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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Вуруд</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/%D0%A0%D0%BE%D2%B3%D0%BD%D0%B0%D0%BC%D0%BE:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%B6%D0%B0:%D0%A1%D0%B0%D2%B3%D0%BC%D0%B8_%D0%BC%D0%B0%D0%BD" title="A list of edits made from this IP address [y]" accesskey="y"><span>Саҳмгузориҳо</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%B6%D0%B0:%D0%91%D0%B0%D2%B3%D1%81%D0%B8_%D0%BC%D0%B0%D0%BD" title="Баҳси пиромуни вироишҳо аз ин нишонаи IP [n]" accesskey="n"><span>Баҳс</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Муҳтавоҳо" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 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id="toc-Осиёи_Миёна" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Осиёи_Миёна"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Осиёи Миёна</span> </div> </a> <ul id="toc-Осиёи_Миёна-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Дар_Аврупо" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Дар_Аврупо"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Дар Аврупо</span> </div> </a> <ul id="toc-Дар_Аврупо-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Аломати_зарб_ва_тақсим" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Аломати_зарб_ва_тақсим"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Аломати зарб ва тақсим</span> </div> </a> <ul id="toc-Аломати_зарб_ва_тақсим-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Аломатҳои_баробари_ва_қавсҳо" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Аломатҳои_баробари_ва_қавсҳо"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Аломатҳои баробари ва қавсҳо</span> </div> </a> <ul id="toc-Аломатҳои_баробари_ва_қавсҳо-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Аломатҳои_калон_ва_хурд" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Аломатҳои_калон_ва_хурд"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Аломатҳои калон ва хурд</span> </div> </a> <ul id="toc-Аломатҳои_калон_ва_хурд-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Таърих_-_Формулаҳои_квадрати_сумма,_куби_сумма,_квадрати_фарқ,_куби_фарқ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Таърих_-_Формулаҳои_квадрати_сумма,_куби_сумма,_квадрати_фарқ,_куби_фарқ"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Таърих - Формулаҳои квадрати сумма, куби сумма, квадрати фарқ, куби фарқ</span> </div> </a> <ul id="toc-Таърих_-_Формулаҳои_квадрати_сумма,_куби_сумма,_квадрати_фарқ,_куби_фарқ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Эзоҳ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Эзоҳ"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Эзоҳ</span> </div> </a> <ul id="toc-Эзоҳ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Сарчашма" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Сарчашма"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Сарчашма</span> </div> </a> <ul id="toc-Сарчашма-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="Муҳтавоҳо" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Алгебра</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 167 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-167" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">167 забон</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Algebra" title="Algebra – африкаанс" lang="af" hreflang="af" data-title="Algebra" data-language-autonym="Afrikaans" data-language-local-name="африкаанс" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Algebra" title="Algebra – Alemannic" lang="gsw" hreflang="gsw" data-title="Algebra" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%88%8D%E1%8C%80%E1%89%A5%E1%88%AB" title="አልጀብራ – амҳарӣ" lang="am" hreflang="am" data-title="አልጀብራ" data-language-autonym="አማርኛ" data-language-local-name="амҳарӣ" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Alchebra" title="Alchebra – Aragonese" lang="an" hreflang="an" data-title="Alchebra" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/R%C4%ABmagiefung" title="Rīmagiefung – Old English" lang="ang" hreflang="ang" data-title="Rīmagiefung" data-language-autonym="Ænglisc" data-language-local-name="Old English" class="interlanguage-link-target"><span>Ænglisc</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – Angika" lang="anp" hreflang="anp" data-title="बीजगणित" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1" title="الجبر – арабӣ" lang="ar" hreflang="ar" data-title="الجبر" data-language-autonym="العربية" data-language-local-name="арабӣ" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1" title="جبر – Egyptian Arabic" lang="arz" hreflang="arz" data-title="جبر" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A7%80%E0%A6%9C%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="বীজগণিত – ассомӣ" lang="as" hreflang="as" data-title="বীজগণিত" data-language-autonym="অসমীয়া" data-language-local-name="ассомӣ" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/%C3%81lxebra" title="Álxebra – Asturian" lang="ast" hreflang="ast" data-title="Álxebra" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/C%C9%99br" title="Cəbr – озарбойҷонӣ" lang="az" hreflang="az" data-title="Cəbr" data-language-autonym="Azərbaycanca" data-language-local-name="озарбойҷонӣ" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1" title="جبر – South Azerbaijani" lang="azb" hreflang="azb" data-title="جبر" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – бошқирдӣ" lang="ba" hreflang="ba" data-title="Алгебра" data-language-autonym="Башҡортса" data-language-local-name="бошқирдӣ" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Algebra" title="Algebra – Samogitian" lang="sgs" hreflang="sgs" data-title="Algebra" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Alhebra" title="Alhebra – Central Bikol" lang="bcl" hreflang="bcl" data-title="Alhebra" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – белорусӣ" lang="be" hreflang="be" data-title="Алгебра" data-language-autonym="Беларуская" data-language-local-name="белорусӣ" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Альгебра – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Альгебра" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – булғорӣ" lang="bg" hreflang="bg" data-title="Алгебра" data-language-autonym="Български" data-language-local-name="булғорӣ" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – Bhojpuri" lang="bh" hreflang="bh" data-title="बीजगणित" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%80%E0%A6%9C%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="বীজগণিত – бинғолӣ" lang="bn" hreflang="bn" data-title="বীজগণিত" data-language-autonym="বাংলা" data-language-local-name="бинғолӣ" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%9A%E0%BD%96%E0%BC%8B%E0%BD%A2%E0%BE%A9%E0%BD%B2%E0%BD%A6%E0%BC%8D" title="ཚབ་རྩིས། – тибетӣ" lang="bo" hreflang="bo" data-title="ཚབ་རྩིས།" data-language-autonym="བོད་ཡིག" data-language-local-name="тибетӣ" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Aljebr" title="Aljebr – бретонӣ" lang="br" hreflang="br" data-title="Aljebr" data-language-autonym="Brezhoneg" data-language-local-name="бретонӣ" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Algebra" title="Algebra – босниягӣ" lang="bs" hreflang="bs" data-title="Algebra" data-language-autonym="Bosanski" data-language-local-name="босниягӣ" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%80lgebra" title="Àlgebra – каталонӣ" lang="ca" hreflang="ca" data-title="Àlgebra" data-language-autonym="Català" data-language-local-name="каталонӣ" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/D%C3%A2i-s%C3%B3" title="Dâi-só – Mindong" lang="cdo" hreflang="cdo" data-title="Dâi-só" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Chechen" lang="ce" hreflang="ce" data-title="Алгебра" data-language-autonym="Нохчийн" data-language-local-name="Chechen" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AC%DB%95%D8%A8%D8%B1" title="جەبر – курдии марказӣ" lang="ckb" hreflang="ckb" data-title="جەبر" data-language-autonym="کوردی" data-language-local-name="курдии марказӣ" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Algebra" title="Algebra – корсиканӣ" lang="co" hreflang="co" data-title="Algebra" data-language-autonym="Corsu" data-language-local-name="корсиканӣ" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Algebra" title="Algebra – чехӣ" lang="cs" hreflang="cs" data-title="Algebra" data-language-autonym="Čeština" data-language-local-name="чехӣ" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Chuvash" lang="cv" hreflang="cv" data-title="Алгебра" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Algebra" title="Algebra – валлӣ" lang="cy" hreflang="cy" data-title="Algebra" data-language-autonym="Cymraeg" data-language-local-name="валлӣ" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Algebra" title="Algebra – даниягӣ" lang="da" hreflang="da" data-title="Algebra" data-language-autonym="Dansk" data-language-local-name="даниягӣ" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Algebra" title="Algebra – немисӣ" lang="de" hreflang="de" data-title="Algebra" data-language-autonym="Deutsch" data-language-local-name="немисӣ" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Cebir" title="Cebir – Zazaki" lang="diq" hreflang="diq" data-title="Cebir" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%86%CE%BB%CE%B3%CE%B5%CE%B2%CF%81%CE%B1" title="Άλγεβρα – юнонӣ" lang="el" hreflang="el" data-title="Άλγεβρα" data-language-autonym="Ελληνικά" data-language-local-name="юнонӣ" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Algebra" title="Algebra – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Algebra" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437796 badge-featuredarticle mw-list-item" title="мақолаҳои баргузида"><a href="https://en.wikipedia.org/wiki/Algebra" title="Algebra – Англисӣ" lang="en" hreflang="en" data-title="Algebra" data-language-autonym="English" data-language-local-name="Англисӣ" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Algebro" title="Algebro – эсперанто" lang="eo" hreflang="eo" data-title="Algebro" data-language-autonym="Esperanto" data-language-local-name="эсперанто" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – испанӣ" lang="es" hreflang="es" data-title="Álgebra" data-language-autonym="Español" data-language-local-name="испанӣ" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Algebra" title="Algebra – эстонӣ" lang="et" hreflang="et" data-title="Algebra" data-language-autonym="Eesti" data-language-local-name="эстонӣ" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Aljebra" title="Aljebra – баскӣ" lang="eu" hreflang="eu" data-title="Aljebra" data-language-autonym="Euskara" data-language-local-name="баскӣ" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1" title="جبر – форсӣ" lang="fa" hreflang="fa" data-title="جبر" data-language-autonym="فارسی" data-language-local-name="форсӣ" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Algebra" title="Algebra – финӣ" lang="fi" hreflang="fi" data-title="Algebra" data-language-autonym="Suomi" data-language-local-name="финӣ" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Alg%C3%B5bra" title="Algõbra – Võro" lang="vro" hreflang="vro" data-title="Algõbra" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Ivakavakadina" title="Ivakavakadina – Fijian" lang="fj" hreflang="fj" data-title="Ivakavakadina" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijian" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Algebra" title="Algebra – фарерӣ" lang="fo" hreflang="fo" data-title="Algebra" data-language-autonym="Føroyskt" data-language-local-name="фарерӣ" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre" title="Algèbre – франсузӣ" lang="fr" hreflang="fr" data-title="Algèbre" data-language-autonym="Français" data-language-local-name="франсузӣ" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Algebra" title="Algebra – Northern Frisian" lang="frr" hreflang="frr" data-title="Algebra" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Algebra" title="Algebra – фризии ғарбӣ" lang="fy" hreflang="fy" data-title="Algebra" data-language-autonym="Frysk" data-language-local-name="фризии ғарбӣ" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Ailg%C3%A9abar" title="Ailgéabar – ирландӣ" lang="ga" hreflang="ga" data-title="Ailgéabar" data-language-autonym="Gaeilge" data-language-local-name="ирландӣ" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E4%BB%A3%E6%95%B8" title="代數 – Gan" lang="gan" hreflang="gan" data-title="代數" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Aj%C3%A8b" title="Ajèb – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Ajèb" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Ailseabra" title="Ailseabra – шотландии гэлӣ" lang="gd" hreflang="gd" data-title="Ailseabra" data-language-autonym="Gàidhlig" data-language-local-name="шотландии гэлӣ" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%81lxebra" title="Álxebra – галисиягӣ" lang="gl" hreflang="gl" data-title="Álxebra" data-language-autonym="Galego" data-language-local-name="галисиягӣ" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – гуаранӣ" lang="gn" hreflang="gn" data-title="Álgebra" data-language-autonym="Avañe'ẽ" data-language-local-name="гуаранӣ" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AC%E0%AB%80%E0%AA%9C%E0%AA%97%E0%AA%A3%E0%AA%BF%E0%AA%A4" title="બીજગણિત – гуҷаротӣ" lang="gu" hreflang="gu" data-title="બીજગણિત" data-language-autonym="ગુજરાતી" data-language-local-name="гуҷаротӣ" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Algeerey" title="Algeerey – Manx" lang="gv" hreflang="gv" data-title="Algeerey" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Algebra" title="Algebra – ҳауса" lang="ha" hreflang="ha" data-title="Algebra" data-language-autonym="Hausa" data-language-local-name="ҳауса" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94" title="אלגברה – ибронӣ" lang="he" hreflang="he" data-title="אלגברה" data-language-autonym="עברית" data-language-local-name="ибронӣ" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – ҳиндӣ" lang="hi" hreflang="hi" data-title="बीजगणित" data-language-autonym="हिन्दी" data-language-local-name="ҳиндӣ" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Algebra" title="Algebra – Fiji Hindi" lang="hif" hreflang="hif" data-title="Algebra" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Algebra" title="Algebra – хорватӣ" lang="hr" hreflang="hr" data-title="Algebra" data-language-autonym="Hrvatski" data-language-local-name="хорватӣ" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Alj%C3%A8b" title="Aljèb – гаитии креолӣ" lang="ht" hreflang="ht" data-title="Aljèb" data-language-autonym="Kreyòl ayisyen" data-language-local-name="гаитии креолӣ" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Algebra" title="Algebra – маҷорӣ" lang="hu" hreflang="hu" data-title="Algebra" data-language-autonym="Magyar" data-language-local-name="маҷорӣ" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D5%B6%D6%80%D5%A1%D5%B0%D5%A1%D5%B7%D5%AB%D5%BE" title="Հանրահաշիվ – арманӣ" lang="hy" hreflang="hy" data-title="Հանրահաշիվ" data-language-autonym="Հայերեն" data-language-local-name="арманӣ" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Algebra" title="Algebra – Байни забонӣ" lang="ia" hreflang="ia" data-title="Algebra" data-language-autonym="Interlingua" data-language-local-name="Байни забонӣ" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Algebra" title="Algebra – Iban" lang="iba" hreflang="iba" data-title="Algebra" data-language-autonym="Jaku Iban" data-language-local-name="Iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Aljabar" title="Aljabar – индонезӣ" lang="id" hreflang="id" data-title="Aljabar" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезӣ" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Alhebra" title="Alhebra – Iloko" lang="ilo" hreflang="ilo" data-title="Alhebra" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Ingush" lang="inh" hreflang="inh" data-title="Алгебра" data-language-autonym="ГӀалгӀай" data-language-local-name="Ingush" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Algebro" title="Algebro – Ido" lang="io" hreflang="io" data-title="Algebro" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Algebra" title="Algebra – исландӣ" lang="is" hreflang="is" data-title="Algebra" data-language-autonym="Íslenska" data-language-local-name="исландӣ" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Algebra" title="Algebra – италиявӣ" lang="it" hreflang="it" data-title="Algebra" data-language-autonym="Italiano" data-language-local-name="италиявӣ" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0%E5%AD%A6" title="代数学 – японӣ" lang="ja" hreflang="ja" data-title="代数学" data-language-autonym="日本語" data-language-local-name="японӣ" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Aljibra" title="Aljibra – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Aljibra" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/alxebra" title="alxebra – Lojban" lang="jbo" hreflang="jbo" data-title="alxebra" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Aljabar" title="Aljabar – Ҷаванизӣ" lang="jv" hreflang="jv" data-title="Aljabar" data-language-autonym="Jawa" data-language-local-name="Ҷаванизӣ" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%9A%E1%83%92%E1%83%94%E1%83%91%E1%83%A0%E1%83%90" title="ალგებრა – гурҷӣ" lang="ka" hreflang="ka" data-title="ალგებრა" data-language-autonym="ქართული" data-language-local-name="гурҷӣ" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Algebra" title="Algebra – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Algebra" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Aljiber" title="Aljiber – Kabyle" lang="kab" hreflang="kab" data-title="Aljiber" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D1%8D" title="Алгебрэ – Kabardian" lang="kbd" hreflang="kbd" data-title="Алгебрэ" data-language-autonym="Адыгэбзэ" data-language-local-name="Kabardian" class="interlanguage-link-target"><span>Адыгэбзэ</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/%C3%91%CA%8A%C5%8B_kal%CA%8A%CA%8A_t%CA%8Am%C9%A9y%C9%9B" title="Ñʊŋ kalʊʊ tʊmɩyɛ – Kabiye" lang="kbp" hreflang="kbp" data-title="Ñʊŋ kalʊʊ tʊmɩyɛ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – қазоқӣ" lang="kk" hreflang="kk" data-title="Алгебра" data-language-autonym="Қазақша" data-language-local-name="қазоқӣ" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AC%E0%B3%80%E0%B2%9C%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಬೀಜಗಣಿತ – каннада" lang="kn" hreflang="kn" data-title="ಬೀಜಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="каннада" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8C%80%EC%88%98%ED%95%99" title="대수학 – кореягӣ" lang="ko" hreflang="ko" data-title="대수학" data-language-autonym="한국어" data-language-local-name="кореягӣ" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Aljebra" title="Aljebra – Cornish" lang="kw" hreflang="kw" data-title="Aljebra" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – қирғизӣ" lang="ky" hreflang="ky" data-title="Алгебра" data-language-autonym="Кыргызча" data-language-local-name="қирғизӣ" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Algebra" title="Algebra – лотинӣ" lang="la" hreflang="la" data-title="Algebra" data-language-autonym="Latina" data-language-local-name="лотинӣ" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Aljebra" title="Aljebra – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Aljebra" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Aligebbula" title="Aligebbula – Ganda" lang="lg" hreflang="lg" data-title="Aligebbula" data-language-autonym="Luganda" data-language-local-name="Ganda" class="interlanguage-link-target"><span>Luganda</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Algebra" title="Algebra – Limburgish" lang="li" hreflang="li" data-title="Algebra" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Algebra" title="Algebra – Ligurian" lang="lij" hreflang="lij" data-title="Algebra" data-language-autonym="Ligure" data-language-local-name="Ligurian" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Algebra" title="Algebra – Lombard" lang="lmo" hreflang="lmo" data-title="Algebra" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%9E%E0%BA%B6%E0%BA%94%E0%BA%8A%E0%BA%B0%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94" title="ພຶດຊະຄະນິດ – лаосӣ" lang="lo" hreflang="lo" data-title="ພຶດຊະຄະນິດ" data-language-autonym="ລາວ" data-language-local-name="лаосӣ" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Algebra" title="Algebra – литвонӣ" lang="lt" hreflang="lt" data-title="Algebra" data-language-autonym="Lietuvių" data-language-local-name="литвонӣ" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Algebra" title="Algebra – латишӣ" lang="lv" hreflang="lv" data-title="Algebra" data-language-autonym="Latviešu" data-language-local-name="латишӣ" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Aljebra" title="Aljebra – малагасӣ" lang="mg" hreflang="mg" data-title="Aljebra" data-language-autonym="Malagasy" data-language-local-name="малагасӣ" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Aljabar" title="Aljabar – Minangkabau" lang="min" hreflang="min" data-title="Aljabar" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – мақдунӣ" lang="mk" hreflang="mk" data-title="Алгебра" data-language-autonym="Македонски" data-language-local-name="мақдунӣ" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B5%80%E0%B4%9C%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="ബീജഗണിതം – малаяламӣ" lang="ml" hreflang="ml" data-title="ബീജഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="малаяламӣ" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – маратҳӣ" lang="mr" hreflang="mr" data-title="बीजगणित" data-language-autonym="मराठी" data-language-local-name="маратҳӣ" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Algebra" title="Algebra – малайӣ" lang="ms" hreflang="ms" data-title="Algebra" data-language-autonym="Bahasa Melayu" data-language-local-name="малайӣ" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Al%C4%A1ebra" title="Alġebra – малтӣ" lang="mt" hreflang="mt" data-title="Alġebra" data-language-autonym="Malti" data-language-local-name="малтӣ" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – Mirandese" lang="mwl" hreflang="mwl" data-title="Álgebra" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%80%E1%80%B9%E1%80%81%E1%80%9B%E1%80%AC%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="အက္ခရာသင်္ချာ – бирманӣ" lang="my" hreflang="my" data-title="အက္ခရာသင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="бирманӣ" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Algebra" title="Algebra – Low German" lang="nds" hreflang="nds" data-title="Algebra" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AC%E0%A4%BF%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बिजगणित – непалӣ" lang="ne" hreflang="ne" data-title="बिजगणित" data-language-autonym="नेपाली" data-language-local-name="непалӣ" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – Newari" lang="new" hreflang="new" data-title="बीजगणित" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nia mw-list-item"><a href="https://nia.wikipedia.org/wiki/Aljabar" title="Aljabar – Nias" lang="nia" hreflang="nia" data-title="Aljabar" data-language-autonym="Li Niha" data-language-local-name="Nias" class="interlanguage-link-target"><span>Li Niha</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Algebra" title="Algebra – голландӣ" lang="nl" hreflang="nl" data-title="Algebra" data-language-autonym="Nederlands" data-language-local-name="голландӣ" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Algebra" title="Algebra – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Algebra" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Algebra" title="Algebra – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Algebra" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Algebra" title="Algebra – Novial" lang="nov" hreflang="nov" data-title="Algebra" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Alg%C3%A8bra" title="Algèbra – окситанӣ" lang="oc" hreflang="oc" data-title="Algèbra" data-language-autonym="Occitan" data-language-local-name="окситанӣ" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Aljebraa" title="Aljebraa – оромо" lang="om" hreflang="om" data-title="Aljebraa" data-language-autonym="Oromoo" data-language-local-name="оромо" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%B2%E0%A8%9C%E0%A8%AC%E0%A8%B0%E0%A8%BE" title="ਅਲਜਬਰਾ – панҷобӣ" lang="pa" hreflang="pa" data-title="ਅਲਜਬਰਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="панҷобӣ" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Algebra" title="Algebra – лаҳистонӣ" lang="pl" hreflang="pl" data-title="Algebra" data-language-autonym="Polski" data-language-local-name="лаҳистонӣ" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/%C3%80lgebra" title="Àlgebra – Piedmontese" lang="pms" hreflang="pms" data-title="Àlgebra" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="الجبرا – Western Punjabi" lang="pnb" hreflang="pnb" data-title="الجبرا" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1" title="الجبر – пушту" lang="ps" hreflang="ps" data-title="الجبر" data-language-autonym="پښتو" data-language-local-name="пушту" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – португалӣ" lang="pt" hreflang="pt" data-title="Álgebra" data-language-autonym="Português" data-language-local-name="португалӣ" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Qillqanancha_kamay" title="Qillqanancha kamay – кечуа" lang="qu" hreflang="qu" data-title="Qillqanancha kamay" data-language-autonym="Runa Simi" data-language-local-name="кечуа" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Algebr%C4%83" title="Algebră – руминӣ" lang="ro" hreflang="ro" data-title="Algebră" data-language-autonym="Română" data-language-local-name="руминӣ" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – русӣ" lang="ru" hreflang="ru" data-title="Алгебра" data-language-autonym="Русский" data-language-local-name="русӣ" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%90%D0%BB%D2%91%D0%B5%D0%B1%D1%80%D0%B0" title="Алґебра – Rusyn" lang="rue" hreflang="rue" data-title="Алґебра" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – саха" lang="sah" hreflang="sah" data-title="Алгебра" data-language-autonym="Саха тыла" data-language-local-name="саха" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/%C3%80lgibbra" title="Àlgibbra – Sicilian" lang="scn" hreflang="scn" data-title="Àlgibbra" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Algebra" title="Algebra – Scots" lang="sco" hreflang="sco" data-title="Algebra" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A2%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="آلجبرا – синдӣ" lang="sd" hreflang="sd" data-title="آلجبرا" data-language-autonym="سنڌي" data-language-local-name="синдӣ" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Algebra" title="Algebra – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Algebra" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Aljibr" title="Aljibr – Tachelhit" lang="shi" hreflang="shi" data-title="Aljibr" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%93%E0%B6%A2_%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%BA" title="වීජ ගණිතය – сингалӣ" lang="si" hreflang="si" data-title="වීජ ගණිතය" data-language-autonym="සිංහල" data-language-local-name="сингалӣ" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Algebra" title="Algebra – Simple English" lang="en-simple" hreflang="en-simple" data-title="Algebra" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Algebra_(discipl%C3%ADna)" title="Algebra (disciplína) – словакӣ" lang="sk" hreflang="sk" data-title="Algebra (disciplína)" data-language-autonym="Slovenčina" data-language-local-name="словакӣ" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Algebra" title="Algebra – словенӣ" lang="sl" hreflang="sl" data-title="Algebra" data-language-autonym="Slovenščina" data-language-local-name="словенӣ" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Aljebra" title="Aljebra – сомалӣ" lang="so" hreflang="so" data-title="Aljebra" data-language-autonym="Soomaaliga" data-language-local-name="сомалӣ" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Algjebra" title="Algjebra – албанӣ" lang="sq" hreflang="sq" data-title="Algjebra" data-language-autonym="Shqip" data-language-local-name="албанӣ" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – сербӣ" lang="sr" hreflang="sr" data-title="Алгебра" data-language-autonym="Српски / srpski" data-language-local-name="сербӣ" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Aljabar" title="Aljabar – Sundanese" lang="su" hreflang="su" data-title="Aljabar" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Algebra" title="Algebra – шведӣ" lang="sv" hreflang="sv" data-title="Algebra" data-language-autonym="Svenska" data-language-local-name="шведӣ" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Aljebra" title="Aljebra – Swahili" lang="sw" hreflang="sw" data-title="Aljebra" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%AF%E0%AE%B1%E0%AF%8D%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="இயற்கணிதம் – тамилӣ" lang="ta" hreflang="ta" data-title="இயற்கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="тамилӣ" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AC%E0%B1%80%E0%B0%9C_%E0%B0%97%E0%B0%A3%E0%B0%BF%E0%B0%A4%E0%B0%82" title="బీజ గణితం – телугу" lang="te" hreflang="te" data-title="బీజ గణితం" data-language-autonym="తెలుగు" data-language-local-name="телугу" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%B5%E0%B8%8A%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" title="พีชคณิต – тайӣ" lang="th" hreflang="th" data-title="พีชคณิต" data-language-autonym="ไทย" data-language-local-name="тайӣ" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Algebra" title="Algebra – туркманӣ" lang="tk" hreflang="tk" data-title="Algebra" data-language-autonym="Türkmençe" data-language-local-name="туркманӣ" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Alhebra" title="Alhebra – Tagalog" lang="tl" hreflang="tl" data-title="Alhebra" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Cebir" title="Cebir – туркӣ" lang="tr" hreflang="tr" data-title="Cebir" data-language-autonym="Türkçe" data-language-local-name="туркӣ" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Tinhlayo-swiyenge" title="Tinhlayo-swiyenge – Tsonga" lang="ts" hreflang="ts" data-title="Tinhlayo-swiyenge" data-language-autonym="Xitsonga" data-language-local-name="Tsonga" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – тоторӣ" lang="tt" hreflang="tt" data-title="Алгебра" data-language-autonym="Татарча / tatarça" data-language-local-name="тоторӣ" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tum mw-list-item"><a href="https://tum.wikipedia.org/wiki/Alijebra" title="Alijebra – Tumbuka" lang="tum" hreflang="tum" data-title="Alijebra" data-language-autonym="ChiTumbuka" data-language-local-name="Tumbuka" class="interlanguage-link-target"><span>ChiTumbuka</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – украинӣ" lang="uk" hreflang="uk" data-title="Алгебра" data-language-autonym="Українська" data-language-local-name="украинӣ" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="الجبرا – урду" lang="ur" hreflang="ur" data-title="الجبرا" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Algebra" title="Algebra – ӯзбекӣ" lang="uz" hreflang="uz" data-title="Algebra" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ӯзбекӣ" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/%C3%80lgebra" title="Àlgebra – Venetian" lang="vec" hreflang="vec" data-title="Àlgebra" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Algebr" title="Algebr – Veps" lang="vep" hreflang="vep" data-title="Algebr" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91" title="Đại số – ветнамӣ" lang="vi" hreflang="vi" data-title="Đại số" data-language-autonym="Tiếng Việt" data-language-local-name="ветнамӣ" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Algebra" title="Algebra – West Flemish" lang="vls" hreflang="vls" data-title="Algebra" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Alhebra" title="Alhebra – Waray" lang="war" hreflang="war" data-title="Alhebra" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0" title="代数 – Wu" lang="wuu" hreflang="wuu" data-title="代数" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-Algebra" title="I-Algebra – Xhosa" lang="xh" hreflang="xh" data-title="I-Algebra" data-language-autonym="IsiXhosa" data-language-local-name="Xhosa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%90%E1%83%9A%E1%83%92%E1%83%94%E1%83%91%E1%83%A0%E1%83%90" title="ალგებრა – Mingrelian" lang="xmf" hreflang="xmf" data-title="ალგებრა" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%9C%D7%92%D7%A2%D7%91%D7%A8%D7%A2" title="אלגעברע – идиш" lang="yi" hreflang="yi" data-title="אלגעברע" data-language-autonym="ייִדיש" data-language-local-name="идиш" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Algebra" title="Algebra – йоруба" lang="yo" hreflang="yo" data-title="Algebra" data-language-autonym="Yorùbá" data-language-local-name="йоруба" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0" title="代数 – хитоӣ" lang="zh" hreflang="zh" data-title="代数" data-language-autonym="中文" data-language-local-name="хитоӣ" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="代數學" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/T%C4%81i-s%C3%B2%CD%98" title="Tāi-sò͘ – Minnan" lang="nan" hreflang="nan" data-title="Tāi-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學 – Cantonese" lang="yue" hreflang="yue" data-title="代數學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q3968#sitelinks-wikipedia" title="Таҳрири пайвандҳои байнизабонӣ" class="wbc-editpage">Вироиши пайвандҳо</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Фазоҳои ном"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">Пинҳон кардан</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Мавод аз Википедиа — донишномаи озод</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="tg" dir="ltr"><table class="plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><figure class="noresize" typeof="mw:File"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D0%B0:%D0%9F%D0%B0%D0%B9%D0%B2%D0%B0%D0%BD%D0%B4%D2%B3%D0%BE_%D0%B1%D0%B0_%D1%81%D0%B0%D1%80%D1%87%D0%B0%D1%88%D0%BC%D0%B0%D2%B3%D0%BE" title="Пайвандҳо ба сарчашмаҳо"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/48px-Question_book-4.svg.png" decoding="async" width="48" height="37" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/72px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/96px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></a><figcaption></figcaption></figure></div></td><td class="mbox-text"><div class="mbox-text-div"><b>Дар ин мақола <a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D0%B0:%D0%9F%D0%B0%D0%B9%D0%B2%D0%B0%D0%BD%D0%B4%D2%B3%D0%BE_%D0%B1%D0%B0_%D1%81%D0%B0%D1%80%D1%87%D0%B0%D1%88%D0%BC%D0%B0%D2%B3%D0%BE" title="Википедиа:Пайвандҳо ба сарчашмаҳо">пайванд ба сарчашмаҳои иттиллот</a> намерасад.</b></div><div class="mbox-textsmall-div hide-when-compact" style="font-size:85%">Иттилоот бояд <a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D0%B0:%D0%98%D1%81%D0%B1%D0%BE%D1%82%D0%BF%D0%B0%D0%B7%D0%B8%D1%80%D3%A3" title="Википедиа:Исботпазирӣ">исботпазир</a> бошад, дар акси ҳол он зери шубҳа ва ҳазф қарор мегирад.<br />Шумо метавонед ин мақоларо <a class="external text" href="https://tg.wikipedia.org/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit">ислоҳ</a> карда, пайвандҳоро ба <a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D0%B0:%D0%A1%D0%B0%D1%80%D1%87%D0%B0%D1%88%D0%BC%D0%B0%D2%B3%D0%BE%D0%B8_%D0%BC%D1%83%D1%8A%D1%82%D0%B0%D0%B1%D0%B0%D1%80" title="Википедиа:Сарчашмаҳои муътабар">сарчашмаҳои муътабар</a> илова намоед.<br />Ин ёддошт дар таърихи <b>{{subst:CURRENTDAY}} {{subst:CURRENTMONTHNAMEGEN}} {{subst:CURRENTYEAR}}</b> гузошта шудааст.</div></td></tr></tbody></table> <p><b>Алгебра</b> (<a href="/wiki/%D0%97%D0%B0%D0%B1%D0%BE%D0%BD%D0%B8_%D0%B0%D1%80%D0%B0%D0%B1%D3%A3" title="Забони арабӣ">ар.</a> <span lang="ar" style="font-size: 110%; font-style: normal; line-height: 1em;">اَلْجَبْرْ</span>‎ «ал-ҷабр» — <i>мукамал кардан) — </i>ҳамчун қисми таркибии илми ҳисоб (<a href="/wiki/%D2%B2%D0%B8%D1%81%D0%BE%D0%B1" title="Ҳисоб">Арифметика</a>) муддати тӯлонӣ бо вай якҷоя инкишоф ёфт. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%90%D0%BA%D1%81:Right_concoid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Right_concoid.svg/220px-Right_concoid.svg.png" decoding="async" width="220" height="236" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Right_concoid.svg/330px-Right_concoid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/af/Right_concoid.svg/440px-Right_concoid.svg.png 2x" data-file-width="560" data-file-height="600" /></a><figcaption>Сеандозаи рости канои тасвиркардашудаи алгебрави тригонометрии муодилавӣ.</figcaption></figure> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Таърихи_пайдоиши_алгебра"><span id=".D0.A2.D0.B0.D1.8A.D1.80.D0.B8.D1.85.D0.B8_.D0.BF.D0.B0.D0.B9.D0.B4.D0.BE.D0.B8.D1.88.D0.B8_.D0.B0.D0.BB.D0.B3.D0.B5.D0.B1.D1.80.D0.B0"></span>Таърихи пайдоиши алгебра</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=1" title="Вироиши қисмат: Таърихи пайдоиши алгебра" class="mw-editsection-visualeditor"><span>вироиш</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=1" title="Edit section's source code: Таърихи пайдоиши алгебра"><span>вироиши манбаъ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Дар доираи илми ҳисоб ҳанӯз 4000 сол пеш бобулиҳо, мисриҳо, баъдтар юнониҳо, хитоиҳо ва ҳиндуиҳои қадим ишораҳои алоҳида истифода бурда, масъалаҳои гуногунро ҳал менамуданд. </p> <div class="mw-heading mw-heading2"><h2 id="Осиёи_Миёна"><span id=".D0.9E.D1.81.D0.B8.D1.91.D0.B8_.D0.9C.D0.B8.D1.91.D0.BD.D0.B0"></span>Осиёи Миёна</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=2" title="Вироиши қисмат: Осиёи Миёна" class="mw-editsection-visualeditor"><span>вироиш</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=2" title="Edit section's source code: Осиёи Миёна"><span>вироиши манбаъ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Махсусан дар <a href="/wiki/%D0%9E%D1%81%D0%B8%D1%91%D0%B8_%D0%9C%D0%B8%D1%91%D0%BD%D0%B0" title="Осиёи Миёна">Осиёи Миёна</a> ва <a href="/wiki/%D2%B2%D0%B8%D0%BD%D0%B4%D1%83%D1%81%D1%82%D0%BE%D0%BD" title="Ҳиндустон">Ҳиндустони</a> асримиёнагӣ (асрҳои IX-XI) ин фанни қадима хеле пеш рафт ва бо кашфиётҳои Навин ғанӣ гашт. Дар нимаи аввали IX донишманди бузурги Шарқ <a href="/wiki/%D0%9C%D1%83%D2%B3%D0%B0%D0%BC%D0%BC%D0%B0%D0%B4%D0%B8_%D0%A5%D0%BE%D1%80%D0%B0%D0%B7%D0%BC%D3%A3" class="mw-redirect" title="Муҳаммади Хоразмӣ">Муҳаммади Хоразмӣ</a> (<a href="/wiki/780" class="mw-redirect" title="780">780</a>-<a href="/wiki/850" class="mw-redirect" title="850">850</a>) асаре бо номи “Ҳисоб ал-ҷабр в-ал-муқобала” иншо намуд, ки дар он илми алгебра ҳамчун фанни мустақил омӯхта шуд. Истилоҳи “aлгебра” дар натиҷа бо <a href="/wiki/%D0%97%D0%B0%D0%B1%D0%BE%D0%BD%D0%B8_%D0%BB%D0%BE%D1%82%D0%B8%D0%BD%D3%A3" title="Забони лотинӣ">забони лотинӣ</a> ба ҳамин шакл тарҷума шудани асари номбурда ба миён омад. Худи Хоразмӣ нахустин шахсе буд, ки ба фанни алгебра асос гузоштааст. </p><p>Беҳтарин падида ва комравоии олимони <a href="/wiki/%D0%9E%D1%81%D0%B8%D1%91%D0%B8_%D0%9C%D0%B8%D1%91%D0%BD%D0%B0" title="Осиёи Миёна">Осиёи Миёна</a> ин аст, ки илми алгебраро чун илми мустақил рӯи кор оварданд. <a href="/wiki/%D0%9C%D1%83%D2%B3%D0%B0%D0%BC%D0%BC%D0%B0%D0%B4%D0%B8_%D0%A5%D0%BE%D1%80%D0%B0%D0%B7%D0%BC%D3%A3" class="mw-redirect" title="Муҳаммади Хоразмӣ">Муҳаммад ибни Мусо Хоразмӣ</a> дар улуми ҷаҳонӣ бо асари «Ҳисоби ҳиндӣ» машҳур гардид ва аз ҷиҳати таърихӣ падидаи илми ал-ҷабр бори аввал дар асари «Китоби мухтасар дар бораи ал-ҷабр ва ал — муқобила» — и ин олими фарҳехта ёд шудааст. Ин асар дар асри XII аз арабӣ ба лотинӣ тарҷума шуда, олимони аврупоӣ ба ҳисоби ҳиндӣ — арабӣ ошно шуданд ва аз ҳамон вақт дар илми риёзии ҷаҳон рақамҳои арабӣ ворид гаштанд.<sup id="cite_ref-Соярӯшанҳои_таърихи_илмҳои_дақиқ_1-0" class="reference"><a href="#cite_note-Соярӯшанҳои_таърихи_илмҳои_дақиқ-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Аввалин китоби <a href="/wiki/%D0%9C%D1%83%D2%B3%D0%B0%D0%BC%D0%BC%D0%B0%D0%B4%D0%B8_%D0%A5%D0%BE%D1%80%D0%B0%D0%B7%D0%BC%D3%A3" class="mw-redirect" title="Муҳаммади Хоразмӣ">Муҳаммади Хоразмӣ</a>, ки ба забони лотинӣ тарҷума ва дар Аврупо ба сифати китоби дарсӣ истифода мешуд, ба пешрафти риёзӣ ва илмҳои дигар таъсири бузург расонида, ба ганҷинаи тамаддуни ҷаҳонӣ шомил шуд. Ин кашфиёти форсро муаррихи маъруфи амрикоӣҶорҷ Сартон (асри ХХ) «ибтидои алгебраи аврупоӣ» ном бурда буд. Баъди Хоразмӣ риёзидонони Осиёи Миёна ва Шарқи Наздик ақидаҳои ӯро оид ба алгебра ҳамчун таълимот дар бораи ҳалли муодилаҳо инкишоф доданд. </p><p>Садаи XI асри заррин аст, ки кашфу халлоқият авҷи аълояшро дар ҳамин аср пайдо кард. Ҷорҷ Сартон дар асари бузурги илмӣ — библиографиаш — «Муқаддима дар таърихи илм» таърихи илми ҷаҳониро ба марҳилаҳои нимасрӣ тақсим мекунад ва пешрафти ҳар кадоми онро ба фаъолияти яке аз шахсиятҳои илмӣ вобаста медонад. Умари Хайёми Нишопурӣ файласуф, шоир, риёзидон, намоянда ва муаррифгари ин аср ба ҳисоб меравад. Ӯ дар китоби «Доир ба исботи масъалаҳои ал-ҷабр ва ал-муқобала» (1069-1071) усули умумии геометрии ҳалли муодилаҳои кубиро кор карда, нуздаҳ намуди ин гуна муодилаҳоро тадқиқ кард ва дар ҳалли муодилаҳои алгебравӣ ба геометрия бартарӣ дод. Ҳамчунин, баъзе аз донишмандони илми риёзӣ тахмин мекунанд, ки Кошонӣ 400 сол пеш аз <a href="/wiki/%D0%A3%D0%BC%D0%B0%D1%80%D0%B8_%D0%A5%D0%B0%D0%B9%D1%91%D0%BC" title="Умари Хайём">Умари Хайём</a>, 600 сол қабл аз Нютон ҷудокунии биномро маълум намуда буд. Файласуф ва донишманди шинохтаи тоҷик А. Турсон дар китоби «Эҳёи Аҷам» овардааст, ки «ин ном иштибоҳан (бо номи Нютон, — Т. А.)» расм шудааст.<sup id="cite_ref-Соярӯшанҳои_таърихи_илмҳои_дақиқ_1-1" class="reference"><a href="#cite_note-Соярӯшанҳои_таърихи_илмҳои_дақиқ-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Ин иштибоҳи таърих дар қисмати аз реша баровардани адад низ ба вуҷуд омадааст. Дар тадқиқоти Кушёр ибни Лабан Ҷилӣ методи аз решаи квадратӣ баровардани ададро вохӯрдан мумкин аст, ки он шабеҳ ба таҳқиқоти Руфинер — Ҳорнер (асри XIX) аст. Усули содатарини аз решаи кубӣ баровардани ададро 800 сол пеш Абулҳасани Насавӣ (асри X-XI; зодаи Нисон) маълум намуда буд. Усули аз таҳти решаи ихтиёрӣ тақрибӣ баровардани адад аввалин бор дар Осиёи Миёна ба вуҷуд омад. Дар ин самт риёзидонони форсу тоҷики асрҳои XV-XVII Кошонӣ, Алқушҷӣ, Баҳовуддини Омулӣ ва Наҷмиддини Алихон низ саҳмгузоранд. Мутаассифона, то кунун ин равия ва афзалияти фаъолияти онҳо мавриди пажӯҳиш қарор нагирифтааст. </p><p>Ташаббуси риёзидонони Осиёи Миёна дар он аср ба ин матлаб ба итмом намерасад. Усули тақрибии ҳалли баъзе аз намудҳои муодилаҳои дараҷаи олӣ дар қисмати фаъолияти илмии кори онҳо қарор дошт. Дар ин асно <a href="/w/index.php?title=%D2%92%D0%B8%D1%91%D1%81%D0%B8%D0%B4%D0%B4%D0%B8%D0%BD_%D0%9A%D0%BE%D1%88%D0%BE%D0%BD%D3%A3&action=edit&redlink=1" class="new" title="Ғиёсиддин Кошонӣ (саҳифа вуҷуд надорад)">Ғиёсиддин Кошонӣ</a> барои ҳалли муодилаи кубӣқоидаи асосии интегратсионии аҷибро кашф намуд, ки ин усулро риёзидони англис Ҳорен дубора дар асри XIX хулосабарорӣ намуд. Дар таркиби усули Кошонӣ, инчунин, усули ҷудокунии решаҳо низ дохил мешавад, ки онро баъдтар Нютон такрор намудааст. Илми алгебра баъди ин дар асарҳои риёзидонҳои минбаъдаи Осиёи Миёна, ки роҷеъ ба мафҳумҳои асосии алгебра (ҳалҳои ҳақиқӣ ва каззобии муодилаҳо, классификатсияи муодилаҳо ва ғайра сермаҳсул кор мекарданд, рушд ёфт. Бахусус, вобастагии байни решаҳо ва коэффитсиентҳои муодилаҳои квардратӣ, ки Наҷмиддини Алихон (асри XVI; Эрон) онро дар рисолаи «Алгебра» кашф намуда, дар адабиёти илмӣ бо назм ифода кардааст, кашфиёти бузург дар риёзӣҳисоб мешавад. Мутаассифона, ин теоремаро риёзидони франсавӣ <a href="/wiki/%D0%A4%D1%80%D0%B0%D0%BD%D1%81%D1%83%D0%B0_%D0%92%D0%B8%D0%B5%D1%82" title="Франсуа Виет">Франсуа Виет</a> дар асри XVII аз нав маълум кард ва он бо номи ӯ (теоремаи Виет) дар илм машҳур гардид. Аз рӯи инсоф ва ҳақиқати илмӣ мебуд, агар муаллифони китобҳои таълимии алгебраи мактабӣ ин вобастагиро бо унвони теоремаи Алихон — Виет номгузорӣ мекарданд.<sup id="cite_ref-Соярӯшанҳои_таърихи_илмҳои_дақиқ_1-2" class="reference"><a href="#cite_note-Соярӯшанҳои_таърихи_илмҳои_дақиқ-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Алгебраи Хоразмӣ дар давоми асрҳои XII – XVI дар тарҷумаи лотиниаш мавриди омӯзиши аврупоиён қарор гирифта, барои дар Ғарб тараққӣ ёфтани ин фанни бостонӣ замина гузошт. То асри XV ҳамаи бузургиҳо, амалҳо бо онҳо, ҳалҳову ҷавобҳои масъалаҳо танҳо бо ибораҳо ифода меёфтанд. Бинобар ҳамин, математикаи то он давра мавҷударо математикаи риторикӣ ё иборавӣ меноманд. </p><p>Ифодаҳои ададӣ, ифодаҳои ҳарфӣ ва аломатҳову ишораҳои оҳиста-оҳиста дар илм ҷои устувореро соҳиб шуданд. </p> <div class="mw-heading mw-heading2"><h2 id="Дар_Аврупо"><span id=".D0.94.D0.B0.D1.80_.D0.90.D0.B2.D1.80.D1.83.D0.BF.D0.BE"></span>Дар Аврупо</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=3" title="Вироиши қисмат: Дар Аврупо" class="mw-editsection-visualeditor"><span>вироиш</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=3" title="Edit section's source code: Дар Аврупо"><span>вироиши манбаъ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Дар нимаи дуюми асри XV дар <a href="/wiki/%D0%98%D1%82%D0%B0%D0%BB%D0%B8%D1%8F" class="mw-redirect" title="Италия">Италия</a>, <a href="/wiki/%D0%9E%D0%BB%D0%BC%D0%BE%D0%BD" title="Олмон">Олмон</a> ва мамлакатҳои дигари <a href="/wiki/%D0%90%D0%B2%D1%80%D1%83%D0%BF%D0%BE" title="Аврупо">Аврупо</a> баъзе аломатҳои алгебравӣ қабул шуданд, ба истифода аз ҳарфҳо асос гузошта буданд. Масалан, дар охири <a href="/wiki/%D0%90%D1%81%D1%80%D0%B8_XV" class="mw-redirect" title="Асри XV">асри XV</a> <a href="/wiki/%D0%9E%D0%BB%D0%B8%D0%BC" title="Олим">олими</a> фаронсавӣ <a href="/wiki/%D0%A4%D1%80%D0%B0%D0%BD%D1%81%D1%83%D0%B0_%D0%92%D0%B8%D0%B5%D1%82" title="Франсуа Виет">Франсуа Виет</a> (<a href="/wiki/1540" class="mw-redirect" title="1540">1540</a>-<a href="/wiki/1603" class="mw-redirect" title="1603">1603</a>) на танҳо барои ифодаи номаълум, балки барои навишти адади дилхоҳ низ ҳарфҳои <a href="/wiki/%D0%90%D0%BB%D0%B8%D1%84%D0%B1%D0%BE%D0%B8_%D0%BB%D0%BE%D1%82%D0%B8%D0%BD%D3%A3" class="mw-redirect" title="Алифбои лотинӣ">алифбои лотиниро</a> истифода бурда, ба кашфи ифодаҳову формулаҳо асос гузошт. Рафта-рафта дар асри XIII дар математика аллакай бузургиҳои гуногунро бо ҳарфҳои гуногун ифода мекардагӣ шуданд. Минбаъд, бо ҳарфҳо низ ҳамаи амалҳои ҳисоб иҷро мешуданд, ки барои ададҳо ҷой доштанд. </p> <div class="mw-heading mw-heading2"><h2 id="Аломати_зарб_ва_тақсим"><span id=".D0.90.D0.BB.D0.BE.D0.BC.D0.B0.D1.82.D0.B8_.D0.B7.D0.B0.D1.80.D0.B1_.D0.B2.D0.B0_.D1.82.D0.B0.D2.9B.D1.81.D0.B8.D0.BC"></span>Аломати зарб ва тақсим</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=4" title="Вироиши қисмат: Аломати зарб ва тақсим" class="mw-editsection-visualeditor"><span>вироиш</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=4" title="Edit section's source code: Аломати зарб ва тақсим"><span>вироиши манбаъ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ба сифати аломати зарб истифода шудани нуқта низ аз ҳамин давра оғоз гардидааст. Барои ифодаи амали тақсим асосан дар <a href="/wiki/%D0%9E%D1%81%D0%B8%D1%91%D0%B8_%D0%9C%D0%B8%D1%91%D0%BD%D0%B0" title="Осиёи Миёна">Осиёи Миёна</a> аломати «-» истфода мешуд. Ҳам аломати зарбу ҳам аломати тақсим (дар шакли ду нуқта) дар охири <a href="/wiki/%D0%90%D1%81%D1%80%D0%B8_XVII" class="mw-redirect" title="Асри XVII">асри XVII</a> аз тарафи математики олмонӣ Г.Лейбнитс (<a href="/wiki/1646" class="mw-redirect" title="1646">1646</a>-<a href="/wiki/1716" class="mw-redirect" title="1716">1716</a>) қабул шудаанд. </p> <div class="mw-heading mw-heading2"><h2 id="Аломатҳои_баробари_ва_қавсҳо"><span id=".D0.90.D0.BB.D0.BE.D0.BC.D0.B0.D1.82.D2.B3.D0.BE.D0.B8_.D0.B1.D0.B0.D1.80.D0.BE.D0.B1.D0.B0.D1.80.D0.B8_.D0.B2.D0.B0_.D2.9B.D0.B0.D0.B2.D1.81.D2.B3.D0.BE"></span>Аломатҳои баробари ва қавсҳо</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=5" title="Вироиши қисмат: Аломатҳои баробари ва қавсҳо" class="mw-editsection-visualeditor"><span>вироиш</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=5" title="Edit section's source code: Аломатҳои баробари ва қавсҳо"><span>вироиши манбаъ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Дар ибтидои <a href="/wiki/%D0%90%D1%81%D1%80%D0%B8_XVII" class="mw-redirect" title="Асри XVII">асри XVII</a> аломатҳои баробарӣ ва қавсҳо дохил гардиданд:қавсҳои нимдавраро математики итолиёӣ Н. Тарталия, қавсҳои квадратиро ҳамватани ӯ Р. Бомбелӣ ва қавсҳои фигуравиро Ф. Виет пешниҳод намуданд. Аз соли <a href="/wiki/1637" class="mw-redirect" title="1637">1637</a> сар карда, аз тарафи математики олмонӣ Р. Декарт (<a href="/wiki/1596" class="mw-redirect" title="1596">1596</a>-<a href="/wiki/1662" class="mw-redirect" title="1662">1662</a>) номаълум бо яке аз ҳарфҳои охири алифбои лотинӣ ва ададҳои додашуда бо яке аз ҳарфҳои авали ҳамин <a href="/w/index.php?title=%D0%90%D0%BB%D0%B8%D1%84%D0%B1%D0%BE&action=edit&redlink=1" class="new" title="Алифбо (саҳифа вуҷуд надорад)">алифбо</a> ишора шудан гирифт. Ҳамин тавр, Декарт аввалин шуда ба рамзҳои алгебравӣ шакли муосирро додааст. </p> <div class="mw-heading mw-heading2"><h2 id="Аломатҳои_калон_ва_хурд"><span id=".D0.90.D0.BB.D0.BE.D0.BC.D0.B0.D1.82.D2.B3.D0.BE.D0.B8_.D0.BA.D0.B0.D0.BB.D0.BE.D0.BD_.D0.B2.D0.B0_.D1.85.D1.83.D1.80.D0.B4"></span>Аломатҳои калон ва хурд</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=6" title="Вироиши қисмат: Аломатҳои калон ва хурд" class="mw-editsection-visualeditor"><span>вироиш</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=6" title="Edit section's source code: Аломатҳои калон ва хурд"><span>вироиши манбаъ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Аломатҳои > («калон») ва < («хурд») соли <a href="/wiki/1631" class="mw-redirect" title="1631">1631</a> аз тарафи Т.Гарриот, аломати баробарӣ бори нахуст аз тарафи Р.Рекорд (соли <a href="/wiki/1557" class="mw-redirect" title="1557">1557</a>) қабул шуданд. Ишорати амали тарҳ низ дар охири асри XV аз тарафи математикҳои олмонӣ пешниҳод шудааст. </p><p>Амалҳо бо дараҷаҳо ва аз ин ҷо бо бисёраъзогиҳо ҳануз аз замони хеле бостон маълум буданд. Танҳо камбуди дар он аст, ки ин амалҳо на бо ишоратҳои ҳарфӣ, балки бо ибораҳо ифода ёфтаанд, ки барои истифодаи ноқулай ҳисоб меёбанд. Аз ибтидои асри XVII cap карда амалҳо бо дараҷаҳо ва якаъзогиҳо ҳамон тавре, ки мо ҳоло бо онҳо одат кардаем, дар <a href="/wiki/%D0%90%D0%B2%D1%80%D1%83%D0%BF%D0%BE" title="Аврупо">Аврупо</a> паҳн гаштан гирифтанд. Аз ин ҷо имкони зарби якаъзогӣ бо якаъзогӣ, якаъзогӣ бо бисёраъзогӣ ва сипас бисёраъзогӣ бо бисёраъзогӣ ба миён омад. Ба ибораи дигар, алгебра оҳиста-оҳиста шакли ҷиддӣву пай дар пайро соҳиб гашта тақрибан дар охирҳои асри XVII ва ибитдои асри XVIII ба ҳамон мундариҷае соҳиб гашт, ки мо ҳоло онро дар мактабҳо меомӯзем. Дар барқароршави ва устуворшавии алгебра ҳамчунин шохаи мустақили математика олимони бисёр мамлакатҳо, хусусан Осиёи Миёна саҳмгузоранд. </p><p>Агар поягузори алгебра ҳамчун илм олими бузург <a href="/wiki/%D0%9C%D1%83%D2%B3%D0%B0%D0%BC%D0%BC%D0%B0%D0%B4_%D0%A5%D0%BE%D1%80%D0%B0%D0%B7%D0%BC%D3%A3" class="mw-redirect" title="Муҳаммад Хоразмӣ">Муҳаммад Хоразмӣ</a> (<a href="/wiki/787" class="mw-redirect" title="787">787</a>-<a href="/wiki/850" class="mw-redirect" title="850">850</a>) ҳисоб ёбад, <a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB%D0%B0%D1%81%D1%83%D1%84" title="Файласуф">файласуф</a> ва математику ситорашиноси дигари форсу тоҷик <a href="/wiki/%D0%A3%D0%BC%D0%B0%D1%80%D0%B8_%D0%A5%D0%B0%D0%B9%D1%91%D0%BC" title="Умари Хайём">Умари Хайём</a> (<a href="/wiki/1048" class="mw-redirect" title="1048">1048</a>-<a href="/wiki/1123" class="mw-redirect" title="1123">1123</a>) пас аз се асри ҳаёти ӯ ин <a href="/wiki/%D0%98%D0%BB%D0%BC" title="Илм">илми</a> бостониро қуввату илҳоми тоза бахшид. </p><p>Дар инкишофи алгебра ҳиссаи олимони итолиёвии <a href="/wiki/%D0%90%D1%81%D1%80%D0%B8_XVI" class="mw-redirect" title="Асри XVI">асри XVI</a> Тарталия (1499-1557) ва Кардано (<a href="/wiki/1501" class="mw-redirect" title="1501">1501</a>-<a href="/wiki/1576" class="mw-redirect" title="1576">1576</a>) олими бузурги олмонӣ Декарт (1596-1650), олими фаронсавӣ Франсуа Виет (1540-1603) низ калон аст. </p><p>Вале ҳеҷ ягон фан, алалхусус математика, ки аз эҳтиёҷоти ҳаррӯзаи инсон пайдо шуда, дар корҳои сохтмонӣ, шинои, баҳри, ҳатто парвозҳои кайҳонӣ ҳамчун ёрдамчии беминнат хидмат мекунад, сукут накарда, ҳамеша ру ба тараққист, инкишоф меёбад, ғанӣ мегардад. Аз ин ҷост, ки дар давоми асрҳои XVII - XIX аз алгебра шохаи нав, аз қабили алгебраи бисёраъзогиҳо ба миён омад. </p><p>Риёзидонони Осиёи Миёна, аз Хоразмӣ cap карда, ифодаҳои дуаъзоги ва сеаъзогии квадратиро ба ду гурӯҳ сода ва мураккаб ҷудо намуда, дар асоси онҳо 6 намуди мухталифи муодилаҳоро ҳал намудаанд. Дар ин кори заҳматталаб инчунин номи олими <a href="/wiki/%D0%A2%D0%BE%D2%B7%D0%B8%D0%BA" class="mw-redirect" title="Тоҷик">тоҷик</a> Алӣ Кушчиро (асри XV), Баҳоваддини Омулӣ, Наҷмиддин Алихонро бо неки ёдоваршудан мумкин аст. Онҳо дар баробари пешниҳод намудани формулаҳои ҳалли муодилаҳои аз бисёраъзогиҳои дараҷаи ду тартибёфта, инчунин муодилаҳои тартиби болотарро низ бо тарзҳои сунъи ҳал намуда, дар назарияи муодилаҳои тартиби се ва чор тағйироти ҷиддӣ ворид сохтаанд. </p> <div class="mw-heading mw-heading2"><h2 id="Таърих_-_Формулаҳои_квадрати_сумма,_куби_сумма,_квадрати_фарқ,_куби_фарқ"><span id=".D0.A2.D0.B0.D1.8A.D1.80.D0.B8.D1.85_-_.D0.A4.D0.BE.D1.80.D0.BC.D1.83.D0.BB.D0.B0.D2.B3.D0.BE.D0.B8_.D0.BA.D0.B2.D0.B0.D0.B4.D1.80.D0.B0.D1.82.D0.B8_.D1.81.D1.83.D0.BC.D0.BC.D0.B0.2C_.D0.BA.D1.83.D0.B1.D0.B8_.D1.81.D1.83.D0.BC.D0.BC.D0.B0.2C_.D0.BA.D0.B2.D0.B0.D0.B4.D1.80.D0.B0.D1.82.D0.B8_.D1.84.D0.B0.D1.80.D2.9B.2C_.D0.BA.D1.83.D0.B1.D0.B8_.D1.84.D0.B0.D1.80.D2.9B"></span>Таърих - Формулаҳои квадрати сумма, куби сумма, квадрати фарқ, куби фарқ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=7" title="Вироиши қисмат: Таърих - Формулаҳои квадрати сумма, куби сумма, квадрати фарқ, куби фарқ" class="mw-editsection-visualeditor"><span>вироиш</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=7" title="Edit section's source code: Таърих - Формулаҳои квадрати сумма, куби сумма, квадрати фарқ, куби фарқ"><span>вироиши манбаъ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Формулаҳои квадрати сумма, куби сумма, квадрати фарқ, куби фарқ, аз замонҳои хеле бостон маълуманд. Хануз пеш аз милод олимони <a href="/wiki/%D0%A5%D0%B8%D1%82%D0%BE%D0%B9" class="mw-redirect" title="Хитой">Хитой</a> формулаҳои мазкурро барои максадҳои амали истифода мебурданд. Вале, азбаски онҳо амалҳои математикиро бо сухан ифода менамуданд, баёни формулахо низ хеле мураккаб буданд. </p><p>Олимони <a href="/wiki/%D0%AE%D0%BD%D0%BE%D0%BD%D0%B8_%D2%9A%D0%B0%D0%B4%D0%B8%D0%BC" class="mw-redirect" title="Юнони Қадим">Юнони Қадим</a> масъалаҳои алгебравиро асосан бо тарзӣ геометрӣ ё шаклхо маънидод менамуданд. Формулаи квадрати фарқро низ ҳангоми а>Ь будан маънидод намудан мумкин аст. Ҳангоми а>0, 6>0 ва с>0 будан формулаи квадрати суммаи се ҷамъшавандаро низ шарҳ додан мумкин аст. <a href="/wiki/%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0" class="mw-disambig" title="Формула">Формулаҳои</a> зарби мухтасарро аз формулаи умумитаре, ки бо номи формулаи биноми Хайём ном дорад, ҳосил намудан мумкин аст. </p><p><a href="/wiki/%D0%A3%D0%BC%D0%B0%D1%80%D0%B8_%D0%A5%D0%B0%D0%B9%D1%91%D0%BC" title="Умари Хайём">Умари Хайём</a> дар «Мушкилоти ҳисоб» ном асараш тарзи ёфтани решаи бутунро бо нишондиҳандаи дилхоҳ натурали аз ададҳои бутун нишон додааст. Дар асари хеш овардааст, ки ӯ тарзи ёфтани решаҳои квадрати ва кубии ҳиндиро (ба формулаҳои квадрат ва куби суммаи ададҳо такя намуда) исбот намудааст. Мутаассифона, ин асари пурарзиш то замони мо боқӣ намондааст. Баъди аз тарафи И. Нютон барои нишондихандаи касри низ ҳосил намудани формулаи Хайём формулаи мазкур бо номи беноми Нютон ёдовар шудааст. Холо дар <a href="/wiki/%D0%A2%D0%B0%D1%8A%D1%80%D0%B8%D1%85" title="Таърих">таърихи</a> математика онро ҳамчун беноми Хайёму Нютон ёдовар мешаванд. </p><p>Соли <a href="/wiki/1556" class="mw-redirect" title="1556">1556</a> математики итолиёӣ Тарталия (1449-1557) дар асараш «Тадқиқоти умумии ададҳо ва ченакҳо» ҷадвали бо ном «коэффитсиентҳои беномиро» ҷой дода буд, ки барои ёфтани коэффитсиентҳои намуди формулаҳои зарби мухтасар дошта хидмат мекард. Масалан, ҳангоми ба дараҷаи ду бардоштани дуаъзогии а+b коэффитсиентҳои 1, 2, 1; ҳангоми ба дараҷаи се бардоштани он коэффитсиентхри 1, 3, 3, 1 ва ғайра ҳосил мешуд (ниг ба коэффитсиентҳои формулаҳои (1-2); (3-4) ва ғайра). Минбаъд Паскал (1623-1662) ҳамин коэффитсиентҳоро дар шакли секунҷа овардааст, ки дар таърих бо номи <a href="/w/index.php?title=%D0%A1%D0%B5%D0%BA%D1%83%D0%BD%D2%B7%D0%B0%D0%B8_%D0%9F%D0%B0%D1%81%D0%BA%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Секунҷаи Паскал (саҳифа вуҷуд надорад)">секунҷаи Паскал</a> ё секунҷаи арифметики маъруф аст. </p> <div class="mw-heading mw-heading2"><h2 id="Эзоҳ"><span id=".D0.AD.D0.B7.D0.BE.D2.B3"></span>Эзоҳ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=8" title="Вироиши қисмат: Эзоҳ" class="mw-editsection-visualeditor"><span>вироиш</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=8" title="Edit section's source code: Эзоҳ"><span>вироиши манбаъ</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Соярӯшанҳои_таърихи_илмҳои_дақиқ-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Соярӯшанҳои_таърихи_илмҳои_дақиқ_1-0">1.0</a></sup> <sup><a href="#cite_ref-Соярӯшанҳои_таърихи_илмҳои_дақиқ_1-1">1.1</a></sup> <sup><a href="#cite_ref-Соярӯшанҳои_таърихи_илмҳои_дақиқ_1-2">1.2</a></sup></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://sadoimardum.tj/maorif/soyar-shan-oi-ta-rihi-ilm-oi-da-i/">Соярӯшанҳои таърихи илмҳои дақиқ</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Сарчашма"><span id=".D0.A1.D0.B0.D1.80.D1.87.D0.B0.D1.88.D0.BC.D0.B0"></span>Сарчашма</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=9" title="Вироиши қисмат: Сарчашма" class="mw-editsection-visualeditor"><span>вироиш</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=9" title="Edit section's source code: Сарчашма"><span>вироиши манбаъ</span></a><span class="mw-editsection-bracket">]</span></span></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Баргирифта аз "<a dir="ltr" href="https://tg.wikipedia.org/w/index.php?title=Алгебра&oldid=1370979">https://tg.wikipedia.org/w/index.php?title=Алгебра&oldid=1370979</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D0%92%D0%B8%D0%B6%D0%B0:%D0%93%D1%83%D1%80%D3%AF%D2%B3%D2%B3%D0%BE" title="Вижа:Гурӯҳҳо">Гурӯҳҳо</a>: <ul><li><a href="/w/index.php?title=%D0%93%D1%83%D1%80%D3%AF%D2%B3:%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%9C%D0%B0%D2%9B%D0%BE%D0%BB%D0%B0%D2%B3%D0%BE_%D0%B1%D0%BE_%D0%BF%D0%B0%D1%80%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D0%B8_%D0%B4%D0%B0%D1%81%D1%82%D0%BD%D0%BE%D1%80%D0%B0%D1%81%D0%B8_%D1%81%D0%B0%D0%BD%D0%B0_%D0%B4%D0%B0%D1%80_%D1%88%D0%B0%D0%B1%D0%BB%D0%BE%D0%BD&action=edit&redlink=1" class="new" title="Гурӯҳ:Википедия:Мақолаҳо бо параметри дастнораси сана дар шаблон (саҳифа вуҷуд надорад)">Википедия:Мақолаҳо бо параметри дастнораси сана дар шаблон</a></li><li><a href="/wiki/%D0%93%D1%83%D1%80%D3%AF%D2%B3:%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Гурӯҳ:Алгебра">Алгебра</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Ин саҳифаро бори охир дар 4 сентябри 2023, 09:35 вироиш карда буданд.</li> <li id="footer-info-copyright">Матн зери иҷозатномаи <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License</a> дастрас мебошад, дигар иҷозатномаҳои иловагӣ низ ба кор бурда мешаванд. 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