowrap">555–</span>556.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Cauchy%2C+Augustin+Louis&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=%3Cspan+class%3D%22nowrap%22%3E555-%3C%2Fspan%3E556&rft.edition=11th&rft.pub=Cambridge+University+Press&rft.date=1911&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFreudenthal2008" class="citation encyclopaedia cs1">Freudenthal, Hans (2008). <a rel="nofollow" class="external text" href="http://www.encyclopedia.com/topic/Augustin-Louis_Cauchy.aspx#1">"Cauchy, Augustin-Louis"</a>. In Gillispie, Charles (ed.). <i><a href="/wiki/Dictionary_of_Scientific_Biography" title="Dictionary of Scientific Biography">Dictionary of Scientific Biography</a></i>. New York: Scribner. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-684-10114-9" title="Special:BookSources/978-0-684-10114-9"><bdi>978-0-684-10114-9</bdi></a> – via American Council of Learned Societies.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Cauchy%2C+Augustin-Louis&rft.btitle=Dictionary+of+Scientific+Biography&rft.place=New+York&rft.pub=Scribner&rft.date=2008&rft.isbn=978-0-684-10114-9&rft.aulast=Freudenthal&rft.aufirst=Hans&rft_id=http%3A%2F%2Fwww.encyclopedia.com%2Ftopic%2FAugustin-Louis_Cauchy.aspx%231&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKline1982" class="citation book cs1">Kline, Morris (1982). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=RNwnUL33epsC"><i>Mathematics: The Loss of Certainty</i></a>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-503085-3" title="Special:BookSources/978-0-19-503085-3"><bdi>978-0-19-503085-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics%3A+The+Loss+of+Certainty&rft.pub=Oxford+University+Press&rft.date=1982&rft.isbn=978-0-19-503085-3&rft.aulast=Kline&rft.aufirst=Morris&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DRNwnUL33epsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFValson1868" class="citation book cs1 cs1-prop-foreign-lang-source">Valson, Claude-Alphonse (1868). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vQ7tw0rVKPsC"><i>La vie et les travaux du baron Cauchy: membre de l'académie des sciences</i></a> [<i>The Life and Works of Baron Cauchy: Member of the Academy of Scinces</i>] (in French). Gauthier-Villars.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=La+vie+et+les+travaux+du+baron+Cauchy%3A+membre+de+l%27acad%C3%A9mie+des+sciences&rft.pub=Gauthier-Villars&rft.date=1868&rft.aulast=Valson&rft.aufirst=Claude-Alphonse&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DvQ7tw0rVKPsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><i>This article incorporates material from the <a href="/wiki/Citizendium" title="Citizendium">Citizendium</a> article "<a href="https://en.citizendium.org/wiki/Augustin-Louis_Cauchy" class="extiw" title="citizendium:Augustin-Louis Cauchy">Augustin-Louis Cauchy</a>", which is licensed under the <a href="/wiki/Wikipedia:Text_of_Creative_Commons_Attribution-ShareAlike_3.0_Unported_License" class="mw-redirect" title="Wikipedia:Text of Creative Commons Attribution-ShareAlike 3.0 Unported License">Creative Commons Attribution-ShareAlike 3.0 Unported License</a> but not under the <a href="/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License" title="Wikipedia:Text of the GNU Free Documentation License">GFDL</a>.</i></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Further_reading">Further reading</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Augustin-Louis_Cauchy&action=edit&section=22" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239549316" /><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBarany2013" class="citation cs2">Barany, Michael (2013), "Stuck in the Middle: Cauchy's Intermediate Value Theorem and the History of Analytic Rigor", <i>Notices of the American Mathematical Society</i>, <b>60</b> (10): <span class="nowrap">1334–</span>1338, <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/10.1090%2Fnoti1049">10.1090/noti1049</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notices+of+the+American+Mathematical+Society&rft.atitle=Stuck+in+the+Middle%3A+Cauchy%27s+Intermediate+Value+Theorem+and+the+History+of+Analytic+Rigor&rft.volume=60&rft.issue=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1334-%3C%2Fspan%3E1338&rft.date=2013&rft_id=info%3Adoi%2F10.1090%2Fnoti1049&rft.aulast=Barany&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBarany2011" class="citation cs2">Barany, Michael (2011), "God, king, and geometry: revisiting the introduction to Cauchy's <i>Cours d'analyse</i>", <i>Historia Mathematica</i>, <b>38</b> (3): <span class="nowrap">368–</span>388, <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%2Fj.hm.2010.12.001">10.1016/j.hm.2010.12.001</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=God%2C+king%2C+and+geometry%3A+revisiting+the+introduction+to+Cauchy%27s+Cours+d%27analyse&rft.volume=38&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E368-%3C%2Fspan%3E388&rft.date=2011&rft_id=info%3Adoi%2F10.1016%2Fj.hm.2010.12.001&rft.aulast=Barany&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li>Boyer, C.: The concepts of the calculus. Hafner Publishing Company, 1949.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBenis-Sinaceur1973" class="citation journal cs1">Benis-Sinaceur, Hourya (1973). <a rel="nofollow" class="external text" href="https://halshs.archives-ouvertes.fr/halshs-01119625/file/1973_RHS_vol26_n2_p97_CauchyBolzano.pdf">"Cauchy et Bolzano"</a> <span class="cs1-format">(PDF)</span>. <i>Revue d'Histoire des Sciences</i>. <b>26</b> (2): <span class="nowrap">97–</span>112. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3406%2Frhs.1973.3315">10.3406/rhs.1973.3315</a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/https://halshs.archives-ouvertes.fr/halshs-01119625/file/1973_RHS_vol26_n2_p97_CauchyBolzano.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2022-10-09.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Revue+d%27Histoire+des+Sciences&rft.atitle=Cauchy+et+Bolzano&rft.volume=26&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E97-%3C%2Fspan%3E112&rft.date=1973&rft_id=info%3Adoi%2F10.3406%2Frhs.1973.3315&rft.aulast=Benis-Sinaceur&rft.aufirst=Hourya&rft_id=https%3A%2F%2Fhalshs.archives-ouvertes.fr%2Fhalshs-01119625%2Ffile%2F1973_RHS_vol26_n2_p97_CauchyBolzano.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFLaugwitz1989" class="citation cs2"><a href="/wiki/Detlef_Laugwitz" title="Detlef Laugwitz">Laugwitz, D.</a> (1989), "Definite values of infinite sums: aspects of the foundations of infinitesimal analysis around 1820", <i>Arch. Hist. Exact Sci.</i>, <b>39</b> (3): <span class="nowrap">195–</span>245, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00329867">10.1007/BF00329867</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:120890300">120890300</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Arch.+Hist.+Exact+Sci.&rft.atitle=Definite+values+of+infinite+sums%3A+aspects+of+the+foundations+of+infinitesimal+analysis+around+1820&rft.volume=39&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E195-%3C%2Fspan%3E245&rft.date=1989&rft_id=info%3Adoi%2F10.1007%2FBF00329867&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120890300%23id-name%3DS2CID&rft.aulast=Laugwitz&rft.aufirst=D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGilain1989" class="citation cs2">Gilain, C. (1989), "Cauchy et le Course d'Analyse de l'École Polytechnique", <i>Bulletin de la Société des amis de la Bibliothèque de l'École polytechnique</i>, <b>5</b>: <span class="nowrap">3–</span>145</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+de+la+Soci%C3%A9t%C3%A9+des+amis+de+la+Biblioth%C3%A8que+de+l%27%C3%89cole+polytechnique&rft.atitle=Cauchy+et+le+Course+d%27Analyse+de+l%27%C3%89cole+Polytechnique&rft.volume=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3-%3C%2Fspan%3E145&rft.date=1989&rft.aulast=Gilain&rft.aufirst=C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGrabiner1981" class="citation book cs1">Grabiner, Judith V. (1981). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/originsofcauchys00judi"><i>The Origins of Cauchy's Rigorous Calculus</i></a></span>. Cambridge: MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-90527-8" title="Special:BookSources/0-387-90527-8"><bdi>0-387-90527-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Origins+of+Cauchy%27s+Rigorous+Calculus&rft.place=Cambridge&rft.pub=MIT+Press&rft.date=1981&rft.isbn=0-387-90527-8&rft.aulast=Grabiner&rft.aufirst=Judith+V.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Foriginsofcauchys00judi&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRassias1989" class="citation book cs1"><a href="/wiki/Themistocles_M._Rassias" title="Themistocles M. Rassias">Rassias, Th. M.</a> (1989). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120325032416/http://www.worldscibooks.com/mathematics/0659.html"><i>Topics in Mathematical Analysis, A Volume Dedicated to the Memory of A. L. Cauchy</i></a>. Singapore, New Jersey, London: World Scientific Co. Archived from <a rel="nofollow" class="external text" href="http://www.worldscibooks.com/mathematics/0659.html">the original</a> on 2012-03-25<span class="reference-accessdate">. Retrieved <span class="nowrap">2011-01-27</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Topics+in+Mathematical+Analysis%2C+A+Volume+Dedicated+to+the+Memory+of+A.+L.+Cauchy&rft.place=Singapore%2C+New+Jersey%2C+London&rft.pub=World+Scientific+Co.&rft.date=1989&rft.aulast=Rassias&rft.aufirst=Th.+M.&rft_id=http%3A%2F%2Fwww.worldscibooks.com%2Fmathematics%2F0659.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSmithies1986" class="citation journal cs1">Smithies, F. (1986). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41133794">"Cauchy's Conception of Rigour in Analysis"</a>. <i>Archive for History of Exact Sciences</i>. <b>36</b> (1): <span class="nowrap">41–</span>61. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00357440">10.1007/BF00357440</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41133794">41133794</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:120781880">120781880</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=Cauchy%27s+Conception+of+Rigour+in+Analysis&rft.volume=36&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E41-%3C%2Fspan%3E61&rft.date=1986&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120781880%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F41133794%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1007%2FBF00357440&rft.aulast=Smithies&rft.aufirst=F.&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F41133794&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation encyclopaedia cs1"><span class="cs1-ws-icon" title="s:The New International Encyclopædia/Cauchy, Augustin Louis"><a class="external text" href="https://en.wikisource.org/wiki/The_New_International_Encyclop%C3%A6dia/Cauchy,_Augustin_Louis">"Cauchy, Augustin Louis" </a></span>. <i><a href="/wiki/New_International_Encyclopedia" class="mw-redirect" title="New International Encyclopedia">New International Encyclopedia</a></i>. 1905.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Cauchy%2C+Augustin+Louis&rft.btitle=New+International+Encyclopedia&rft.date=1905&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" 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=Augustin-Louis_Cauchy&action=edit&section=23" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style 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class="mw-redirect" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Cauchy.html">"Augustin-Louis Cauchy"</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=Augustin-Louis+Cauchy&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%2FCauchy.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAugustin-Louis+Cauchy" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20050617084840/http://planetmath.org/encyclopedia/CauchyCriterionForConvergence.html">Cauchy criterion for convergence</a> at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (archived June 17, 2005)</li> <li><a rel="nofollow" class="external text" href="http://portail.mathdoc.fr/cgi-bin/oetoc?id=OE_CAUCHY_1_1">Augustin-Louis Cauchy – Œuvres complètes</a> (in 2 series) Gallica-Math</li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=55177">Augustin-Louis Cauchy</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="http://math.berkeley.edu/~robin/Cauchy/">Augustin-Louis Cauchy – Cauchy's Life</a> by <a href="/wiki/Robin_Hartshorne" title="Robin Hartshorne">Robin Hartshorne</a></li></ul> <div class="navbox-styles"><style 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