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class="vector-toc-list"> <li id="toc-Saint_Petersburg" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Saint_Petersburg"> <div class="vector-toc-text"> 2.1 Saint Petersburg </div> </a> <ul id="toc-Saint_Petersburg-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Berlin" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Berlin"> <div class="vector-toc-text"> 2.2 Berlin </div> </a> <ul id="toc-Berlin-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Return_to_Russia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Return_to_Russia"> <div class="vector-toc-text"> 2.3 Return to Russia </div> </a> <ul id="toc-Return_to_Russia-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Personal_life" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Personal_life"> <div class="vector-toc-text"> 3 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href="#Contributions_to_mathematics_and_physics"> <div class="vector-toc-text"> 4 Contributions to mathematics and physics </div> </a> <button aria-controls="toc-Contributions_to_mathematics_and_physics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Contributions to mathematics and physics subsection </button> <ul id="toc-Contributions_to_mathematics_and_physics-sublist" class="vector-toc-list"> <li id="toc-Mathematical_notation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mathematical_notation"> <div class="vector-toc-text"> 4.1 Mathematical notation </div> </a> <ul id="toc-Mathematical_notation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Analysis"> <div class="vector-toc-text"> 4.2 Analysis </div> </a> <ul id="toc-Analysis-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"> 4.3 Number theory </div> </a> <ul id="toc-Number_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Graph_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Graph_theory"> <div class="vector-toc-text"> 4.4 Graph theory </div> </a> <ul id="toc-Graph_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physics,_astronomy,_and_engineering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Physics,_astronomy,_and_engineering"> <div class="vector-toc-text"> 4.5 Physics, astronomy, and engineering </div> </a> <ul id="toc-Physics,_astronomy,_and_engineering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Logic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Logic"> <div class="vector-toc-text"> 4.6 Logic </div> </a> <ul id="toc-Logic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Music" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Music"> <div class="vector-toc-text"> 4.7 Music </div> </a> <ul id="toc-Music-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Personal_philosophy_and_religious_beliefs" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Personal_philosophy_and_religious_beliefs"> <div class="vector-toc-text"> 5 Personal philosophy and religious beliefs </div> </a> <ul id="toc-Personal_philosophy_and_religious_beliefs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Commemorations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Commemorations"> <div class="vector-toc-text"> 6 Commemorations </div> </a> <ul id="toc-Commemorations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Selected_bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Selected_bibliography"> <div class="vector-toc-text"> 7 Selected bibliography </div> </a> <ul id="toc-Selected_bibliography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> 8 Notes </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 9 References </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle References subsection </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> 9.1 Sources </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> 10 Further reading </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 11 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Leonhard Euler</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 158 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-158" aria-hidden="true" > 158 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ady mw-list-item"><a href="https://ady.wikipedia.org/wiki/%D0%AD%D0%B9%D0%BB%D0%B5%D1%80,_%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4" title="Эйлер, Леонард – Adyghe" lang="ady" hreflang="ady" data-title="Эйлер, Леонард" data-language-autonym="Адыгабзэ" data-language-local-name="Adyghe" class="interlanguage-link-target">Адыгабзэ</a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Afrikaans" lang="af" hreflang="af" data-title="Leonhard Euler" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Alemannic" lang="gsw" hreflang="gsw" data-title="Leonhard Euler" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target">Alemannisch</a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%8C%E1%8B%AE%E1%8A%93%E1%88%AD%E1%8B%B5_%E1%8A%A6%E1%8B%AD%E1%88%88%E1%88%AD" title="ሌዮናርድ ኦይለር – Amharic" lang="am" hreflang="am" data-title="ሌዮናርድ ኦይለር" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target">አማርኛ</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%84%D9%8A%D9%88%D9%86%D9%87%D8%A7%D8%B1%D8%AA_%D8%A3%D9%88%D9%8A%D9%84%D8%B1" title="ليونهارت أويلر – Arabic" lang="ar" hreflang="ar" data-title="ليونهارت أويلر" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Aragonese" lang="an" hreflang="an" data-title="Leonhard Euler" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B2%E0%A6%BF%E0%A6%85%27%E0%A6%A8%E0%A6%BE%E0%A7%B0%E0%A7%8D%E0%A6%A1_%E0%A6%85%E0%A6%87%E0%A6%B2%E0%A6%BE%E0%A7%B0" title="লিঅ'নাৰ্ড অইলাৰ – Assamese" lang="as" hreflang="as" data-title="লিঅ'নাৰ্ড অইলাৰ" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target">অসমীয়া</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Asturian" lang="ast" hreflang="ast" data-title="Leonhard Euler" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Guarani" lang="gn" hreflang="gn" data-title="Leonhard Euler" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" class="interlanguage-link-target">Avañe'ẽ</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Leonard_Eyler" title="Leonard Eyler – Azerbaijani" lang="az" hreflang="az" data-title="Leonard Eyler" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%84%D8%A6%D9%88%D9%86%D8%A7%D8%B1%D8%AF_%D8%A7%D9%88%DB%8C%D9%84%D8%B1" title="لئونارد اویلر – South Azerbaijani" lang="azb" hreflang="azb" data-title="لئونارد اویلر" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target">تۆرکجه</a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Balinese" lang="ban" hreflang="ban" data-title="Leonhard Euler" data-language-autonym="Basa Bali" data-language-local-name="Balinese" class="interlanguage-link-target">Basa Bali</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B2%E0%A7%87%E0%A6%93%E0%A6%A8%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A1_%E0%A6%85%E0%A6%AF%E0%A6%BC%E0%A6%B2%E0%A6%BE%E0%A6%B0" title="লেওনার্ড অয়লার – Bangla" lang="bn" hreflang="bn" data-title="লেওনার্ড অয়লার" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Minnan" lang="nan" hreflang="nan" data-title="Leonhard Euler" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Bashkir" lang="ba" hreflang="ba" data-title="Леонард Эйлер" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target">Башҡортса</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9B%D0%B5%D0%B0%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леанард Эйлер – Belarusian" lang="be" hreflang="be" data-title="Леанард Эйлер" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9B%D0%B5%D0%B0%D0%BD%D0%B0%D1%80%D0%B4_%D0%9E%D0%B9%D0%BB%D0%B5%D1%80" title="Леанард Ойлер – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Леанард Ойлер" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target">Беларуская (тарашкевіца)</a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%B2%E0%A4%BF%E0%A4%AF%E0%A5%8B%E0%A4%A8%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%91%E0%A4%AF%E0%A4%B2%E0%A4%B0" title="लियोनार्ड ऑयलर – Bhojpuri" lang="bh" hreflang="bh" data-title="लियोनार्ड ऑयलर" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target">भोजपुरी</a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Central Bikol" lang="bcl" hreflang="bcl" data-title="Leonhard Euler" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target">Bikol Central</a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Bislama" lang="bi" hreflang="bi" data-title="Leonhard Euler" data-language-autonym="Bislama" data-language-local-name="Bislama" class="interlanguage-link-target">Bislama</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%9E%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Ойлер – Bulgarian" lang="bg" hreflang="bg" data-title="Леонард Ойлер" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Bosnian" lang="bs" hreflang="bs" data-title="Leonhard Euler" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Breton" lang="br" hreflang="br" data-title="Leonhard Euler" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target">Brezhoneg</a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Леонард Эйлер" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target">Буряад</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Catalan" lang="ca" hreflang="ca" data-title="Leonhard Euler" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Chuvash" lang="cv" hreflang="cv" data-title="Леонард Эйлер" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Cebuano" lang="ceb" hreflang="ceb" data-title="Leonhard Euler" data-language-autonym="Cebuano" data-language-local-name="Cebuano" class="interlanguage-link-target">Cebuano</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Czech" lang="cs" hreflang="cs" data-title="Leonhard Euler" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-tum mw-list-item"><a href="https://tum.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Tumbuka" lang="tum" hreflang="tum" data-title="Leonhard Euler" data-language-autonym="ChiTumbuka" data-language-local-name="Tumbuka" class="interlanguage-link-target">ChiTumbuka</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Welsh" lang="cy" hreflang="cy" data-title="Leonhard Euler" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Danish" lang="da" hreflang="da" data-title="Leonhard Euler" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%A3%D9%88%D9%8A%D9%84%D8%B1" title="أويلر – Moroccan Arabic" lang="ary" hreflang="ary" data-title="أويلر" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target">الدارجة</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/Leonhard_Euler" title="Leonhard Euler – German" lang="de" hreflang="de" data-title="Leonhard Euler" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Estonian" lang="et" hreflang="et" data-title="Leonhard Euler" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%AD%CE%BF%CE%BD%CE%B1%CF%81%CE%BD%CF%84_%CE%8C%CE%B9%CE%BB%CE%B5%CF%81" title="Λέοναρντ Όιλερ – Greek" lang="el" hreflang="el" data-title="Λέοναρντ Όιλερ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://es.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Spanish" lang="es" hreflang="es" data-title="Leonhard Euler" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Esperanto" lang="eo" hreflang="eo" data-title="Leonhard Euler" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Leonard_Euler" title="Leonard Euler – Extremaduran" lang="ext" hreflang="ext" data-title="Leonard Euler" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target">Estremeñu</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Basque" lang="eu" hreflang="eu" data-title="Leonhard Euler" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%84%D8%A6%D9%88%D9%86%D8%A7%D8%B1%D8%AF_%D8%A7%D9%88%DB%8C%D9%84%D8%B1" title="لئونارد اویلر – Persian" lang="fa" hreflang="fa" data-title="لئونارد اویلر" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Fiji Hindi" lang="hif" hreflang="hif" data-title="Leonhard Euler" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target">Fiji Hindi</a></li><li class="interlanguage-link interwiki-fr badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://fr.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – French" lang="fr" hreflang="fr" data-title="Leonhard Euler" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Western Frisian" lang="fy" hreflang="fy" data-title="Leonhard Euler" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target">Frysk</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Irish" lang="ga" hreflang="ga" data-title="Leonhard Euler" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Scottish Gaelic" lang="gd" hreflang="gd" data-title="Leonhard Euler" data-language-autonym="Gàidhlig" data-language-local-name="Scottish Gaelic" class="interlanguage-link-target">Gàidhlig</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Galician" lang="gl" hreflang="gl" data-title="Leonhard Euler" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E6%AD%90%E6%8B%89" title="歐拉 – Gan" lang="gan" hreflang="gan" data-title="歐拉" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target">贛語</a></li><li class="interlanguage-link interwiki-got mw-list-item"><a href="https://got.wikipedia.org/wiki/%F0%90%8C%BB%F0%90%8C%B9%F0%90%8D%85%F0%90%8C%B0%F0%90%8C%B7%F0%90%8C%B0%F0%90%8D%82%F0%90%8C%B3%F0%90%8C%BF%F0%90%8D%83_%F0%90%8C%B4%F0%90%8D%85%F0%90%8C%BB%F0%90%8C%B0%F0%90%8C%B9%F0%90%8D%82" title="𐌻𐌹𐍅𐌰𐌷𐌰𐍂𐌳𐌿𐍃 𐌴𐍅𐌻𐌰𐌹𐍂 – Gothic" lang="got" hreflang="got" data-title="𐌻𐌹𐍅𐌰𐌷𐌰𐍂𐌳𐌿𐍃 𐌴𐍅𐌻𐌰𐌹𐍂" data-language-autonym="𐌲𐌿𐍄𐌹𐍃𐌺" data-language-local-name="Gothic" class="interlanguage-link-target">𐌲𐌿𐍄𐌹𐍃𐌺</a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Kalmyk" lang="xal" hreflang="xal" data-title="Леонард Эйлер" data-language-autonym="Хальмг" data-language-local-name="Kalmyk" class="interlanguage-link-target">Хальмг</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A0%88%EC%98%A8%ED%95%98%EB%A5%B4%ED%8A%B8_%EC%98%A4%EC%9D%BC%EB%9F%AC" title="레온하르트 오일러 – Korean" lang="ko" hreflang="ko" data-title="레온하르트 오일러" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Hausa" lang="ha" hreflang="ha" data-title="Leonhard Euler" data-language-autonym="Hausa" data-language-local-name="Hausa" class="interlanguage-link-target">Hausa</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BC%D5%A5%D5%B8%D5%B6%D5%A1%D6%80%D5%A4_%D4%B7%D5%B5%D5%AC%D5%A5%D6%80" title="Լեոնարդ Էյլեր – Armenian" lang="hy" hreflang="hy" data-title="Լեոնարդ Էյլեր" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B2%E0%A4%BF%E0%A4%AF%E0%A5%8B%E0%A4%A8%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%93%E0%A4%87%E0%A4%B2%E0%A4%B0" title="लियोनार्ड ओइलर – Hindi" lang="hi" hreflang="hi" data-title="लियोनार्ड ओइलर" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Croatian" lang="hr" hreflang="hr" data-title="Leonhard Euler" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Ido" lang="io" hreflang="io" data-title="Leonhard Euler" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target">Ido</a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Iloko" lang="ilo" hreflang="ilo" data-title="Leonhard Euler" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target">Ilokano</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Indonesian" lang="id" hreflang="id" data-title="Leonhard Euler" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Interlingua" lang="ia" hreflang="ia" data-title="Leonhard Euler" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target">Interlingua</a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%AD%D0%B9%D0%BB%D0%B5%D1%80,_%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4" title="Эйлер, Леонард – Ossetic" lang="os" hreflang="os" data-title="Эйлер, Леонард" data-language-autonym="Ирон" data-language-local-name="Ossetic" class="interlanguage-link-target">Ирон</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Icelandic" lang="is" hreflang="is" data-title="Leonhard Euler" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Eulero" title="Eulero – Italian" lang="it" hreflang="it" data-title="Eulero" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9C%D7%90%D7%95%D7%A0%D7%A8%D7%93_%D7%90%D7%95%D7%99%D7%9C%D7%A8" title="לאונרד אוילר – Hebrew" lang="he" hreflang="he" data-title="לאונרד אוילר" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Javanese" lang="jv" hreflang="jv" data-title="Leonhard Euler" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target">Jawa</a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Kabiye" lang="kbp" hreflang="kbp" data-title="Leonhard Euler" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target">Kabɩyɛ</a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B2%E0%B2%BF%E0%B2%AF%E0%B3%8A%E0%B2%A8%E0%B2%BE%E0%B2%B0%E0%B3%8D%E0%B2%A1%E0%B3%8D_%E0%B2%AF%E0%B3%82%E0%B2%B2%E0%B2%B0%E0%B3%8D" title="ಲಿಯೊನಾರ್ಡ್ ಯೂಲರ್ – Kannada" lang="kn" hreflang="kn" data-title="ಲಿಯೊನಾರ್ಡ್ ಯೂಲರ್" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9A%E1%83%94%E1%83%9D%E1%83%9C%E1%83%90%E1%83%A0%E1%83%93_%E1%83%94%E1%83%98%E1%83%9A%E1%83%94%E1%83%A0%E1%83%98" title="ლეონარდ ეილერი – Georgian" lang="ka" hreflang="ka" data-title="ლეონარდ ეილერი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Kazakh" lang="kk" hreflang="kk" data-title="Леонард Эйлер" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Cornish" lang="kw" hreflang="kw" data-title="Leonhard Euler" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target">Kernowek</a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Leonard_Euler" title="Leonard Euler – Swahili" lang="sw" hreflang="sw" data-title="Leonard Euler" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target">Kiswahili</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Haitian Creole" lang="ht" hreflang="ht" data-title="Leonhard Euler" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Leonhard Euler" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target">Kriyòl gwiyannen</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Kyrgyz" lang="ky" hreflang="ky" data-title="Леонард Эйлер" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Leonhardus_Eulerus" title="Leonhardus Eulerus – Latin" lang="la" hreflang="la" data-title="Leonhardus Eulerus" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Leonards_Eilers" title="Leonards Eilers – Latvian" lang="lv" hreflang="lv" data-title="Leonards Eilers" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Luxembourgish" lang="lb" hreflang="lb" data-title="Leonhard Euler" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target">Lëtzebuergesch</a></li><li class="interlanguage-link interwiki-lez mw-list-item"><a href="https://lez.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Lezghian" lang="lez" hreflang="lez" data-title="Леонард Эйлер" data-language-autonym="Лезги" data-language-local-name="Lezghian" class="interlanguage-link-target">Лезги</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Lithuanian" lang="lt" hreflang="lt" data-title="Leonhard Euler" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Limburgish" lang="li" hreflang="li" data-title="Leonhard Euler" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target">Limburgs</a></li><li class="interlanguage-link interwiki-olo mw-list-item"><a href="https://olo.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Livvi-Karelian" lang="olo" hreflang="olo" data-title="Leonhard Euler" data-language-autonym="Livvinkarjala" data-language-local-name="Livvi-Karelian" class="interlanguage-link-target">Livvinkarjala</a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/leonard.euler" title="leonard.euler – Lojban" lang="jbo" hreflang="jbo" data-title="leonard.euler" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target">La .lojban.</a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Lombard" lang="lmo" hreflang="lmo" data-title="Leonhard Euler" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target">Lombard</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Hungarian" lang="hu" hreflang="hu" data-title="Leonhard Euler" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%B2%E0%A4%BF%E0%A4%AF%E0%A5%8B%E0%A4%A8%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%93%E0%A4%87%E0%A4%B2%E0%A4%B0" title="लियोनार्ड ओइलर – Maithili" lang="mai" hreflang="mai" data-title="लियोनार्ड ओइलर" data-language-autonym="मैथिली" data-language-local-name="Maithili" class="interlanguage-link-target">मैथिली</a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://mk.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%9E%D1%98%D0%BB%D0%B5%D1%80" title="Леонард Ојлер – Macedonian" lang="mk" hreflang="mk" data-title="Леонард Ојлер" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Malagasy" lang="mg" hreflang="mg" data-title="Leonhard Euler" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target">Malagasy</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B2%E0%B5%86%E0%B4%AF%E0%B5%BB%E0%B4%B9%E0%B4%BE%E0%B5%BC%E0%B4%9F%E0%B5%8D_%E0%B4%93%E0%B4%AF%E0%B5%8D%E0%B4%B2%E0%B5%BC" title="ലെയൻഹാർട് ഓയ്ലർ – Malayalam" lang="ml" hreflang="ml" data-title="ലെയൻഹാർട് ഓയ്ലർ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B2%E0%A4%BF%E0%A4%93%E0%A4%A8%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%91%E0%A4%AF%E0%A4%B2%E0%A4%B0" title="लिओनार्ड ऑयलर – Marathi" lang="mr" hreflang="mr" data-title="लिओनार्ड ऑयलर" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%9A%E1%83%94%E1%83%9D%E1%83%9C%E1%83%90%E1%83%A0%E1%83%93_%E1%83%94%E1%83%98%E1%83%9A%E1%83%94%E1%83%A0%E1%83%98" title="ლეონარდ ეილერი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ლეონარდ ეილერი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target">მარგალური</a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%84%D9%8A%D9%88%D9%86%D8%A7%D8%B1%D8%AF_%D9%8A%D9%88%D9%84%D8%B1" title="ليونارد يولر – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ليونارد يولر" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target">مصرى</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Malay" lang="ms" hreflang="ms" data-title="Leonhard Euler" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Mirandese" lang="mwl" hreflang="mwl" data-title="Leonhard Euler" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target">Mirandés</a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Mongolian" lang="mn" hreflang="mn" data-title="Леонард Эйлер" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target">Монгол</a></li><li class="interlanguage-link interwiki-my badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://my.wikipedia.org/wiki/%E1%80%9C%E1%80%AE%E1%80%9A%E1%80%BD%E1%80%94%E1%80%BA%E1%80%9F%E1%80%90%E1%80%BA_%E1%80%A1%E1%80%BD%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%9C%E1%80%AC" title="လီယွန်ဟတ် အွိုင်လာ – Burmese" lang="my" hreflang="my" data-title="လီယွန်ဟတ် အွိုင်လာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Dutch" lang="nl" hreflang="nl" data-title="Leonhard Euler" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B2%E0%A4%BF%E0%A4%AF%E0%A5%8B%E0%A4%A8%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%AF%E0%A5%81%E0%A4%B2%E0%A4%B0" title="लियोनार्ड युलर – Newari" lang="new" hreflang="new" data-title="लियोनार्ड युलर" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target">नेपाल भाषा</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%AC%E3%82%AA%E3%83%B3%E3%83%8F%E3%83%AB%E3%83%88%E3%83%BB%E3%82%AA%E3%82%A4%E3%83%A9%E3%83%BC" title="レオンハルト・オイラー – Japanese" lang="ja" hreflang="ja" data-title="レオンハルト・オイラー" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%AD%D0%B9%D0%BB%D0%B5%D1%80,_%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4" title="Эйлер, Леонард – Chechen" lang="ce" hreflang="ce" data-title="Эйлер, Леонард" data-language-autonym="Нохчийн" data-language-local-name="Chechen" class="interlanguage-link-target">Нохчийн</a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Northern Frisian" lang="frr" hreflang="frr" data-title="Leonhard Euler" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target">Nordfriisk</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Leonhard Euler" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Leonhard Euler" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Occitan" lang="oc" hreflang="oc" data-title="Leonhard Euler" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Liyoonaardi_Ooyiler" title="Liyoonaardi Ooyiler – Oromo" lang="om" hreflang="om" data-title="Liyoonaardi Ooyiler" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target">Oromoo</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Uzbek" lang="uz" hreflang="uz" data-title="Leonhard Euler" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B2%E0%A8%BF%E0%A8%93%E0%A8%A8%E0%A8%B9%E0%A8%BE%E0%A8%B0%E0%A8%A1_%E0%A8%87%E0%A8%93%E0%A8%B2%E0%A8%B0" title="ਲਿਓਨਹਾਰਡ ਇਓਲਰ – Punjabi" lang="pa" hreflang="pa" data-title="ਲਿਓਨਹਾਰਡ ਇਓਲਰ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%84%DB%8C%D9%88%D9%86%DB%81%D8%A7%D8%B1%DA%88_%D8%A7%D9%88%DB%8C%D9%84%D8%B1" title="لیونہارڈ اویلر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="لیونہارڈ اویلر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%84%DB%8C%D9%88%D9%86%D8%A7%D8%B1%DA%89_%D8%A7%DB%8C%D9%88%D9%84%D8%B1" title="لیونارډ ایولر – Pashto" lang="ps" hreflang="ps" data-title="لیونارډ ایولر" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Lionaad_Yuula" title="Lionaad Yuula – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Lionaad Yuula" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target">Patois</a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%9B%E1%9F%81%E1%9E%A2%E1%9E%BB%E1%9E%93%E1%9E%A0%E1%9E%B6%E1%9E%8A_%E1%9E%A2%E1%9E%99%E1%9E%9B%E1%9F%90%E1%9E%9A" title="លេអុនហាដ អយល័រ – Khmer" lang="km" hreflang="km" data-title="លេអុនហាដ អយល័រ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target">ភាសាខ្មែរ</a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Piedmontese" lang="pms" hreflang="pms" data-title="Leonhard Euler" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target">Piemontèis</a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Low German" lang="nds" hreflang="nds" data-title="Leonhard Euler" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target">Plattdüütsch</a></li><li class="interlanguage-link interwiki-pl badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://pl.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Polish" lang="pl" hreflang="pl" data-title="Leonhard Euler" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Portuguese" lang="pt" hreflang="pt" data-title="Leonhard Euler" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Leonard_Euler" title="Leonard Euler – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Leonard Euler" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target">Qaraqalpaqsha</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Romanian" lang="ro" hreflang="ro" data-title="Leonhard Euler" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%95%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Ейлер – Rusyn" lang="rue" hreflang="rue" data-title="Леонард Ейлер" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target">Русиньскый</a></li><li class="interlanguage-link interwiki-ru badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%B9%D0%BB%D0%B5%D1%80,_%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4" title="Эйлер, Леонард – Russian" lang="ru" hreflang="ru" data-title="Эйлер, Леонард" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Yakut" lang="sah" hreflang="sah" data-title="Леонард Эйлер" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target">Саха тыла</a></li><li class="interlanguage-link interwiki-szy mw-list-item"><a href="https://szy.wikipedia.org/wiki/Li-ang-ha-te._Yu-la" title="Li-ang-ha-te. Yu-la – Sakizaya" lang="szy" hreflang="szy" data-title="Li-ang-ha-te. Yu-la" data-language-autonym="Sakizaya" data-language-local-name="Sakizaya" class="interlanguage-link-target">Sakizaya</a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%B2%E0%A4%BF%E0%A4%AF%E0%A5%8B%E0%A4%A8%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%93%E0%A4%87%E0%A4%B2%E0%A4%B0" title="लियोनार्ड ओइलर – Sanskrit" lang="sa" hreflang="sa" data-title="लियोनार्ड ओइलर" data-language-autonym="संस्कृतम्" data-language-local-name="Sanskrit" class="interlanguage-link-target">संस्कृतम्</a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%9E%E1%B1%A4%E1%B1%AD%E1%B1%9A%E1%B1%B1%E1%B1%A6%E1%B1%9F%E1%B1%A8%E1%B1%B0_%E1%B1%A4%E1%B1%A3%E1%B1%9E%E1%B1%9F%E1%B1%A8" title="ᱞᱤᱭᱚᱱᱦᱟᱨᱰ ᱤᱣᱞᱟᱨ – Santali" lang="sat" hreflang="sat" data-title="ᱞᱤᱭᱚᱱᱦᱟᱨᱰ ᱤᱣᱞᱟᱨ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="Santali" class="interlanguage-link-target">ᱥᱟᱱᱛᱟᱲᱤ</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Scots" lang="sco" hreflang="sco" data-title="Leonhard Euler" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Leonard_Euler" title="Leonard Euler – Albanian" lang="sq" hreflang="sq" data-title="Leonard Euler" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Liunardu_Euleru" title="Liunardu Euleru – Sicilian" lang="scn" hreflang="scn" data-title="Liunardu Euleru" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target">Sicilianu</a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%BD%E0%B7%92%E0%B6%BA%E0%B7%9D%E0%B6%B1%E0%B7%8A%E0%B7%84%E0%B7%8F%E0%B6%A9%E0%B7%8A_%E0%B6%94%E0%B6%BA%E0%B7%92%E0%B6%BD%E0%B6%BB%E0%B7%8A" title="ලියෝන්හාඩ් ඔයිලර් – Sinhala" lang="si" hreflang="si" data-title="ලියෝන්හාඩ් ඔයිලර්" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target">සිංහල</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Simple English" lang="en-simple" hreflang="en-simple" data-title="Leonhard Euler" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Slovak" lang="sk" hreflang="sk" data-title="Leonhard Euler" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://sl.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Slovenian" lang="sl" hreflang="sl" data-title="Leonhard Euler" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%84%DB%8C%DB%86%D9%86%D8%A7%D8%B1%D8%AF_%D8%A6%DB%86%DB%8C%D9%84%DB%95%D8%B1" title="لیۆنارد ئۆیلەر – Central Kurdish" lang="ckb" hreflang="ckb" data-title="لیۆنارد ئۆیلەر" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-sr badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://sr.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%9E%D1%98%D0%BB%D0%B5%D1%80" title="Леонард Ојлер – Serbian" lang="sr" hreflang="sr" data-title="Леонард Ојлер" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Leonhard Euler" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Sundanese" lang="su" hreflang="su" data-title="Leonhard Euler" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target">Sunda</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Finnish" lang="fi" hreflang="fi" data-title="Leonhard Euler" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Swedish" lang="sv" hreflang="sv" data-title="Leonhard Euler" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Tagalog" lang="tl" hreflang="tl" data-title="Leonhard Euler" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B2%E0%AE%BF%E0%AE%AF%E0%AF%8B%E0%AE%A9%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%9F%E0%AF%81_%E0%AE%86%E0%AE%AF%E0%AF%8D%E0%AE%B2%E0%AE%B0%E0%AF%8D" title="லியோனார்டு ஆய்லர் – Tamil" lang="ta" hreflang="ta" data-title="லியோனார்டு ஆய்லர்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Leonard_Euler" title="Leonard Euler – Kabyle" lang="kab" hreflang="kab" data-title="Leonard Euler" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target">Taqbaylit</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Tatar" lang="tt" hreflang="tt" data-title="Леонард Эйлер" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B2%E0%B0%BF%E0%B0%AF%E0%B1%8A%E0%B0%A8%E0%B1%8D%E2%80%8C%E0%B0%B9%E0%B0%BE%E0%B0%B0%E0%B1%8D%E0%B0%A1%E0%B1%8D_%E0%B0%86%E0%B0%AF%E0%B0%BF%E0%B0%B2%E0%B0%B0%E0%B1%8D" title="లియొన్‌హార్డ్ ఆయిలర్ – Telugu" lang="te" hreflang="te" data-title="లియొన్‌హార్డ్ ఆయిలర్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%A5%E0%B8%AD%E0%B9%87%E0%B8%AD%E0%B8%99%E0%B8%AE%E0%B8%B2%E0%B8%A3%E0%B9%8C%E0%B8%97_%E0%B8%AD%E0%B9%87%E0%B8%AD%E0%B8%A2%E0%B9%80%E0%B8%A5%E0%B8%AD%E0%B8%A3%E0%B9%8C" title="เลอ็อนฮาร์ท อ็อยเลอร์ – Thai" lang="th" hreflang="th" data-title="เลอ็อนฮาร์ท อ็อยเลอร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Эйлер – Tajik" lang="tg" hreflang="tg" data-title="Леонард Эйлер" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target">Тоҷикӣ</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Turkish" lang="tr" hreflang="tr" data-title="Leonhard Euler" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Leonard_E%C3%BDler" title="Leonard Eýler – Turkmen" lang="tk" hreflang="tk" data-title="Leonard Eýler" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target">Türkmençe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%95%D0%B9%D0%BB%D0%B5%D1%80" title="Леонард Ейлер – Ukrainian" lang="uk" hreflang="uk" data-title="Леонард Ейлер" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur badge-Q17559452 badge-recommendedarticle mw-list-item" title="recommended article"><a href="https://ur.wikipedia.org/wiki/%D9%84%DB%8C%D9%88%D9%86%DB%81%D8%A7%D8%B1%DA%88_%D8%A7%D9%88%DB%8C%D9%84%D8%B1" title="لیونہارڈ اویلر – Urdu" lang="ur" hreflang="ur" data-title="لیونہارڈ اویلر" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Eiler_Leonard" title="Eiler Leonard – Veps" lang="vep" hreflang="vep" data-title="Eiler Leonard" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target">Vepsän kel’</a></li><li class="interlanguage-link interwiki-vi badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://vi.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Vietnamese" lang="vi" hreflang="vi" data-title="Leonhard Euler" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-vo mw-list-item"><a href="https://vo.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Volapük" lang="vo" hreflang="vo" data-title="Leonhard Euler" data-language-autonym="Volapük" data-language-local-name="Volapük" class="interlanguage-link-target">Volapük</a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Euleri_Leonhard" title="Euleri Leonhard – Võro" lang="vro" hreflang="vro" data-title="Euleri Leonhard" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target">Võro</a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%AD%90%E6%8B%89" title="歐拉 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="歐拉" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target">文言</a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Waray" lang="war" hreflang="war" data-title="Leonhard Euler" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target">Winaray</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%90%8A%E6%98%82%E5%93%88%E5%BE%B7%C2%B7%E6%AD%90%E6%8B%89" title="萊昂哈德·歐拉 – Wu" lang="wuu" hreflang="wuu" data-title="萊昂哈德·歐拉" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%9C%D7%A2%D7%90%D7%A0%D7%94%D7%90%D7%A8%D7%93_%D7%90%D7%95%D7%99%D7%9C%D7%A2%D7%A8" title="לעאנהארד אוילער – Yiddish" lang="yi" hreflang="yi" data-title="לעאנהארד אוילער" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target">ייִדיש</a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Yoruba" lang="yo" hreflang="yo" data-title="Leonhard Euler" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target">Yorùbá</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%9D%8E%E5%AE%89%E7%B4%8D%C2%B7%E6%AD%90%E6%8B%89" title="李安納·歐拉 – Cantonese" lang="yue" hreflang="yue" data-title="李安納·歐拉" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Zazaki" lang="diq" hreflang="diq" data-title="Leonhard Euler" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target">Zazaki</a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Samogitian" lang="sgs" hreflang="sgs" data-title="Leonhard Euler" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target">Žemaitėška</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%90%8A%E6%98%82%E5%93%88%E5%BE%B7%C2%B7%E6%AD%90%E6%8B%89" title="萊昂哈德·歐拉 – Chinese" lang="zh" hreflang="zh" data-title="萊昂哈德·歐拉" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li><li class="interlanguage-link interwiki-btm mw-list-item"><a href="https://btm.wikipedia.org/wiki/Leonhard_Euler" title="Leonhard Euler – Batak Mandailing" lang="btm" hreflang="btm" data-title="Leonhard Euler" data-language-autonym="Batak Mandailing" data-language-local-name="Batak Mandailing" class="interlanguage-link-target">Batak Mandailing</a></li> </ul> <div class="after-portlet after-portlet-lang"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q7604#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div 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For other uses, see <a href="/wiki/Euler_(disambiguation)" class="mw-disambig" title="Euler (disambiguation)">Euler (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">Leonhard Euler</div></th></tr><tr><td colspan="2" class="infobox-image"><a href="/wiki/File:Leonhard_Euler_-_Jakob_Emanuel_Handmann_(Kunstmuseum_Basel).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Leonhard_Euler_-_Jakob_Emanuel_Handmann_%28Kunstmuseum_Basel%29.jpg/220px-Leonhard_Euler_-_Jakob_Emanuel_Handmann_%28Kunstmuseum_Basel%29.jpg" decoding="async" width="220" height="284" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Leonhard_Euler_-_Jakob_Emanuel_Handmann_%28Kunstmuseum_Basel%29.jpg/330px-Leonhard_Euler_-_Jakob_Emanuel_Handmann_%28Kunstmuseum_Basel%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Leonhard_Euler_-_Jakob_Emanuel_Handmann_%28Kunstmuseum_Basel%29.jpg/440px-Leonhard_Euler_-_Jakob_Emanuel_Handmann_%28Kunstmuseum_Basel%29.jpg 2x" data-file-width="4672" data-file-height="6040" /></a><div class="infobox-caption">Portrait by <a href="/wiki/Jakob_Emanuel_Handmann" title="Jakob Emanuel Handmann">Jakob Emanuel Handmann</a>, 1753</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data">(1707-04-15)15 April 1707 <div style="display:inline" class="birthplace"><a href="/wiki/Basel" title="Basel">Basel</a>, <a href="/wiki/Swiss_Confederacy" class="mw-redirect" title="Swiss Confederacy">Swiss Confederacy</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">18 September 1783(1783-09-18) (aged 76) [<a href="/wiki/Adoption_of_the_Gregorian_calendar#Adoption_in_Eastern_Europe" title="Adoption of the Gregorian calendar">OS</a>: 7 September 1783] <div style="display:inline" class="deathplace"><a href="/wiki/Saint_Petersburg" title="Saint Petersburg">Saint Petersburg</a>, <a href="/wiki/Russian_Empire" title="Russian Empire">Russian Empire</a></div></td></tr><tr><th scope="row" class="infobox-label">Education</th><td class="infobox-data"><a href="/wiki/University_of_Basel" title="University of Basel">University of Basel</a> (<a href="/wiki/MPhil" class="mw-redirect" title="MPhil">MPhil</a>)</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"><ul><li><a href="/wiki/Contributions_of_Leonhard_Euler_to_mathematics" title="Contributions of Leonhard Euler to mathematics">Contributions</a></li><li><a href="/wiki/List_of_things_named_after_Leonhard_Euler" class="mw-redirect" title="List of things named after Leonhard Euler">namesakes</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Spouses</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"> <ul><li><style data-mw-deduplicate="TemplateStyles:r1151524712">.mw-parser-output .marriage-line-margin2px{line-height:0;margin-bottom:-2px}.mw-parser-output .marriage-line-margin3px{line-height:0;margin-bottom:-3px}.mw-parser-output .marriage-display-ws{display:inline;white-space:nowrap}</style></li></ul> <div class="marriage-display-ws"><div style="display:inline-block;line-height:normal;margin-top:1px;white-space:normal;">Katharina Gsell</div> <div class="marriage-line-margin2px"></div> <div style="display:inline-block;margin-bottom:1px;"></div>(<abbr title="married">m.</abbr> 1734; died 1773)</div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1151524712"></li></ul> <div class="marriage-display-ws"><div style="display:inline-block;line-height:normal;margin-top:1px;white-space:normal;">Salome Abigail Gsell</div> <div class="marriage-line-margin2px"></div> <div style="display:inline-block;margin-bottom:1px;"></div>(<abbr title="married">m.</abbr> 1776)</div> </div></td></tr><tr><th scope="row" class="infobox-label">Children</th><td class="infobox-data">13, including <a href="/wiki/Johann_Euler" title="Johann Euler">Johann</a></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><a href="/wiki/Fellow_of_the_Royal_Society" title="Fellow of the Royal Society">FRS</a> (1747)</td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546">Scientific career</td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><div class="hlist"><ul><li><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></li><li><a href="/wiki/Physics" title="Physics">Physics</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/Imperial_Russian_Academy_of_Sciences" class="mw-redirect" title="Imperial Russian Academy of Sciences">Imperial Russian Academy of Sciences</a></li><li><a href="/wiki/Prussian_Academy_of_Sciences" title="Prussian Academy of Sciences">Berlin Academy</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><a rel="nofollow" class="external text" href="https://scholarlycommons.pacific.edu/euler-works/2/">Dissertatio physica de sono (Physical dissertation on sound)</a> (1726)</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann Bernoulli</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><a href="/wiki/Johann_Hennert" class="mw-redirect" title="Johann Hennert">Johann Hennert</a></td></tr><tr><th scope="row" class="infobox-label">Other notable students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/Nicolas_Fuss" title="Nicolas Fuss">Nicolas Fuss</a></li><li><a href="/wiki/Stepan_Rumovsky" title="Stepan Rumovsky">Stepan Rumovsky</a></li><li><a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Joseph-Louis Lagrange</a> (epistolary correspondent)<a href="#cite_note-2">[a]</a></li><li><a href="/wiki/Anders_Johan_Lexell" title="Anders Johan Lexell">Anders Johan Lexell</a></li></ul></div></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th colspan="2" class="infobox-header">Signature</th></tr><tr><td colspan="2" class="infobox-full-data"><a href="/wiki/File:Euler%27s_signature.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Euler%27s_signature.svg/150px-Euler%27s_signature.svg.png" decoding="async" width="150" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Euler%27s_signature.svg/225px-Euler%27s_signature.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Euler%27s_signature.svg/300px-Euler%27s_signature.svg.png 2x" data-file-width="627" data-file-height="147" /></a></td></tr></tbody></table> Leonhard Euler (<a href="/wiki/Help:IPA/English" title="Help:IPA/English">/ˈɔɪlər/</a> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key">OY-lər</a>;<a href="#cite_note-7">[b]</a> <style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style>German: <a href="/wiki/Help:IPA/Standard_German" title="Help:IPA/Standard German">[ˈleːɔnhaʁt ˈʔɔʏlɐ]</a> <span data-nosnippet="" id="ooui-php-1" class="ext-phonos-PhonosButton noexcerpt ext-phonos-PhonosButton-emptylabel oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/e\/ef\/De-Leonhard_Euler.ogg\/De-Leonhard_Euler.ogg.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"De-Leonhard Euler.ogg"},"classes":["ext-phonos-PhonosButton","noexcerpt","ext-phonos-PhonosButton-emptylabel"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/e/ef/De-Leonhard_Euler.ogg/De-Leonhard_Euler.ogg.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"></a><a href="/wiki/File:De-Leonhard_Euler.ogg" title="File:De-Leonhard Euler.ogg">ⓘ</a>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1177148991">Swiss Standard German: <a href="/wiki/Help:IPA/Standard_German" title="Help:IPA/Standard German">[ˈleɔnhard ˈɔʏlər]</a>; 15 April 1707 – 18 September 1783) was a <a href="/wiki/Old_Swiss_Confederacy" title="Old Swiss Confederacy">Swiss</a> <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, <a href="/wiki/Physicist" title="Physicist">physicist</a>, <a href="/wiki/Astronomer" title="Astronomer">astronomer</a>, <a href="/wiki/Geographer" title="Geographer">geographer</a>, <a href="/wiki/Logician" class="mw-redirect" title="Logician">logician</a>, and <a href="/wiki/Engineer" title="Engineer">engineer</a> who founded the studies of <a href="/wiki/Graph_theory" title="Graph theory">graph theory</a> and <a href="/wiki/Topology" title="Topology">topology</a> and made pioneering and influential discoveries in many other branches of mathematics such as <a href="/wiki/Analytic_number_theory" title="Analytic number theory">analytic number theory</a>, <a href="/wiki/Complex_analysis" title="Complex analysis">complex analysis</a>, and <a href="/wiki/Infinitesimal_calculus" class="mw-redirect" title="Infinitesimal calculus">infinitesimal calculus</a>. He introduced much of modern mathematical terminology and <a href="/wiki/Mathematical_notation" title="Mathematical notation">notation</a>, including the notion of a <a href="/wiki/Mathematical_function" class="mw-redirect" title="Mathematical function">mathematical function</a>.<a href="#cite_note-FOOTNOTEDunham199917-8">[6]</a> He is also known for his work in <a href="/wiki/Mechanics" title="Mechanics">mechanics</a>, <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, <a href="/wiki/Optics" title="Optics">optics</a>, <a href="/wiki/Astronomy" title="Astronomy">astronomy</a>, and <a href="/wiki/Music_theory" title="Music theory">music theory</a>.<a href="#cite_note-:0-9">[7]</a> Euler is regarded as one of the greatest, most prolific mathematicians in history and the greatest of the 18th century. Several great mathematicians who produced their work after Euler's death have recognised his importance in the field as shown by quotes attributed to many of them: <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Pierre-Simon Laplace</a> expressed Euler's influence on mathematics by stating, "Read Euler, read Euler, he is the master of us all."<a href="#cite_note-Laplace-10">[8]</a><a href="#cite_note-fn2-11">[c]</a> <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a> wrote: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it."<a href="#cite_note-Grinstein-12">[9]</a><a href="#cite_note-fn3-14">[d]</a> His 866 publications and his correspondence are being collected in the <a href="/wiki/Opera_Omnia_Leonhard_Euler" title="Opera Omnia Leonhard Euler">Opera Omnia Leonhard Euler</a> which, when completed, will consist of 81 <a href="/wiki/Quarto" title="Quarto">quartos</a>.<a href="#cite_note-ivb-15">[11]</a><a href="#cite_note-series_ii_done-16">[12]</a><a href="#cite_note-FOOTNOTEGautschi20083-17">[13]</a> He spent most of his adult life in <a href="/wiki/Saint_Petersburg" title="Saint Petersburg">Saint Petersburg</a>, Russia, and in <a href="/wiki/Berlin" title="Berlin">Berlin</a>, then the capital of <a href="/wiki/Kingdom_of_Prussia" title="Kingdom of Prussia">Prussia</a>. Euler is credited for popularizing the Greek letter <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"> (lowercase <a href="/wiki/Pi_(letter)" title="Pi (letter)">pi</a>) to denote <a href="/wiki/Pi" title="Pi">the ratio of a circle's circumference to its diameter</a>, as well as first using the notation <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.418ex; height:2.843ex;" alt="{\displaystyle f(x)}"> for the value of a function, the letter <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"> to express the <a href="/wiki/Imaginary_unit" title="Imaginary unit">imaginary unit</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {-1}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ea1ea9ac61e6e1e84ac39130f78143c18865719" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.906ex; height:3.009ex;" alt="{\displaystyle {\sqrt {-1}}}">, the Greek letter <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Sigma }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e1f558f53cda207614abdf90162266c70bc5c1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Sigma }"> (capital <a href="/wiki/Sigma" title="Sigma">sigma</a>) to express <a href="/wiki/Summation" title="Summation">summations</a>, the Greek letter <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32769037c408874e1890f77554c65f39c523ebe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \Delta }"> (capital <a href="/wiki/Delta_(letter)" title="Delta (letter)">delta</a>) for <a href="/wiki/Finite_difference" title="Finite difference">finite differences</a>, and lowercase letters to represent the sides of a triangle while representing the angles as capital letters.<a href="#cite_note-assad-18">[14]</a> He gave the current definition of the constant <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}">, the base of the <a href="/wiki/Natural_logarithm" title="Natural logarithm">natural logarithm</a>, now known as <a href="/wiki/Euler%27s_number" class="mw-redirect" title="Euler's number">Euler's number</a>.<a href="#cite_note-britannica-19">[15]</a> Euler is also credited with being the first to develop <a href="/wiki/Graph_theory" title="Graph theory">graph theory</a> (partly as a solution for the problem of the <a href="/wiki/Seven_Bridges_of_K%C3%B6nigsberg" title="Seven Bridges of Königsberg">Seven Bridges of Königsberg</a>, which is also considered the first practical application of topology). He also became famous for, among many other accomplishments, providing a solution to several unsolved problems in number theory and analysis, including the famous <a href="/wiki/Basel_problem" title="Basel problem">Basel problem</a>. Euler has also been credited for discovering that the sum of the numbers of vertices and faces minus the number of edges of a <a href="/wiki/Polyhedron" title="Polyhedron">polyhedron</a> equals 2, a number now commonly known as the <a href="/wiki/Euler_characteristic" title="Euler characteristic">Euler characteristic</a>. In the field of physics, Euler reformulated <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a>'s <a href="/wiki/Laws_of_physics" class="mw-redirect" title="Laws of physics">laws of physics</a> into <a href="/wiki/Euler%27s_laws_of_motion" title="Euler's laws of motion">new laws</a> in his two-volume work <a href="/wiki/Mechanica" title="Mechanica">Mechanica</a> to better explain the motion of <a href="/wiki/Rigid_bodies" class="mw-redirect" title="Rigid bodies">rigid bodies</a>. He also made substantial contributions to the study of <a href="/wiki/Euler%E2%80%93Bernoulli_beam_theory" title="Euler–Bernoulli beam theory">elastic deformations</a> of solid objects. <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Early_life">Early life</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=1" title="Edit section: Early life">edit</a>]</div> Leonhard Euler was born on 15 April 1707, in <a href="/wiki/Basel" title="Basel">Basel</a> to Paul III Euler, a pastor of the <a href="/wiki/Reformed_Church" class="mw-redirect" title="Reformed Church">Reformed Church</a>, and Marguerite (née Brucker), whose ancestors include a number of well-known scholars in the classics.<a href="#cite_note-FOOTNOTEGautschi20084-20">[16]</a> He was the oldest of four children, having two younger sisters, Anna Maria and Maria Magdalena, and a younger brother, Johann Heinrich.<a href="#cite_note-FOOTNOTECalinger201611-21">[17]</a><a href="#cite_note-FOOTNOTEGautschi20084-20">[16]</a> Soon after the birth of Leonhard, the Euler family moved from Basel to the town of <a href="/wiki/Riehen" title="Riehen">Riehen</a>, Switzerland, where his father became pastor in the local church and Leonhard spent most of his childhood.<a href="#cite_note-FOOTNOTEGautschi20084-20">[16]</a> From a young age, Euler received schooling in mathematics from his father, who had taken courses from <a href="/wiki/Jacob_Bernoulli" title="Jacob Bernoulli">Jacob Bernoulli</a> some years earlier at the <a href="/wiki/University_of_Basel" title="University of Basel">University of Basel</a>. Around the age of eight, Euler was sent to live at his maternal grandmother's house and enrolled in the Latin school in Basel. In addition, he received private tutoring from Johannes Burckhardt, a young theologian with a keen interest in mathematics.<a href="#cite_note-FOOTNOTEGautschi20084-20">[16]</a> In 1720, at thirteen years of age, Euler enrolled at the <a href="/wiki/University_of_Basel" title="University of Basel">University of Basel</a>.<a href="#cite_note-:0-9">[7]</a> Attending university at such a young age was not unusual at the time.<a href="#cite_note-FOOTNOTEGautschi20084-20">[16]</a> The course on elementary mathematics was given by <a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann Bernoulli</a>, the younger brother of the deceased Jacob Bernoulli (who had taught Euler's father). Johann Bernoulli and Euler soon got to know each other better. Euler described Bernoulli in his autobiography:<a href="#cite_note-FOOTNOTEGautschi20085-22">[18]</a> <dl><dd>"the famous professor Johann Bernoulli [...] made it a special pleasure for himself to help me along in the mathematical sciences. Private lessons, however, he refused because of his busy schedule. However, he gave me a far more salutary advice, which consisted in myself getting a hold of some of the more difficult mathematical books and working through them with great diligence, and should I encounter some objections or difficulties, he offered me free access to him every Saturday afternoon, and he was gracious enough to comment on the collected difficulties, which was done with such a desired advantage that, when he resolved one of my objections, ten others at once disappeared, which certainly is the best method of making happy progress in the mathematical sciences."</dd></dl> It was during this time that Euler, backed by Bernoulli, obtained his father's consent to become a mathematician instead of a pastor.<a href="#cite_note-FOOTNOTECalinger1996124-23">[19]</a><a href="#cite_note-zum_werk_leonhard-24">[20]</a> In 1723, Euler received a <a href="/wiki/Master_of_Philosophy" title="Master of Philosophy">Master of Philosophy</a> with a dissertation that compared the philosophies of <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> and <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>.<a href="#cite_note-FOOTNOTEGautschi20084-20">[16]</a> Afterwards, he enrolled in the theological faculty of the University of Basel.<a href="#cite_note-zum_werk_leonhard-24">[20]</a> In 1726, Euler completed a dissertation on the <a href="/wiki/Speed_of_sound" title="Speed of sound">propagation of sound</a> with the title De Sono<a href="#cite_note-FOOTNOTECalinger201632-25">[21]</a><a href="#cite_note-17cent-26">[22]</a> with which he unsuccessfully attempted to obtain a position at the University of Basel.<a href="#cite_note-FOOTNOTECalinger1996125-27">[23]</a> In 1727, he entered the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">Paris Academy</a> prize competition (offered annually and later biennially by the academy beginning in 1720)<a href="#cite_note-paris-acad-28">[24]</a> for the first time. The problem posed that year was to find the best way to place the <a href="/wiki/Mast_(sailing)" title="Mast (sailing)">masts</a> on a ship. <a href="/wiki/Pierre_Bouguer" title="Pierre Bouguer">Pierre Bouguer</a>, who became known as "the father of naval architecture", won and Euler took second place.<a href="#cite_note-FOOTNOTECalinger1996156-29">[25]</a> Over the years, Euler entered this competition 15 times,<a href="#cite_note-paris-acad-28">[24]</a> winning 12 of them.<a href="#cite_note-FOOTNOTECalinger1996156-29">[25]</a> <div class="mw-heading mw-heading2"><h2 id="Career">Career</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=2" title="Edit section: Career">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Saint_Petersburg">Saint Petersburg</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=3" title="Edit section: Saint Petersburg">edit</a>]</div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:The_Soviet_Union_1957_CPA_2000_stamp,_Portrait_of_Leonhard_Euler_(1707-1783).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/The_Soviet_Union_1957_CPA_2000_stamp%2C_Portrait_of_Leonhard_Euler_%281707-1783%29.jpg/220px-The_Soviet_Union_1957_CPA_2000_stamp%2C_Portrait_of_Leonhard_Euler_%281707-1783%29.jpg" decoding="async" width="220" height="158" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/The_Soviet_Union_1957_CPA_2000_stamp%2C_Portrait_of_Leonhard_Euler_%281707-1783%29.jpg/330px-The_Soviet_Union_1957_CPA_2000_stamp%2C_Portrait_of_Leonhard_Euler_%281707-1783%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/The_Soviet_Union_1957_CPA_2000_stamp%2C_Portrait_of_Leonhard_Euler_%281707-1783%29.jpg/440px-The_Soviet_Union_1957_CPA_2000_stamp%2C_Portrait_of_Leonhard_Euler_%281707-1783%29.jpg 2x" data-file-width="2009" data-file-height="1447" /></a><figcaption>1957 <a href="/wiki/Soviet_Union" title="Soviet Union">Soviet Union</a> stamp commemorating the 250th birthday of Euler. The text says: 250 years from the birth of the great mathematician, academician Leonhard Euler.</figcaption></figure> Johann Bernoulli's two sons, <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel</a> and <a href="/wiki/Nicolaus_II_Bernoulli" title="Nicolaus II Bernoulli">Nicolaus</a>, entered into service at the <a href="/wiki/Russian_Academy_of_Sciences" title="Russian Academy of Sciences">Imperial Russian Academy of Sciences</a> in <a href="/wiki/Saint_Petersburg" title="Saint Petersburg">Saint Petersburg</a> in 1725, leaving Euler with the assurance they would recommend him to a post when one was available.<a href="#cite_note-FOOTNOTECalinger1996125-27">[23]</a> On 31 July 1726, Nicolaus died of appendicitis after spending less than a year in Russia.<a href="#cite_note-FOOTNOTECalinger1996121–166-30">[26]</a><a href="#cite_note-mactutor-31">[27]</a> When Daniel assumed his brother's position in the mathematics/physics division, he recommended that the post in physiology that he had vacated be filled by his friend Euler.<a href="#cite_note-FOOTNOTECalinger1996125-27">[23]</a> In November 1726, Euler eagerly accepted the offer, but delayed making the trip to Saint Petersburg while he unsuccessfully applied for a physics professorship at the University of Basel.<a href="#cite_note-FOOTNOTECalinger1996125-27">[23]</a> Euler arrived in Saint Petersburg in May 1727.<a href="#cite_note-FOOTNOTECalinger1996125-27">[23]</a><a href="#cite_note-zum_werk_leonhard-24">[20]</a> He was promoted from his junior post in the medical department of the academy to a position in the mathematics department. He lodged with Daniel Bernoulli with whom he worked in close collaboration.<a href="#cite_note-FOOTNOTECalinger1996126–127-32">[28]</a> Euler mastered Russian, settled into life in Saint Petersburg and took on an additional job as a medic in the <a href="/wiki/Imperial_Russian_Navy" title="Imperial Russian Navy">Russian Navy</a>.<a href="#cite_note-FOOTNOTECalinger1996127-33">[29]</a> The academy at Saint Petersburg, established by <a href="/wiki/Peter_the_Great" title="Peter the Great">Peter the Great</a>, was intended to improve education in Russia and to close the scientific gap with Western Europe. As a result, it was made especially attractive to foreign scholars like Euler.<a href="#cite_note-FOOTNOTECalinger1996156-29">[25]</a> The academy's benefactress, <a href="/wiki/Catherine_I_of_Russia" title="Catherine I of Russia">Catherine I</a>, who had continued the progressive policies of her late husband, died before Euler's arrival to Saint Petersburg.<a href="#cite_note-FOOTNOTECalinger1996126-34">[30]</a> The Russian conservative nobility then gained power upon the ascension of the twelve-year-old <a href="/wiki/Peter_II_of_Russia" title="Peter II of Russia">Peter II</a>.<a href="#cite_note-FOOTNOTECalinger1996126-34">[30]</a> The nobility, suspicious of the academy's foreign scientists, cut funding for Euler and his colleagues and prevented the entrance of foreign and non-aristocratic students into the Gymnasium and universities.<a href="#cite_note-FOOTNOTECalinger1996126-34">[30]</a> Conditions improved slightly after the death of Peter II in 1730 and the German-influenced <a href="/wiki/Anna_of_Russia" title="Anna of Russia">Anna of Russia</a> assumed power.<a href="#cite_note-FOOTNOTECalinger1996128-35">[31]</a> Euler swiftly rose through the ranks in the academy and was made a professor of physics in 1731.<a href="#cite_note-FOOTNOTECalinger1996128-35">[31]</a> He also left the Russian Navy, refusing a promotion to <a href="/wiki/Lieutenant_(navy)" title="Lieutenant (navy)">lieutenant</a>.<a href="#cite_note-FOOTNOTECalinger1996128-35">[31]</a> Two years later, Daniel Bernoulli, fed up with the censorship and hostility he faced at Saint Petersburg, left for Basel. Euler succeeded him as the head of the mathematics department.<a href="#cite_note-FOOTNOTECalinger1996128–129-36">[32]</a> In January 1734, he married Katharina Gsell (1707–1773), a daughter of <a href="/wiki/Georg_Gsell" title="Georg Gsell">Georg Gsell</a>.<a href="#cite_note-FOOTNOTEGekkerEuler2007[httpsbooksgooglecombooksidTa9bz1wv79ACpgPA402_402]-37">[33]</a> <a href="/wiki/Frederick_the_Great" title="Frederick the Great">Frederick II</a> had made an attempt to recruit the services of Euler for his newly established <a href="/wiki/Prussian_Academy_of_Sciences" title="Prussian Academy of Sciences">Berlin Academy</a> in 1740, but Euler initially preferred to stay in St Petersburg.<a href="#cite_note-FOOTNOTECalinger1996157–158-38">[34]</a> But after Empress Anna died and Frederick II agreed to pay 1600 <a href="/wiki/%C3%89cu" title="Écu">ecus</a> (the same as Euler earned in Russia) he agreed to move to Berlin. In 1741, he requested permission to leave to Berlin, arguing he was in need of a milder climate for his eyesight.<a href="#cite_note-FOOTNOTECalinger1996157–158-38">[34]</a> The Russian academy gave its consent and would pay him 200 rubles per year as one of its active members.<a href="#cite_note-FOOTNOTECalinger1996157–158-38">[34]</a> <div class="mw-heading mw-heading3"><h3 id="Berlin">Berlin</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=4" title="Edit section: Berlin">edit</a>]</div> Concerned about the continuing turmoil in Russia, Euler left St. Petersburg in June 1741 to take up a post at the <a href="/wiki/Prussian_Academy_of_Sciences" title="Prussian Academy of Sciences">Berlin Academy</a>, which he had been offered by <a href="/wiki/Frederick_the_Great_of_Prussia" class="mw-redirect" title="Frederick the Great of Prussia">Frederick the Great of Prussia</a>.<a href="#cite_note-FOOTNOTEGautschi20087-39">[35]</a> He lived for 25 years in <a href="/wiki/Berlin" title="Berlin">Berlin</a>, where he wrote several hundred articles.<a href="#cite_note-zum_werk_leonhard-24">[20]</a> In 1748 his text on functions called the <a href="/wiki/Introductio_in_analysin_infinitorum" title="Introductio in analysin infinitorum">Introductio in analysin infinitorum</a> was published and in 1755 a text on <a href="/wiki/Differential_calculus" title="Differential calculus">differential calculus</a> called the <a href="/wiki/Institutiones_calculi_differentialis" title="Institutiones calculi differentialis">Institutiones calculi differentialis</a> was published.<a href="#cite_note-dartm-40">[36]</a><a href="#cite_note-FOOTNOTEDunham1999xxiv–xxv-41">[37]</a> In 1755, 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><a href="#cite_note-sten-42">[38]</a> and of the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a>.<a href="#cite_note-volumes-43">[39]</a> Notable students of Euler in Berlin included <a href="/wiki/Stepan_Rumovsky" title="Stepan Rumovsky">Stepan Rumovsky</a>, later considered as the first Russian astronomer.<a href="#cite_note-BEA-44">[40]</a><a href="#cite_note-ClarkGolinski1999-45">[41]</a> In 1748 he declined an offer from the University of Basel to succeed the recently deceased Johann Bernoulli.<a href="#cite_note-zum_werk_leonhard-24">[20]</a> In 1753 he bought a house in <a href="/wiki/Charlottenburg" title="Charlottenburg">Charlottenburg</a>, in which he lived with his family and widowed mother.<a href="#cite_note-zum_300_knobloch-46">[42]</a><a href="#cite_note-FOOTNOTEGautschi20088–9-47">[43]</a> Euler became the tutor for <a href="/wiki/Friederike_Charlotte_of_Brandenburg-Schwedt" title="Friederike Charlotte of Brandenburg-Schwedt">Friederike Charlotte of Brandenburg-Schwedt</a>, the Princess of <a href="/wiki/Anhalt-Dessau" title="Anhalt-Dessau">Anhalt-Dessau</a> and Frederick's niece. He wrote over 200 letters to her in the early 1760s, which were later compiled into a volume entitled <a href="/wiki/Letters_to_a_German_Princess" title="Letters to a German Princess">Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess</a>.<a href="#cite_note-Digital_Copy_of_"Letters_to_a_German_Princess"-48">[44]</a> This work contained Euler's exposition on various subjects pertaining to physics and mathematics and offered valuable insights into Euler's personality and religious beliefs. It was translated into multiple languages, published across Europe and in the United States, and became more widely read than any of his mathematical works. The popularity of the Letters testifies to Euler's ability to communicate scientific matters effectively to a lay audience, a rare ability for a dedicated research scientist.<a href="#cite_note-FOOTNOTEDunham1999xxiv–xxv-41">[37]</a> Despite Euler's immense contribution to the academy's prestige and having been put forward as a candidate for its presidency by <a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">Jean le Rond d'Alembert</a>, <a href="/wiki/Frederick_II_of_Prussia" class="mw-redirect" title="Frederick II of Prussia">Frederick II</a> named himself as its president.<a href="#cite_note-FOOTNOTEGautschi20088–9-47">[43]</a> The Prussian king had a large circle of intellectuals in his court, and he found the mathematician unsophisticated and ill-informed on matters beyond numbers and figures. Euler was a simple, devoutly religious man who never questioned the existing social order or conventional beliefs. He was, in many ways, the polar opposite of <a href="/wiki/Voltaire" title="Voltaire">Voltaire</a>, who enjoyed a high place of prestige at Frederick's court. Euler was not a skilled debater and often made it a point to argue subjects that he knew little about, making him the frequent target of Voltaire's wit.<a href="#cite_note-FOOTNOTEDunham1999xxiv–xxv-41">[37]</a> Frederick also expressed disappointment with Euler's practical engineering abilities, stating: <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">I wanted to have a water jet in my garden: Euler calculated the force of the wheels necessary to raise the water to a reservoir, from where it should fall back through channels, finally spurting out in <a href="/wiki/Sanssouci" title="Sanssouci">Sanssouci</a>. My mill was carried out geometrically and could not raise a mouthful of water closer than fifty paces to the reservoir. Vanity of vanities! Vanity of geometry!<a href="#cite_note-fredlett-49">[45]</a></blockquote> However, the disappointment was almost surely unwarranted from a technical perspective. Euler's calculations look likely to be correct, even if Euler's interactions with Frederick and those constructing his fountain may have been dysfunctional.<a href="#cite_note-Lynch-50">[46]</a> Throughout his stay in Berlin, Euler maintained a strong connection to the academy in St. Petersburg and also published 109 papers in Russia.<a href="#cite_note-vucinich-51">[47]</a> He also assisted students from the St. Petersburg academy and at times accommodated Russian students in his house in Berlin.<a href="#cite_note-vucinich-51">[47]</a> In 1760, with the <a href="/wiki/Seven_Years%27_War" title="Seven Years' War">Seven Years' War</a> raging, Euler's farm in Charlottenburg was sacked by advancing Russian troops.<a href="#cite_note-zum_300_knobloch-46">[42]</a> Upon learning of this event, <a href="/wiki/Ivan_Saltykov" title="Ivan Saltykov">General Ivan Petrovich Saltykov</a> paid compensation for the damage caused to Euler's estate, with <a href="/wiki/Empress_Elizabeth" class="mw-redirect" title="Empress Elizabeth">Empress Elizabeth</a> of Russia later adding a further payment of 4000 rubles—an exorbitant amount at the time.<a href="#cite_note-gindikin-52">[48]</a> Euler decided to leave Berlin in 1766 and return to Russia.<a href="#cite_note-FOOTNOTEGautschi20089-53">[49]</a> During his Berlin years (1741–1766), Euler was at the peak of his productivity. He wrote 380 works, 275 of which were published.<a href="#cite_note-math_at_prussian-54">[50]</a> This included 125 memoirs in the Berlin Academy and over 100 memoirs sent to the <a href="/wiki/Russian_Academy_of_Sciences" title="Russian Academy of Sciences">St. Petersburg Academy</a>, which had retained him as a member and paid him an annual stipend. Euler's Introductio in Analysin Infinitorum was published in two parts in 1748. In addition to his own research, Euler supervised the library, the observatory, the botanical garden, and the publication of calendars and maps from which the academy derived income.<a href="#cite_note-historian's_craft-55">[51]</a> He was even involved in the design of the water fountains at <a href="/wiki/Sanssouci" title="Sanssouci">Sanssouci</a>, the King's summer palace.<a href="#cite_note-fountains-56">[52]</a> <div class="mw-heading mw-heading3"><h3 id="Return_to_Russia">Return to Russia</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=5" title="Edit section: Return to Russia">edit</a>]</div> The political situation in Russia stabilized after <a href="/wiki/Catherine_the_Great" title="Catherine the Great">Catherine the Great's</a> accession to the throne, so in 1766 Euler accepted an invitation to return to the St. Petersburg Academy. His conditions were quite exorbitant—a 3000 ruble annual salary, a pension for his wife, and the promise of high-ranking appointments for his sons. At the university he was assisted by his student <a href="/wiki/Anders_Johan_Lexell" title="Anders Johan Lexell">Anders Johan Lexell</a>.<a href="#cite_note-lexell's_theorem-57">[53]</a> While living in St. Petersburg, a fire in 1771 destroyed his home.<a href="#cite_note-thiele-58">[54]</a> <div class="mw-heading mw-heading2"><h2 id="Personal_life">Personal life</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=6" title="Edit section: Personal life">edit</a>]</div> On 7 January 1734, he married Katharina Gsell (1707–1773), daughter of <a href="/wiki/Georg_Gsell" title="Georg Gsell">Georg Gsell</a>, a painter from the Academy Gymnasium in Saint Petersburg.<a href="#cite_note-FOOTNOTEGekkerEuler2007[httpsbooksgooglecombooksidTa9bz1wv79ACpgPA402_402]-37">[33]</a> The young couple bought a house by the <a href="/wiki/Neva_River" class="mw-redirect" title="Neva River">Neva River</a>. Of their thirteen children, only five survived childhood,<a href="#cite_note-novaacta-59">[55]</a> three sons and two daughters.<a href="#cite_note-FOOTNOTECalinger1996129-60">[56]</a> Their first son was <a href="/wiki/Johann_Euler" title="Johann Euler">Johann Albrecht Euler</a>, whose godfather was <a href="/wiki/Christian_Goldbach" title="Christian Goldbach">Christian Goldbach</a>.<a href="#cite_note-FOOTNOTECalinger1996129-60">[56]</a> Three years after his wife's death in 1773,<a href="#cite_note-thiele-58">[54]</a> Euler married her half-sister, Salome Abigail Gsell (1723–1794).<a href="#cite_note-FOOTNOTEGekkerEuler2007[httpsbooksgooglecombooksidTa9bz1wv79ACpgPA405_405]-61">[57]</a> This marriage lasted until his death in 1783. His brother Johann Heinrich settled in St. Petersburg in 1735 and was employed as a painter at the academy.<a href="#cite_note-FOOTNOTECalinger1996157–158-38">[34]</a> Early in his life, Euler memorized the entirety of the <a href="/wiki/Aeneid" title="Aeneid">Aeneid</a> by <a href="/wiki/Virgil" title="Virgil">Virgil</a>, and by old age, could recite the entirety of the poem, along with stating the first and last sentence on each page of the edition from which he had learnt it.<a href="#cite_note-62">[58]</a><a href="#cite_note-63">[59]</a> <div class="mw-heading mw-heading3"><h3 id="Eyesight_deterioration">Eyesight deterioration</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=7" title="Edit section: Eyesight deterioration">edit</a>]</div> Euler's <a href="/wiki/Eyesight" class="mw-redirect" title="Eyesight">eyesight</a> worsened throughout his mathematical career. In 1738, three years after nearly expiring from fever,<a href="#cite_note-FOOTNOTEGautschi20086-64">[60]</a> he became almost blind in his right eye. Euler blamed the <a href="/wiki/Cartography" title="Cartography">cartography</a> he performed for the St. Petersburg Academy for his condition,<a href="#cite_note-blindness-65">[61]</a> but the cause of his blindness remains the subject of speculation.<a href="#cite_note-righteye-66">[62]</a><a href="#cite_note-bullock-67">[63]</a> Euler's vision in that eye worsened throughout his stay in Germany, to the extent that Frederick referred to him as "<a href="/wiki/Cyclopes" title="Cyclopes">Cyclops</a>". Euler remarked on his loss of vision, stating "Now I will have fewer distractions."<a href="#cite_note-blindness-65">[61]</a> In 1766 a <a href="/wiki/Cataract" title="Cataract">cataract</a> in his left eye was discovered. Though <a href="/wiki/Couching_(ophthalmology)" title="Couching (ophthalmology)">couching of the cataract</a> temporarily improved his vision, complications ultimately rendered him almost totally blind in the left eye as well.<a href="#cite_note-volumes-43">[39]</a> However, his condition appeared to have little effect on his productivity. With the aid of his scribes, Euler's productivity in many areas of study increased;<a href="#cite_note-FOOTNOTEGautschi20089–10-68">[64]</a> and, in 1775, he produced, on average, one mathematical paper every week.<a href="#cite_note-volumes-43">[39]</a> <div class="mw-heading mw-heading3"><h3 id="Death">Death</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=8" title="Edit section: Death">edit</a>]</div> In St. Petersburg on 18 September 1783, after a lunch with his family, Euler was discussing the newly discovered planet <a href="/wiki/Uranus" title="Uranus">Uranus</a> and its <a href="/wiki/Orbit" title="Orbit">orbit</a> with <a href="/wiki/Anders_Johan_Lexell" title="Anders Johan Lexell">Anders Johan Lexell</a> when he collapsed and died from a <a href="/wiki/Brain_hemorrhage" class="mw-redirect" title="Brain hemorrhage">brain hemorrhage</a>.<a href="#cite_note-righteye-66">[62]</a> <a href="/w/index.php?title=Jacob_von_Staehlin&action=edit&redlink=1" class="new" title="Jacob von Staehlin (page does not exist)">Jacob von Staehlin</a> [<a href="https://de.wikipedia.org/wiki/Jacob_von_Staehlin" class="extiw" title="de:Jacob von Staehlin">de</a>] wrote a short obituary for the <a href="/wiki/Russian_Academy_of_Sciences" title="Russian Academy of Sciences">Russian Academy of Sciences</a> and Russian mathematician <a href="/wiki/Nicolas_Fuss" title="Nicolas Fuss">Nicolas Fuss</a>, one of Euler's disciples, wrote a more detailed eulogy,<a href="#cite_note-novaacta-59">[55]</a> which he delivered at a memorial meeting. In his eulogy for the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy</a>, French mathematician and philosopher <a href="/wiki/Marquis_de_Condorcet" title="Marquis de Condorcet">Marquis de Condorcet</a>, wrote: <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Euler_Grave_at_Alexander_Nevsky_Monastry.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Euler_Grave_at_Alexander_Nevsky_Monastry.jpg/220px-Euler_Grave_at_Alexander_Nevsky_Monastry.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Euler_Grave_at_Alexander_Nevsky_Monastry.jpg/330px-Euler_Grave_at_Alexander_Nevsky_Monastry.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Euler_Grave_at_Alexander_Nevsky_Monastry.jpg/440px-Euler_Grave_at_Alexander_Nevsky_Monastry.jpg 2x" data-file-width="1536" data-file-height="1024" /></a><figcaption>Euler's grave at the <a href="/wiki/Alexander_Nevsky_Lavra" title="Alexander Nevsky Lavra">Alexander Nevsky Monastery</a></figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote">il cessa de calculer et de vivre— ... he ceased to calculate and to live.<a href="#cite_note-condorcet-69">[65]</a></blockquote> Euler was buried next to Katharina at the <a href="/wiki/Smolensk_Lutheran_Cemetery" class="mw-redirect" title="Smolensk Lutheran Cemetery">Smolensk Lutheran Cemetery</a> on <a href="/wiki/Vasilievsky_Island" class="mw-redirect" title="Vasilievsky Island">Vasilievsky Island</a>. In 1837, the <a href="/wiki/Russian_Academy_of_Sciences" title="Russian Academy of Sciences">Russian Academy of Sciences</a> installed a new monument, replacing his overgrown grave plaque. To commemorate the 250th anniversary of Euler's birth in 1957, his tomb was moved to the <a href="/wiki/Lazarevskoe_Cemetery" title="Lazarevskoe Cemetery">Lazarevskoe Cemetery</a> at the <a href="/wiki/Alexander_Nevsky_Monastery" class="mw-redirect" title="Alexander Nevsky Monastery">Alexander Nevsky Monastery</a>.<a href="#cite_note-FOOTNOTECalinger2016530–536-70">[66]</a> <div class="mw-heading mw-heading2"><h2 id="Contributions_to_mathematics_and_physics">Contributions to mathematics and physics</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=9" title="Edit section: Contributions to mathematics and physics">edit</a>]</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/Contributions_of_Leonhard_Euler_to_mathematics" title="Contributions of Leonhard Euler to mathematics">Contributions of Leonhard Euler to mathematics</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output 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.mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r1238256010">.mw-parser-output .e-mathematical-constant-sidebar{width:20em}.mw-parser-output .e-mathematical-constant-sidebar .sidebar-title-with-pretitle{font-size:130%}.mw-parser-output .e-mathematical-constant-sidebar .sidebar-heading{border-top:#aaa 1px solid}</style><table class="sidebar nomobile nowraplinks hlist e-mathematical-constant-sidebar"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:E_(mathematical_constant)" title="Category:E (mathematical constant)">a series of articles</a> on the</td></tr><tr><th class="sidebar-title-with-pretitle">mathematical constant <a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e</a></th></tr><tr><td class="sidebar-image"><a href="/wiki/File:Euler%27s_formula.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/180px-Euler%27s_formula.svg.png" decoding="async" width="180" height="185" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/270px-Euler%27s_formula.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/360px-Euler%27s_formula.svg.png 2x" data-file-width="760" data-file-height="782" /></a></td></tr><tr><th class="sidebar-heading"> Properties</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Natural_logarithm" title="Natural logarithm">Natural logarithm</a></li> <li><a href="/wiki/Exponential_function" title="Exponential function">Exponential function</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Applications</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Compound_interest" title="Compound interest">compound interest</a></li> <li><a href="/wiki/Euler%27s_identity" title="Euler's identity">Euler's identity</a></li> <li><a href="/wiki/Euler%27s_formula" title="Euler's formula">Euler's formula</a></li> <li><a href="/wiki/Half-life" title="Half-life">half-lives</a> <ul><li>exponential <a href="/wiki/Exponential_growth" title="Exponential growth">growth</a> and <a href="/wiki/Exponential_decay" title="Exponential decay">decay</a></li></ul></li></ul></td> </tr><tr><th class="sidebar-heading"> Defining e</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Proof_that_e_is_irrational" title="Proof that e is irrational">proof that e is irrational</a></li> <li><a href="/wiki/List_of_representations_of_e" title="List of representations of e">representations of e</a></li> <li><a href="/wiki/Lindemann%E2%80%93Weierstrass_theorem" title="Lindemann–Weierstrass theorem">Lindemann–Weierstrass theorem</a></li></ul></td> </tr><tr><th class="sidebar-heading"> People</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/John_Napier" title="John Napier">John Napier</a></li> <li><a class="mw-selflink selflink">Leonhard Euler</a> </li></ul></td> </tr><tr><th class="sidebar-heading"> Related topics</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Schanuel%27s_conjecture" title="Schanuel's conjecture">Schanuel's conjecture</a></li></ul></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:E_(mathematical_constant)" title="Template:E (mathematical constant)"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:E_(mathematical_constant)" title="Template talk:E (mathematical constant)"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:E_(mathematical_constant)" title="Special:EditPage/Template:E (mathematical constant)"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> Euler worked in almost all areas of mathematics, including <a href="/wiki/Geometry" title="Geometry">geometry</a>, <a href="/wiki/Infinitesimal_calculus" class="mw-redirect" title="Infinitesimal calculus">infinitesimal calculus</a>, <a href="/wiki/Trigonometry" title="Trigonometry">trigonometry</a>, <a href="/wiki/Algebra" title="Algebra">algebra</a>, and <a href="/wiki/Number_theory" title="Number theory">number theory</a>, as well as <a href="/wiki/Continuum_physics" class="mw-redirect" title="Continuum physics">continuum physics</a>, <a href="/wiki/Lunar_theory" title="Lunar theory">lunar theory</a>, and other areas of <a href="/wiki/Physics" title="Physics">physics</a>. He is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 <a href="/wiki/Quarto_(text)" class="mw-redirect" title="Quarto (text)">quarto</a> volumes.<a href="#cite_note-volumes-43">[39]</a> Euler's name is associated with a <a href="/wiki/List_of_topics_named_after_Leonhard_Euler" title="List of topics named after Leonhard Euler">large number of topics</a>. Euler's work averages 800 pages a year from 1725 to 1783. He also wrote over 4500 letters and hundreds of manuscripts. It has been estimated that Leonhard Euler was the author of a quarter of the combined output in mathematics, physics, mechanics, astronomy, and navigation in the 18th century.<a href="#cite_note-assad-18">[14]</a> <div class="mw-heading mw-heading3"><h3 id="Mathematical_notation">Mathematical notation</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=10" title="Edit section: Mathematical notation">edit</a>]</div> Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">function</a><a href="#cite_note-FOOTNOTEDunham199917-8">[6]</a> and was the first to write f(x) to denote the function f applied to the argument x. He also introduced the modern notation for the <a href="/wiki/Trigonometric_functions" title="Trigonometric functions">trigonometric functions</a>, the letter e for the base of the <a href="/wiki/Natural_logarithm" title="Natural logarithm">natural logarithm</a> (now also known as <a href="/wiki/Euler%27s_number" class="mw-redirect" title="Euler's number">Euler's number</a>), the Greek letter <a href="/wiki/Sigma" title="Sigma">Σ</a> for summations and the letter i to denote the <a href="/wiki/Imaginary_unit" title="Imaginary unit">imaginary unit</a>.<a href="#cite_note-Boyer-71">[67]</a> The use of the Greek letter <a href="/wiki/Pi_(letter)" title="Pi (letter)">π</a> to denote the <a href="/wiki/Pi" title="Pi">ratio of a circle's circumference to its diameter</a> was also popularized by Euler, although it originated with <a href="/wiki/Welsh_people" title="Welsh people">Welsh</a> mathematician <a href="/wiki/William_Jones_(mathematician)" title="William Jones (mathematician)">William Jones</a>.<a href="#cite_note-arndt-72">[68]</a> <div class="mw-heading mw-heading3"><h3 id="Analysis">Analysis</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=11" title="Edit section: Analysis">edit</a>]</div> The development of <a href="/wiki/Infinitesimal_calculus" class="mw-redirect" title="Infinitesimal calculus">infinitesimal calculus</a> was at the forefront of 18th-century mathematical research, and the <a href="/wiki/Bernoulli_family" title="Bernoulli family">Bernoullis</a>—family friends of Euler—were responsible for much of the early progress in the field. Thanks to their influence, studying calculus became the major focus of Euler's work. While some of Euler's proofs are not acceptable by modern standards of <a href="/wiki/Mathematical_rigor" class="mw-redirect" title="Mathematical rigor">mathematical rigour</a><a href="#cite_note-Basel-73">[69]</a> (in particular his reliance on the principle of the <a href="/wiki/Generality_of_algebra" title="Generality of algebra">generality of algebra</a>), his ideas led to many great advances. Euler is well known in <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">analysis</a> for his frequent use and development of <a href="/wiki/Power_series" title="Power series">power series</a>, the expression of functions as sums of infinitely many terms,<a href="#cite_note-FOOTNOTEFerraro2008155-74">[70]</a> such as <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{x}=\sum _{n=0}^{\infty }{x^{n} \over n!}=\lim _{n\to \infty }\left({\frac {1}{0!}}+{\frac {x}{1!}}+{\frac {x^{2}}{2!}}+\cdots +{\frac {x^{n}}{n!}}\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mrow> <mi>n</mi> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>0</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mrow> <mn>1</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mrow> <mi>n</mi> <mo>!</mo> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{x}=\sum _{n=0}^{\infty }{x^{n} \over n!}=\lim _{n\to \infty }\left({\frac {1}{0!}}+{\frac {x}{1!}}+{\frac {x^{2}}{2!}}+\cdots +{\frac {x^{n}}{n!}}\right).}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c95b9b62c1f21a1131cd62f7c18bee48d1dfe8d2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:50.674ex; height:6.843ex;" alt="{\displaystyle e^{x}=\sum _{n=0}^{\infty }{x^{n} \over n!}=\lim _{n\to \infty }\left({\frac {1}{0!}}+{\frac {x}{1!}}+{\frac {x^{2}}{2!}}+\cdots +{\frac {x^{n}}{n!}}\right).}"> Euler's use of power series enabled him to solve the <a href="/wiki/Basel_problem" title="Basel problem">Basel problem</a>, finding the sum of the reciprocals of squares of every natural number, in 1735 (he provided a more elaborate argument in 1741). The Basel problem was originally posed by <a href="/wiki/Pietro_Mengoli" title="Pietro Mengoli">Pietro Mengoli</a> in 1644, and by the 1730s was a famous open problem, popularized by <a href="/wiki/Jacob_Bernoulli" title="Jacob Bernoulli">Jacob Bernoulli</a> and unsuccessfully attacked by many of the leading mathematicians of the time. Euler found that:<a href="#cite_note-Morris_PhD_thesis-75">[71]</a><a href="#cite_note-FOOTNOTEDunham1999-76">[72]</a><a href="#cite_note-Basel-73">[69]</a> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{n=1}^{\infty }{1 \over n^{2}}=\lim _{n\to \infty }\left({\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+\cdots +{\frac {1}{n^{2}}}\right)={\frac {\pi ^{2}}{6}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>6</mn> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{n=1}^{\infty }{1 \over n^{2}}=\lim _{n\to \infty }\left({\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+\cdots +{\frac {1}{n^{2}}}\right)={\frac {\pi ^{2}}{6}}.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a9cfed0433da9faf896f688da37124e613ab17d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:51.705ex; height:6.843ex;" alt="{\displaystyle \sum _{n=1}^{\infty }{1 \over n^{2}}=\lim _{n\to \infty }\left({\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+\cdots +{\frac {1}{n^{2}}}\right)={\frac {\pi ^{2}}{6}}.}"> Euler introduced the constant <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma =\lim _{n\rightarrow \infty }\left(1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+\cdots +{\frac {1}{n}}-\ln(n)\right)\approx 0.5772,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mo>−</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mo>≈</mo> <mn>0.5772</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma =\lim _{n\rightarrow \infty }\left(1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+\cdots +{\frac {1}{n}}-\ln(n)\right)\approx 0.5772,}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6033037ea808e643a618f024f60b88c1f060e4f2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:56.944ex; height:6.176ex;" alt="{\displaystyle \gamma =\lim _{n\rightarrow \infty }\left(1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+\cdots +{\frac {1}{n}}-\ln(n)\right)\approx 0.5772,}"> now known as <a href="/wiki/Euler%27s_constant" title="Euler's constant">Euler's constant</a> or the Euler–Mascheroni constant, and studied its relationship with the <a href="/wiki/Harmonic_series_(mathematics)" title="Harmonic series (mathematics)">harmonic series</a>, the <a href="/wiki/Gamma_function" title="Gamma function">gamma function</a>, and values of the <a href="/wiki/Riemann_zeta_function" title="Riemann zeta function">Riemann zeta function</a>.<a href="#cite_note-lagarias-77">[73]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Euler%27s_formula.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/220px-Euler%27s_formula.svg.png" decoding="async" width="220" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/330px-Euler%27s_formula.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Euler%27s_formula.svg/440px-Euler%27s_formula.svg.png 2x" data-file-width="760" data-file-height="782" /></a><figcaption>A geometric interpretation of <a href="/wiki/Euler%27s_formula" title="Euler's formula">Euler's formula</a></figcaption></figure> Euler introduced the use of the <a href="/wiki/Exponential_function" title="Exponential function">exponential function</a> and <a href="/wiki/Logarithms" class="mw-redirect" title="Logarithms">logarithms</a> in <a href="/wiki/Analytic_proof" title="Analytic proof">analytic proofs</a>. He discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and <a href="/wiki/Complex_number" title="Complex number">complex numbers</a>, thus greatly expanding the scope of mathematical applications of logarithms.<a href="#cite_note-Boyer-71">[67]</a> He also defined the exponential function for complex numbers and discovered its relation to the <a href="/wiki/Trigonometric_function" class="mw-redirect" title="Trigonometric function">trigonometric functions</a>. For any <a href="/wiki/Real_number" title="Real number">real number</a> <a href="/wiki/%CE%A6" class="mw-redirect" title="Φ">φ</a> (taken to be radians), <a href="/wiki/Euler%27s_formula" title="Euler's formula">Euler's formula</a> states that the <a href="/wiki/Exponential_function#On_the_complex_plane" title="Exponential function">complex exponential</a> function satisfies <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{i\varphi }=\cos \varphi +i\sin \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>φ</mi> </mrow> </msup> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mo>+</mo> <mi>i</mi> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{i\varphi }=\cos \varphi +i\sin \varphi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5645926e79cc461626d5f06ef8106c5f84b7187" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.868ex; height:3.176ex;" alt="{\displaystyle e^{i\varphi }=\cos \varphi +i\sin \varphi }"> which was called "the most remarkable formula in mathematics" by <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a>.<a href="#cite_note-Feynman-78">[74]</a> A special case of the above formula is known as <a href="/wiki/Euler%27s_identity" title="Euler's identity">Euler's identity</a>, <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{i\pi }+1=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>π</mi> </mrow> </msup> <mo>+</mo> <mn>1</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{i\pi }+1=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7464809a40f9e486de3a454745f572fbf8bb256" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.089ex; height:2.843ex;" alt="{\displaystyle e^{i\pi }+1=0}"> Euler elaborated the theory of higher <a href="/wiki/Transcendental_function" title="Transcendental function">transcendental functions</a> by introducing the <a href="/wiki/Gamma_function" title="Gamma function">gamma function</a><a href="#cite_note-FOOTNOTEFerraro2008159-79">[75]</a><a href="#cite_note-davis-80">[76]</a> and introduced a new method for solving <a href="/wiki/Quartic_equation" title="Quartic equation">quartic equations</a>.<a href="#cite_note-nickalls-81">[77]</a> He found a way to calculate integrals with complex limits, foreshadowing the development of modern <a href="/wiki/Complex_analysis" title="Complex analysis">complex analysis</a>. He invented the <a href="/wiki/Calculus_of_variations" title="Calculus of variations">calculus of variations</a> and formulated the <a href="/wiki/Euler%E2%80%93Lagrange_equation" title="Euler–Lagrange equation">Euler–Lagrange equation</a> for reducing <a href="/wiki/Mathematical_optimization" title="Mathematical optimization">optimization problems</a> in this area to the solution of <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a>. Euler pioneered the use of analytic methods to solve number theory problems. In doing so, he united two disparate branches of mathematics and introduced a new field of study, <a href="/wiki/Analytic_number_theory" title="Analytic number theory">analytic number theory</a>. In breaking ground for this new field, Euler created the theory of <a href="/wiki/Generalized_hypergeometric_series" class="mw-redirect" title="Generalized hypergeometric series">hypergeometric series</a>, <a href="/wiki/Q-series" class="mw-redirect" title="Q-series">q-series</a>, <a href="/wiki/Hyperbolic_functions" title="Hyperbolic functions">hyperbolic trigonometric functions</a>, and the analytic theory of <a href="/wiki/Generalized_continued_fraction" class="mw-redirect" title="Generalized continued fraction">continued fractions</a>. For example, he proved the <a href="/wiki/Infinitude_of_primes" class="mw-redirect" title="Infinitude of primes">infinitude of primes</a> using the divergence of the <a href="/wiki/Harmonic_series_(mathematics)" title="Harmonic series (mathematics)">harmonic series</a>, and he used analytic methods to gain some understanding of the way <a href="/wiki/Prime_numbers" class="mw-redirect" title="Prime numbers">prime numbers</a> are distributed. Euler's work in this area led to the development of the <a href="/wiki/Prime_number_theorem" title="Prime number theorem">prime number theorem</a>.<a href="#cite_note-FOOTNOTEDunham1999Ch._3,_Ch._4-82">[78]</a> <div class="mw-heading mw-heading3"><h3 id="Number_theory">Number theory</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=12" title="Edit section: Number theory">edit</a>]</div> Euler's interest in number theory can be traced to the influence of <a href="/wiki/Christian_Goldbach" title="Christian Goldbach">Christian Goldbach</a>,<a href="#cite_note-FOOTNOTECalinger1996130-83">[79]</a> his friend in the St. Petersburg Academy.<a href="#cite_note-FOOTNOTEGautschi20086-64">[60]</a> Much of Euler's early work on number theory was based on the work of <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a>. Euler developed some of Fermat's ideas and disproved some of his conjectures, such as his conjecture that all numbers of the form <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle 2^{2^{n}}+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle 2^{2^{n}}+1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2b835070d924d2556ec07501e18d07a09c6d5bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.184ex; height:2.843ex;" alt="{\textstyle 2^{2^{n}}+1}"> (<a href="/wiki/Fermat_numbers" class="mw-redirect" title="Fermat numbers">Fermat numbers</a>) are prime.<a href="#cite_note-FOOTNOTEDunham19997-84">[80]</a> Euler linked the nature of prime distribution with ideas in analysis. He proved that <a href="/wiki/Proof_that_the_sum_of_the_reciprocals_of_the_primes_diverges" class="mw-redirect" title="Proof that the sum of the reciprocals of the primes diverges">the sum of the reciprocals of the primes diverges</a>. In doing so, he discovered the connection between the <a href="/wiki/Riemann_zeta_function" title="Riemann zeta function">Riemann zeta function</a> and prime numbers; this is known as the <a href="/wiki/Proof_of_the_Euler_product_formula_for_the_Riemann_zeta_function" title="Proof of the Euler product formula for the Riemann zeta function">Euler product formula for the Riemann zeta function</a>.<a href="#cite_note-patterson-85">[81]</a> Euler invented the <a href="/wiki/Totient_function" class="mw-redirect" title="Totient function">totient function</a> φ(n), the number of positive integers less than or equal to the integer n that are <a href="/wiki/Coprime" class="mw-redirect" title="Coprime">coprime</a> to n. Using properties of this function, he generalized <a href="/wiki/Fermat%27s_little_theorem" title="Fermat's little theorem">Fermat's little theorem</a> to what is now known as <a href="/wiki/Euler%27s_theorem" title="Euler's theorem">Euler's theorem</a>.<a href="#cite_note-shiu-86">[82]</a> He contributed significantly to the theory of <a href="/wiki/Perfect_number" title="Perfect number">perfect numbers</a>, which had fascinated mathematicians since <a href="/wiki/Euclid" title="Euclid">Euclid</a>. He proved that the relationship shown between even perfect numbers and <a href="/wiki/Mersenne_prime" title="Mersenne prime">Mersenne primes</a> (which he had earlier proved) was one-to-one, a result otherwise known as the <a href="/wiki/Euclid%E2%80%93Euler_theorem" title="Euclid–Euler theorem">Euclid–Euler theorem</a>.<a href="#cite_note-stillwell-87">[83]</a> Euler also conjectured the law of <a href="/wiki/Quadratic_reciprocity" title="Quadratic reciprocity">quadratic reciprocity</a>. The concept is regarded as a fundamental theorem within number theory, and his ideas paved the way for the work of <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a>, particularly <a href="/wiki/Disquisitiones_Arithmeticae" title="Disquisitiones Arithmeticae">Disquisitiones Arithmeticae</a>.<a href="#cite_note-FOOTNOTEDunham1999Ch._1,_Ch._4-88">[84]</a> By 1772 Euler had proved that 231 − 1 = <a href="/wiki/2147483647" class="mw-redirect" title="2147483647">2,147,483,647</a> is a Mersenne prime. It may have remained the <a href="/wiki/Largest_known_prime" class="mw-redirect" title="Largest known prime">largest known prime</a> until 1867.<a href="#cite_note-caldwell-89">[85]</a> Euler also contributed major developments to the theory of <a href="/wiki/Partitions_of_an_integer" class="mw-redirect" title="Partitions of an integer">partitions of an integer</a>.<a href="#cite_note-hopwil-90">[86]</a> <div class="mw-heading mw-heading3"><h3 id="Graph_theory">Graph theory</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=13" title="Edit section: Graph theory">edit</a>]</div> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/File:Konigsberg_bridges.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/5d/Konigsberg_bridges.png" decoding="async" width="302" height="238" class="mw-file-element" data-file-width="302" data-file-height="238" /></a><figcaption>Map of <a href="/wiki/K%C3%B6nigsberg" title="Königsberg">Königsberg</a> in Euler's time showing the actual layout of the <a href="/wiki/Seven_Bridges_of_K%C3%B6nigsberg" title="Seven Bridges of Königsberg">seven bridges</a>, highlighting the river <a href="/wiki/Pregolya" title="Pregolya">Pregel</a> and the bridges</figcaption></figure> In 1735, Euler presented a solution to the problem known as the <a href="/wiki/Seven_Bridges_of_K%C3%B6nigsberg" title="Seven Bridges of Königsberg">Seven Bridges of Königsberg</a>.<a href="#cite_note-bridge-91">[87]</a> The city of <a href="/wiki/K%C3%B6nigsberg" title="Königsberg">Königsberg</a>, <a href="/wiki/Kingdom_of_Prussia" title="Kingdom of Prussia">Prussia</a> was set on the <a href="/wiki/Pregolya" title="Pregolya">Pregel</a> River, and included two large islands that were connected to each other and the mainland by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point. It is not possible: there is no <a href="/wiki/Eulerian_path" title="Eulerian path">Eulerian circuit</a>. This solution is considered to be the first theorem of <a href="/wiki/Graph_theory" title="Graph theory">graph theory</a>.<a href="#cite_note-bridge-91">[87]</a> Euler also discovered the <a href="/wiki/Planar_graph#Euler's_formula" title="Planar graph">formula</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V-E+F=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>−</mo> <mi>E</mi> <mo>+</mo> <mi>F</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V-E+F=2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/759601e482258ff7a359a7db381abf60372c5b06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:15.245ex; height:2.343ex;" alt="{\displaystyle V-E+F=2}"> relating the number of vertices, edges, and faces of a <a href="/wiki/Convex_polytope" title="Convex polytope">convex polyhedron</a>,<a href="#cite_note-FOOTNOTERicheson2012-92">[88]</a> and hence of a <a href="/wiki/Planar_graph" title="Planar graph">planar graph</a>. The constant in this formula is now known as the <a href="/wiki/Euler_characteristic" title="Euler characteristic">Euler characteristic</a> for the graph (or other mathematical object), and is related to the <a href="/wiki/Genus_(mathematics)" title="Genus (mathematics)">genus</a> of the object.<a href="#cite_note-gibbons-93">[89]</a> The study and generalization of this formula, specifically by <a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a><a href="#cite_note-Cauchy-94">[90]</a> and <a href="/wiki/Simon_Antoine_Jean_L%27Huilier" title="Simon Antoine Jean L'Huilier">L'Huilier</a>,<a href="#cite_note-Lhuillier-95">[91]</a> is at the origin of <a href="/wiki/Topology" title="Topology">topology</a>.<a href="#cite_note-FOOTNOTERicheson2012-92">[88]</a> <div class="mw-heading mw-heading3"><h3 id="Physics,_astronomy,_and_engineering">Physics, astronomy, and engineering</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=14" title="Edit section: Physics, astronomy, and engineering">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle" style="padding-left:0.9em;padding-right:0.9em;"><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></th></tr><tr><td class="sidebar-image"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">F</mtext> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2ad0a6d6780c3abc5247abd82bd8a2249d56ff3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.318ex; height:5.509ex;" alt="{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}"><div class="sidebar-caption" style="font-size:90%;padding:0.6em 0;font-style:italic;"><a href="/wiki/Second_law_of_motion" class="mw-redirect" title="Second law of motion">Second law of motion</a></div></td></tr><tr><th class="sidebar-heading" style="font-weight: bold; display:block;margin-bottom:1.0em;"> <div class="hlist"> <ul><li><a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">History</a></li> <li><a href="/wiki/Timeline_of_classical_mechanics" title="Timeline of classical mechanics">Timeline</a></li> <li><a href="/wiki/List_of_textbooks_on_classical_mechanics_and_quantum_mechanics" title="List of textbooks on classical mechanics and quantum mechanics">Textbooks</a></li></ul> </div></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Branches</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Applied_mechanics" title="Applied mechanics">Applied</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum</a></li> <li><a href="/wiki/Analytical_dynamics" class="mw-redirect" title="Analytical dynamics">Dynamics</a></li> <li><a href="/wiki/Classical_field_theory" title="Classical field theory">Field theory</a></li> <li><a href="/wiki/Kinematics" title="Kinematics">Kinematics</a></li> <li><a href="/wiki/Kinetics_(physics)" title="Kinetics (physics)">Kinetics</a></li> <li><a href="/wiki/Statics" title="Statics">Statics</a></li> <li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical mechanics</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Fundamentals</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Acceleration" title="Acceleration">Acceleration</a></li> <li><a href="/wiki/Angular_momentum" title="Angular momentum">Angular momentum</a></li> <li><a href="/wiki/Couple_(mechanics)" title="Couple (mechanics)">Couple</a></li> <li><a href="/wiki/D%27Alembert%27s_principle" title="D'Alembert's principle">D'Alembert's principle</a></li> <li><a href="/wiki/Energy" title="Energy">Energy</a> <ul><li><a href="/wiki/Kinetic_energy#Newtonian_kinetic_energy" title="Kinetic energy">kinetic</a></li> <li><a href="/wiki/Potential_energy" title="Potential energy">potential</a></li></ul></li> <li><a href="/wiki/Force" title="Force">Force</a></li> <li><a href="/wiki/Frame_of_reference" title="Frame of reference">Frame of reference</a></li> <li><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial frame of reference</a></li> <li><a href="/wiki/Impulse_(physics)" title="Impulse (physics)">Impulse</a></li> <li><a href="/wiki/Inertia" title="Inertia">Inertia</a> / <a href="/wiki/Moment_of_inertia" title="Moment of inertia">Moment of inertia</a></li> <li><a href="/wiki/Mass" title="Mass">Mass</a></li> <li> <a href="/wiki/Mechanical_power_(physics)" class="mw-redirect" title="Mechanical power (physics)">Mechanical power</a></li> <li><a href="/wiki/Work_(physics)" title="Work (physics)">Mechanical work</a></li> <li> <a href="/wiki/Moment_(physics)" title="Moment (physics)">Moment</a></li> <li><a href="/wiki/Momentum" title="Momentum">Momentum</a></li> <li><a href="/wiki/Space" title="Space">Space</a></li> <li><a href="/wiki/Speed" title="Speed">Speed</a></li> <li><a href="/wiki/Time" title="Time">Time</a></li> <li><a href="/wiki/Torque" title="Torque">Torque</a></li> <li><a href="/wiki/Velocity" title="Velocity">Velocity</a></li> <li><a href="/wiki/Virtual_work" title="Virtual work">Virtual work</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Formulations</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"> <ul><li><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a></div></li> <li><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical mechanics</a> <div class="plainlist"><ul><li><a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian mechanics</a></li><li><a href="/wiki/Hamiltonian_mechanics" title="Hamiltonian mechanics">Hamiltonian mechanics</a></li><li><a href="/wiki/Routhian_mechanics" title="Routhian mechanics">Routhian mechanics</a></li><li><a href="/wiki/Hamilton%E2%80%93Jacobi_equation" title="Hamilton–Jacobi equation">Hamilton–Jacobi equation</a></li><li><a href="/wiki/Appell%27s_equation_of_motion" title="Appell's equation of motion">Appell's equation of motion</a></li><li><a href="/wiki/Koopman%E2%80%93von_Neumann_classical_mechanics" title="Koopman–von Neumann classical mechanics">Koopman–von Neumann mechanics</a></li></ul></div></div></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Core topics</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Damping" title="Damping">Damping</a></li> <li><a href="/wiki/Displacement_(geometry)" title="Displacement (geometry)">Displacement</a></li> <li><a href="/wiki/Equations_of_motion" title="Equations of motion">Equations of motion</a></li> <li><a href="/wiki/Euler%27s_laws_of_motion" title="Euler's laws of motion">Euler's laws of motion</a></li> <li><a href="/wiki/Fictitious_force" title="Fictitious force">Fictitious force</a></li> <li><a href="/wiki/Friction" title="Friction">Friction</a></li> <li><a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">Harmonic oscillator</a></li></ul> </div> <ul><li><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial</a> / <a href="/wiki/Non-inertial_reference_frame" title="Non-inertial reference frame">Non-inertial reference frame</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Motion" title="Motion">Motion</a> (<a href="/wiki/Linear_motion" title="Linear motion">linear</a>)</li> <li><a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a></li> <li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a></li> <li><a href="/wiki/Relative_velocity" title="Relative velocity">Relative velocity</a></li> <li><a href="/wiki/Rigid_body" title="Rigid body">Rigid body</a> <ul><li><a href="/wiki/Rigid_body_dynamics" title="Rigid body dynamics">dynamics</a></li> <li><a href="/wiki/Euler%27s_equations_(rigid_body_dynamics)" title="Euler's equations (rigid body dynamics)">Euler's equations</a></li></ul></li> <li><a href="/wiki/Simple_harmonic_motion" title="Simple harmonic motion">Simple harmonic motion</a></li> <li><a href="/wiki/Vibration" title="Vibration">Vibration</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)"><a href="/wiki/Rotation_around_a_fixed_axis" title="Rotation around a fixed axis">Rotation</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Circular_motion" title="Circular motion">Circular motion</a></li> <li><a href="/wiki/Rotating_reference_frame" title="Rotating reference frame">Rotating reference frame</a></li> <li><a href="/wiki/Centripetal_force" title="Centripetal force">Centripetal force</a></li> <li><a href="/wiki/Centrifugal_force" title="Centrifugal force">Centrifugal force</a> <ul><li><a href="/wiki/Reactive_centrifugal_force" title="Reactive centrifugal force">reactive</a></li></ul></li> <li><a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis force</a></li> <li><a href="/wiki/Pendulum_(mechanics)" title="Pendulum (mechanics)">Pendulum</a></li> <li><a href="/wiki/Tangential_speed" title="Tangential speed">Tangential speed</a></li> <li><a href="/wiki/Rotational_frequency" title="Rotational frequency">Rotational frequency</a></li></ul> </div> <ul><li><a href="/wiki/Angular_acceleration" title="Angular acceleration">Angular acceleration</a> / <a href="/wiki/Angular_displacement" title="Angular displacement">displacement</a> / <a href="/wiki/Angular_frequency" title="Angular frequency">frequency</a> / <a href="/wiki/Angular_velocity" title="Angular velocity">velocity</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a></li> <li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Jeremiah_Horrocks" title="Jeremiah Horrocks">Horrocks</a></li> <li><a href="/wiki/Edmond_Halley" title="Edmond Halley">Halley</a></li> <li><a href="/wiki/Pierre_Louis_Maupertuis" title="Pierre Louis Maupertuis">Maupertuis</a></li> <li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a></li> <li><a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann Bernoulli</a></li> <li><a class="mw-selflink selflink">Euler</a></li> <li><a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">d'Alembert</a></li> <li><a href="/wiki/Alexis_Clairaut" title="Alexis Clairaut">Clairaut</a></li> <li><a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Lagrange</a></li> <li><a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Laplace</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/William_Rowan_Hamilton" title="William Rowan Hamilton">Hamilton</a></li> <li><a href="/wiki/Carl_Gustav_Jacob_Jacobi" title="Carl Gustav Jacob Jacobi">Jacobi</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li> <li><a href="/wiki/Edward_Routh" title="Edward Routh">Routh</a></li> <li><a href="/wiki/Joseph_Liouville" title="Joseph Liouville">Liouville</a></li> <li><a href="/wiki/Paul_%C3%89mile_Appell" title="Paul Émile Appell">Appell</a></li> <li><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a></li> <li><a href="/wiki/Bernard_Koopman" title="Bernard Koopman">Koopman</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><a 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href="/wiki/Template_talk:Classical_mechanics" title="Template talk:Classical mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Classical_mechanics" title="Special:EditPage/Template:Classical mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> Some of Euler's greatest successes were in solving real-world problems analytically, and in describing numerous applications of the <a href="/wiki/Bernoulli_numbers" class="mw-redirect" title="Bernoulli numbers">Bernoulli numbers</a>, <a href="/wiki/Fourier_series" title="Fourier series">Fourier series</a>, <a href="/wiki/Euler_number" class="mw-redirect" title="Euler number">Euler numbers</a>, the constants <a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e</a> and <a href="/wiki/Pi" title="Pi">π</a>, continued fractions, and integrals. He integrated <a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Leibniz</a>'s <a href="/wiki/Differential_calculus" title="Differential calculus">differential calculus</a> with Newton's <a href="/wiki/Method_of_Fluxions" title="Method of Fluxions">Method of Fluxions</a>, and developed tools that made it easier to apply calculus to physical problems. He made great strides in improving the <a href="/wiki/Numerical_approximation" class="mw-redirect" title="Numerical approximation">numerical approximation</a> of integrals, inventing what are now known as the <a href="/wiki/Euler_approximations" class="mw-redirect" title="Euler approximations">Euler approximations</a>. The most notable of these approximations are <a href="/wiki/Euler%27s_method" class="mw-redirect" title="Euler's method">Euler's method</a><a href="#cite_note-butcher-96">[92]</a> and the <a href="/wiki/Euler%E2%80%93Maclaurin_formula" title="Euler–Maclaurin formula">Euler–Maclaurin formula</a>.<a href="#cite_note-FOOTNOTECalinger201696,_137-97">[93]</a><a href="#cite_note-FOOTNOTEFerraro2008171–180Chapter_14:_Euler's_derivation_of_the_Euler–Maclaurin_summation_formula-98">[94]</a><a href="#cite_note-mills-99">[95]</a> Euler helped develop the <a href="/wiki/Euler%E2%80%93Bernoulli_beam_equation" class="mw-redirect" title="Euler–Bernoulli beam equation">Euler–Bernoulli beam equation</a>, which became a cornerstone of engineering.<a href="#cite_note-ojalvo-100">[96]</a> Besides successfully applying his analytic tools to problems in <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a>, Euler applied these techniques to celestial problems. His work in astronomy was recognized by multiple <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">Paris Academy</a> Prizes over the course of his career. His accomplishments include determining with great accuracy the <a href="/wiki/Orbit" title="Orbit">orbits</a> of <a href="/wiki/Comet" title="Comet">comets</a> and other celestial bodies, understanding the nature of comets, and calculating the <a href="/wiki/Solar_parallax" class="mw-redirect" title="Solar parallax">parallax</a> of the Sun. His calculations contributed to the development of accurate <a href="/wiki/History_of_longitude" title="History of longitude">longitude tables</a>.<a href="#cite_note-yousch-101">[97]</a> Euler made important contributions in <a href="/wiki/Optics" title="Optics">optics</a>.<a href="#cite_note-davidson-102">[98]</a> He disagreed with Newton's <a href="/wiki/Corpuscular_theory_of_light" title="Corpuscular theory of light">corpuscular theory of light</a>,<a href="#cite_note-FOOTNOTECalinger1996152–153-103">[99]</a> which was the prevailing theory of the time. His 1740s papers on optics helped ensure that the <a href="/wiki/Wave_theory_of_light" class="mw-redirect" title="Wave theory of light">wave theory of light</a> proposed by <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a> would become the dominant mode of thought, at least until the development of the <a href="/wiki/Wave-particle_duality" class="mw-redirect" title="Wave-particle duality">quantum theory of light</a>.<a href="#cite_note-optics-104">[100]</a> In <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, Euler was the first to predict the phenomenon of <a href="/wiki/Cavitation" title="Cavitation">cavitation</a>, in 1754, long before its first observation in the late 19th century, and the <a href="/wiki/Euler_number_(physics)" title="Euler number (physics)">Euler number</a> used in fluid flow calculations comes from his related work on the efficiency of <a href="/wiki/Turbine" title="Turbine">turbines</a>.<a href="#cite_note-li-105">[101]</a> In 1757 he published an important set of equations for <a href="/wiki/Inviscid_flow" title="Inviscid flow">inviscid flow</a> in <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, that are now known as the <a href="/wiki/Euler_equations_(fluid_dynamics)" title="Euler equations (fluid dynamics)">Euler equations</a>.<a href="#cite_note-euler2-106">[102]</a> Euler is well known in <a href="/wiki/Structural_engineering" title="Structural engineering">structural engineering</a> for his formula giving <a href="/wiki/Euler%27s_critical_load" title="Euler's critical load">Euler's critical load</a>, the critical <a href="/wiki/Buckling" title="Buckling">buckling</a> load of an ideal strut, which depends only on its length and <a href="/wiki/Flexural_rigidity" title="Flexural rigidity">flexural stiffness</a>.<a href="#cite_note-FOOTNOTEGautschi200822-107">[103]</a> <div class="mw-heading mw-heading3"><h3 id="Logic">Logic</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=15" title="Edit section: Logic">edit</a>]</div> Euler is credited with using <a href="/wiki/Closed_curve" class="mw-redirect" title="Closed curve">closed curves</a> to illustrate <a href="/wiki/Syllogism" title="Syllogism">syllogistic</a> reasoning (1768). These diagrams have become known as <a href="/wiki/Euler_diagram" title="Euler diagram">Euler diagrams</a>.<a href="#cite_note-logic-108">[104]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Euler_Diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Euler_Diagram.svg/170px-Euler_Diagram.svg.png" decoding="async" width="170" height="151" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Euler_Diagram.svg/255px-Euler_Diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Euler_Diagram.svg/340px-Euler_Diagram.svg.png 2x" data-file-width="323" data-file-height="287" /></a><figcaption>An Euler diagram</figcaption></figure> An Euler diagram is a <a href="/wiki/Diagram" title="Diagram">diagrammatic</a> means of representing <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">sets</a> and their relationships. Euler diagrams consist of simple closed curves (usually circles) in the plane that depict <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">sets</a>. Each Euler curve divides the plane into two regions or "zones": the interior, which symbolically represents the <a href="/wiki/Element_(mathematics)" title="Element (mathematics)">elements</a> of the set, and the exterior, which represents all elements that are not members of the set. The sizes or shapes of the curves are not important; the significance of the diagram is in how they overlap. The spatial relationships between the regions bounded by each curve (overlap, containment or neither) corresponds to set-theoretic relationships (<a href="/wiki/Intersection_(set_theory)" title="Intersection (set theory)">intersection</a>, <a href="/wiki/Subset" title="Subset">subset</a>, and <a href="/wiki/Disjoint_sets" title="Disjoint sets">disjointness</a>). Curves whose interior zones do not intersect represent <a href="/wiki/Disjoint_sets" title="Disjoint sets">disjoint sets</a>. Two curves whose interior zones intersect represent sets that have common elements; the zone inside both curves represents the set of elements common to both sets (the <a href="/wiki/Intersection_(set_theory)" title="Intersection (set theory)">intersection</a> of the sets). A curve that is contained completely within the interior zone of another represents a <a href="/wiki/Subset" title="Subset">subset</a> of it. Euler diagrams (and their refinement to <a href="/wiki/Venn_diagram" title="Venn diagram">Venn diagrams</a>) were incorporated as part of instruction in <a href="/wiki/Set_theory" title="Set theory">set theory</a> as part of the <a href="/wiki/New_math" class="mw-redirect" title="New math">new math</a> movement in the 1960s.<a href="#cite_note-lemanski-109">[105]</a> Since then, they have come into wide use as a way of visualizing combinations of characteristics.<a href="#cite_note-rodgers-110">[106]</a> <div class="mw-heading mw-heading3"><h3 id="Music">Music</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=16" title="Edit section: Music">edit</a>]</div> One of Euler's more unusual interests was the application of <a href="/wiki/Music_and_mathematics" title="Music and mathematics">mathematical ideas in music</a>. In 1739 he wrote the Tentamen novae theoriae musicae (Attempt at a New Theory of Music), hoping to eventually incorporate <a href="/wiki/Musical_theory" class="mw-redirect" title="Musical theory">musical theory</a> as part of mathematics. This part of his work, however, did not receive wide attention and was once described as too mathematical for musicians and too musical for mathematicians.<a href="#cite_note-FOOTNOTECalinger1996144–145-111">[107]</a> Even when dealing with music, Euler's approach is mainly mathematical,<a href="#cite_note-pesic-112">[108]</a> for instance, his introduction of <a href="/wiki/Binary_logarithm" title="Binary logarithm">binary logarithms</a> as a way of numerically describing the subdivision of <a href="/wiki/Octave" title="Octave">octaves</a> into fractional parts.<a href="#cite_note-tegg-113">[109]</a> His writings on music are not particularly numerous (a few hundred pages, in his total production of about thirty thousand pages), but they reflect an early preoccupation and one that remained with him throughout his life.<a href="#cite_note-pesic-112">[108]</a> A first point of Euler's musical theory is the definition of "genres", i.e. of possible divisions of the octave using the prime numbers 3 and 5. Euler describes 18 such genres, with the general definition 2mA, where A is the "exponent" of the genre (i.e. the sum of the exponents of 3 and 5) and 2m (where "m is an indefinite number, small or large, so long as the sounds are perceptible"<a href="#cite_note-FOOTNOTEEuler1739115-114">[110]</a>), expresses that the relation holds independently of the number of octaves concerned. The first genre, with A = 1, is the octave itself (or its duplicates); the second genre, 2m.3, is the octave divided by the fifth (fifth + fourth, C–G–C); the third genre is 2m.5, major third + minor sixth (C–E–C); the fourth is 2m.32, two-fourths and a tone (C–F–B♭–C); the fifth is 2m.3.5 (C–E–G–B–C); etc. Genres 12 (2m.33.5), 13 (2m.32.52) and 14 (2m.3.53) are corrected versions of the <a href="/wiki/Genus_(music)" title="Genus (music)">diatonic, chromatic and enharmonic</a>, respectively, of the Ancients. Genre 18 (2m.33.52) is the "diatonico-chromatic", "used generally in all compositions",<a href="#cite_note-emery-115">[111]</a> and which turns out to be identical with the system described by <a href="/wiki/Johann_Mattheson" title="Johann Mattheson">Johann Mattheson</a>.<a href="#cite_note-mattheson-116">[112]</a> Euler later envisaged the possibility of describing genres including the prime number 7.<a href="#cite_note-perret-117">[113]</a> Euler devised a specific graph, the Speculum musicum,<a href="#cite_note-FOOTNOTEEuler1739147-118">[114]</a><a href="#cite_note-de_harmoniae-119">[115]</a> to illustrate the diatonico-chromatic genre, and discussed paths in this graph for specific intervals, recalling his interest in the Seven Bridges of Königsberg (see <a href="#Graph_theory">above</a>). The device drew renewed interest as the <a href="/wiki/Tonnetz" title="Tonnetz">Tonnetz</a> in <a href="/wiki/Neo-Riemannian_theory" title="Neo-Riemannian theory">Neo-Riemannian theory</a> (see also <a href="/wiki/Lattice_(music)" title="Lattice (music)">Lattice (music)</a>).<a href="#cite_note-gollin-120">[116]</a> Euler further used the principle of the "exponent" to propose a derivation of the gradus suavitatis (degree of suavity, of agreeableness) of intervals and chords from their prime factors – one must keep in mind that he considered just intonation, i.e. 1 and the prime numbers 3 and 5 only.<a href="#cite_note-lindley-121">[117]</a> Formulas have been proposed extending this system to any number of prime numbers, e.g. in the form <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds=\sum _{i}(k_{i}p_{i}-k_{i})+1,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>s</mi> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <mo stretchy="false">(</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds=\sum _{i}(k_{i}p_{i}-k_{i})+1,}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c5aac04394db2fad22495e6b816ca969486659c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:24.05ex; height:5.509ex;" alt="{\displaystyle ds=\sum _{i}(k_{i}p_{i}-k_{i})+1,}"> where pi are prime numbers and ki their exponents.<a href="#cite_note-bailhache-122">[118]</a> <div class="mw-heading mw-heading2"><h2 id="Personal_philosophy_and_religious_beliefs">Personal philosophy and religious beliefs</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=17" title="Edit section: Personal philosophy and religious beliefs">edit</a>]</div> Euler was a religious person throughout his life.<a href="#cite_note-zum_werk_leonhard-24">[20]</a> Much of what is known of Euler's religious beliefs can be deduced from his <a href="/wiki/Letters_to_a_German_Princess" title="Letters to a German Princess">Letters to a German Princess</a> and an earlier work, Rettung der Göttlichen Offenbahrung gegen die Einwürfe der Freygeister (Defense of the Divine Revelation against the Objections of the Freethinkers). These works show that Euler was a devout Christian who believed the Bible to be inspired; the Rettung was primarily an argument for the <a href="/wiki/Biblical_inspiration" title="Biblical inspiration">divine inspiration of scripture</a>.<a href="#cite_note-theology-123">[119]</a><a href="#cite_note-Ho2-124">[120]</a> Euler opposed the concepts of <a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Leibniz's</a> <a href="/wiki/Monadism" class="mw-redirect" title="Monadism">monadism</a> and the philosophy of <a href="/wiki/Christian_Wolff_(philosopher)" title="Christian Wolff (philosopher)">Christian Wolff</a>.<a href="#cite_note-FOOTNOTECalinger1996123-125">[121]</a> Euler insisted that knowledge is founded in part on the basis of precise quantitative laws, something that monadism and Wolffian science were unable to provide. Euler also labelled Wolff's ideas as "heathen and atheistic".<a href="#cite_note-wolff-126">[122]</a> There is a famous legend<a href="#cite_note-diderot-127">[123]</a> inspired by Euler's arguments with secular <a href="/wiki/Philosophers" class="mw-redirect" title="Philosophers">philosophers</a> over religion, which is set during Euler's second stint at the St. Petersburg Academy. The French philosopher <a href="/wiki/Denis_Diderot" title="Denis Diderot">Denis Diderot</a> was visiting Russia on Catherine the Great's invitation. However, the Empress was alarmed that the philosopher's arguments for <a href="/wiki/Atheism" title="Atheism">atheism</a> were influencing members of her court, and so Euler was asked to confront the Frenchman. Diderot was informed that a learned mathematician had produced a proof of the <a href="/wiki/Existence_of_God" title="Existence of God">existence of God</a>: he agreed to view the proof as it was presented in court. Euler appeared, advanced toward Diderot, and in a tone of perfect conviction announced this <a href="/wiki/Non_sequitur_(literary_device)" title="Non sequitur (literary device)">non-sequitur</a>: "Sir, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {a+b^{n}}{n}}=x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>=</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a+b^{n}}{n}}=x}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9b6f284cf65106c41ec725c0c4b648bb881c444" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.551ex; height:5.343ex;" alt="{\displaystyle {\frac {a+b^{n}}{n}}=x}">, hence God exists –reply!" Diderot, to whom (says the story) all mathematics was gibberish, stood dumbstruck as peals of laughter erupted from the court. Embarrassed, he asked to leave Russia, a request that was graciously granted by the Empress. However amusing the anecdote may be, it is <a href="https://en.wiktionary.org/wiki/apocryphal" class="extiw" title="wikt:apocryphal">apocryphal</a>, given that Diderot himself did research in mathematics.<a href="#cite_note-persee-128">[124]</a> The legend was apparently first told by <a href="/wiki/Dieudonn%C3%A9_Thi%C3%A9bault" title="Dieudonné Thiébault">Dieudonné Thiébault</a> with embellishment by <a href="/wiki/Augustus_De_Morgan" title="Augustus De Morgan">Augustus De Morgan</a>.<a href="#cite_note-diderot-127">[123]</a> <div class="mw-heading mw-heading2"><h2 id="Commemorations">Commemorations</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=18" title="Edit section: Commemorations">edit</a>]</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/List_of_things_named_after_Leonhard_Euler" class="mw-redirect" title="List of things named after Leonhard Euler">List of things named after Leonhard Euler</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Euler-10_Swiss_Franc_banknote_(front).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Euler-10_Swiss_Franc_banknote_%28front%29.jpg/220px-Euler-10_Swiss_Franc_banknote_%28front%29.jpg" decoding="async" width="220" height="107" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Euler-10_Swiss_Franc_banknote_%28front%29.jpg/330px-Euler-10_Swiss_Franc_banknote_%28front%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Euler-10_Swiss_Franc_banknote_%28front%29.jpg/440px-Euler-10_Swiss_Franc_banknote_%28front%29.jpg 2x" data-file-width="3204" data-file-height="1558" /></a><figcaption>Euler portrait on the sixth series of the <a href="/wiki/Swiss_Franc" class="mw-redirect" title="Swiss Franc">10 Franc</a> banknote</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CHF10_7_front_horizontal.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/CHF10_7_front_horizontal.jpg/220px-CHF10_7_front_horizontal.jpg" decoding="async" width="220" height="107" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/CHF10_7_front_horizontal.jpg/330px-CHF10_7_front_horizontal.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/CHF10_7_front_horizontal.jpg/440px-CHF10_7_front_horizontal.jpg 2x" data-file-width="1074" data-file-height="520" /></a><figcaption>Euler portrait on the seventh series of the 10 Franc banknote</figcaption></figure> Euler was featured on both the sixth<a href="#cite_note-swiss6-129">[125]</a> and seventh<a href="#cite_note-swiss7-130">[126]</a> series of the Swiss 10-<a href="/wiki/Swiss_franc" title="Swiss franc">franc</a> banknote and on numerous Swiss, German, and Russian postage stamps. In 1782 he was elected 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>.<a href="#cite_note-aaas-131">[127]</a> The <a href="/wiki/Asteroid" title="Asteroid">asteroid</a> <a href="/wiki/2002_Euler" title="2002 Euler">2002 Euler</a> was named in his honour.<a href="#cite_note-schmadel-132">[128]</a> <div class="mw-heading mw-heading2"><h2 id="Selected_bibliography">Selected bibliography</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=19" title="Edit section: Selected bibliography">edit</a>]</div> Euler has <a href="/wiki/Contributions_of_Leonhard_Euler_to_mathematics#Works" title="Contributions of Leonhard Euler to mathematics">an extensive bibliography</a>. His books include: <ul><li><a href="/wiki/Mechanica" title="Mechanica">Mechanica</a> (1736)</li> <li><a rel="nofollow" class="external text" href="https://www.loc.gov/item/04028085/">Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici latissimo sensu accepti (1744)</a><a href="#cite_note-fraser-133">[129]</a> (A method for finding curved lines enjoying properties of maximum or minimum, or solution of isoperimetric problems in the broadest accepted sense)<a href="#cite_note-dartm2-134">[130]</a></li> <li><a href="/wiki/Introductio_in_analysin_infinitorum" title="Introductio in analysin infinitorum">Introductio in analysin infinitorum</a> (1748)<a href="#cite_note-reich-135">[131]</a><a href="#cite_note-ferraro-136">[132]</a> (Introduction to Analysis of the Infinite)<a href="#cite_note-revaninf-137">[133]</a></li> <li><a href="/wiki/Institutiones_calculi_differentialis" title="Institutiones calculi differentialis">Institutiones calculi differentialis</a> (1755)<a href="#cite_note-ferraro-136">[132]</a><a href="#cite_note-demidov-138">[134]</a> (Foundations of differential calculus)</li> <li><a href="/wiki/Elements_of_Algebra" title="Elements of Algebra">Vollständige Anleitung zur Algebra</a> (1765)<a href="#cite_note-ferraro-136">[132]</a> (Elements of Algebra)</li> <li><a href="/wiki/Institutiones_calculi_integralis" title="Institutiones calculi integralis">Institutiones calculi integralis</a> (1768–1770)<a href="#cite_note-ferraro-136">[132]</a> (Foundations of integral calculus)</li> <li><a href="/wiki/Letters_to_a_German_Princess" title="Letters to a German Princess">Letters to a German Princess</a> (1768–1772)<a href="#cite_note-FOOTNOTEDunham1999xxiv–xxv-41">[37]</a></li> <li>Dioptrica, published in three volumes beginning in 1769<a href="#cite_note-davidson-102">[98]</a></li></ul> It took until 1830 for the bulk of Euler's posthumous works to be individually published,<a href="#cite_note-kleinert-139">[135]</a> with an additional batch of 61 unpublished works discovered by <a href="/w/index.php?title=Paul_Heinrich_von_Fuss&action=edit&redlink=1" class="new" title="Paul Heinrich von Fuss (page does not exist)">Paul Heinrich von Fuss</a> (Euler's great-grandson and <a href="/wiki/Nicolas_Fuss" title="Nicolas Fuss">Nicolas Fuss</a>'s son) and published as a collection in 1862.<a href="#cite_note-kleinert-139">[135]</a><a href="#cite_note-fuss-140">[136]</a> A chronological catalog of Euler's works was compiled by Swedish mathematician <a href="/wiki/Gustaf_Enestr%C3%B6m" title="Gustaf Eneström">Gustaf Eneström</a> and published from 1910 to 1913.<a href="#cite_note-FOOTNOTECalinger2016ix–x-141">[137]</a> The catalog, known as the Eneström index, numbers Euler's works from E1 to E866.<a href="#cite_note-enestrom-142">[138]</a> The Euler Archive was started at <a href="/wiki/Dartmouth_College" title="Dartmouth College">Dartmouth College</a><a href="#cite_note-archive-start-143">[139]</a> before moving to the <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a><a href="#cite_note-archive-move-144">[140]</a> and, most recently, to <a href="/wiki/University_of_the_Pacific_(United_States)" title="University of the Pacific (United States)">University of the Pacific</a> in 2017.<a href="#cite_note-euler_archive-145">[141]</a> In 1907, the <a href="/wiki/Swiss_Academies_of_Arts_and_Sciences" title="Swiss Academies of Arts and Sciences">Swiss Academy of Sciences</a> created the <a href="/wiki/Euler_Commission" class="mw-redirect" title="Euler Commission">Euler Commission</a> and charged it with the publication of Euler's complete works. After several delays in the 19th century,<a href="#cite_note-kleinert-139">[135]</a> the first volume of the <a href="/wiki/Opera_Omnia_Leonhard_Euler" title="Opera Omnia Leonhard Euler">Opera Omnia</a>, was published in 1911.<a href="#cite_note-pluss-146">[142]</a> However, the discovery of new manuscripts continued to increase the magnitude of this project. Fortunately, the publication of Euler's Opera Omnia has made steady progress, with over 70 volumes (averaging 426 pages each) published by 2006 and 80 volumes published by 2022.<a href="#cite_note-new_look-147">[143]</a><a href="#cite_note-series_ii_done-16">[12]</a><a href="#cite_note-assad-18">[14]</a> These volumes are organized into four series. The first series compiles the works on analysis, algebra, and number theory; it consists of 29 volumes and numbers over 14,000 pages. The 31 volumes of Series II, amounting to 10,660 pages, contain the works on mechanics, astronomy, and engineering. Series III contains 12 volumes on physics. Series IV, which contains the massive amount of Euler's correspondence, unpublished manuscripts, and notes only began compilation in 1967. After publishing 8 print volumes in Series IV, the project decided in 2022 to publish its remaining projected volumes in Series IV in online format only.<a href="#cite_note-series_ii_done-16">[12]</a><a href="#cite_note-pluss-146">[142]</a><a href="#cite_note-assad-18">[14]</a> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><a href="/wiki/File:Acta_Eruditorum_-_II_geometria,_1744_%E2%80%93_BEIC_13411238.jpg" class="mw-file-description" title="Illustration from Solutio problematis... a. 1743 propositi published in Acta Eruditorum, 1744"><img alt="Illustration from Solutio problematis... a. 1743 propositi published in Acta Eruditorum, 1744" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Acta_Eruditorum_-_II_geometria%2C_1744_%E2%80%93_BEIC_13411238.jpg/191px-Acta_Eruditorum_-_II_geometria%2C_1744_%E2%80%93_BEIC_13411238.jpg" decoding="async" width="191" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Acta_Eruditorum_-_II_geometria%2C_1744_%E2%80%93_BEIC_13411238.jpg/286px-Acta_Eruditorum_-_II_geometria%2C_1744_%E2%80%93_BEIC_13411238.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Acta_Eruditorum_-_II_geometria%2C_1744_%E2%80%93_BEIC_13411238.jpg/381px-Acta_Eruditorum_-_II_geometria%2C_1744_%E2%80%93_BEIC_13411238.jpg 2x" data-file-width="1154" data-file-height="1211" /></a></div> <div class="gallerytext">Illustration from Solutio problematis... a. 1743 propositi published in <a href="/wiki/Acta_Eruditorum" title="Acta Eruditorum">Acta Eruditorum</a>, 1744</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><a href="/wiki/File:Methodus_inveniendi_-_Leonhard_Euler_-_1744.jpg" class="mw-file-description" title="The title page of Euler's Methodus inveniendi lineas curvas"><img alt="The title page of Euler's Methodus inveniendi lineas curvas" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Methodus_inveniendi_-_Leonhard_Euler_-_1744.jpg/144px-Methodus_inveniendi_-_Leonhard_Euler_-_1744.jpg" decoding="async" width="144" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Methodus_inveniendi_-_Leonhard_Euler_-_1744.jpg/216px-Methodus_inveniendi_-_Leonhard_Euler_-_1744.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Methodus_inveniendi_-_Leonhard_Euler_-_1744.jpg/288px-Methodus_inveniendi_-_Leonhard_Euler_-_1744.jpg 2x" data-file-width="2715" data-file-height="3763" /></a></div> <div class="gallerytext">The title page of Euler's Methodus inveniendi lineas curvas</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><a href="/wiki/File:Leonhard_Euler_World_Map_AD1760.jpg" class="mw-file-description" title="Euler's 1760 world map"><img alt="Euler's 1760 world map" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Leonhard_Euler_World_Map_AD1760.jpg/200px-Leonhard_Euler_World_Map_AD1760.jpg" decoding="async" width="200" height="172" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Leonhard_Euler_World_Map_AD1760.jpg/300px-Leonhard_Euler_World_Map_AD1760.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Leonhard_Euler_World_Map_AD1760.jpg/400px-Leonhard_Euler_World_Map_AD1760.jpg 2x" data-file-width="2615" data-file-height="2252" /></a></div> <div class="gallerytext">Euler's 1760 world map</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><a href="/wiki/File:Euler_Tab._Geogr._Africae_1753_UTA.jpg" class="mw-file-description" title="Euler's 1753 map of Africa"><img alt="Euler's 1753 map of Africa" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Euler_Tab._Geogr._Africae_1753_UTA.jpg/200px-Euler_Tab._Geogr._Africae_1753_UTA.jpg" decoding="async" width="200" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Euler_Tab._Geogr._Africae_1753_UTA.jpg/300px-Euler_Tab._Geogr._Africae_1753_UTA.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Euler_Tab._Geogr._Africae_1753_UTA.jpg/400px-Euler_Tab._Geogr._Africae_1753_UTA.jpg 2x" data-file-width="4755" data-file-height="3938" /></a></div> <div class="gallerytext">Euler's 1753 map of Africa</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=20" title="Edit section: Notes">edit</a>]</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-2"><a href="#cite_ref-2">^</a> Euler is listed by an <a href="/wiki/Academic_genealogy" title="Academic genealogy">academic genealogy</a> as the equivalent to the <a href="/wiki/Doctoral_advisor" title="Doctoral advisor">doctoral advisor</a> of Lagrange.<a href="#cite_note-mathg-1">[1]</a> </li> <li id="cite_note-7"><a href="#cite_ref-7">^</a> The pronunciation <a href="/wiki/Help:IPA/English" title="Help:IPA/English">/ˈjuːlər/</a> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key">YOO-lər</a> is considered incorrect.<a href="#cite_note-oxford-3">[2]</a><a href="#cite_note-merriam-4">[3]</a><a href="#cite_note-amer_heritage-5">[4]</a><a href="#cite_note-nets,_puzzles-6">[5]</a> </li> <li id="cite_note-fn2-11"><a href="#cite_ref-fn2_11-0">^</a> The quote appeared in <a href="/wiki/Gugliemo_Libri" class="mw-redirect" title="Gugliemo Libri">Gugliemo Libri</a>'s review of a recently published collection of correspondence among eighteenth-century mathematicians: "... nous rappellerions que Laplace lui même, ... ne cessait de répéter aux jeunes mathématiciens ces paroles mémorables que nous avons entendues de sa propre bouche : 'Lisez Euler, lisez Euler, c'est notre maître à tous.'" [... we would recall that Laplace himself, ... never ceased to repeat to young mathematicians these memorable words that we heard from his own mouth: 'Read Euler, read Euler, he is our master in everything.']<a href="#cite_note-148">[144]</a> </li> <li id="cite_note-fn3-14"><a href="#cite_ref-fn3_14-0">^</a> This quote appeared in a letter from Gauss to <a href="/wiki/Paul_Fuss" title="Paul Fuss">Paul Fuss</a> dated September 11, 1849:<a href="#cite_note-fussletter-13">[10]</a> "Die besondere Herausgabe der kleinern Eulerschen Abhandlungen ist gewiß etwas höchst verdienstliches, [...] und das Studium aller Eulerschen Arbeiten doch stets die beste durch nichts anderes zu ersetzende Schule für die verschiedenen mathematischen Gebiete bleiben wird." [The special publication of the smaller Euler treatises is certainly something highly deserving, [...] and the study of all Euler's works will always remain the best school for the various mathematical fields, which cannot be replaced by anything else.] </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=21" title="Edit section: References">edit</a>]</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-mathg-1"><a href="#cite_ref-mathg_1-0">^</a> <a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=38586">Leonhard Euler</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a> Retrieved 2 July 2021; <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220827210526/https://mathgenealogy.org/id.php?id=38586">Archived</a> </li> <li id="cite_note-oxford-3"><a href="#cite_ref-oxford_3-0">^</a> <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 encyclopaedia cs1">"Euler". <a href="/wiki/Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a> (2nd ed.). <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. 1989.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euler&rft.btitle=Oxford+English+Dictionary&rft.edition=2nd&rft.pub=Oxford+University+Press&rft.date=1989&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-merriam-4"><a href="#cite_ref-merriam_4-0">^</a> <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.merriam-webster.com/dictionary/Euler">"Euler"</a>. <a href="/wiki/Webster%27s_Dictionary" title="Webster's Dictionary">Merriam–Webster's Online Dictionary</a>. 2009. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090425165621/http://www.merriam-webster.com/dictionary/euler">Archived</a> from the original on 25 April 2009. Retrieved 5 June 2009.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euler&rft.btitle=Merriam%E2%80%93Webster%27s+Online+Dictionary&rft.date=2009&rft_id=http%3A%2F%2Fwww.merriam-webster.com%2Fdictionary%2FEuler&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-amer_heritage-5"><a href="#cite_ref-amer_heritage_5-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="http://ahdictionary.com/word/search.html?q=Euler%2C+Leonhard&submit.x=40&submit.y=16">"Euler, Leonhard"</a>. <a href="/wiki/The_American_Heritage_Dictionary_of_the_English_Language" title="The American Heritage Dictionary of the English Language">The American Heritage Dictionary of the English Language</a> (5th ed.). Boston: <a href="/wiki/Houghton_Mifflin_Harcourt" title="Houghton Mifflin Harcourt">Houghton Mifflin Company</a>. 2011. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131004213455/http://ahdictionary.com/word/search.html?q=Euler%2C+Leonhard&submit.x=40&submit.y=16">Archived</a> from the original on 4 October 2013. Retrieved 30 May 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euler%2C+Leonhard&rft.btitle=The+American+Heritage+Dictionary+of+the+English+Language&rft.place=Boston&rft.edition=5th&rft.pub=Houghton+Mifflin+Company&rft.date=2011&rft_id=http%3A%2F%2Fahdictionary.com%2Fword%2Fsearch.html%3Fq%3DEuler%252C%2BLeonhard%26submit.x%3D40%26submit.y%3D16&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-nets,_puzzles-6"><a href="#cite_ref-nets,_puzzles_6-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHiggins2007" class="citation book cs1">Higgins, Peter M. (2007). <a rel="nofollow" class="external text" href="https://archive.org/details/netspuzzlespostm00higg">Nets, Puzzles, and Postmen: An Exploration of Mathematical Connections</a>. <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. p. <a rel="nofollow" class="external text" href="https://archive.org/details/netspuzzlespostm00higg/page/n51">43</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-921842-4" title="Special:BookSources/978-0-19-921842-4"><bdi>978-0-19-921842-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nets%2C+Puzzles%2C+and+Postmen%3A+An+Exploration+of+Mathematical+Connections&rft.pages=43&rft.pub=Oxford+University+Press&rft.date=2007&rft.isbn=978-0-19-921842-4&rft.aulast=Higgins&rft.aufirst=Peter+M.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnetspuzzlespostm00higg&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTEDunham199917-8">^ <a href="#cite_ref-FOOTNOTEDunham199917_8-0">a</a> <a href="#cite_ref-FOOTNOTEDunham199917_8-1">b</a> <a href="#CITEREFDunham1999">Dunham 1999</a>, p. 17. </li> <li id="cite_note-:0-9">^ <a href="#cite_ref-:0_9-0">a</a> <a href="#cite_ref-:0_9-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDebnath2010" class="citation book cs1"><a href="/wiki/Lokenath_Debnath" title="Lokenath Debnath">Debnath, Lokenath</a> (2010). <a rel="nofollow" class="external text" href="https://archive.org/details/legacyofleonhard0000debn">The Legacy of Leonhard Euler : A Tricentennial Tribute</a>. London: Imperial College Press. pp. vii. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-84816-525-0" title="Special:BookSources/978-1-84816-525-0"><bdi>978-1-84816-525-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Legacy+of+Leonhard+Euler+%3A+A+Tricentennial+Tribute&rft.place=London&rft.pages=vii&rft.pub=Imperial+College+Press&rft.date=2010&rft.isbn=978-1-84816-525-0&rft.aulast=Debnath&rft.aufirst=Lokenath&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Flegacyofleonhard0000debn&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-Laplace-10"><a href="#cite_ref-Laplace_10-0">^</a> <a href="#CITEREFDunham1999">Dunham 1999</a>, p. xiii "Lisez Euler, lisez Euler, c'est notre maître à tous." </li> <li id="cite_note-Grinstein-12"><a href="#cite_ref-Grinstein_12-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrinsteinLipsey2001" class="citation encyclopaedia cs1">Grinstein, Louise; Lipsey, Sally I. (2001). "Euler, Leonhard (1707–1783)". Encyclopedia of Mathematics Education. <a href="/wiki/Routledge" title="Routledge">Routledge</a>. p. 235. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-415-76368-4" title="Special:BookSources/978-0-415-76368-4"><bdi>978-0-415-76368-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euler%2C+Leonhard+%281707%E2%80%931783%29&rft.btitle=Encyclopedia+of+Mathematics+Education&rft.pages=235&rft.pub=Routledge&rft.date=2001&rft.isbn=978-0-415-76368-4&rft.aulast=Grinstein&rft.aufirst=Louise&rft.au=Lipsey%2C+Sally+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-fussletter-13"><a href="#cite_ref-fussletter_13-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFußGauß1849" class="citation web cs1">Fuß, Paul Heinrich; Gauß, Carl Friedrich (11 September 1849). <a rel="nofollow" class="external text" href="https://gauss.adw-goe.de/handle/gauss/218">"Carl Friedrich Gauß → Paul Heinrich Fuß, Göttingen, 1849 Sept. 11"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Carl+Friedrich+Gau%C3%9F+%E2%86%92+Paul+Heinrich+Fu%C3%9F%2C+G%C3%B6ttingen%2C+1849+Sept.+11&rft.date=1849-09-11&rft.aulast=Fu%C3%9F&rft.aufirst=Paul+Heinrich&rft.au=Gau%C3%9F%2C+Carl+Friedrich&rft_id=https%3A%2F%2Fgauss.adw-goe.de%2Fhandle%2Fgauss%2F218&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-ivb-15"><a href="#cite_ref-ivb_15-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220911205554/https://bez.unibas.ch/de/projekte/opera-omnia-leonhard-euler/">"Leonhardi Euleri Opera Omnia (LEOO)"</a>. Bernoulli Euler Center. Archived from <a rel="nofollow" class="external text" href="https://bez.unibas.ch/de/projekte/opera-omnia-leonhard-euler/">the original</a> on 11 September 2022. Retrieved 11 September 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Bernoulli+Euler+Center&rft.atitle=Leonhardi+Euleri+Opera+Omnia+%28LEOO%29&rft_id=https%3A%2F%2Fbez.unibas.ch%2Fde%2Fprojekte%2Fopera-omnia-leonhard-euler%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-series_ii_done-16">^ <a href="#cite_ref-series_ii_done_16-0">a</a> <a href="#cite_ref-series_ii_done_16-1">b</a> <a href="#cite_ref-series_ii_done_16-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220911182123/https://bernoulli-euler-gesellschaft.ch/en/opera_omnia">"The works"</a>. Bernoulli-Euler Society. Archived from <a rel="nofollow" class="external text" href="https://bernoulli-euler-gesellschaft.ch/en/opera_omnia">the original</a> on 11 September 2022. Retrieved 11 September 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Bernoulli-Euler+Society&rft.atitle=The+works&rft_id=https%3A%2F%2Fbernoulli-euler-gesellschaft.ch%2Fen%2Fopera_omnia&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTEGautschi20083-17"><a href="#cite_ref-FOOTNOTEGautschi20083_17-0">^</a> <a href="#CITEREFGautschi2008">Gautschi 2008</a>, p. 3. </li> <li id="cite_note-assad-18">^ <a href="#cite_ref-assad_18-0">a</a> <a href="#cite_ref-assad_18-1">b</a> <a href="#cite_ref-assad_18-2">c</a> <a href="#cite_ref-assad_18-3">d</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAssad2007" class="citation journal cs1">Assad, Arjang A. (2007). <a rel="nofollow" class="external text" href="https://onlinelibrary.wiley.com/doi/10.1002/net.20158">"Leonhard Euler: A brief appreciation"</a>. Networks. 49 (3): 190–198. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fnet.20158">10.1002/net.20158</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:11298706">11298706</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Networks&rft.atitle=Leonhard+Euler%3A+A+brief+appreciation&rft.volume=49&rft.issue=3&rft.pages=190-198&rft.date=2007&rft_id=info%3Adoi%2F10.1002%2Fnet.20158&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A11298706%23id-name%3DS2CID&rft.aulast=Assad&rft.aufirst=Arjang+A.&rft_id=https%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fnet.20158&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-britannica-19"><a href="#cite_ref-britannica_19-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoyer2021" class="citation encyclopaedia cs1"><a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer">Boyer, Carl B</a> (1 June 2021). <a rel="nofollow" class="external text" href="https://www.britannica.com/biography/Leonhard-Euler">"Leonhard Euler"</a>. <a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Encyclopedia Britannica</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210503204248/https://www.britannica.com/biography/Leonhard-Euler">Archived</a> from the original on 3 May 2021. Retrieved 27 May 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Leonhard+Euler&rft.btitle=Encyclopedia+Britannica&rft.date=2021-06-01&rft.aulast=Boyer&rft.aufirst=Carl+B&rft_id=https%3A%2F%2Fwww.britannica.com%2Fbiography%2FLeonhard-Euler&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTEGautschi20084-20">^ <a href="#cite_ref-FOOTNOTEGautschi20084_20-0">a</a> <a href="#cite_ref-FOOTNOTEGautschi20084_20-1">b</a> <a href="#cite_ref-FOOTNOTEGautschi20084_20-2">c</a> <a href="#cite_ref-FOOTNOTEGautschi20084_20-3">d</a> <a href="#cite_ref-FOOTNOTEGautschi20084_20-4">e</a> <a href="#cite_ref-FOOTNOTEGautschi20084_20-5">f</a> <a href="#CITEREFGautschi2008">Gautschi 2008</a>, p. 4. </li> <li id="cite_note-FOOTNOTECalinger201611-21"><a href="#cite_ref-FOOTNOTECalinger201611_21-0">^</a> <a href="#CITEREFCalinger2016">Calinger 2016</a>, p. 11. </li> <li id="cite_note-FOOTNOTEGautschi20085-22"><a href="#cite_ref-FOOTNOTEGautschi20085_22-0">^</a> <a href="#CITEREFGautschi2008">Gautschi 2008</a>, p. 5. </li> <li id="cite_note-FOOTNOTECalinger1996124-23"><a href="#cite_ref-FOOTNOTECalinger1996124_23-0">^</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, p. 124. </li> <li id="cite_note-zum_werk_leonhard-24">^ <a href="#cite_ref-zum_werk_leonhard_24-0">a</a> <a href="#cite_ref-zum_werk_leonhard_24-1">b</a> <a href="#cite_ref-zum_werk_leonhard_24-2">c</a> <a href="#cite_ref-zum_werk_leonhard_24-3">d</a> <a href="#cite_ref-zum_werk_leonhard_24-4">e</a> <a href="#cite_ref-zum_werk_leonhard_24-5">f</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKnoblochLouhivaaraWinkler1983" class="citation book cs1"><a href="/wiki/Eberhard_Knobloch" title="Eberhard Knobloch">Knobloch, Eberhard</a>; Louhivaara, I. S.; Winkler, J., eds. (May 1983). <a rel="nofollow" class="external text" href="https://link.springer.com/content/pdf/bfm%3A978-3-0348-7121-1%2F1.pdf">Zum Werk Leonhard Eulers: Vorträge des Euler-Kolloquiums im Mai 1983 in Berlin</a> (PDF). <a href="/wiki/Birkh%C3%A4user_Verlag" class="mw-redirect" title="Birkhäuser Verlag">Birkhäuser Verlag</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-0348-7121-1">10.1007/978-3-0348-7121-1</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-0348-7122-8" title="Special:BookSources/978-3-0348-7122-8"><bdi>978-3-0348-7122-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Zum+Werk+Leonhard+Eulers%3A+Vortr%C3%A4ge+des+Euler-Kolloquiums+im+Mai+1983+in+Berlin&rft.pub=Birkh%C3%A4user+Verlag&rft.date=1983-05&rft_id=info%3Adoi%2F10.1007%2F978-3-0348-7121-1&rft.isbn=978-3-0348-7122-8&rft_id=https%3A%2F%2Flink.springer.com%2Fcontent%2Fpdf%2Fbfm%253A978-3-0348-7121-1%252F1.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTECalinger201632-25"><a href="#cite_ref-FOOTNOTECalinger201632_25-0">^</a> <a href="#CITEREFCalinger2016">Calinger 2016</a>, p. 32. </li> <li id="cite_note-17cent-26"><a href="#cite_ref-17cent_26-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEuler1727" class="citation book cs1 cs1-prop-foreign-lang-source">Euler, Leonhard (1727). <a rel="nofollow" class="external text" href="https://scholarlycommons.pacific.edu/euler-works/2/">Dissertatio physica de sono</a> [Physical dissertation on sound] (in Latin). Basel: E. and J. R. Thurnisiorum. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210606192503/https://scholarlycommons.pacific.edu/euler-works/2/">Archived</a> from the original on 6 June 2021. Retrieved 6 June 2021 – via Euler archive.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dissertatio+physica+de+sono&rft.place=Basel&rft.pub=E.+and+J.+R.+Thurnisiorum&rft.date=1727&rft.aulast=Euler&rft.aufirst=Leonhard&rft_id=https%3A%2F%2Fscholarlycommons.pacific.edu%2Feuler-works%2F2%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> Translated into English as <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBruce" class="citation web cs1">Bruce, Ian. <a rel="nofollow" class="external text" href="http://www.17centurymaths.com/contents/euler/e002tr.pdf">"Euler's Dissertation De Sono : E002"</a> (PDF). Some Mathematical Works of the 17th & 18th Centuries, including Newton's Principia, Euler's Mechanica, Introductio in Analysin, etc., translated mainly from Latin into English. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160610171755/http://www.17centurymaths.com/contents/euler/e002tr.pdf">Archived</a> (PDF) from the original on 10 June 2016. Retrieved 12 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Some+Mathematical+Works+of+the+17th+%26+18th+Centuries%2C+including+Newton%27s+Principia%2C+Euler%27s+Mechanica%2C+Introductio+in+Analysin%2C+etc.%2C+translated+mainly+from+Latin+into+English&rft.atitle=Euler%27s+Dissertation+De+Sono+%3A+E002&rft.aulast=Bruce&rft.aufirst=Ian&rft_id=http%3A%2F%2Fwww.17centurymaths.com%2Fcontents%2Feuler%2Fe002tr.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTECalinger1996125-27">^ <a href="#cite_ref-FOOTNOTECalinger1996125_27-0">a</a> <a href="#cite_ref-FOOTNOTECalinger1996125_27-1">b</a> <a href="#cite_ref-FOOTNOTECalinger1996125_27-2">c</a> <a href="#cite_ref-FOOTNOTECalinger1996125_27-3">d</a> <a href="#cite_ref-FOOTNOTECalinger1996125_27-4">e</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, p. 125. </li> <li id="cite_note-paris-acad-28">^ <a href="#cite_ref-paris-acad_28-0">a</a> <a href="#cite_ref-paris-acad_28-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://eulerarchive.maa.org/historica/places/paris.html">"The Paris Academy"</a>. Euler Archive. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210730064357/http://eulerarchive.maa.org/historica/places/paris.html">Archived</a> from the original on 30 July 2021. Retrieved 29 July 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Euler+Archive&rft.atitle=The+Paris+Academy&rft_id=http%3A%2F%2Feulerarchive.maa.org%2Fhistorica%2Fplaces%2Fparis.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTECalinger1996156-29">^ <a href="#cite_ref-FOOTNOTECalinger1996156_29-0">a</a> <a href="#cite_ref-FOOTNOTECalinger1996156_29-1">b</a> <a href="#cite_ref-FOOTNOTECalinger1996156_29-2">c</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, p. 156. </li> <li id="cite_note-FOOTNOTECalinger1996121–166-30"><a href="#cite_ref-FOOTNOTECalinger1996121–166_30-0">^</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, pp. 121–166. </li> <li id="cite_note-mactutor-31"><a href="#cite_ref-mactutor_31-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs1">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a> <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Bernoulli_Nicolaus(II).html">"Nicolaus (II) Bernoulli"</a>. <a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a>. <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=Nicolaus+%28II%29+Bernoulli&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%2FBernoulli_Nicolaus%28II%29.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> Retrieved 2 July 2021. </li> <li id="cite_note-FOOTNOTECalinger1996126–127-32"><a href="#cite_ref-FOOTNOTECalinger1996126–127_32-0">^</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, pp. 126–127. </li> <li id="cite_note-FOOTNOTECalinger1996127-33"><a href="#cite_ref-FOOTNOTECalinger1996127_33-0">^</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, p. 127. </li> <li id="cite_note-FOOTNOTECalinger1996126-34">^ <a href="#cite_ref-FOOTNOTECalinger1996126_34-0">a</a> <a href="#cite_ref-FOOTNOTECalinger1996126_34-1">b</a> <a href="#cite_ref-FOOTNOTECalinger1996126_34-2">c</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, p. 126. </li> <li id="cite_note-FOOTNOTECalinger1996128-35">^ <a href="#cite_ref-FOOTNOTECalinger1996128_35-0">a</a> <a href="#cite_ref-FOOTNOTECalinger1996128_35-1">b</a> <a href="#cite_ref-FOOTNOTECalinger1996128_35-2">c</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, p. 128. </li> <li id="cite_note-FOOTNOTECalinger1996128–129-36"><a href="#cite_ref-FOOTNOTECalinger1996128–129_36-0">^</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, pp. 128–129. </li> <li id="cite_note-FOOTNOTEGekkerEuler2007[httpsbooksgooglecombooksidTa9bz1wv79ACpgPA402_402]-37">^ <a href="#cite_ref-FOOTNOTEGekkerEuler2007[httpsbooksgooglecombooksidTa9bz1wv79ACpgPA402_402]_37-0">a</a> <a href="#cite_ref-FOOTNOTEGekkerEuler2007[httpsbooksgooglecombooksidTa9bz1wv79ACpgPA402_402]_37-1">b</a> <a href="#CITEREFGekkerEuler2007">Gekker & Euler 2007</a>, p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Ta9bz1wv79AC&pg=PA402">402</a>. </li> <li id="cite_note-FOOTNOTECalinger1996157–158-38">^ <a href="#cite_ref-FOOTNOTECalinger1996157–158_38-0">a</a> <a href="#cite_ref-FOOTNOTECalinger1996157–158_38-1">b</a> <a href="#cite_ref-FOOTNOTECalinger1996157–158_38-2">c</a> <a href="#cite_ref-FOOTNOTECalinger1996157–158_38-3">d</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, pp. 157–158. </li> <li id="cite_note-FOOTNOTEGautschi20087-39"><a href="#cite_ref-FOOTNOTEGautschi20087_39-0">^</a> <a href="#CITEREFGautschi2008">Gautschi 2008</a>, p. 7. </li> <li id="cite_note-dartm-40"><a href="#cite_ref-dartm_40-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEuler1787" class="citation journal cs1 cs1-prop-foreign-lang-source"><a class="mw-selflink selflink">Euler, Leonhard</a> (1787). <a rel="nofollow" class="external text" href="https://scholarlycommons.pacific.edu/euler-works/212/">"Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum"</a> [Foundations of Differential Calculus, with Applications to Finite Analysis and Series]. 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Retrieved 8 June 2021 – via Euler Archive.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Academiae+Imperialis+Scientiarum+Petropolitanae&rft.atitle=Institutiones+calculi+differentialis+cum+eius+usu+in+analysi+finitorum+ac+doctrina+serierum&rft.volume=1&rft.pages=1-880&rft.date=1787&rft.aulast=Euler&rft.aufirst=Leonhard&rft_id=https%3A%2F%2Fscholarlycommons.pacific.edu%2Feuler-works%2F212%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTEDunham1999xxiv–xxv-41">^ <a href="#cite_ref-FOOTNOTEDunham1999xxiv–xxv_41-0">a</a> <a href="#cite_ref-FOOTNOTEDunham1999xxiv–xxv_41-1">b</a> <a href="#cite_ref-FOOTNOTEDunham1999xxiv–xxv_41-2">c</a> <a href="#cite_ref-FOOTNOTEDunham1999xxiv–xxv_41-3">d</a> <a href="#CITEREFDunham1999">Dunham 1999</a>, pp. xxiv–xxv. </li> <li id="cite_note-sten-42"><a href="#cite_ref-sten_42-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStén2014" class="citation book cs1">Stén, Johan C.-E. 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Vol. 17. <a href="/wiki/Birkh%C3%A4user" title="Birkhäuser">Birkhäuser</a>. pp. 119–135. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-00618-5_7">10.1007/978-3-319-00618-5_7</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-00617-8" title="Special:BookSources/978-3-319-00617-8"><bdi>978-3-319-00617-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Academic+events+in+Saint+Petersburg&rft.btitle=A+Comet+of+the+Enlightenment&rft.series=Vita+Mathematica&rft.pages=119-135&rft.pub=Birkh%C3%A4user&rft.date=2014&rft_id=info%3Adoi%2F10.1007%2F978-3-319-00618-5_7&rft.isbn=978-3-319-00617-8&rft.aulast=St%C3%A9n&rft.aufirst=Johan+C.-E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> See in particular footnote 37, p. 131. </li> <li id="cite_note-volumes-43">^ <a href="#cite_ref-volumes_43-0">a</a> <a href="#cite_ref-volumes_43-1">b</a> <a href="#cite_ref-volumes_43-2">c</a> <a href="#cite_ref-volumes_43-3">d</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFinkel1897" class="citation journal cs1">Finkel, B. 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"Biography – Leonhard Euler". <a href="/wiki/The_American_Mathematical_Monthly" title="The American Mathematical Monthly">The American Mathematical Monthly</a>. 4 (12): 297–302. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2968971">10.2307/2968971</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/2968971">2968971</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1514436">1514436</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=Biography+%E2%80%93+Leonhard+Euler&rft.volume=4&rft.issue=12&rft.pages=297-302&rft.date=1897&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1514436%23id-name%3DMR&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2968971%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F2968971&rft.aulast=Finkel&rft.aufirst=B.+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-BEA-44"><a href="#cite_ref-BEA_44-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTrimbleWilliamsBracherJarrell2007" class="citation book cs1"><a href="/wiki/Virginia_Louise_Trimble" title="Virginia Louise Trimble">Trimble, Virginia</a>; Williams, Thomas; Bracher, Katherine; Jarrell, Richard; Marché, Jordan D.; Ragep, F. 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(2007). <a href="/wiki/Biographical_Encyclopedia_of_Astronomers" title="Biographical Encyclopedia of Astronomers">Biographical Encyclopedia of Astronomers</a>. <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer Science+Business Media</a>. p. 992. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-30400-7" title="Special:BookSources/978-0-387-30400-7"><bdi>978-0-387-30400-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Biographical+Encyclopedia+of+Astronomers&rft.pages=992&rft.pub=Springer+Science%2BBusiness+Media&rft.date=2007&rft.isbn=978-0-387-30400-7&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> Available at <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210422142741/https://books.google.com/books?id=t-BF1CHkc50C&pg=PA992">Archive.org</a> </li> <li id="cite_note-ClarkGolinski1999-45"><a href="#cite_ref-ClarkGolinski1999_45-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClarkGolinskiSchaffer1999" class="citation book cs1">Clark, William; Golinski, Jan; Schaffer, Simon (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ttGgd6mec1MC&pg=PA395">The Sciences in Enlightened Europe</a>. <a href="/wiki/University_of_Chicago_Press" title="University of Chicago Press">University of Chicago Press</a>. p. 395. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-10940-4" title="Special:BookSources/978-0-226-10940-4"><bdi>978-0-226-10940-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210422142742/https://books.google.com/books?id=ttGgd6mec1MC&pg=PA395">Archived</a> from the original on 22 April 2021. 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Mitteilungen der Deutschen Mathematiker-Vereinigung. 15 (4): 276–288. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fdmvm-2007-0092">10.1515/dmvm-2007-0092</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:122271644">122271644</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mitteilungen+der+Deutschen+Mathematiker-Vereinigung&rft.atitle=Leonhard+Euler+1707%E2%80%931783.+Zum+300.+Geburtstag+eines+langj%C3%A4hrigen+Wahlberliners&rft.volume=15&rft.issue=4&rft.pages=276-288&rft.date=2007&rft_id=info%3Adoi%2F10.1515%2Fdmvm-2007-0092&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122271644%23id-name%3DS2CID&rft.aulast=Knobloch&rft.aufirst=Eberhard&rft_id=https%3A%2F%2Fdoi.org%2F10.1515%252Fdmvm-2007-0092&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTEGautschi20088–9-47">^ <a href="#cite_ref-FOOTNOTEGautschi20088–9_47-0">a</a> <a href="#cite_ref-FOOTNOTEGautschi20088–9_47-1">b</a> <a href="#CITEREFGautschi2008">Gautschi 2008</a>, pp. 8–9. </li> <li id="cite_note-Digital_Copy_of_"Letters_to_a_German_Princess"-48"><a href="#cite_ref-Digital_Copy_of_"Letters_to_a_German_Princess"_48-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEuler1802" class="citation book cs1"><a class="mw-selflink selflink">Euler, Leonhard</a> (1802). <a href="/wiki/Letters_to_a_German_Princess" title="Letters to a German Princess">Letters of Euler on Different Subjects of Physics and Philosophy, Addressed to a German Princess</a>. 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Retrieved 26 December 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Irish+Times&rft.atitle=Euler+and+the+failed+fountain+of+Sanssouci+%E2%80%94+that%27s+maths%3A+Frederick+the+Great+ignored+the+advice+of+a+genius+in+maths+and+physics&rft.date=2017-09&rft.aulast=Lynch&rft.aufirst=Peter&rft_id=https%3A%2F%2Fwww.irishtimes.com%2Fnews%2Fscience%2Feuler-and-the-failed-fountain-of-sanssouci-1.3205969&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-vucinich-51">^ <a href="#cite_ref-vucinich_51-0">a</a> <a href="#cite_ref-vucinich_51-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVucinich1960" class="citation journal cs1"><a href="/wiki/Alexander_Vucinich" title="Alexander Vucinich">Vucinich, Alexander</a> (1960). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2708192">"Mathematics in Russian Culture"</a>. <a href="/wiki/Journal_of_the_History_of_Ideas" title="Journal of the History of Ideas">Journal of the History of Ideas</a>. 21 (2): 164–165. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2708192">10.2307/2708192</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0022-5037">0022-5037</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/2708192">2708192</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210803030757/https://www.jstor.org/stable/2708192">Archived</a> from the original on 3 August 2021. Retrieved 3 August 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+History+of+Ideas&rft.atitle=Mathematics+in+Russian+Culture&rft.volume=21&rft.issue=2&rft.pages=164-165&rft.date=1960&rft.issn=0022-5037&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2708192%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F2708192&rft.aulast=Vucinich&rft.aufirst=Alexander&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2708192&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-gindikin-52"><a href="#cite_ref-gindikin_52-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGindikin2007" class="citation book cs1"><a href="/wiki/Simon_Gindikin" title="Simon Gindikin">Gindikin, Simon</a> (2007). "Leonhard Euler". Tales of Mathematicians and Physicists. <a href="/wiki/Springer_Publishing" title="Springer Publishing">Springer Publishing</a>. pp. 171–212. <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%2F978-0-387-48811-0_7">10.1007/978-0-387-48811-0_7</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-48811-0" title="Special:BookSources/978-0-387-48811-0"><bdi>978-0-387-48811-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Leonhard+Euler&rft.btitle=Tales+of+Mathematicians+and+Physicists&rft.pages=171-212&rft.pub=Springer+Publishing&rft.date=2007&rft_id=info%3Adoi%2F10.1007%2F978-0-387-48811-0_7&rft.isbn=978-0-387-48811-0&rft.aulast=Gindikin&rft.aufirst=Simon&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> See in particular <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Ng1Vn4byYHUC&pg=PA182">p. 182</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210610074839/https://books.google.com/books?id=Ng1Vn4byYHUC&pg=PA182">Archived</a> 10 June 2021 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. </li> <li id="cite_note-FOOTNOTEGautschi20089-53"><a href="#cite_ref-FOOTNOTEGautschi20089_53-0">^</a> <a href="#CITEREFGautschi2008">Gautschi 2008</a>, p. 9. </li> <li id="cite_note-math_at_prussian-54"><a href="#cite_ref-math_at_prussian_54-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKnobloch1998" class="citation book cs1"><a href="/wiki/Eberhard_Knobloch" title="Eberhard Knobloch">Knobloch, Eberhard</a> (1998). "Mathematics at the Prussian Academy of Sciences 1700–1810". In Begehr, Heinrich; <a href="/wiki/Helmut_Koch" title="Helmut Koch">Koch, Helmut</a>; Kramer, Jürg; <a href="/wiki/Norbert_Schappacher" title="Norbert Schappacher">Schappacher, Norbert</a>; Thiele, Ernst-Jochen (eds.). Mathematics in Berlin. Basel: <a href="/wiki/Birkh%C3%A4user" title="Birkhäuser">Birkhäuser Basel</a>. pp. 1–8. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-0348-8787-8_1">10.1007/978-3-0348-8787-8_1</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-7643-5943-0" title="Special:BookSources/978-3-7643-5943-0"><bdi>978-3-7643-5943-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Mathematics+at+the+Prussian+Academy+of+Sciences+1700%E2%80%931810&rft.btitle=Mathematics+in+Berlin&rft.place=Basel&rft.pages=1-8&rft.pub=Birkh%C3%A4user+Basel&rft.date=1998&rft_id=info%3Adoi%2F10.1007%2F978-3-0348-8787-8_1&rft.isbn=978-3-7643-5943-0&rft.aulast=Knobloch&rft.aufirst=Eberhard&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-historian's_craft-55"><a href="#cite_ref-historian's_craft_55-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThiele2005" class="citation book cs1"><a href="/wiki/R%C3%BCdiger_Thiele" title="Rüdiger Thiele">Thiele, Rüdiger</a> (2005). "The Mathematics and Science of Leonhard Euler (1707–1783)". Mathematics and the Historian's Craft. CMS Books in Mathematics. New York: <a href="/wiki/Springer_Publishing" title="Springer Publishing">Springer Publishing</a>. pp. 81–140. <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%2F0-387-28272-6_6">10.1007/0-387-28272-6_6</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-25284-1" title="Special:BookSources/978-0-387-25284-1"><bdi>978-0-387-25284-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Mathematics+and+Science+of+Leonhard+Euler+%281707%E2%80%931783%29&rft.btitle=Mathematics+and+the+Historian%27s+Craft&rft.place=New+York&rft.series=CMS+Books+in+Mathematics&rft.pages=81-140&rft.pub=Springer+Publishing&rft.date=2005&rft_id=info%3Adoi%2F10.1007%2F0-387-28272-6_6&rft.isbn=978-0-387-25284-1&rft.aulast=Thiele&rft.aufirst=R%C3%BCdiger&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-fountains-56"><a href="#cite_ref-fountains_56-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEckert2002" class="citation journal cs1">Eckert, Michael (2002). "Euler and the Fountains of Sanssouci". <a href="/wiki/Archive_for_History_of_Exact_Sciences" title="Archive for History of Exact Sciences">Archive for History of Exact Sciences</a>. 56 (6): 451–468. <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%2Fs004070200054">10.1007/s004070200054</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0003-9519">0003-9519</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:121790508">121790508</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=Euler+and+the+Fountains+of+Sanssouci&rft.volume=56&rft.issue=6&rft.pages=451-468&rft.date=2002&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121790508%23id-name%3DS2CID&rft.issn=0003-9519&rft_id=info%3Adoi%2F10.1007%2Fs004070200054&rft.aulast=Eckert&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-lexell's_theorem-57"><a href="#cite_ref-lexell's_theorem_57-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaeharaMartini2017" class="citation journal cs1">Maehara, Hiroshi; Martini, Horst (2017). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/10.4169/amer.math.monthly.124.4.337">"On Lexell's Theorem"</a>. <a href="/wiki/The_American_Mathematical_Monthly" title="The American Mathematical Monthly">The American Mathematical Monthly</a>. 124 (4): 337–344. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4169%2Famer.math.monthly.124.4.337">10.4169/amer.math.monthly.124.4.337</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-9890">0002-9890</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/10.4169/amer.math.monthly.124.4.337">10.4169/amer.math.monthly.124.4.337</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:125175471">125175471</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210820093951/https://www.jstor.org/stable/10.4169/amer.math.monthly.124.4.337">Archived</a> from the original on 20 August 2021. Retrieved 16 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=On+Lexell%27s+Theorem&rft.volume=124&rft.issue=4&rft.pages=337-344&rft.date=2017&rft.issn=0002-9890&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A125175471%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F10.4169%2Famer.math.monthly.124.4.337%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.4169%2Famer.math.monthly.124.4.337&rft.aulast=Maehara&rft.aufirst=Hiroshi&rft.au=Martini%2C+Horst&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F10.4169%2Famer.math.monthly.124.4.337&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-thiele-58">^ <a href="#cite_ref-thiele_58-0">a</a> <a href="#cite_ref-thiele_58-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThiele2005" class="citation book cs1"><a href="/wiki/R%C3%BCdiger_Thiele" title="Rüdiger Thiele">Thiele, Rüdiger</a> (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3ZTedZtwYMoC&pg=PA81+">"The mathematics and science of Leonhard Euler"</a>. In Kinyon, Michael; <a href="/wiki/Glen_Van_Brummelen" title="Glen Van Brummelen">van Brummelen, Glen</a> (eds.). Mathematics and the Historian's Craft: The Kenneth O. May Lectures. <a href="/wiki/Springer_Publishing" title="Springer Publishing">Springer Publishing</a>. pp. 81–140. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-25284-1" title="Special:BookSources/978-0-387-25284-1"><bdi>978-0-387-25284-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+mathematics+and+science+of+Leonhard+Euler&rft.btitle=Mathematics+and+the+Historian%27s+Craft%3A+The+Kenneth+O.+May+Lectures&rft.pages=81-140&rft.pub=Springer+Publishing&rft.date=2005&rft.isbn=978-0-387-25284-1&rft.aulast=Thiele&rft.aufirst=R%C3%BCdiger&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D3ZTedZtwYMoC%26pg%3DPA81%2B&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-novaacta-59">^ <a href="#cite_ref-novaacta_59-0">a</a> <a href="#cite_ref-novaacta_59-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFuss1783" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Nicolas_Fuss" title="Nicolas Fuss">Fuss, Nicolas</a> (1783). <a rel="nofollow" class="external text" href="https://www.biodiversitylibrary.org/item/38629#page/177/mode/1up">"Éloge de M. Léonhard Euler"</a> [Eulogy for Leonhard Euler]. Nova Acta Academiae Scientiarum Imperialis Petropolitanae (in French). 1: 159–212. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210820093949/https://www.biodiversitylibrary.org/item/38629#page/177/mode/1up">Archived</a> from the original on 20 August 2021. Retrieved 19 May 2018 – via Bioheritage Diversity Library.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nova+Acta+Academiae+Scientiarum+Imperialis+Petropolitanae&rft.atitle=%C3%89loge+de+M.+L%C3%A9onhard+Euler&rft.volume=1&rft.pages=159-212&rft.date=1783&rft.aulast=Fuss&rft.aufirst=Nicolas&rft_id=https%3A%2F%2Fwww.biodiversitylibrary.org%2Fitem%2F38629%23page%2F177%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> Translated into English as <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www-history.mcs.st-and.ac.uk/~history/Extras/Euler_Fuss_Eulogy.html">"Eulogy of Leonhard Euler by Nicolas Fuss"</a>. <a href="/wiki/MacTutor_History_of_Mathematics_archive" class="mw-redirect" title="MacTutor History of Mathematics archive">MacTutor History of Mathematics archive</a>. Translated by Glaus, John S. D. <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20181226041204/http://www-history.mcs.st-and.ac.uk/~history/Extras/Euler_Fuss_Eulogy.html">Archived</a> from the original on 26 December 2018. Retrieved 30 August 2006.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MacTutor+History+of+Mathematics+archive&rft.atitle=Eulogy+of+Leonhard+Euler+by+Nicolas+Fuss&rft_id=http%3A%2F%2Fwww-history.mcs.st-and.ac.uk%2F~history%2FExtras%2FEuler_Fuss_Eulogy.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTECalinger1996129-60">^ <a href="#cite_ref-FOOTNOTECalinger1996129_60-0">a</a> <a href="#cite_ref-FOOTNOTECalinger1996129_60-1">b</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, p. 129. </li> <li id="cite_note-FOOTNOTEGekkerEuler2007[httpsbooksgooglecombooksidTa9bz1wv79ACpgPA405_405]-61"><a href="#cite_ref-FOOTNOTEGekkerEuler2007[httpsbooksgooglecombooksidTa9bz1wv79ACpgPA405_405]_61-0">^</a> <a href="#CITEREFGekkerEuler2007">Gekker & Euler 2007</a>, p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Ta9bz1wv79AC&pg=PA405">405</a>. </li> <li id="cite_note-62"><a href="#cite_ref-62">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMeade1999" class="citation web cs1">Meade, Phil (27 November 1999). <a rel="nofollow" class="external text" href="https://www.newscientist.com/letter/mg16422147-400-uncommon-talent/">"Letter: Uncommon talent"</a>. www.newscientist.com. Retrieved 22 September 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.newscientist.com&rft.atitle=Letter%3A+Uncommon+talent&rft.date=1999-11-27&rft.aulast=Meade&rft.aufirst=Phil&rft_id=https%3A%2F%2Fwww.newscientist.com%2Fletter%2Fmg16422147-400-uncommon-talent%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-63"><a href="#cite_ref-63">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNahin2017" class="citation book cs1"><a href="/wiki/Paul_J._Nahin" title="Paul J. Nahin">Nahin, Paul J.</a> (2017). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=m3GYDwAAQBAJ&dq=aeneid+euler&pg=PA326">Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills</a>. Princeton Science Library. Princeton Oxford: Princeton University Press. p. 326. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-17591-1" title="Special:BookSources/978-0-691-17591-1"><bdi>978-0-691-17591-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dr.+Euler%27s+Fabulous+Formula%3A+Cures+Many+Mathematical+Ills&rft.place=Princeton+Oxford&rft.series=Princeton+Science+Library&rft.pages=326&rft.pub=Princeton+University+Press&rft.date=2017&rft.isbn=978-0-691-17591-1&rft.aulast=Nahin&rft.aufirst=Paul+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dm3GYDwAAQBAJ%26dq%3Daeneid%2Beuler%26pg%3DPA326&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTEGautschi20086-64">^ <a href="#cite_ref-FOOTNOTEGautschi20086_64-0">a</a> <a href="#cite_ref-FOOTNOTEGautschi20086_64-1">b</a> <a href="#CITEREFGautschi2008">Gautschi 2008</a>, p. 6. </li> <li id="cite_note-blindness-65">^ <a href="#cite_ref-blindness_65-0">a</a> <a href="#cite_ref-blindness_65-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEves1969" class="citation book cs1"><a href="/wiki/Howard_Eves" title="Howard Eves">Eves, Howard W.</a> (1969). "Euler's blindness". In Mathematical Circles: A Selection of Mathematical Stories and Anecdotes, Quadrants III and IV. Prindle, Weber, & Schmidt. p. 48. <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/260534353">260534353</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euler%27s+blindness&rft.btitle=In+Mathematical+Circles%3A+A+Selection+of+Mathematical+Stories+and+Anecdotes%2C+Quadrants+III+and+IV&rft.pages=48&rft.pub=Prindle%2C+Weber%2C+%26+Schmidt&rft.date=1969&rft_id=info%3Aoclcnum%2F260534353&rft.aulast=Eves&rft.aufirst=Howard+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> Also quoted by <a href="#CITEREFRicheson2012">Richeson (2012)</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kv2EDwAAQBAJ&pg=PA17">p. 17</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210616115732/https://books.google.com/books?id=kv2EDwAAQBAJ&pg=PA17">Archived</a> 16 June 2021 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, cited to Eves. </li> <li id="cite_note-righteye-66">^ <a href="#cite_ref-righteye_66-0">a</a> <a href="#cite_ref-righteye_66-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAsensiAsensi2013" class="citation journal cs1">Asensi, Victor; Asensi, Jose M. 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Davidson">Davidson, Michael W.</a> (February 2011). <a rel="nofollow" class="external text" href="https://doi.org/10.1017%2Fs1551929511000046">"Pioneers in Optics: Leonhard Euler and Étienne-Louis Malus"</a>. 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Académie Royale des Sciences et des Belles-Lettres de Berlin, Mémoires (in French). 11: 217–273. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210506203208/https://scholarlycommons.pacific.edu/euler-works/225/">Archived</a> from the original on 6 May 2021. Retrieved 12 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acad%C3%A9mie+Royale+des+Sciences+et+des+Belles-Lettres+de+Berlin%2C+M%C3%A9moires&rft.atitle=Principes+g%C3%A9n%C3%A9raux+de+l%27%C3%A9tat+d%27%C3%A9quilibre+d%27un+fluide&rft.volume=11&rft.pages=217-273&rft.date=1757&rft.aulast=Euler&rft.aufirst=Leonhard&rft_id=https%3A%2F%2Fscholarlycommons.pacific.edu%2Feuler-works%2F225%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> Translated into English as <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrisch2008" class="citation arxiv cs1"><a href="/wiki/Uriel_Frisch" title="Uriel Frisch">Frisch, Uriel</a> (2008). 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On the valuation of logic diagrams"</a>. Logic-Philosophical Studies. 14: 98–122.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Logic-Philosophical+Studies&rft.atitle=Means+or+end%3F+On+the+valuation+of+logic+diagrams&rft.volume=14&rft.pages=98-122&rft.date=2016&rft.aulast=Lemanski&rft.aufirst=Jens&rft_id=https%3A%2F%2Fphilarchive.org%2Frec%2FLEMMOE&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-rodgers-110"><a href="#cite_ref-rodgers_110-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRodgers2014" class="citation journal cs1">Rodgers, Peter (June 2014). <a rel="nofollow" class="external text" href="https://kar.kent.ac.uk/35163/1/JVLC_Euler_Survey.pdf">"A survey of Euler diagrams"</a> (PDF). Journal of Visual Languages & Computing. 25 (3): 134–155. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jvlc.2013.08.006">10.1016/j.jvlc.2013.08.006</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:2571971">2571971</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210820093951/https://kar.kent.ac.uk/35163/1/JVLC_Euler_Survey.pdf">Archived</a> (PDF) from the original on 20 August 2021. 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Music and the Making of Modern Science. <a href="/wiki/MIT_Press" title="MIT Press">MIT Press</a>. pp. 133–160. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-02727-4" title="Special:BookSources/978-0-262-02727-4"><bdi>978-0-262-02727-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210610064542/https://books.google.com/books?id=HfPvAwAAQBAJ&pg=PA133">Archived</a> from the original on 10 June 2021. Retrieved 10 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euler%3A+the+mathematics+of+musical+sadness%3B+Euler%3A+from+sound+to+light&rft.btitle=Music+and+the+Making+of+Modern+Science&rft.pages=133-160&rft.pub=MIT+Press&rft.date=2014&rft.isbn=978-0-262-02727-4&rft.aulast=Pesic&rft.aufirst=Peter&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHfPvAwAAQBAJ%26pg%3DPA133&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-tegg-113"><a href="#cite_ref-tegg_113-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTegg1829" class="citation encyclopaedia cs1"><a href="/wiki/Thomas_Tegg" title="Thomas Tegg">Tegg, Thomas</a> (1829). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=E-ZTAAAAYAAJ&pg=PA142">"Binary logarithms"</a>. London encyclopaedia; or, Universal dictionary of science, art, literature and practical mechanics: comprising a popular view of the present state of knowledge, Volume 4. pp. 142–143. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210523051211/https://books.google.com/books?id=E-ZTAAAAYAAJ&pg=PA142">Archived</a> from the original on 23 May 2021. Retrieved 13 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Binary+logarithms&rft.btitle=London+encyclopaedia%3B+or%2C+Universal+dictionary+of+science%2C+art%2C+literature+and+practical+mechanics%3A+comprising+a+popular+view+of+the+present+state+of+knowledge%2C+Volume+4&rft.pages=142-143&rft.date=1829&rft.aulast=Tegg&rft.aufirst=Thomas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DE-ZTAAAAYAAJ%26pg%3DPA142&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTEEuler1739115-114"><a href="#cite_ref-FOOTNOTEEuler1739115_114-0">^</a> <a href="#CITEREFEuler1739">Euler 1739</a>, p. 115. </li> <li id="cite_note-emery-115"><a href="#cite_ref-emery_115-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEmery2000" class="citation book cs1">Emery, Eric (2000). Temps et musique. Lausanne: L'Âge d'homme. pp. 344–345.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Temps+et+musique&rft.place=Lausanne&rft.pages=344-345&rft.pub=L%27%C3%82ge+d%27homme&rft.date=2000&rft.aulast=Emery&rft.aufirst=Eric&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-mattheson-116"><a href="#cite_ref-mattheson_116-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMattheson1731" class="citation book cs1"><a href="/wiki/Johann_Mattheson" title="Johann Mattheson">Mattheson, Johannes</a> (1731). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_yRxDAAAAcAAJ">Grosse General-Baß-Schule</a>. Vol. I. Hamburg. pp. 104–106. <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/30006387">30006387</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Grosse+General-Ba%C3%9F-Schule&rft.place=Hamburg&rft.pages=104-106&rft.date=1731&rft_id=info%3Aoclcnum%2F30006387&rft.aulast=Mattheson&rft.aufirst=Johannes&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_yRxDAAAAcAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> Mentioned by Euler. Also: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMattheson1719" class="citation book cs1">Mattheson, Johannes (1719). <a rel="nofollow" class="external text" href="https://archive.org/details/exemplarischeor00mattgoog">Exemplarische Organisten-Probe</a>. Hamburg. pp. 57–59.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Exemplarische+Organisten-Probe&rft.place=Hamburg&rft.pages=57-59&rft.date=1719&rft.aulast=Mattheson&rft.aufirst=Johannes&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fexemplarischeor00mattgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-perret-117"><a href="#cite_ref-perret_117-0">^</a> See: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPerret1926" class="citation book cs1">Perret, Wilfrid (1926). Some Questions of Musical Theory. Cambridge: W. Heffer & Sons. pp. 60–62. <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/3212114">3212114</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Some+Questions+of+Musical+Theory&rft.place=Cambridge&rft.pages=60-62&rft.pub=W.+Heffer+%26+Sons&rft.date=1926&rft_id=info%3Aoclcnum%2F3212114&rft.aulast=Perret&rft.aufirst=Wilfrid&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.huygens-fokker.org/microtonality/efg.html">"What is an Euler-Fokker genus?"</a>. Microtonality. <a href="/wiki/Huygens-Fokker_Foundation" title="Huygens-Fokker Foundation">Huygens-Fokker Foundation</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150521074006/http://www.huygens-fokker.org/microtonality/efg.html">Archived</a> from the original on 21 May 2015. Retrieved 12 June 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Microtonality&rft.atitle=What+is+an+Euler-Fokker+genus%3F&rft_id=http%3A%2F%2Fwww.huygens-fokker.org%2Fmicrotonality%2Fefg.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li></ul> </li> <li id="cite_note-FOOTNOTEEuler1739147-118"><a href="#cite_ref-FOOTNOTEEuler1739147_118-0">^</a> <a href="#CITEREFEuler1739">Euler 1739</a>, p. 147. </li> <li id="cite_note-de_harmoniae-119"><a href="#cite_ref-de_harmoniae_119-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEuler1774" class="citation journal cs1"><a class="mw-selflink selflink">Euler, Leonhard</a> (1774). <a rel="nofollow" class="external text" href="https://scholarlycommons.pacific.edu/euler-works/457/">"De harmoniae veris principiis per speculum musicum repraesentatis"</a>. Novi Commentarii Academiae Scientiarum Petropolitanae. 18. Eneström index 457: 330–353. Retrieved 12 September 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Novi+Commentarii+Academiae+Scientiarum+Petropolitanae&rft.atitle=De+harmoniae+veris+principiis+per+speculum+musicum+repraesentatis&rft.volume=18&rft.pages=330-353&rft.date=1774&rft.aulast=Euler&rft.aufirst=Leonhard&rft_id=https%3A%2F%2Fscholarlycommons.pacific.edu%2Feuler-works%2F457%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-gollin-120"><a href="#cite_ref-gollin_120-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGollin2009" class="citation conference cs1">Gollin, Edward (2009). "Combinatorial and transformational aspects of Euler's Speculum Musicum". In Klouche, T.; Noll, Th. (eds.). Mathematics and Computation in Music: First International Conference, MCM 2007 Berlin, Germany, May 18–20, 2007, Revised Selected Papers. Communications in Computer and Information Science. Vol. 37. Springer. pp. 406–411. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-04579-0_40">10.1007/978-3-642-04579-0_40</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-04578-3" title="Special:BookSources/978-3-642-04578-3"><bdi>978-3-642-04578-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Combinatorial+and+transformational+aspects+of+Euler%27s+Speculum+Musicum&rft.btitle=Mathematics+and+Computation+in+Music%3A+First+International+Conference%2C+MCM+2007+Berlin%2C+Germany%2C+May+18%E2%80%9320%2C+2007%2C+Revised+Selected+Papers&rft.series=Communications+in+Computer+and+Information+Science&rft.pages=406-411&rft.pub=Springer&rft.date=2009&rft_id=info%3Adoi%2F10.1007%2F978-3-642-04579-0_40&rft.isbn=978-3-642-04578-3&rft.aulast=Gollin&rft.aufirst=Edward&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-lindley-121"><a href="#cite_ref-lindley_121-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLindleyTurner-Smith1993" class="citation book cs1"><a href="/wiki/Mark_Lindley" title="Mark Lindley">Lindley, Mark</a>; Turner-Smith, Ronald (1993). <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/27789639">Mathematical Models of Musical Scales : A New Approach</a>. Bonn: Verlag für Systematische Musikwissenschaft. pp. 234–239. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783922626664" title="Special:BookSources/9783922626664"><bdi>9783922626664</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/27789639">27789639</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Models+of+Musical+Scales+%3A+A+New+Approach&rft.place=Bonn&rft.pages=234-239&rft.pub=Verlag+f%C3%BCr+Systematische+Musikwissenschaft&rft.date=1993&rft_id=info%3Aoclcnum%2F27789639&rft.isbn=9783922626664&rft.aulast=Lindley&rft.aufirst=Mark&rft.au=Turner-Smith%2C+Ronald&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F27789639&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> See also <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNolan2002" class="citation book cs1">Nolan, Catherine (2002). "Music Theory and Mathematics". In Christensen, Th. (ed.). The Cambridge History of Western Music Theory. New York: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. pp. 278–279. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781139053471" title="Special:BookSources/9781139053471"><bdi>9781139053471</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/828741887">828741887</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Music+Theory+and+Mathematics&rft.btitle=The+Cambridge+History+of+Western+Music+Theory&rft.place=New+York&rft.pages=278-279&rft.pub=Cambridge+University+Press&rft.date=2002&rft_id=info%3Aoclcnum%2F828741887&rft.isbn=9781139053471&rft.aulast=Nolan&rft.aufirst=Catherine&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-bailhache-122"><a href="#cite_ref-bailhache_122-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBailhache1997" class="citation web cs1 cs1-prop-foreign-lang-source">Bailhache, Patrice (17 January 1997). <a rel="nofollow" class="external text" href="http://patrice.bailhache.free.fr/thmusique/euler.html">"La Musique traduite en Mathématiques: Leonhard Euler"</a>. Communication au colloque du Centre François Viète, "Problèmes de traduction au XVIIIe siècle", Nantes (in French). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151128063721/http://patrice.bailhache.free.fr/thmusique/euler.html">Archived</a> from the original on 28 November 2015. Retrieved 12 June 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Communication+au+colloque+du+Centre+Fran%C3%A7ois+Vi%C3%A8te%2C+%22Probl%C3%A8mes+de+traduction+au+XVIIIe+si%C3%A8cle%22%2C+Nantes&rft.atitle=La+Musique+traduite+en+Math%C3%A9matiques%3A+Leonhard+Euler&rft.date=1997-01-17&rft.aulast=Bailhache&rft.aufirst=Patrice&rft_id=http%3A%2F%2Fpatrice.bailhache.free.fr%2Fthmusique%2Feuler.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-theology-123"><a href="#cite_ref-theology_123-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEuler1747" class="citation book cs1 cs1-prop-foreign-lang-source"><a class="mw-selflink selflink">Euler, Leonhard</a> (1747). <a rel="nofollow" class="external text" href="https://scholarlycommons.pacific.edu/euler-works/92/">Rettung der Göttlichen Offenbahrung gegen die Einwürfe der Freygeister</a> [Defense of divine revelation against the objections of the freethinkers] (in German). Eneström index 92. Berlin: Ambrosius Haude and Johann Carl Spener. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210612231041/https://scholarlycommons.pacific.edu/euler-works/92/">Archived</a> from the original on 12 June 2021. Retrieved 12 June 2021 – via Euler Archive.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Rettung+der+G%C3%B6ttlichen+Offenbahrung+gegen+die+Einw%C3%BCrfe+der+Freygeister&rft.place=Berlin&rft.pub=Ambrosius+Haude+and+Johann+Carl+Spener&rft.date=1747&rft.aulast=Euler&rft.aufirst=Leonhard&rft_id=https%3A%2F%2Fscholarlycommons.pacific.edu%2Feuler-works%2F92%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-Ho2-124"><a href="#cite_ref-Ho2_124-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarquis_de_Condorcet1805" class="citation book cs1"><a href="/wiki/Marquis_de_Condorcet" title="Marquis de Condorcet">Marquis de Condorcet</a> (1805). <a rel="nofollow" class="external text" href="http://www.math.dartmouth.edu/~euler/docs/translations/E092trans.pdf">Comparison to the Last Edition of Euler's Letters Published by de Condorcet, with the Original Edition: A Defense of the Revelation Against the Objections of Freethinkers, by Mr. Euler Followed by Thoughts by the Author on Religion, Omitted From the Last Edition of his Letters to a Princess of Germany</a> (PDF). Translated by Ho, Andie. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150428184622/https://math.dartmouth.edu/~euler/docs/translations/E092trans.pdf">Archived</a> (PDF) from the original on 28 April 2015. Retrieved 26 July 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Comparison+to+the+Last+Edition+of+Euler%27s+Letters+Published+by+de+Condorcet%2C+with+the+Original+Edition%3A+A+Defense+of+the+Revelation+Against+the+Objections+of+Freethinkers%2C+by+Mr.+Euler+Followed+by+Thoughts+by+the+Author+on+Religion%2C+Omitted+From+the+Last+Edition+of+his+Letters+to+a+Princess+of+Germany&rft.date=1805&rft.au=Marquis+de+Condorcet&rft_id=http%3A%2F%2Fwww.math.dartmouth.edu%2F~euler%2Fdocs%2Ftranslations%2FE092trans.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTECalinger1996123-125"><a href="#cite_ref-FOOTNOTECalinger1996123_125-0">^</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, p. 123. </li> <li id="cite_note-wolff-126"><a href="#cite_ref-wolff_126-0">^</a> <a href="#CITEREFCalinger1996">Calinger 1996</a>, pp. 153–154 </li> <li id="cite_note-diderot-127">^ <a href="#cite_ref-diderot_127-0">a</a> <a href="#cite_ref-diderot_127-1">b</a> See: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrown1942" class="citation journal cs1">Brown, B. H. (May 1942). "The Euler–Diderot anecdote". <a href="/wiki/The_American_Mathematical_Monthly" title="The American Mathematical Monthly">The American Mathematical Monthly</a>. 49 (5): 302–303. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2303096">10.2307/2303096</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/2303096">2303096</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=The+Euler%E2%80%93Diderot+anecdote&rft.volume=49&rft.issue=5&rft.pages=302-303&rft.date=1942-05&rft_id=info%3Adoi%2F10.2307%2F2303096&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2303096%23id-name%3DJSTOR&rft.aulast=Brown&rft.aufirst=B.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGillings1954" class="citation journal cs1">Gillings, R. J. (February 1954). "The so-called Euler–Diderot incident". <a href="/wiki/The_American_Mathematical_Monthly" title="The American Mathematical Monthly">The American Mathematical Monthly</a>. 61 (2): 77–80. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2307789">10.2307/2307789</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/2307789">2307789</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=The+so-called+Euler%E2%80%93Diderot+incident&rft.volume=61&rft.issue=2&rft.pages=77-80&rft.date=1954-02&rft_id=info%3Adoi%2F10.2307%2F2307789&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2307789%23id-name%3DJSTOR&rft.aulast=Gillings&rft.aufirst=R.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStruik1967" class="citation book cs1"><a href="/wiki/Dirk_Jan_Struik" title="Dirk Jan Struik">Struik, Dirk J.</a> (1967). <a rel="nofollow" class="external text" href="https://archive.org/details/concisehistoryof0000stru_m6j1/page/129">A Concise History of Mathematics</a> (3rd revised ed.). <a href="/wiki/Dover_Books" class="mw-redirect" title="Dover Books">Dover Books</a>. p. <a rel="nofollow" class="external text" href="https://archive.org/details/concisehistoryof0000stru_m6j1/page/129">129</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-60255-4" title="Special:BookSources/978-0-486-60255-4"><bdi>978-0-486-60255-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Concise+History+of+Mathematics&rft.pages=129&rft.edition=3rd+revised&rft.pub=Dover+Books&rft.date=1967&rft.isbn=978-0-486-60255-4&rft.aulast=Struik&rft.aufirst=Dirk+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fconcisehistoryof0000stru_m6j1%2Fpage%2F129&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li></ul> </li> <li id="cite_note-persee-128"><a href="#cite_ref-persee_128-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarty1988" class="citation journal cs1 cs1-prop-foreign-lang-source">Marty, Jacques (1988). <a rel="nofollow" class="external text" href="http://www.persee.fr/web/revues/home/prescript/article/rde_0769-0886_1988_num_4_1_954">"Quelques aspects des travaux de Diderot en " mathématiques mixtes ""</a> [Some aspects of Diderot's work in general mathematics]. Recherches sur Diderot et sur l'Encyclopédie (in French). 4 (1): 145–147. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150924214645/http://www.persee.fr/web/revues/home/prescript/article/rde_0769-0886_1988_num_4_1_954">Archived</a> from the original on 24 September 2015. Retrieved 20 April 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Recherches+sur+Diderot+et+sur+l%27Encyclop%C3%A9die&rft.atitle=Quelques+aspects+des+travaux+de+Diderot+en+%22+math%C3%A9matiques+mixtes+%22&rft.volume=4&rft.issue=1&rft.pages=145-147&rft.date=1988&rft.aulast=Marty&rft.aufirst=Jacques&rft_id=http%3A%2F%2Fwww.persee.fr%2Fweb%2Frevues%2Fhome%2Fprescript%2Farticle%2Frde_0769-0886_1988_num_4_1_954&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-swiss6-129"><a href="#cite_ref-swiss6_129-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.snb.ch/de/iabout/cash/history/id/cash_history_serie6#t7">"Schweizerische Nationalbank (SNB) – Sechste Banknotenserie (1976)"</a>. <a href="/wiki/Swiss_National_Bank" title="Swiss National Bank">Swiss National Bank</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210503140326/https://www.snb.ch/de/iabout/cash/history/id/cash_history_serie6#t7">Archived</a> from the original on 3 May 2021. Retrieved 15 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Swiss+National+Bank&rft.atitle=Schweizerische+Nationalbank+%28SNB%29+%E2%80%93+Sechste+Banknotenserie+%281976%29&rft_id=https%3A%2F%2Fwww.snb.ch%2Fde%2Fiabout%2Fcash%2Fhistory%2Fid%2Fcash_history_serie6%23t7&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-swiss7-130"><a href="#cite_ref-swiss7_130-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.snb.ch/de/iabout/cash/history/id/cash_history_serie7#t7">"Schweizerische Nationalbank (SNB) – Siebte Banknotenserie (1984)"</a>. <a href="/wiki/Swiss_National_Bank" title="Swiss National Bank">Swiss National Bank</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210423025734/https://www.snb.ch/de/iabout/cash/history/id/cash_history_serie7#t7">Archived</a> from the original on 23 April 2021. Retrieved 15 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Swiss+National+Bank&rft.atitle=Schweizerische+Nationalbank+%28SNB%29+%E2%80%93+Siebte+Banknotenserie+%281984%29&rft_id=https%3A%2F%2Fwww.snb.ch%2Fde%2Fiabout%2Fcash%2Fhistory%2Fid%2Fcash_history_serie7%23t7&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-aaas-131"><a href="#cite_ref-aaas_131-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://www.amacad.org/sites/default/files/academy/multimedia/pdfs/publications/bookofmembers/ChapterE.pdf">"E"</a> (PDF). Members of the American Academy of Arts & Sciences, 1780–2017. <a href="/wiki/American_Academy_of_Arts_and_Sciences" title="American Academy of Arts and Sciences">American Academy of Arts and Sciences</a>. pp. 164–179. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190218021302/https://www.amacad.org/sites/default/files/academy/multimedia/pdfs/publications/bookofmembers/ChapterE.pdf">Archived</a> (PDF) from the original on 18 February 2019. Retrieved 17 February 2019.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=E&rft.btitle=Members+of+the+American+Academy+of+Arts+%26+Sciences%2C+1780%E2%80%932017&rft.pages=164-179&rft.pub=American+Academy+of+Arts+and+Sciences&rft_id=https%3A%2F%2Fwww.amacad.org%2Fsites%2Fdefault%2Ffiles%2Facademy%2Fmultimedia%2Fpdfs%2Fpublications%2Fbookofmembers%2FChapterE.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> Entry for Euler is on p. 177. </li> <li id="cite_note-schmadel-132"><a href="#cite_ref-schmadel_132-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmadel2007" class="citation encyclopaedia cs1"><a href="/wiki/Lutz_D._Schmadel" title="Lutz D. Schmadel">Schmadel, Lutz D.</a>, ed. (2007). "(2002) Euler". Dictionary of Minor Planet Names. <a href="/wiki/Berlin" title="Berlin">Berlin</a>, <a href="/wiki/Heidelberg" title="Heidelberg">Heidelberg</a>: <a href="/wiki/Springer_Publishing" title="Springer Publishing">Springer Publishing</a>. p. 162. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-540-29925-7_2003">10.1007/978-3-540-29925-7_2003</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-29925-7" title="Special:BookSources/978-3-540-29925-7"><bdi>978-3-540-29925-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=%282002%29+Euler&rft.btitle=Dictionary+of+Minor+Planet+Names&rft.place=Berlin%2C+Heidelberg&rft.pages=162&rft.pub=Springer+Publishing&rft.date=2007&rft_id=info%3Adoi%2F10.1007%2F978-3-540-29925-7_2003&rft.isbn=978-3-540-29925-7&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-fraser-133"><a href="#cite_ref-fraser_133-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFraser2005" class="citation book cs1">Fraser, Craig G. (11 February 2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UdGBy8iLpocC&pg=PA168">Leonhard Euler's 1744 book on the calculus of variations</a>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-045744-4" title="Special:BookSources/978-0-08-045744-4"><bdi>978-0-08-045744-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Leonhard+Euler%27s+1744+book+on+the+calculus+of+variations&rft.pub=Elsevier&rft.date=2005-02-11&rft.isbn=978-0-08-045744-4&rft.aulast=Fraser&rft.aufirst=Craig+G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUdGBy8iLpocC%26pg%3DPA168&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> In <a href="#CITEREFGrattan-Guinness2005">Grattan-Guinness 2005</a>, pp. 168–180 </li> <li id="cite_note-dartm2-134"><a href="#cite_ref-dartm2_134-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEuler1744" class="citation book cs1 cs1-prop-foreign-lang-source">Euler, Leonhard (1744). <a rel="nofollow" class="external text" href="https://scholarlycommons.pacific.edu/euler-works/65/">Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti</a> [A method for finding curved lines enjoying properties of maximum or minimum, or solution of isoperimetric problems in the broadest accepted sense] (in Latin). Bosquet. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210608223653/https://scholarlycommons.pacific.edu/euler-works/65/">Archived</a> from the original on 8 June 2021. Retrieved 8 June 2021 – via Euler archive.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Methodus+inveniendi+lineas+curvas+maximi+minimive+proprietate+gaudentes%2C+sive+solutio+problematis+isoperimetrici+lattissimo+sensu+accepti&rft.pub=Bosquet&rft.date=1744&rft.aulast=Euler&rft.aufirst=Leonhard&rft_id=https%3A%2F%2Fscholarlycommons.pacific.edu%2Feuler-works%2F65%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-reich-135"><a href="#cite_ref-reich_135-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReich2005" class="citation book cs1"><a href="/wiki/Karin_Reich" title="Karin Reich">Reich, Karin</a> (11 February 2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UdGBy8iLpocC&pg=PA181">'Introduction' to analysis</a>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-045744-4" title="Special:BookSources/978-0-08-045744-4"><bdi>978-0-08-045744-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%27Introduction%27+to+analysis&rft.pub=Elsevier&rft.date=2005-02-11&rft.isbn=978-0-08-045744-4&rft.aulast=Reich&rft.aufirst=Karin&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUdGBy8iLpocC%26pg%3DPA181&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> In <a href="#CITEREFGrattan-Guinness2005">Grattan-Guinness 2005</a>, pp. 181–190 </li> <li id="cite_note-ferraro-136">^ <a href="#cite_ref-ferraro_136-0">a</a> <a href="#cite_ref-ferraro_136-1">b</a> <a href="#cite_ref-ferraro_136-2">c</a> <a href="#cite_ref-ferraro_136-3">d</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFerraro2007" class="citation book cs1">Ferraro, Giovanni (2007). "Euler's treatises on infinitesimal analysis: Introductio in analysin infinitorum, institutiones calculi differentialis, institutionum calculi integralis". In Baker, Roger (ed.). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220912015017/http://oak.ucc.nau.edu/cgg/Ferraro%20entire.pdf">Euler Reconsidered: Tercentenary Essays</a> (PDF). Heber City, UT: Kendrick Press. pp. 39–101. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=2384378">2384378</a>. Archived from <a rel="nofollow" class="external text" href="http://oak.ucc.nau.edu/cgg/Ferraro%20entire.pdf">the original</a> (PDF) on 12 September 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euler%27s+treatises+on+infinitesimal+analysis%3A+Introductio+in+analysin+infinitorum%2C+institutiones+calculi+differentialis%2C+institutionum+calculi+integralis&rft.btitle=Euler+Reconsidered%3A+Tercentenary+Essays&rft.place=Heber+City%2C+UT&rft.pages=39-101&rft.pub=Kendrick+Press&rft.date=2007&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D2384378%23id-name%3DMR&rft.aulast=Ferraro&rft.aufirst=Giovanni&rft_id=http%3A%2F%2Foak.ucc.nau.edu%2Fcgg%2FFerraro%2520entire.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-revaninf-137"><a href="#cite_ref-revaninf_137-0">^</a> Reviews of Introduction to Analysis of the Infinite: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAiton" class="citation journal cs1">Aiton, E. J. "Introduction to analysis of the infinite. Book I. Transl. by John D. Blanton. (English)". <a href="/wiki/ZbMATH" class="mw-redirect" title="ZbMATH">zbMATH</a>. <a href="/wiki/Zbl_(identifier)" class="mw-redirect" title="Zbl (identifier)">Zbl</a> <a rel="nofollow" class="external text" href="https://zbmath.org/?format=complete&q=an:0657.01013">0657.01013</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=zbMATH&rft.atitle=Introduction+to+analysis+of+the+infinite.+Book+I.+Transl.+by+John+D.+Blanton.+%28English%29&rft_id=https%3A%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A0657.01013%23id-name%3DZbl&rft.aulast=Aiton&rft.aufirst=E.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShiu1990" class="citation journal cs1">Shiu, P. (December 1990). "Introduction to analysis of the infinite (Book II), by Leonard Euler (translated by John D. Blanton)". <a href="/wiki/The_Mathematical_Gazette" title="The Mathematical Gazette">The Mathematical Gazette</a>. 74 (470): 392–393. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F3618156">10.2307/3618156</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/3618156">3618156</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Mathematical+Gazette&rft.atitle=Introduction+to+analysis+of+the+infinite+%28Book+II%29%2C+by+Leonard+Euler+%28translated+by+John+D.+Blanton%29.&rft.volume=74&rft.issue=470&rft.pages=392-393&rft.date=1990-12&rft_id=info%3Adoi%2F10.2307%2F3618156&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F3618156%23id-name%3DJSTOR&rft.aulast=Shiu&rft.aufirst=P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFŞtefănescu" class="citation journal cs1">Ştefănescu, Doru. "Euler, Leonhard Introduction to analysis of the infinite. Book I. Translated from the Latin and with an introduction by John D. Blanton". <a href="/wiki/Mathematical_Reviews" title="Mathematical Reviews">Mathematical Reviews</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1025504">1025504</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematical+Reviews&rft.atitle=Euler%2C+Leonhard+Introduction+to+analysis+of+the+infinite.+Book+I.+Translated+from+the+Latin+and+with+an+introduction+by+John+D.+Blanton.&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1025504%23id-name%3DMR&rft.aulast=%C5%9Etef%C4%83nescu&rft.aufirst=Doru&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li></ul> </li> <li id="cite_note-demidov-138"><a href="#cite_ref-demidov_138-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDemidov2005" class="citation book cs1">Demidov, S. S. (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UdGBy8iLpocC&pg=PA191">Treatise on the differential calculus</a>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0080457444" title="Special:BookSources/978-0080457444"><bdi>978-0080457444</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210618015909/https://books.google.com/books?id=UdGBy8iLpocC&pg=PA191">Archived</a> from the original on 18 June 2021. Retrieved 12 November 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Treatise+on+the+differential+calculus&rft.pub=Elsevier&rft.date=2005&rft.isbn=978-0080457444&rft.aulast=Demidov&rft.aufirst=S.+S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUdGBy8iLpocC%26pg%3DPA191&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> In <a href="#CITEREFGrattan-Guinness2005">Grattan-Guinness 2005</a>, pp. 191–198. </li> <li id="cite_note-kleinert-139">^ <a href="#cite_ref-kleinert_139-0">a</a> <a href="#cite_ref-kleinert_139-1">b</a> <a href="#cite_ref-kleinert_139-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKleinert2015" class="citation journal cs1">Kleinert, Andreas (2015). <a rel="nofollow" class="external text" href="https://doi.org/10.4467%2F23921749pkhn_pau.16.002.5258">"Leonhardi Euleri Opera omnia: Editing the works and correspondence of Leonhard Euler"</a>. Prace Komisji Historii Nauki PAU. 14. <a href="/wiki/Jagiellonian_University" title="Jagiellonian University">Jagiellonian University</a>: 13–35. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4467%2F23921749pkhn_pau.16.002.5258">10.4467/23921749pkhn_pau.16.002.5258</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Prace+Komisji+Historii+Nauki+PAU&rft.atitle=Leonhardi+Euleri+Opera+omnia%3A+Editing+the+works+and+correspondence+of+Leonhard+Euler&rft.volume=14&rft.pages=13-35&rft.date=2015&rft_id=info%3Adoi%2F10.4467%2F23921749pkhn_pau.16.002.5258&rft.aulast=Kleinert&rft.aufirst=Andreas&rft_id=https%3A%2F%2Fdoi.org%2F10.4467%252F23921749pkhn_pau.16.002.5258&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-fuss-140"><a href="#cite_ref-fuss_140-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEulerFussFuss1862" class="citation book cs1"><a class="mw-selflink selflink">Euler, Leonhard</a>; <a href="/wiki/Nicolas_Fuss" title="Nicolas Fuss">Fuss, Nikola Ivanovich</a>; Fuss, Paul (1862). Opera postuma mathematica et physica anno 1844 detecta quae Academiae scientiarum petropolitanae obtulerunt ejusque auspicus ediderunt auctoris pronepotes Paulus Henricus Fuss et Nicolaus Fuss. <a href="/wiki/Russian_Academy_of_Sciences" title="Russian Academy of Sciences">Imperatorskaia akademīia nauk (Russia)</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/9094558695">9094558695</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Opera+postuma+mathematica+et+physica+anno+1844+detecta+quae+Academiae+scientiarum+petropolitanae+obtulerunt+ejusque+auspicus+ediderunt+auctoris+pronepotes+Paulus+Henricus+Fuss+et+Nicolaus+Fuss.&rft.pub=Imperatorskaia+akadem%C4%ABia+nauk+%28Russia%29&rft.date=1862&rft_id=info%3Aoclcnum%2F9094558695&rft.aulast=Euler&rft.aufirst=Leonhard&rft.au=Fuss%2C+Nikola+Ivanovich&rft.au=Fuss%2C+Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-FOOTNOTECalinger2016ix–x-141"><a href="#cite_ref-FOOTNOTECalinger2016ix–x_141-0">^</a> <a href="#CITEREFCalinger2016">Calinger 2016</a>, pp. ix–x. </li> <li id="cite_note-enestrom-142"><a href="#cite_ref-enestrom_142-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://scholarlycommons.pacific.edu/euler-works/">"The Eneström Index"</a>. Euler Archive. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210809104204/https://scholarlycommons.pacific.edu/euler-works/">Archived</a> from the original on 9 August 2021. Retrieved 27 May 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Euler+Archive&rft.atitle=The+Enestr%C3%B6m+Index&rft_id=https%3A%2F%2Fscholarlycommons.pacific.edu%2Feuler-works%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-archive-start-143"><a href="#cite_ref-archive-start_143-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKnapp2007" class="citation news cs1">Knapp, Susan (19 February 2007). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100528022155/http://www.dartmouth.edu/~vox/0607/0219/euler.html">"Dartmouth students build online archive of historic mathematician"</a>. Vox of Dartmouth. <a href="/wiki/Dartmouth_College" title="Dartmouth College">Dartmouth College</a>. Archived from <a rel="nofollow" class="external text" href="http://www.dartmouth.edu/~vox/0607/0219/euler.html">the original</a> on 28 May 2010.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Vox+of+Dartmouth&rft.atitle=Dartmouth+students+build+online+archive+of+historic+mathematician&rft.date=2007-02-19&rft.aulast=Knapp&rft.aufirst=Susan&rft_id=http%3A%2F%2Fwww.dartmouth.edu%2F~vox%2F0607%2F0219%2Feuler.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-archive-move-144"><a href="#cite_ref-archive-move_144-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKlyve2011" class="citation magazine cs1">Klyve, Dominic (June–July 2011). <a rel="nofollow" class="external text" href="http://digitaleditions.walsworthprintgroup.com/article/Euler+Archive+Moves+To+MAA+Website/757939/72837/article.html">"Euler Archive Moves To MAA Website"</a>. <a href="/wiki/MAA_FOCUS" title="MAA FOCUS">MAA FOCUS</a>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. Retrieved 9 January 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=MAA+FOCUS&rft.atitle=Euler+Archive+Moves+To+MAA+Website&rft.date=2011-06%2F2011-07&rft.aulast=Klyve&rft.aufirst=Dominic&rft_id=http%3A%2F%2Fdigitaleditions.walsworthprintgroup.com%2Farticle%2FEuler%2BArchive%2BMoves%2BTo%2BMAA%2BWebsite%2F757939%2F72837%2Farticle.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-euler_archive-145"><a href="#cite_ref-euler_archive_145-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20210607074500/https://scholarlycommons.pacific.edu/euler/">"The Euler Archive"</a>. <a href="/wiki/University_of_the_Pacific_(United_States)" title="University of the Pacific (United States)">University of the Pacific</a>. Archived from <a rel="nofollow" class="external text" href="https://scholarlycommons.pacific.edu/euler/">the original</a> on 7 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=University+of+the+Pacific&rft.atitle=The+Euler+Archive&rft_id=https%3A%2F%2Fscholarlycommons.pacific.edu%2Feuler%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-pluss-146">^ <a href="#cite_ref-pluss_146-0">a</a> <a href="#cite_ref-pluss_146-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlüss" class="citation web cs1">Plüss, Matthias. <a rel="nofollow" class="external text" href="http://www.snf.ch/de/fokusForschung/newsroom/Seiten/news-160620-horizonte-der-goethe-der-mathematik.aspx">"Der Goethe der Mathematik"</a>. <a href="/wiki/Swiss_National_Science_Foundation" title="Swiss National Science Foundation">Swiss National Science Foundation</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210624195156/http://www.snf.ch/de/fokusForschung/newsroom/Seiten/news-160620-horizonte-der-goethe-der-mathematik.aspx">Archived</a> from the original on 24 June 2021. Retrieved 16 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Swiss+National+Science+Foundation&rft.atitle=Der+Goethe+der+Mathematik&rft.aulast=Pl%C3%BCss&rft.aufirst=Matthias&rft_id=http%3A%2F%2Fwww.snf.ch%2Fde%2FfokusForschung%2Fnewsroom%2FSeiten%2Fnews-160620-horizonte-der-goethe-der-mathematik.aspx&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-new_look-147"><a href="#cite_ref-new_look_147-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVaradarajan2006" class="citation book cs1"><a href="/wiki/Veeravalli_S._Varadarajan" title="Veeravalli S. Varadarajan">Varadarajan, V. S.</a> (2006). <a rel="nofollow" class="external text" href="http://worldcat.org/oclc/803144928">Euler through time : a new look at old themes</a>. <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-3580-7" title="Special:BookSources/978-0-8218-3580-7"><bdi>978-0-8218-3580-7</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/803144928">803144928</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Euler+through+time+%3A+a+new+look+at+old+themes&rft.pub=American+Mathematical+Society&rft.date=2006&rft_id=info%3Aoclcnum%2F803144928&rft.isbn=978-0-8218-3580-7&rft.aulast=Varadarajan&rft.aufirst=V.+S.&rft_id=http%3A%2F%2Fworldcat.org%2Foclc%2F803144928&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> <li id="cite_note-148"><a href="#cite_ref-148">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLibri1846" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Guglielmo_Libri_Carucci_dalla_Sommaja" title="Guglielmo Libri Carucci dalla Sommaja">Libri, Gugliemo</a> (January 1846). <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k57253t/f52.image.langEN">"Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIe siècle, ..."</a> [Mathematical and physical correspondence of some famous geometers of the eighteenth century, ...]. <a href="/wiki/Journal_des_s%C3%A7avans" title="Journal des sçavans">Journal des Savants</a> (in French): 51. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180809113402/https://gallica.bnf.fr/ark:/12148/bpt6k57253t/f52.image.langEN">Archived</a> from the original on 9 August 2018. Retrieved 7 April 2014.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+des+Savants&rft.atitle=Correspondance+math%C3%A9matique+et+physique+de+quelques+c%C3%A9l%C3%A8bres+g%C3%A9om%C3%A8tres+du+XVIIIe+si%C3%A8cle%2C+...&rft.pages=51&rft.date=1846-01&rft.aulast=Libri&rft.aufirst=Gugliemo&rft_id=http%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k57253t%2Ff52.image.langEN&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=22" title="Edit section: Sources">edit</a>]</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-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCalinger1996" class="citation journal cs1">Calinger, Ronald (1996). <a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fhmat.1996.0015">"Leonhard Euler: The First St. Petersburg Years (1727–1741)"</a>. <a href="/wiki/Historia_Mathematica" title="Historia Mathematica">Historia Mathematica</a>. 23 (2): 121–166. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fhmat.1996.0015">10.1006/hmat.1996.0015</a>.</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=Leonhard+Euler%3A+The+First+St.+Petersburg+Years+%281727%E2%80%931741%29&rft.volume=23&rft.issue=2&rft.pages=121-166&rft.date=1996&rft_id=info%3Adoi%2F10.1006%2Fhmat.1996.0015&rft.aulast=Calinger&rft.aufirst=Ronald&rft_id=https%3A%2F%2Fdoi.org%2F10.1006%252Fhmat.1996.0015&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCalinger2016" class="citation book cs1">Calinger, Ronald (2016). <a rel="nofollow" class="external text" href="http://press.princeton.edu/titles/10531.html">Leonhard Euler: Mathematical Genius in the Enlightenment</a>. <a href="/wiki/Princeton_University_Press" title="Princeton University Press">Princeton University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-11927-4" title="Special:BookSources/978-0-691-11927-4"><bdi>978-0-691-11927-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170713153106/http://press.princeton.edu/titles/10531.html">Archived</a> from the original on 13 July 2017. Retrieved 4 January 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Leonhard+Euler%3A+Mathematical+Genius+in+the+Enlightenment&rft.pub=Princeton+University+Press&rft.date=2016&rft.isbn=978-0-691-11927-4&rft.aulast=Calinger&rft.aufirst=Ronald&rft_id=http%3A%2F%2Fpress.princeton.edu%2Ftitles%2F10531.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunham1999" class="citation book cs1"><a href="/wiki/William_Dunham_(mathematician)" title="William Dunham (mathematician)">Dunham, William</a> (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=uKOVNvGOkhQC">Euler: The Master of Us All</a>. Dolciani Mathematical Expositions. Vol. 22. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-328-3" title="Special:BookSources/978-0-88385-328-3"><bdi>978-0-88385-328-3</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210613213855/https://books.google.com/books?id=uKOVNvGOkhQC">Archived</a> from the original on 13 June 2021. Retrieved 12 November 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Euler%3A+The+Master+of+Us+All&rft.series=Dolciani+Mathematical+Expositions&rft.pub=Mathematical+Association+of+America&rft.date=1999&rft.isbn=978-0-88385-328-3&rft.aulast=Dunham&rft.aufirst=William&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DuKOVNvGOkhQC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEuler1739" class="citation book cs1 cs1-prop-foreign-lang-source"><a class="mw-selflink selflink">Euler, Leonhard</a> (1739). <a rel="nofollow" class="external text" href="https://scholarlycommons.pacific.edu/euler-works/33/">Tentamen novae theoriae musicae</a> [An attempt at a new theory of music, exposed in all clearness, according to the most well-founded principles of harmony] (in Latin). St. Petersburg: <a href="/wiki/Russian_Academy_of_Sciences" title="Russian Academy of Sciences">Imperial Academy of Sciences</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210612225827/https://scholarlycommons.pacific.edu/euler-works/33/">Archived</a> from the original on 12 June 2021. Retrieved 12 June 2021 – via Euler archive.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Tentamen+novae+theoriae+musicae&rft.place=St.+Petersburg&rft.pub=Imperial+Academy+of+Sciences&rft.date=1739&rft.aulast=Euler&rft.aufirst=Leonhard&rft_id=https%3A%2F%2Fscholarlycommons.pacific.edu%2Feuler-works%2F33%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFerraro2008" class="citation book cs1">Ferraro, Giovanni (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vLBJSmA9zgAC">The Rise and Development of the Theory of Series up to the Early 1820s</a>. <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer Science+Business Media</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-73467-5" title="Special:BookSources/978-0-387-73467-5"><bdi>978-0-387-73467-5</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210529072644/https://books.google.com/books?id=vLBJSmA9zgAC">Archived</a> from the original on 29 May 2021. Retrieved 27 May 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Rise+and+Development+of+the+Theory+of+Series+up+to+the+Early+1820s&rft.pub=Springer+Science%2BBusiness+Media&rft.date=2008&rft.isbn=978-0-387-73467-5&rft.aulast=Ferraro&rft.aufirst=Giovanni&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DvLBJSmA9zgAC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGekkerEuler2007" class="citation book cs1">Gekker, I. R.; Euler, A. A. (2007). "Leonhard Euler's family and descendants". In <a href="/wiki/Nikolay_Bogolyubov" title="Nikolay Bogolyubov">Bogolyubov, Nikolaĭ Nikolaevich</a>; Mikhaĭlov, G. K.; <a href="/wiki/Adolph_P._Yushkevich" title="Adolph P. Yushkevich">Yushkevich, Adolph Pavlovich</a> (eds.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Ta9bz1wv79AC">Euler and Modern Science</a>. Translated by Robert Burns. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-564-5" title="Special:BookSources/978-0-88385-564-5"><bdi>978-0-88385-564-5</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160518041806/https://books.google.com/books?id=Ta9bz1wv79AC">Archived</a> from the original on 18 May 2016. Retrieved 12 November 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Leonhard+Euler%27s+family+and+descendants&rft.btitle=Euler+and+Modern+Science&rft.pub=Mathematical+Association+of+America&rft.date=2007&rft.isbn=978-0-88385-564-5&rft.aulast=Gekker&rft.aufirst=I.+R.&rft.au=Euler%2C+A.+A.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DTa9bz1wv79AC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGautschi2008" class="citation journal cs1"><a href="/wiki/Walter_Gautschi" title="Walter Gautschi">Gautschi, Walter</a> (2008). "Leonhard Euler: His Life, the Man, and His Works". <a href="/wiki/SIAM_Review" class="mw-redirect" title="SIAM Review">SIAM Review</a>. 50 (1): 3–33. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008SIAMR..50....3G">2008SIAMR..50....3G</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.177.8766">10.1.1.177.8766</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2F070702710">10.1137/070702710</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0036-1445">0036-1445</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/20454060">20454060</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SIAM+Review&rft.atitle=Leonhard+Euler%3A+His+Life%2C+the+Man%2C+and+His+Works&rft.volume=50&rft.issue=1&rft.pages=3-33&rft.date=2008&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F20454060%23id-name%3DJSTOR&rft_id=info%3Abibcode%2F2008SIAMR..50....3G&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.177.8766%23id-name%3DCiteSeerX&rft.issn=0036-1445&rft_id=info%3Adoi%2F10.1137%2F070702710&rft.aulast=Gautschi&rft.aufirst=Walter&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrattan-Guinness2005" class="citation book cs1"><a href="/wiki/Ivor_Grattan-Guinness" title="Ivor Grattan-Guinness">Grattan-Guinness, Ivor</a>, ed. (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UdGBy8iLpocC">Landmark Writings in Western Mathematics 1640–1940</a>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-045744-4" title="Special:BookSources/978-0-08-045744-4"><bdi>978-0-08-045744-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Landmark+Writings+in+Western+Mathematics+1640%E2%80%931940&rft.pub=Elsevier&rft.date=2005&rft.isbn=978-0-08-045744-4&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUdGBy8iLpocC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRicheson2012" class="citation book cs1"><a href="/wiki/David_Richeson" title="David Richeson">Richeson, David S.</a> (2012). <a href="/wiki/Euler%27s_Gem" title="Euler's Gem">Euler's Gem: The Polyhedron Formula and the Birth of Topology</a>. <a href="/wiki/Princeton_University_Press" title="Princeton University Press">Princeton University Press</a>. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=KUYLhOVkaV4C&pg=PA17">p. 17</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4008-3856-1" title="Special:BookSources/978-1-4008-3856-1"><bdi>978-1-4008-3856-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Euler%27s+Gem%3A+The+Polyhedron+Formula+and+the+Birth+of+Topology&rft.pages=p.+17&rft.pub=Princeton+University+Press&rft.date=2012&rft.isbn=978-1-4008-3856-1&rft.aulast=Richeson&rft.aufirst=David+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=23" title="Edit section: Further reading">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239549316"><div class="refbegin refbegin-columns references-column-width" style="column-width: 60em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBradleyD'AntonioSandifer2007" class="citation book cs1">Bradley, Robert E.; D'Antonio, Lawrence A.; Sandifer, Charles Edward (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=tK_KRmTf9nUC">Euler at 300: An Appreciation</a>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-565-2" title="Special:BookSources/978-0-88385-565-2"><bdi>978-0-88385-565-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Euler+at+300%3A+An+Appreciation&rft.pub=Mathematical+Association+of+America&rft.date=2007&rft.isbn=978-0-88385-565-2&rft.aulast=Bradley&rft.aufirst=Robert+E.&rft.au=D%27Antonio%2C+Lawrence+A.&rft.au=Sandifer%2C+Charles+Edward&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DtK_KRmTf9nUC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBradleySandifer2007" class="citation book cs1">Bradley, Robert E.; Sandifer, Charles Edward, eds. (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=75vJL_Y-PvsC">Leonhard Euler: Life, Work and Legacy</a>. Studies in the History and Philosophy of Mathematics. Vol. 5. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-52728-8" title="Special:BookSources/978-0-444-52728-8"><bdi>978-0-444-52728-8</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210619153753/https://books.google.com/books?id=75vJL_Y-PvsC">Archived</a> from the original on 19 June 2021. Retrieved 8 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Leonhard+Euler%3A+Life%2C+Work+and+Legacy&rft.series=Studies+in+the+History+and+Philosophy+of+Mathematics&rft.pub=Elsevier&rft.date=2007&rft.isbn=978-0-444-52728-8&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D75vJL_Y-PvsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunham2007" class="citation book cs1"><a href="/wiki/William_Dunham_(mathematician)" title="William Dunham (mathematician)">Dunham, William</a> (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=A6by_UpQikIC">The Genius of Euler: Reflections on his Life and Work</a>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-558-4" title="Special:BookSources/978-0-88385-558-4"><bdi>978-0-88385-558-4</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+Genius+of+Euler%3A+Reflections+on+his+Life+and+Work&rft.pub=Mathematical+Association+of+America&rft.date=2007&rft.isbn=978-0-88385-558-4&rft.aulast=Dunham&rft.aufirst=William&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DA6by_UpQikIC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHascherPapadopoulos2015" class="citation book cs1 cs1-prop-foreign-lang-source">Hascher, Xavier; Papadopoulos, Athanase, eds. (2015). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=KVcGrgEACAAJ">Leonhard Euler : Mathématicien, physicien et théoricien de la musique</a> (in French). Paris: CNRS Editions. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-2-271-08331-9" title="Special:BookSources/978-2-271-08331-9"><bdi>978-2-271-08331-9</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210608215959/https://books.google.com/books?id=KVcGrgEACAAJ">Archived</a> from the original on 8 June 2021. Retrieved 8 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Leonhard+Euler+%3A+Math%C3%A9maticien%2C+physicien+et+th%C3%A9oricien+de+la+musique&rft.place=Paris&rft.pub=CNRS+Editions&rft.date=2015&rft.isbn=978-2-271-08331-9&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DKVcGrgEACAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSandifer2007" class="citation book cs1">Sandifer, C. Edward (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=CvBxLr_0uBQC">The Early Mathematics of Leonhard Euler</a>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-559-1" title="Special:BookSources/978-0-88385-559-1"><bdi>978-0-88385-559-1</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+Early+Mathematics+of+Leonhard+Euler&rft.pub=Mathematical+Association+of+America&rft.date=2007&rft.isbn=978-0-88385-559-1&rft.aulast=Sandifer&rft.aufirst=C.+Edward&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DCvBxLr_0uBQC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSandifer2007" class="citation book cs1">Sandifer, C. Edward (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=sohHs7ExOsYC">How Euler Did It</a>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-563-8" title="Special:BookSources/978-0-88385-563-8"><bdi>978-0-88385-563-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=How+Euler+Did+It&rft.pub=Mathematical+Association+of+America&rft.date=2007&rft.isbn=978-0-88385-563-8&rft.aulast=Sandifer&rft.aufirst=C.+Edward&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DsohHs7ExOsYC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSandifer2015" class="citation book cs1">Sandifer, C. Edward (2015). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3c6iBQAAQBAJ">How Euler Did Even More</a>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-584-3" title="Special:BookSources/978-0-88385-584-3"><bdi>978-0-88385-584-3</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210616065630/https://books.google.com/books?id=3c6iBQAAQBAJ">Archived</a> from the original on 16 June 2021. Retrieved 8 June 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=How+Euler+Did+Even+More&rft.pub=Mathematical+Association+of+America&rft.date=2015&rft.isbn=978-0-88385-584-3&rft.aulast=Sandifer&rft.aufirst=C.+Edward&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D3c6iBQAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchattschneider1983" class="citation journal cs1"><a href="/wiki/Doris_Schattschneider" title="Doris Schattschneider">Schattschneider, Doris</a>, ed. (November 1983). "A Tribute to Leonhard Euler 1707–1783 (special issue)". <a href="/wiki/Mathematics_Magazine" title="Mathematics Magazine">Mathematics Magazine</a>. 56 (5). <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/i326726">i326726</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematics+Magazine&rft.atitle=A+Tribute+to+Leonhard+Euler+1707%E2%80%931783+%28special+issue%29&rft.volume=56&rft.issue=5&rft.date=1983-11&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2Fi326726%23id-name%3DJSTOR&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Leonhard_Euler&action=edit&section=24" title="Edit section: External links">edit</a>]</div> <style 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sistersitebox plainlinks"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-abovebelow"> Leonhard Euler at Wikipedia's <a href="/wiki/Wikipedia:Wikimedia_sister_projects" title="Wikipedia:Wikimedia sister projects">sister projects</a></div> <div class="side-box-flex"> <div class="side-box-text plainlist"><ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="20" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /><a href="https://commons.wikimedia.org/wiki/Leonhard_Euler" class="extiw" title="c:Leonhard Euler">Media</a> from Commons</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/23px-Wikiquote-logo.svg.png" decoding="async" width="23" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/35px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/46px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /><a href="https://en.wikiquote.org/wiki/Leonhard_Euler" class="extiw" title="q:Leonhard Euler">Quotations</a> from Wikiquote</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/26px-Wikisource-logo.svg.png" decoding="async" width="26" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/39px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/51px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /><a href="https://en.wikisource.org/wiki/Author:Leonhard_Euler" class="extiw" title="s:Author:Leonhard Euler">Texts</a> from Wikisource</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/27px-Wikidata-logo.svg.png" decoding="async" width="27" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/41px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/54px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /><a href="https://www.wikidata.org/wiki/q7604" class="extiw" title="d:q7604">Data</a> from Wikidata</li></ul></div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=38586">Leonhard Euler</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://eulerarchive.maa.org/">The Euler Archive</a>: Composition of Euler works with translations into English</li> <li><a rel="nofollow" class="external text" href="http://lettre.digital/euler/">Opera-Bernoulli-Euler</a> (compiled works of Euler, Bernoulli family, and contemporary peers)</li> <li><a rel="nofollow" class="external text" href="http://www.euler-2007.ch/en/index.htm">Euler Tercentenary 2007</a></li> <li><a rel="nofollow" class="external text" href="http://www.eulersociety.org/">The Euler Society</a></li> <li><a rel="nofollow" class="external text" href="https://euler.bbaw.de/">Euleriana</a> at the <a href="/wiki/Berlin-Brandenburg_Academy_of_Sciences_and_Humanities" title="Berlin-Brandenburg Academy of Sciences and Humanities">Berlin-Brandenburg Academy of Sciences and Humanities</a></li> <li><a rel="nofollow" class="external text" href="http://www.math.dartmouth.edu/~euler/historica/family-tree.html">Euler Family Tree</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110518054936/http://friedrich.uni-trier.de/oeuvres/20/219/">Euler's Correspondence with Frederick the Great, King of Prussia</a></li> <li><a rel="nofollow" class="external text" href="https://librivox.org/author/12395">Works by Leonhard Euler</a> at <a href="/wiki/LibriVox" title="LibriVox">LibriVox</a> (public domain audiobooks) <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/15px-Speaker_Icon.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/23px-Speaker_Icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/30px-Speaker_Icon.svg.png 2x" data-file-width="500" data-file-height="500" /></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs1">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a> <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Euler.html">"Leonhard Euler"</a>. <a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a>. <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=Leonhard+Euler&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%2FEuler.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunham2009" class="citation web cs1"><a href="/wiki/William_Dunham_(mathematician)" title="William Dunham (mathematician)">Dunham, William</a> (24 September 2009). <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=h-DV26x6n_Q">"An Evening with Leonhard Euler"</a>. YouTube. <a href="/wiki/Muhlenberg_College" title="Muhlenberg College">Muhlenberg College</a>: philoctetesctr (published 9 November 2009).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=YouTube&rft.atitle=An+Evening+with+Leonhard+Euler&rft.date=2009-09-24&rft.aulast=Dunham&rft.aufirst=William&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3Dh-DV26x6n_Q&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"> (talk given by <a href="/wiki/William_Dunham_(mathematician)" title="William Dunham (mathematician)">William Dunham</a> at )</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunham2008" class="citation web cs1">Dunham, William (14 October 2008). <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=fEWj93XjON0">"A Tribute to Euler – William Dunham"</a>. YouTube. Muhlenberg College: PoincareDuality (published 23 November 2011).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=YouTube&rft.atitle=A+Tribute+to+Euler+%E2%80%93+William+Dunham&rft.date=2008-10-14&rft.aulast=Dunham&rft.aufirst=William&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DfEWj93XjON0&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALeonhard+Euler" class="Z3988"></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output 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class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Leonhard_Euler" title="Template:Leonhard Euler"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Leonhard_Euler" title="Template talk:Leonhard Euler"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Leonhard_Euler" title="Special:EditPage/Template:Leonhard Euler"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Leonhard_Euler" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Leonhard Euler</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Euler%E2%80%93Lagrange_equation" title="Euler–Lagrange equation">Euler–Lagrange equation</a></li> <li><a href="/wiki/Euler%E2%80%93Lotka_equation" title="Euler–Lotka equation">Euler–Lotka equation</a></li> <li><a href="/wiki/Euler%E2%80%93Maclaurin_formula" title="Euler–Maclaurin formula">Euler–Maclaurin formula</a></li> <li><a href="/wiki/Euler%E2%80%93Maruyama_method" title="Euler–Maruyama method">Euler–Maruyama method</a></li> <li><a href="/wiki/Euler%E2%80%93Mascheroni_constant" class="mw-redirect" title="Euler–Mascheroni constant">Euler–Mascheroni constant</a></li> <li><a href="/wiki/Euler%E2%80%93Poisson%E2%80%93Darboux_equation" title="Euler–Poisson–Darboux equation">Euler–Poisson–Darboux equation</a></li> <li><a href="/wiki/Euler%E2%80%93Rodrigues_formula" title="Euler–Rodrigues formula">Euler–Rodrigues formula</a></li> <li><a href="/wiki/Euler%E2%80%93Tricomi_equation" title="Euler–Tricomi equation">Euler–Tricomi equation</a></li> <li><a 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theorem">Euler's theorem</a></li> <li><a href="/wiki/Euler_equations_(fluid_dynamics)" title="Euler equations (fluid dynamics)">Euler equations (fluid dynamics)</a></li> <li><a href="/wiki/Euler_function" title="Euler function">Euler function</a></li> <li><a href="/wiki/Euler_method" title="Euler method">Euler method</a></li> <li><a href="/wiki/Euler_numbers" title="Euler numbers">Euler numbers</a></li> <li><a href="/wiki/Euler_number_(physics)" title="Euler number (physics)">Euler number (physics)</a></li> <li><a href="/wiki/Euler%E2%80%93Bernoulli_beam_theory" title="Euler–Bernoulli beam theory">Euler–Bernoulli beam theory</a></li> <li><a href="/wiki/List_of_things_named_after_Leonhard_Euler" class="mw-redirect" title="List of things named after Leonhard Euler">Namesakes</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" 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title="Criticism of nonstandard analysis">Criticism of nonstandard analysis</a></li> <li><a href="/wiki/The_Analyst" title="The Analyst">The Analyst</a></li> <li><a href="/wiki/The_Method_of_Mechanical_Theorems" title="The Method of Mechanical Theorems">The Method of Mechanical Theorems</a></li> <li><a href="/wiki/Cavalieri%27s_principle" title="Cavalieri's principle">Cavalieri's principle</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><a href="/wiki/File:German_integral.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/German_integral.gif/50px-German_integral.gif" decoding="async" width="50" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/German_integral.gif/75px-German_integral.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/b/b5/German_integral.gif 2x" data-file-width="84" data-file-height="155" /></a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related branches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nonstandard_analysis" title="Nonstandard analysis">Nonstandard analysis</a></li> <li><a href="/wiki/Nonstandard_calculus" title="Nonstandard calculus">Nonstandard calculus</a></li> <li><a href="/wiki/Internal_set_theory" title="Internal set theory">Internal set theory</a></li> <li><a href="/wiki/Synthetic_differential_geometry" title="Synthetic differential geometry">Synthetic differential geometry</a></li> <li><a href="/wiki/Smooth_infinitesimal_analysis" title="Smooth infinitesimal analysis">Smooth infinitesimal analysis</a></li> <li><a href="/wiki/Constructive_nonstandard_analysis" title="Constructive nonstandard analysis">Constructive nonstandard analysis</a></li> <li><a href="/wiki/Infinitesimal_strain_theory" title="Infinitesimal strain theory">Infinitesimal strain theory (physics)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formalizations</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Differential_(mathematics)" title="Differential (mathematics)">Differentials</a></li> <li><a href="/wiki/Hyperreal_number" title="Hyperreal number">Hyperreal numbers</a></li> <li><a href="/wiki/Dual_number" title="Dual number">Dual numbers</a></li> <li><a href="/wiki/Surreal_number" title="Surreal number">Surreal numbers</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Individual concepts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Standard_part_function" title="Standard part function">Standard part function</a></li> <li><a href="/wiki/Transfer_principle" title="Transfer principle">Transfer principle</a></li> <li><a href="/wiki/Hyperinteger" title="Hyperinteger">Hyperinteger</a></li> <li><a href="/wiki/Increment_theorem" title="Increment theorem">Increment theorem</a></li> <li><a href="/wiki/Monad_(nonstandard_analysis)" title="Monad (nonstandard analysis)">Monad</a></li> <li><a href="/wiki/Internal_set" title="Internal set">Internal set</a></li> <li><a href="/wiki/Levi-Civita_field" title="Levi-Civita field">Levi-Civita field</a></li> <li><a href="/wiki/Hyperfinite_set" title="Hyperfinite set">Hyperfinite set</a></li> <li><a href="/wiki/Law_of_continuity" title="Law of continuity">Law of continuity</a></li> <li><a href="/wiki/Overspill" title="Overspill">Overspill</a></li> <li><a href="/wiki/Microcontinuity" title="Microcontinuity">Microcontinuity</a></li> <li><a href="/wiki/Transcendental_law_of_homogeneity" title="Transcendental law of homogeneity">Transcendental law of homogeneity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematicians</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a></li> <li><a href="/wiki/Abraham_Robinson" title="Abraham Robinson">Abraham Robinson</a></li> <li><a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Augustin-Louis Cauchy</a></li> <li><a class="mw-selflink selflink">Leonhard Euler</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Textbooks</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;font-style:italic;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Analyse_des_Infiniment_Petits_pour_l%27Intelligence_des_Lignes_Courbes" title="Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes">Analyse des Infiniment Petits</a></li> <li><a href="/wiki/Elementary_Calculus:_An_Infinitesimal_Approach" title="Elementary Calculus: An Infinitesimal Approach">Elementary Calculus</a></li> <li><a href="/wiki/Cours_d%27Analyse" title="Cours d'Analyse">Cours d'Analyse</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Differential_equations" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Differential_equations_topics" title="Template:Differential equations topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Differential_equations_topics" title="Template talk:Differential equations topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Differential_equations_topics" title="Special:EditPage/Template:Differential equations topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Differential_equations" style="font-size:114%;margin:0 4em"><a href="/wiki/Differential_equation" title="Differential equation">Differential equations</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Classification</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Operations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Differential_operator" title="Differential operator">Differential operator</a></li> <li><a href="/wiki/Notation_for_differentiation" title="Notation for differentiation">Notation for differentiation</a></li> <li><a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">Ordinary</a></li> <li><a href="/wiki/Partial_differential_equation" title="Partial differential equation">Partial</a></li> <li><a href="/wiki/Differential-algebraic_system_of_equations" title="Differential-algebraic system of equations">Differential-algebraic</a></li> <li><a href="/wiki/Integro-differential_equation" title="Integro-differential equation">Integro-differential</a></li> <li><a href="/wiki/Fractional_differential_equations" class="mw-redirect" title="Fractional differential equations">Fractional</a></li> <li><a href="/wiki/Linear_differential_equation" title="Linear differential equation">Linear</a></li> <li><a href="/wiki/Non-linear_differential_equation" class="mw-redirect" title="Non-linear differential equation">Non-linear</a></li> <li><a href="/wiki/Holonomic_function" title="Holonomic function">Holonomic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Attributes of variables</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dependent_and_independent_variables" title="Dependent and independent variables">Dependent and independent variables</a></li> <li><a href="/wiki/Homogeneous_differential_equation" title="Homogeneous differential equation">Homogeneous</a></li> <li><a href="/wiki/Non-homogeneous_differential_equation" class="mw-redirect" title="Non-homogeneous differential equation">Nonhomogeneous</a></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Coupled</a></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Decoupled</a></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Order</a></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Degree</a></li> <li><a href="/wiki/Autonomous_system_(mathematics)" title="Autonomous system (mathematics)">Autonomous</a></li> <li><a href="/wiki/Exact_differential_equation" title="Exact differential equation">Exact differential equation</a></li> <li><a href="/wiki/Jet_bundle#Partial_differential_equations" title="Jet bundle">On jet bundles</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Relation to processes</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Difference_equation" class="mw-redirect" title="Difference equation">Difference</a> (discrete analogue)</li> <li><a href="/wiki/Stochastic_differential_equation" title="Stochastic differential equation">Stochastic</a> <ul><li><a href="/wiki/Stochastic_partial_differential_equation" title="Stochastic partial differential equation">Stochastic partial</a></li></ul></li> <li><a href="/wiki/Delay_differential_equation" title="Delay differential equation">Delay</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Solutions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Existence/uniqueness</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem" title="Picard–Lindelöf theorem">Picard–Lindelöf theorem</a></li> <li><a href="/wiki/Peano_existence_theorem" title="Peano existence theorem">Peano existence theorem</a></li> <li><a href="/wiki/Carath%C3%A9odory%27s_existence_theorem" title="Carathéodory's existence theorem">Carathéodory's existence theorem</a></li> <li><a href="/wiki/Cauchy%E2%80%93Kowalevski_theorem" class="mw-redirect" title="Cauchy–Kowalevski theorem">Cauchy–Kowalevski theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Solution topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wronskian" title="Wronskian">Wronskian</a></li> <li><a href="/wiki/Phase_portrait" title="Phase portrait">Phase portrait</a></li> <li><a href="/wiki/Phase_space" title="Phase space">Phase space</a></li> <li><a href="/wiki/Lyapunov_stability" title="Lyapunov stability">Lyapunov stability</a></li> <li><a href="/wiki/Asymptotic_stability" class="mw-redirect" title="Asymptotic stability">Asymptotic stability</a></li> <li><a href="/wiki/Exponential_stability" title="Exponential stability">Exponential stability</a></li> <li><a href="/wiki/Rate_of_convergence" title="Rate of convergence">Rate of convergence</a></li> <li><a href="/wiki/Power_series_solution_of_differential_equations" title="Power series solution of differential equations">Series solutions</a></li> <li><a href="/wiki/Integral" title="Integral">Integral</a> solutions</li> <li><a href="/wiki/Numerical_integration" title="Numerical integration">Numerical integration</a></li> <li><a href="/wiki/Dirac_delta_function" title="Dirac delta function">Dirac delta function</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Solution methods</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_mathematical_jargon#Proof_techniques" class="mw-redirect" title="List of mathematical jargon">Inspection</a></li> <li><a href="/wiki/Integration_by_substitution" title="Integration by substitution">Substitution</a></li> <li><a href="/wiki/Separation_of_variables" title="Separation of variables">Separation of variables</a></li> <li><a href="/wiki/Method_of_undetermined_coefficients" title="Method of undetermined coefficients">Method of undetermined coefficients</a></li> <li><a href="/wiki/Variation_of_parameters" title="Variation of parameters">Variation of parameters</a></li> <li><a href="/wiki/Integrating_factor" title="Integrating factor">Integrating factor</a></li> <li><a href="/wiki/Integral_transform" title="Integral transform">Integral transforms</a></li> <li><a href="/wiki/Euler_method" title="Euler method">Euler method</a></li> <li><a href="/wiki/Finite_difference_method" title="Finite difference method">Finite difference method</a></li> <li><a href="/wiki/Crank%E2%80%93Nicolson_method" title="Crank–Nicolson method">Crank–Nicolson method</a></li> <li><a href="/wiki/Runge%E2%80%93Kutta_methods" title="Runge–Kutta methods">Runge–Kutta methods</a></li> <li><a href="/wiki/Finite_element_method" title="Finite element method">Finite element method</a></li> <li><a href="/wiki/Finite_volume_method" title="Finite volume method">Finite volume method</a></li> <li><a href="/wiki/Galerkin_method" title="Galerkin method">Galerkin method</a></li> <li><a href="/wiki/Perturbation_theory" title="Perturbation theory">Perturbation theory</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Examples</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_named_differential_equations" title="List of named differential equations">List of named differential equations</a></li> <li><a href="/wiki/List_of_linear_ordinary_differential_equations" title="List of linear ordinary differential equations">List of linear ordinary differential equations</a></li> <li><a href="/wiki/List_of_nonlinear_ordinary_differential_equations" title="List of nonlinear ordinary differential equations">List of nonlinear ordinary differential equations</a></li> <li><a href="/wiki/List_of_nonlinear_partial_differential_equations" title="List of nonlinear partial differential equations">List of nonlinear partial differential equations</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematicians</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a></li> <li><a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a></li> <li><a class="mw-selflink selflink">Leonhard Euler</a></li> <li><a href="/wiki/Jacob_Bernoulli" title="Jacob Bernoulli">Jacob Bernoulli</a></li> <li><a href="/wiki/%C3%89mile_Picard" title="Émile Picard">Émile Picard</a></li> <li><a href="/wiki/J%C3%B3zef_Maria_Hoene-Wro%C5%84ski" title="Józef Maria Hoene-Wroński">Józef Maria Hoene-Wroński</a></li> <li><a href="/wiki/Ernst_Leonard_Lindel%C3%B6f" title="Ernst Leonard Lindelöf">Ernst Lindelöf</a></li> <li><a href="/wiki/Rudolf_Lipschitz" title="Rudolf Lipschitz">Rudolf Lipschitz</a></li> <li><a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Joseph-Louis Lagrange</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Augustin-Louis Cauchy</a></li> <li><a href="/wiki/John_Crank" title="John Crank">John Crank</a></li> <li><a href="/wiki/Phyllis_Nicolson" title="Phyllis Nicolson">Phyllis Nicolson</a></li> <li><a href="/wiki/Carl_David_Tolm%C3%A9_Runge" class="mw-redirect" title="Carl David Tolmé Runge">Carl David Tolmé Runge</a></li> <li><a href="/wiki/Martin_Kutta" title="Martin Kutta">Martin Kutta</a></li> <li><a href="/wiki/Sofya_Kovalevskaya" title="Sofya Kovalevskaya">Sofya Kovalevskaya</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Calculus" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Calculus_topics" title="Template:Calculus topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Calculus_topics" title="Template talk:Calculus topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Calculus_topics" title="Special:EditPage/Template:Calculus topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Calculus" style="font-size:114%;margin:0 4em"><a href="/wiki/Calculus" title="Calculus">Calculus</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Precalculus" title="Precalculus">Precalculus</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Binomial_theorem" title="Binomial theorem">Binomial theorem</a></li> <li><a href="/wiki/Concave_function" title="Concave function">Concave function</a></li> <li><a href="/wiki/Continuous_function" title="Continuous function">Continuous function</a></li> <li><a href="/wiki/Factorial" title="Factorial">Factorial</a></li> <li><a href="/wiki/Finite_difference" title="Finite difference">Finite difference</a></li> <li><a href="/wiki/Free_variables_and_bound_variables" title="Free variables and bound variables">Free variables and bound variables</a></li> <li><a href="/wiki/Graph_of_a_function" title="Graph of a function">Graph of a function</a></li> <li><a href="/wiki/Linear_function" title="Linear function">Linear function</a></li> <li><a href="/wiki/Radian" title="Radian">Radian</a></li> <li><a href="/wiki/Rolle%27s_theorem" title="Rolle's theorem">Rolle's theorem</a></li> <li><a href="/wiki/Secant_line" title="Secant line">Secant</a></li> <li><a href="/wiki/Slope" title="Slope">Slope</a></li> <li><a href="/wiki/Tangent" title="Tangent">Tangent</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">Limits</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Indeterminate_form" title="Indeterminate form">Indeterminate form</a></li> <li><a href="/wiki/Limit_of_a_function" title="Limit of a function">Limit of a function</a> <ul><li><a href="/wiki/One-sided_limit" title="One-sided limit">One-sided limit</a></li></ul></li> <li><a href="/wiki/Limit_of_a_sequence" title="Limit of a sequence">Limit of a sequence</a></li> <li><a href="/wiki/Order_of_approximation" title="Order of approximation">Order of approximation</a></li> <li><a href="/wiki/(%CE%B5,_%CE%B4)-definition_of_limit" class="mw-redirect" title="(ε, δ)-definition of limit">(ε, δ)-definition of limit</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Differential_calculus" title="Differential calculus">Differential calculus</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Derivative" title="Derivative">Derivative</a></li> <li><a href="/wiki/Second_derivative" title="Second derivative">Second derivative</a></li> <li><a href="/wiki/Partial_derivative" title="Partial derivative">Partial derivative</a></li> <li><a href="/wiki/Differential_(mathematics)" title="Differential (mathematics)">Differential</a></li> <li><a href="/wiki/Differential_operator" title="Differential operator">Differential operator</a></li> <li><a href="/wiki/Mean_value_theorem" title="Mean value theorem">Mean value theorem</a></li> <li><a href="/wiki/Notation_for_differentiation" title="Notation for differentiation">Notation</a> <ul><li><a href="/wiki/Leibniz%27s_notation" title="Leibniz's notation">Leibniz's notation</a></li> <li><a href="/wiki/Newton%27s_notation_for_differentiation" class="mw-redirect" title="Newton's notation for differentiation">Newton's notation</a></li></ul></li> <li><a href="/wiki/Differentiation_rules" title="Differentiation rules">Rules of differentiation</a> <ul><li><a href="/wiki/Linearity_of_differentiation" title="Linearity of differentiation">linearity</a></li> <li><a href="/wiki/Power_rule" title="Power rule">Power</a></li> <li><a href="/wiki/Sum_rule_in_differentiation" class="mw-redirect" title="Sum rule in differentiation">Sum</a></li> <li><a href="/wiki/Chain_rule" title="Chain rule">Chain</a></li> <li><a href="/wiki/L%27H%C3%B4pital%27s_rule" title="L'Hôpital's rule">L'Hôpital's</a></li> <li><a href="/wiki/Product_rule" title="Product rule">Product</a> <ul><li><a href="/wiki/General_Leibniz_rule" title="General Leibniz rule">General Leibniz's rule</a></li></ul></li> <li><a href="/wiki/Quotient_rule" title="Quotient rule">Quotient</a></li></ul></li> <li>Other techniques <ul><li><a href="/wiki/Implicit_differentiation" class="mw-redirect" title="Implicit differentiation">Implicit differentiation</a></li> <li><a href="/wiki/Inverse_functions_and_differentiation" class="mw-redirect" title="Inverse functions and differentiation">Inverse functions and differentiation</a></li> <li><a href="/wiki/Logarithmic_derivative" title="Logarithmic derivative">Logarithmic derivative</a></li> <li><a href="/wiki/Related_rates" title="Related rates">Related rates</a></li></ul></li> <li><a href="/wiki/Stationary_point" title="Stationary point">Stationary points</a> <ul><li><a href="/wiki/First_derivative_test" class="mw-redirect" title="First derivative test">First derivative test</a></li> <li><a href="/wiki/Second_derivative_test" class="mw-redirect" title="Second derivative test">Second derivative test</a></li> <li><a href="/wiki/Extreme_value_theorem" title="Extreme value theorem">Extreme value theorem</a></li> <li><a href="/wiki/Maximum_and_minimum" title="Maximum and minimum">Maximum and minimum</a></li></ul></li> <li>Further applications <ul><li><a href="/wiki/Newton%27s_method" title="Newton's method">Newton's method</a></li> <li><a href="/wiki/Taylor%27s_theorem" title="Taylor's theorem">Taylor's theorem</a></li></ul></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Differential equation</a> <ul><li><a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">Ordinary differential equation</a></li> <li><a href="/wiki/Partial_differential_equation" title="Partial differential equation">Partial differential equation</a></li> <li><a href="/wiki/Stochastic_differential_equation" title="Stochastic differential equation">Stochastic differential equation</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Integral_calculus" class="mw-redirect" title="Integral calculus">Integral calculus</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Antiderivative" title="Antiderivative">Antiderivative</a></li> <li><a href="/wiki/Arc_length" title="Arc length">Arc length</a></li> <li><a href="/wiki/Riemann_integral" title="Riemann integral">Riemann integral</a></li> <li><a href="/wiki/Integral#Properties" title="Integral">Basic properties</a></li> <li><a href="/wiki/Constant_of_integration" title="Constant of integration">Constant of integration</a></li> <li><a href="/wiki/Fundamental_theorem_of_calculus" title="Fundamental theorem of calculus">Fundamental theorem of calculus</a> <ul><li><a href="/wiki/Leibniz_integral_rule" title="Leibniz integral rule">Differentiating under the integral sign</a></li></ul></li> <li><a href="/wiki/Integration_by_parts" title="Integration by parts">Integration by parts</a></li> <li><a href="/wiki/Integration_by_substitution" title="Integration by substitution">Integration by substitution</a> <ul><li><a href="/wiki/Trigonometric_substitution" title="Trigonometric substitution">trigonometric</a></li> <li><a href="/wiki/Euler_substitution" title="Euler substitution">Euler</a></li> <li><a href="/wiki/Tangent_half-angle_substitution" title="Tangent half-angle substitution">Tangent half-angle substitution</a></li></ul></li> <li><a href="/wiki/Partial_fractions_in_integration" class="mw-redirect" title="Partial fractions in integration">Partial fractions in integration</a> <ul><li><a href="/wiki/Quadratic_integral" title="Quadratic integral">Quadratic integral</a></li></ul></li> <li><a href="/wiki/Trapezoidal_rule" title="Trapezoidal rule">Trapezoidal rule</a></li> <li>Volumes <ul><li><a href="/wiki/Disc_integration" title="Disc integration">Washer method</a></li> <li><a href="/wiki/Shell_integration" title="Shell integration">Shell method</a></li></ul></li> <li><a href="/wiki/Integral_equation" title="Integral equation">Integral equation</a></li> <li><a href="/wiki/Integro-differential_equation" title="Integro-differential equation">Integro-differential equation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Vector_calculus" title="Vector calculus">Vector calculus</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Derivatives <ul><li><a href="/wiki/Curl_(mathematics)" title="Curl (mathematics)">Curl</a></li> <li><a href="/wiki/Directional_derivative" title="Directional derivative">Directional derivative</a></li> <li><a href="/wiki/Divergence" title="Divergence">Divergence</a></li> <li><a href="/wiki/Gradient" title="Gradient">Gradient</a></li> <li><a href="/wiki/Laplace_operator" title="Laplace operator">Laplacian</a></li></ul></li> <li>Basic theorems <ul><li><a href="/wiki/Fundamental_Theorem_of_Line_Integrals" class="mw-redirect" title="Fundamental Theorem of Line Integrals">Line integrals</a></li> <li><a href="/wiki/Green%27s_theorem" title="Green's theorem">Green's</a></li> <li><a href="/wiki/Stokes%27_theorem" title="Stokes' theorem">Stokes'</a></li> <li><a href="/wiki/Divergence_theorem" title="Divergence theorem">Gauss'</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Multivariable_calculus" title="Multivariable calculus">Multivariable calculus</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Divergence_theorem" title="Divergence theorem">Divergence theorem</a></li> <li><a href="/wiki/Geometric_calculus" title="Geometric calculus">Geometric</a></li> <li><a href="/wiki/Hessian_matrix" title="Hessian matrix">Hessian matrix</a></li> <li><a href="/wiki/Jacobian_matrix_and_determinant" title="Jacobian matrix and determinant">Jacobian matrix and determinant</a></li> <li><a href="/wiki/Lagrange_multiplier" title="Lagrange multiplier">Lagrange multiplier</a></li> <li><a href="/wiki/Line_integral" title="Line integral">Line integral</a></li> <li><a href="/wiki/Matrix_calculus" title="Matrix calculus">Matrix</a></li> <li><a href="/wiki/Multiple_integral" title="Multiple integral">Multiple integral</a></li> <li><a href="/wiki/Partial_derivative" title="Partial derivative">Partial derivative</a></li> <li><a href="/wiki/Surface_integral" title="Surface integral">Surface integral</a></li> <li><a href="/wiki/Volume_integral" title="Volume integral">Volume integral</a></li> <li>Advanced topics <ul><li><a href="/wiki/Differential_form" title="Differential form">Differential forms</a></li> <li><a href="/wiki/Exterior_derivative" title="Exterior derivative">Exterior derivative</a></li> <li><a href="/wiki/Generalized_Stokes%27_theorem" class="mw-redirect" title="Generalized Stokes' theorem">Generalized Stokes' theorem</a></li> <li><a href="/wiki/Tensor_calculus" class="mw-redirect" title="Tensor calculus">Tensor calculus</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sequences and series</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arithmetico-geometric_sequence" title="Arithmetico-geometric sequence">Arithmetico-geometric sequence</a></li> <li>Types of series <ul><li><a href="/wiki/Alternating_series" title="Alternating series">Alternating</a></li> <li><a href="/wiki/Binomial_series" title="Binomial series">Binomial</a></li> <li><a href="/wiki/Fourier_series" title="Fourier series">Fourier</a></li> <li><a href="/wiki/Geometric_series" title="Geometric series">Geometric</a></li> <li><a href="/wiki/Harmonic_series_(mathematics)" title="Harmonic series (mathematics)">Harmonic</a></li> <li><a href="/wiki/Infinite_series" class="mw-redirect" title="Infinite series">Infinite</a></li> <li><a href="/wiki/Power_series" title="Power series">Power</a> <ul><li><a href="/wiki/Maclaurin_series" class="mw-redirect" title="Maclaurin series">Maclaurin</a></li> <li><a href="/wiki/Taylor_series" title="Taylor series">Taylor</a></li></ul></li> <li><a href="/wiki/Telescoping_series" title="Telescoping series">Telescoping</a></li></ul></li> <li>Tests of convergence <ul><li><a href="/wiki/Abel%27s_test" title="Abel's test">Abel's</a></li> <li><a href="/wiki/Alternating_series_test" title="Alternating series test">Alternating series</a></li> <li><a href="/wiki/Cauchy_condensation_test" title="Cauchy condensation test">Cauchy condensation</a></li> <li><a href="/wiki/Direct_comparison_test" title="Direct comparison test">Direct comparison</a></li> <li><a href="/wiki/Dirichlet%27s_test" title="Dirichlet's test">Dirichlet's</a></li> <li><a href="/wiki/Integral_test_for_convergence" title="Integral test for convergence">Integral</a></li> <li><a href="/wiki/Limit_comparison_test" title="Limit comparison test">Limit comparison</a></li> <li><a href="/wiki/Ratio_test" title="Ratio test">Ratio</a></li> <li><a href="/wiki/Root_test" title="Root test">Root</a></li> <li><a href="/wiki/Term_test" class="mw-redirect" title="Term test">Term</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Special functions and numbers</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bernoulli_number" title="Bernoulli number">Bernoulli numbers</a></li> <li><a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e (mathematical constant)</a></li> <li><a href="/wiki/Exponential_function" title="Exponential function">Exponential function</a></li> <li><a href="/wiki/Natural_logarithm" title="Natural logarithm">Natural logarithm</a></li> <li><a href="/wiki/Stirling%27s_approximation" title="Stirling's approximation">Stirling's approximation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/History_of_calculus" title="History of calculus">History of calculus</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adequality" title="Adequality">Adequality</a></li> <li><a href="/wiki/Brook_Taylor" title="Brook Taylor">Brook Taylor</a></li> <li><a href="/wiki/Colin_Maclaurin" title="Colin Maclaurin">Colin Maclaurin</a></li> <li><a href="/wiki/Generality_of_algebra" title="Generality of algebra">Generality of algebra</a></li> <li><a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a></li> <li><a href="/wiki/Infinitesimal" title="Infinitesimal">Infinitesimal</a></li> <li><a href="/wiki/Infinitesimal_calculus" class="mw-redirect" title="Infinitesimal calculus">Infinitesimal calculus</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a></li> <li><a href="/wiki/Fluxion" title="Fluxion">Fluxion</a></li> <li><a href="/wiki/Law_of_Continuity" class="mw-redirect" title="Law of Continuity">Law of Continuity</a></li> <li><a class="mw-selflink selflink">Leonhard Euler</a></li> <li><a href="/wiki/Method_of_Fluxions" title="Method of Fluxions">Method of Fluxions</a></li> <li><a href="/wiki/The_Method_of_Mechanical_Theorems" title="The Method of Mechanical Theorems">The Method of Mechanical Theorems</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Integrals" scope="row" class="navbox-group" style="width:1%;text-align:left"><a href="/wiki/Lists_of_integrals" title="Lists of integrals">Integrals</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_integrals_of_rational_functions" title="List of integrals of rational functions">rational functions</a></li> <li><a href="/wiki/List_of_integrals_of_irrational_functions" title="List of integrals of irrational functions">irrational functions</a></li> <li><a href="/wiki/List_of_integrals_of_exponential_functions" title="List of integrals of exponential functions">exponential functions</a></li> <li><a href="/wiki/List_of_integrals_of_logarithmic_functions" title="List of integrals of logarithmic functions">logarithmic functions</a></li> <li><a href="/wiki/List_of_integrals_of_hyperbolic_functions" title="List of integrals of hyperbolic functions">hyperbolic functions</a> <ul><li><a href="/wiki/List_of_integrals_of_inverse_hyperbolic_functions" title="List of integrals of inverse hyperbolic functions">inverse</a></li></ul></li> <li><a href="/wiki/List_of_integrals_of_trigonometric_functions" title="List of integrals of trigonometric functions">trigonometric functions</a> <ul><li><a href="/wiki/List_of_integrals_of_inverse_trigonometric_functions" title="List of integrals of inverse trigonometric functions">inverse</a></li> <li><a href="/wiki/Integral_of_the_secant_function" title="Integral of the secant function">Secant</a></li> <li><a href="/wiki/Integral_of_secant_cubed" title="Integral of secant cubed">Secant cubed</a></li></ul></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_limits" title="List of limits">List of limits</a></li> <li><a href="/wiki/Differentiation_rules" title="Differentiation rules">List of derivatives</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous topics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Complex calculus <ul><li><a href="/wiki/Contour_integral" class="mw-redirect" title="Contour integral">Contour integral</a></li></ul></li> <li>Differential geometry <ul><li><a href="/wiki/Manifold" title="Manifold">Manifold</a></li> <li><a href="/wiki/Curvature" title="Curvature">Curvature</a></li> <li><a href="/wiki/Differential_geometry_of_curves" class="mw-redirect" title="Differential geometry of curves">of curves</a></li> <li><a href="/wiki/Differential_geometry_of_surfaces" title="Differential geometry of surfaces">of surfaces</a></li> <li><a href="/wiki/Tensor" title="Tensor">Tensor</a></li></ul></li> <li><a href="/wiki/Euler%E2%80%93Maclaurin_formula" title="Euler–Maclaurin formula">Euler–Maclaurin formula</a></li> <li><a href="/wiki/Gabriel%27s_horn" title="Gabriel's horn">Gabriel's horn</a></li> <li><a href="/wiki/Integration_Bee" title="Integration Bee">Integration Bee</a></li> <li><a href="/wiki/Proof_that_22/7_exceeds_%CF%80" title="Proof that 22/7 exceeds π">Proof that 22/7 exceeds π</a></li> <li><a href="/wiki/Regiomontanus%27_angle_maximization_problem" title="Regiomontanus' angle maximization problem">Regiomontanus' angle maximization problem</a></li> <li><a href="/wiki/Steinmetz_solid" title="Steinmetz solid">Steinmetz solid</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Topics_in_continuum_mechanics" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Topics_in_continuum_mechanics" title="Template:Topics in continuum mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Topics_in_continuum_mechanics" title="Template talk:Topics in continuum mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Topics_in_continuum_mechanics" title="Special:EditPage/Template:Topics in continuum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Topics_in_continuum_mechanics" style="font-size:114%;margin:0 4em">Topics in <a href="/wiki/Continuum_mechanics" title="Continuum mechanics">continuum mechanics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Divisions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Solid_mechanics" title="Solid mechanics">Solid mechanics</a></li> <li><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a></li> <li><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></li> <li><a href="/wiki/Vibrations" class="mw-redirect" title="Vibrations">Vibrations</a></li> <li><a href="/wiki/Rigid_body_dynamics" title="Rigid body dynamics">Rigid body dynamics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Laws and Definitions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <dl><dt>Laws</dt></dl> <ul><li><a href="/wiki/Conservation_of_mass" title="Conservation of mass">Conservation of mass</a></li> <li><a href="/wiki/Momentum" title="Momentum">Conservation of momentum</a> <ul><li><a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier-Stokes</a></li> <li><a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli</a></li> <li><a href="/wiki/Poiseuille_equation" class="mw-redirect" title="Poiseuille equation">Poiseuille</a></li> <li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes</a></li> <li><a href="/wiki/Pascal%27s_law" title="Pascal's law">Pascal</a></li></ul></li> <li><a href="/wiki/Conservation_of_energy" title="Conservation of energy">Conservation of energy</a></li> <li><a href="/wiki/Clausius%E2%80%93Duhem_inequality" title="Clausius–Duhem inequality">Entropy inequality</a></li></ul> <dl><dt>Definitions</dt></dl> <ul><li><a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">Stress</a> <ul><li><a href="/wiki/Cauchy_stress_tensor" title="Cauchy stress tensor">Cauchy stress</a></li> <li><a href="/wiki/Stress_measures" class="mw-redirect" title="Stress measures">Stress measures</a></li></ul></li> <li><a href="/wiki/Deformation_(mechanics)" class="mw-redirect" title="Deformation (mechanics)">Deformation</a></li> <li><a href="/wiki/Infinitesimal_strain_theory" title="Infinitesimal strain theory">Small strain</a> <ul><li><a href="/wiki/Antiplane_shear" title="Antiplane shear">Antiplane shear</a></li></ul></li> <li><a href="/wiki/Finite_strain_theory" title="Finite strain theory">Large strain</a></li> <li><a href="/wiki/Compatibility_(mechanics)" title="Compatibility (mechanics)">Compatibility</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Solid_mechanics" title="Solid mechanics">Solid</a> and <a href="/wiki/Structural_mechanics" title="Structural mechanics">Structural mechanics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <dl><dt><a href="/wiki/Solid" title="Solid">Solids</a></dt></dl> <ul><li><a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">Elasticity</a> <ul><li><a href="/wiki/Linear_elasticity" title="Linear elasticity">linear</a></li> <li><a href="/wiki/Hooke%27s_law" title="Hooke's law">Hooke's law</a></li> <li><a href="/wiki/Transverse_isotropy" title="Transverse isotropy">Transverse isotropy</a></li> <li><a href="/wiki/Orthotropic_material" title="Orthotropic material">Orthotropy</a></li> <li><a href="/wiki/Hyperelastic_material" title="Hyperelastic material">hyperelasticity</a> <ul><li><a href="/wiki/Elasticity_of_cell_membranes" title="Elasticity of cell membranes">Membrane elasticity</a></li></ul></li> <li><a href="/wiki/Equation_of_state" title="Equation of state">Equation of state</a> <ul><li><a href="/wiki/Hugoniot_elastic_limit" class="mw-redirect" title="Hugoniot elastic limit">Hugoniot</a></li> <li><a href="/wiki/Equation_of_state#Jones–Wilkins–Lee_equation_of_state_for_explosives_(JWL_equation)" title="Equation of state">JWL</a></li></ul></li> <li><a href="/wiki/Hypoelastic_material" title="Hypoelastic material">hypoelasticity</a></li> <li><a href="/wiki/Cauchy_elastic_material" title="Cauchy elastic material">Cauchy elasticity</a></li> <li><a href="/wiki/Viscoelasticity" title="Viscoelasticity">Viscoelasticity</a> <ul><li><a href="/wiki/Creep_(deformation)" title="Creep (deformation)">Creep</a></li> <li><a href="/wiki/Creep_and_shrinkage_of_concrete" title="Creep and shrinkage of concrete">Concrete creep</a></li></ul></li></ul></li> <li><a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">Plasticity</a> <ul><li><a href="/wiki/Rock_mass_plasticity" title="Rock mass plasticity">Rock mass plasticity</a></li> <li><a href="/wiki/Viscoplasticity" title="Viscoplasticity">Viscoplasticity</a></li> <li><a href="/wiki/Yield_surface" title="Yield surface">Yield criterion</a> <ul><li><a href="/wiki/Bresler%E2%80%93Pister_yield_criterion" title="Bresler–Pister yield criterion">Bresler-Pister</a></li></ul></li></ul></li> <li><a href="/wiki/Contact_mechanics" title="Contact mechanics">Contact mechanics</a> <ul><li><a href="/wiki/Contact_mechanics" title="Contact mechanics">Frictionless</a></li> <li><a href="/wiki/Frictional_contact_mechanics" title="Frictional contact mechanics">Frictional</a></li></ul></li></ul> <dl><dt><a href="/wiki/Failure" title="Failure">Material failure theory</a></dt></dl> <ul><li><a href="/wiki/Drucker_stability" title="Drucker stability">Drucker stability</a></li> <li><a href="/wiki/Material_failure_theory" title="Material failure theory">Material failure theory</a></li> <li><a href="/wiki/Fatigue_(material)" title="Fatigue (material)">Fatigue</a></li> <li><a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture mechanics</a> <ul><li><a href="/wiki/J-integral" title="J-integral">J-integral</a></li> <li><a href="/wiki/Compact_tension_specimen" title="Compact tension specimen">Compact tension specimen</a></li></ul></li> <li><a href="/wiki/Damage_mechanics" title="Damage mechanics">Damage mechanics</a> <ul><li><a href="/wiki/Johnson-Holmquist_damage_model" class="mw-redirect" title="Johnson-Holmquist damage model">Johnson-Holmquist</a></li></ul></li></ul> <dl><dt><a href="/wiki/Structural_mechanics" title="Structural mechanics">Structures</a></dt></dl> <ul><li><a href="/wiki/Bending" title="Bending">Bending</a> <ul><li><a href="/wiki/Bending_moment" title="Bending moment">Bending moment</a></li> <li><a href="/wiki/Bending_of_plates" title="Bending of plates">Bending of plates</a></li> <li><a href="/wiki/Sandwich_theory" title="Sandwich theory">Sandwich theory</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <dl><dt><a href="/wiki/Fluid" title="Fluid">Fluids</a></dt></dl> <ul><li><a href="/wiki/Fluid_statics" class="mw-redirect" title="Fluid statics">Fluid statics</a></li> <li><a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Fluid dynamics</a></li> <li><a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a></li> <li><a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a></li> <li><a href="/wiki/Poiseuille_equation" class="mw-redirect" title="Poiseuille equation">Poiseuille equation</a></li> <li><a href="/wiki/Buoyancy" title="Buoyancy">Buoyancy</a></li> <li><a href="/wiki/Viscosity" title="Viscosity">Viscosity</a> <ul><li><a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian</a></li> <li><a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">Non-Newtonian</a></li></ul></li> <li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a></li> <li><a href="/wiki/Pascal%27s_law" title="Pascal's law">Pascal's law</a></li> <li><a href="/wiki/Pressure" title="Pressure">Pressure</a></li> <li><a href="/wiki/Liquid" title="Liquid">Liquids</a></li> <li><a href="/wiki/Surface_tension" title="Surface tension">Surface tension</a></li> <li><a href="/wiki/Capillary_action" title="Capillary action">Capillary action</a></li></ul> <dl><dt><a href="/wiki/Gas" title="Gas">Gases</a></dt></dl> <ul><li><a href="/wiki/Atmosphere" title="Atmosphere">Atmosphere</a></li> <li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a href="/wiki/Charles%27s_law" title="Charles's law">Charles's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a></li></ul> <dl><dt><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></dt></dl> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Acoustic_theory" title="Acoustic theory">Acoustic theory</a></li> <li><a href="/wiki/Aeroacoustics" title="Aeroacoustics">Aeroacoustics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Rheology" title="Rheology">Rheology</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Viscoelasticity" title="Viscoelasticity">Viscoelasticity</a></li> <li><a href="/wiki/Smart_fluid" title="Smart fluid">Smart fluids</a> <ul><li><a href="/wiki/Magnetorheological_fluid" title="Magnetorheological fluid">Magnetorheological</a></li> <li><a href="/wiki/Electrorheological_fluid" title="Electrorheological fluid">Electrorheological</a></li> <li><a href="/wiki/Ferrofluid" title="Ferrofluid">Ferrofluids</a></li></ul></li> <li><a href="/wiki/Rheometry" title="Rheometry">Rheometry</a></li> <li><a href="/wiki/Rheometer" title="Rheometer">Rheometer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Scientist" title="Scientist">Scientists</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Robert_Boyle" title="Robert Boyle">Boyle</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li> <li><a href="/wiki/Jacques_Charles" title="Jacques Charles">Charles</a></li> <li><a class="mw-selflink selflink">Euler</a></li> <li><a href="/wiki/Joseph_Louis_Gay-Lussac" title="Joseph Louis Gay-Lussac">Gay-Lussac</a></li> <li><a href="/wiki/Robert_Hooke" title="Robert Hooke">Hooke</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Claude-Louis_Navier" title="Claude-Louis Navier">Navier</a></li> <li><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">Stokes</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Award" title="Award">Awards</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Eringen_Medal" title="Eringen Medal">Eringen Medal</a></li> <li><a href="/wiki/William_Prager_Medal" title="William Prager Medal">William Prager Medal</a></li></ul> </div></td></tr></tbody></table></div></div></td></tr></tbody></table></div> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 0}.mw-parser-output .portal-bar-related{font-size:100%;justify-content:flex-start}.mw-parser-output .portal-bar-unbordered{padding:0 1.7em;margin-left:0}.mw-parser-output .portal-bar-header{margin:0 1em 0 0.5em;flex:0 0 auto;min-height:24px}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;flex:0 1 auto;padding:0.15em 0;column-gap:1em;align-items:baseline;margin:0;list-style:none}.mw-parser-output .portal-bar-content-related{margin:0;list-style:none}.mw-parser-output .portal-bar-item{display:inline-block;margin:0.15em 0.2em;min-height:24px;line-height:24px}@media screen and 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class="portal-bar noprint metadata noviewer portal-bar-bordered" role="navigation" aria-label="Portals"><a href="/wiki/Wikipedia:Contents/Portals" title="Wikipedia:Contents/Portals">Portals</a>:<ul class="portal-bar-content"><li class="portal-bar-item"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/19px-P_vip.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/28px-P_vip.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/37px-P_vip.svg.png 2x" data-file-width="1911" data-file-height="1944" /> <a href="/wiki/Portal:Biography" title="Portal:Biography">Biography</a></li><li class="portal-bar-item"><a href="/wiki/File:Chess.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Chess.svg/19px-Chess.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Chess.svg/29px-Chess.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Chess.svg/38px-Chess.svg.png 2x" data-file-width="512" data-file-height="512" /></a> <a href="/wiki/Portal:Chess" title="Portal:Chess">Chess</a></li><li class="portal-bar-item"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/19px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/29px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/38px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a> <a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics</a></li><li class="portal-bar-item"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Arithmetic_symbols.svg/19px-Arithmetic_symbols.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Arithmetic_symbols.svg/29px-Arithmetic_symbols.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Arithmetic_symbols.svg/38px-Arithmetic_symbols.svg.png 2x" data-file-width="210" data-file-height="210" /> <a href="/wiki/Portal:Arithmetic" title="Portal:Arithmetic">Arithmetic</a></li><li class="portal-bar-item"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/17px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="17" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/26px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/34px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a> <a href="/wiki/Portal:Physics" title="Portal:Physics">Physics</a></li><li class="portal-bar-item"><a href="/wiki/File:Nuvola_apps_kcmsystem.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Nuvola_apps_kcmsystem.svg/19px-Nuvola_apps_kcmsystem.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Nuvola_apps_kcmsystem.svg/29px-Nuvola_apps_kcmsystem.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Nuvola_apps_kcmsystem.svg/38px-Nuvola_apps_kcmsystem.svg.png 2x" data-file-width="128" data-file-height="128" /></a> <a href="/wiki/Portal:Engineering" title="Portal:Engineering">Engineering</a></li><li class="portal-bar-item"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/GClef.svg/7px-GClef.svg.png" decoding="async" width="7" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/GClef.svg/10px-GClef.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/GClef.svg/14px-GClef.svg.png 2x" data-file-width="15" data-file-height="41" /> <a href="/wiki/Portal:Music" title="Portal:Music">Music</a></li><li class="portal-bar-item"><a href="/wiki/File:Nuvola_apps_kalzium.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/19px-Nuvola_apps_kalzium.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/29px-Nuvola_apps_kalzium.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/38px-Nuvola_apps_kalzium.svg.png 2x" data-file-width="128" data-file-height="128" /></a> <a href="/wiki/Portal:Science" title="Portal:Science">Science</a></li><li class="portal-bar-item"><img alt="image" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Newton%27s_reflecting_telescope.jpg/17px-Newton%27s_reflecting_telescope.jpg" decoding="async" width="17" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Newton%27s_reflecting_telescope.jpg/26px-Newton%27s_reflecting_telescope.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Newton%27s_reflecting_telescope.jpg/34px-Newton%27s_reflecting_telescope.jpg 2x" data-file-width="1140" data-file-height="1276" /> <a href="/wiki/Portal:History_of_Science" class="mw-redirect" title="Portal:History of Science">History of Science</a></li><li class="portal-bar-item"><img alt="flag" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/19px-Flag_of_Switzerland.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/29px-Flag_of_Switzerland.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/38px-Flag_of_Switzerland.svg.png 2x" data-file-width="512" data-file-height="512" /> <a href="/wiki/Portal:Switzerland" 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class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8034&url_prefix=https://opac.vatlib.it/auth/detail/&id=495/144041">Vatican</a></li><li><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007260793905171">Israel</a></li><li><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058521606606706">Catalonia</a></li><li><a rel="nofollow" class="external text" href="https://opac.kbr.be/LIBRARY/doc/AUTHORITY/16927424">Belgium</a><ul><li><a rel="nofollow" class="external text" href="https://opac.kbr.be/LIBRARY/doc/AUTHORITY/14687716">2</a></li></ul></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA01184372?l=en">CiNii</a></li><li><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=38586">Mathematics Genealogy Project</a></li><li><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:euler.leonhard">zbMATH</a></li><li><a rel="nofollow" class="external text" href="https://dblp.org/pid/07/718">DBLP</a></li><li><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/64415">MathSciNet</a></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/817527">Trove</a></li><li><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd118531379.html?language=en">Deutsche Biographie</a></li><li><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/118531379">DDB</a></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://www.idref.fr/028115481">IdRef</a></li><li><a rel="nofollow" class="external text" href="https://hls-dhs-dss.ch/fr/articles/018751">Historical Dictionary of Switzerland</a></li><li><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w66d66q0">SNAC</a></li><li><a rel="nofollow" class="external text" href="https://rism.online/people/61623">RISM</a></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Leonhard_Euler&oldid=1258980360">https://en.wikipedia.org/w/index.php?title=Leonhard_Euler&oldid=1258980360</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Leonhard_Euler" title="Category:Leonhard Euler">Leonhard Euler</a></li><li><a href="/wiki/Category:1707_births" title="Category:1707 births">1707 births</a></li><li><a href="/wiki/Category:1783_deaths" title="Category:1783 deaths">1783 deaths</a></li><li><a href="/wiki/Category:18th-century_writers_in_Latin" title="Category:18th-century writers in Latin">18th-century writers in Latin</a></li><li><a href="/wiki/Category:18th-century_male_writers" title="Category:18th-century male writers">18th-century male 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[\"CITEREFTrimbleWilliamsBracherJarrell2007\"] = 1,\n [\"CITEREFVaradarajan2006\"] = 1,\n [\"CITEREFVucinich1960\"] = 1,\n [\"CITEREFWannerHairer2005\"] = 1,\n [\"CITEREFYouschkevitch1971\"] = 1,\n [\"CITEREFŞtefănescu\"] = 1,\n}\ntemplate_list = table#1 {\n [\"-\\\"\"] = 1,\n [\"Authority control\"] = 1,\n [\"Awrap\"] = 1,\n [\"Birth date\"] = 1,\n [\"Blockquote\"] = 2,\n [\"Bracket\"] = 1,\n [\"Calculus topics\"] = 1,\n [\"Cite arXiv\"] = 1,\n [\"Cite book\"] = 57,\n [\"Cite conference\"] = 1,\n [\"Cite encyclopedia\"] = 7,\n [\"Cite journal\"] = 38,\n [\"Cite magazine\"] = 1,\n [\"Cite news\"] = 2,\n [\"Cite thesis\"] = 1,\n [\"Cite web\"] = 18,\n [\"Classical mechanics\"] = 1,\n [\"DEFAULTSORT:Euler, Leonhard\"] = 1,\n [\"Death date and age\"] = 1,\n [\"Differential equations topics\"] = 1,\n [\"E (mathematical constant)\"] = 1,\n [\"Efn\"] = 5,\n [\"Featured article\"] = 1,\n [\"Harvnb\"] = 5,\n [\"Harvtxt\"] = 1,\n [\"Hlist\"] = 2,\n [\"IPA\"] = 2,\n [\"IPAc-en\"] = 2,\n [\"Ill\"] = 1,\n [\"Infinitesimals\"] = 1,\n [\"Infobox scientist\"] = 1,\n [\"Lang\"] = 2,\n [\"Leonhard Euler\"] = 1,\n [\"Librivox author\"] = 1,\n [\"MacTutor\"] = 1,\n [\"MacTutor Biography\"] = 1,\n [\"Main\"] = 2,\n [\"Marriage\"] = 2,\n [\"Math\"] = 4,\n [\"MathGenealogy\"] = 2,\n [\"Music\"] = 1,\n [\"Navboxes\"] = 1,\n [\"Notelist\"] = 1,\n [\"Nowrap\"] = 1,\n [\"Pi\"] = 1,\n [\"Plainlist\"] = 1,\n [\"Portal bar\"] = 1,\n [\"R\"] = 2,\n [\"Redirect\"] = 1,\n [\"Refbegin\"] = 2,\n [\"Refend\"] = 2,\n [\"Reflist\"] = 1,\n [\"Respell\"] = 2,\n [\"Sfn\"] = 70,\n [\"Short description\"] = 1,\n [\"Sister project links\"] = 1,\n [\"Spaced ndash\"] = 1,\n [\"Topics in continuum mechanics\"] = 1,\n [\"Ubl\"] = 2,\n [\"Use dmy dates\"] = 1,\n [\"Webarchive\"] = 2,\n}\narticle_whitelist = table#1 {\n}\ntable#1 {\n [\"size\"] = \"tiny\",\n}\n","limitreport-profile":[["?","360","18.2"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::callParserFunction","340","17.2"],["dataWrapper \u003Cmw.lua:672\u003E","180","9.1"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::getAllExpandedArguments","140","7.1"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::gsub","120","6.1"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::find","100","5.1"],["recursiveClone \u003CmwInit.lua:45\u003E","60","3.0"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::getEntity","60","3.0"],["type","40","2.0"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::match","40","2.0"],["[others]","540","27.3"]]},"cachereport":{"origin":"mw-web.codfw.main-f69cdc8f6-qdh76","timestamp":"20241123111934","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Leonhard Euler","url":"https:\/\/en.wikipedia.org\/wiki\/Leonhard_Euler","sameAs":"http:\/\/www.wikidata.org\/entity\/Q7604","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q7604","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2001-06-29T01:27:51Z","dateModified":"2024-11-22T18:25:56Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/f\/f9\/Leonhard_Euler_-_Jakob_Emanuel_Handmann_%28Kunstmuseum_Basel%29.jpg","headline":"Swiss mathematician, physicist, and engineer (1707\u20131783)"}</script> </body> </html>