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</span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/%D0%9C%D0%B0%D1%85%D1%81%D1%83%D1%81:%D0%AD%D2%99%D0%BB%D3%99%D2%AF" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Википедия эсендә эҙләү [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Эҙләү</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input 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class="vector-appearance-landmark" aria-label="Уҡыу көйләүҙәре"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Измените внешний вид страницы, размер, ширину и цвет шрифта." > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Уҡыу көйләүҙәре" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Уҡыу көйләүҙәре</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=ba" class=""><span>Иғәнә</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%9C%D0%B0%D1%85%D1%81%D1%83%D1%81:%D0%98%D2%AB%D3%99%D0%BF_%D1%8F%D2%99%D1%8B%D1%83%D1%8B_%D1%8F%D2%BB%D0%B0%D1%83&returnto=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4+%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B" title="Мотлаҡ булмаһа ла, иҫәп яҙмаһы төҙөргә һәм системала танылырға тәҡдим итәбеҙ" class=""><span>Теркәлеү</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%9C%D0%B0%D1%85%D1%81%D1%83%D1%81:%D0%A2%D0%B0%D0%BD%D1%8B%D0%BB%D1%8B%D1%83&returnto=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4+%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B" title="Бында теркәлеү үтергә була, әммә мотлаҡ түгел [o]" accesskey="o" class=""><span>Танылыу</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Күберәк мөмкинлектәр" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Шәхси ҡоралдар" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Шәхси ҡоралдар</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Ҡатнашыусы менюһы" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=ba"><span>Иғәнә</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9C%D0%B0%D1%85%D1%81%D1%83%D1%81:%D0%98%D2%AB%D3%99%D0%BF_%D1%8F%D2%99%D1%8B%D1%83%D1%8B_%D1%8F%D2%BB%D0%B0%D1%83&returnto=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4+%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B" title="Мотлаҡ булмаһа ла, иҫәп яҙмаһы төҙөргә һәм системала танылырға тәҡдим итәбеҙ"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Теркәлеү</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9C%D0%B0%D1%85%D1%81%D1%83%D1%81:%D0%A2%D0%B0%D0%BD%D1%8B%D0%BB%D1%8B%D1%83&returnto=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4+%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B" title="Бында теркәлеү үтергә була, әммә мотлаҡ түгел [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Танылыу</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"> Танылмаған мөхәррирҙәр өсөн бит <a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%A0%D3%99%D1%85%D0%B8%D0%BC_%D0%B8%D1%82%D0%B5%D0%B3%D0%B5%D2%99" aria-label="Мөхәррирләү тураһында ентеклерәк"><span>Күберәк белергә</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%9C%D0%B0%D1%85%D1%81%D1%83%D1%81:%D3%A8%D0%BB%D3%A9%D1%88%D3%A9%D0%BC" title="Был IP-адрестан яһалған төҙәтеүҙәр [y]" accesskey="y"><span>Өлөш</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%9C%D0%B0%D1%85%D1%81%D1%83%D1%81:%D3%98%D2%A3%D0%B3%D3%99%D0%BC%D3%99_%D0%B1%D0%B8%D1%82%D0%B5%D0%BC" title="IP-адресығыҙ өсөн фекер алышыу бите [n]" accesskey="n"><span>Фекер алышыу</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 id="mw-dismissablenotice-anonplace"></div><script>(function(){var node=document.getElementById("mw-dismissablenotice-anonplace");if(node){node.outerHTML="\u003Cdiv class=\"mw-dismissable-notice\"\u003E\u003Cdiv class=\"mw-dismissable-notice-close\"\u003E[\u003Ca tabindex=\"0\" role=\"button\"\u003Eйәшерергә\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv id=\"localNotice\" data-nosnippet=\"\"\u003E\u003Cdiv class=\"sitenotice\" lang=\"ba\" dir=\"ltr\"\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></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="Сайт"> <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="Йөкмәткеһе" 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 class="vector-pinnable-header-label">Йөкмәткеһе</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ҡабырға панеленә күсерергә</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">йәшерергә</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Башы</div> </a> </li> <li id="toc-Төп_мәғлүмәттәр" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Төп_мәғлүмәттәр"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Төп мәғлүмәттәр</span> </div> </a> <ul id="toc-Төп_мәғлүмәттәр-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Аксиоматика" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Аксиоматика"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Аксиоматика</span> </div> </a> <ul id="toc-Аксиоматика-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Тамғалауҙар_системалары" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Тамғалауҙар_системалары"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Тамғалауҙар системалары</span> </div> </a> <ul id="toc-Тамғалауҙар_системалары-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Шулай_уҡ_ҡарағыҙ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Шулай_уҡ_ҡарағыҙ"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Шулай уҡ ҡарағыҙ</span> </div> </a> <ul id="toc-Шулай_уҡ_ҡарағыҙ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Әҙәбиәт" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Әҙәбиәт"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Әҙәбиәт</span> </div> </a> <ul id="toc-Әҙәбиәт-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="Йөкмәткеһе" 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="Йөкмәткене күрһәтергә/йәшерергә" > <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">Йөкмәткене күрһәтергә/йәшерергә</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">Евклид геометрияһы</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="Икенсе телдәге мәҡәләгә күсегеҙ. 83 телдә уҡырға була" > <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-83" 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">83 тел</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/Euklidiese_meetkunde" title="Euklidiese meetkunde — африкаанс" lang="af" hreflang="af" data-title="Euklidiese meetkunde" data-language-autonym="Afrikaans" data-language-local-name="африкаанс" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A9%E1%8A%AD%E1%88%8A%E1%8B%B3%E1%8B%8A_%E1%8C%82%E1%8B%8E%E1%88%9C%E1%89%B5%E1%88%AA" title="ዩክሊዳዊ ጂዎሜትሪ — амхарский" lang="am" hreflang="am" data-title="ዩክሊዳዊ ጂዎሜትሪ" data-language-autonym="አማርኛ" data-language-local-name="амхарский" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%87%D9%86%D8%AF%D8%B3%D8%A9_%D8%A5%D9%82%D9%84%D9%8A%D8%AF%D9%8A%D8%A9" title="هندسة إقليدية — арабский" lang="ar" hreflang="ar" data-title="هندسة إقليدية" data-language-autonym="العربية" data-language-local-name="арабский" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Xeometr%C3%ADa_eucl%C3%ADdea" title="Xeometría euclídea — астурийский" lang="ast" hreflang="ast" data-title="Xeometría euclídea" data-language-autonym="Asturianu" data-language-local-name="астурийский" 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/Evklid_h%C9%99nd%C9%99s%C9%99si" title="Evklid həndəsəsi — азербайджанский" lang="az" hreflang="az" data-title="Evklid həndəsəsi" data-language-autonym="Azərbaycanca" data-language-local-name="азербайджанский" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Euclidean_geometry" title="Euclidean geometry — Central Bikol" lang="bcl" hreflang="bcl" data-title="Euclidean geometry" 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%AD%D1%9E%D0%BA%D0%BB%D1%96%D0%B4%D0%B0%D0%B2%D0%B0_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Эўклідава геаметрыя — белорусский" lang="be" hreflang="be" data-title="Эўклідава геаметрыя" data-language-autonym="Беларуская" data-language-local-name="белорусский" 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%AD%D1%9E%D0%BA%D0%BB%D1%96%D0%B4%D0%B0%D0%B2%D0%B0_%D0%B3%D0%B5%D0%B0%D0%BC%D1%8D%D1%82%D1%80%D1%8B%D1%8F" title="Эўклідава геамэтрыя — белорусский (тарашкевица)" lang="be-tarask" hreflang="be-tarask" data-title="Эўклідава геамэтрыя" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="белорусский (тарашкевица)" 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%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Евклидова геометрия — болгарский" lang="bg" hreflang="bg" data-title="Евклидова геометрия" data-language-autonym="Български" data-language-local-name="болгарский" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%87%E0%A6%89%E0%A6%95%E0%A7%8D%E0%A6%B2%E0%A6%BF%E0%A6%A1%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%9C%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A6%BF" title="ইউক্লিডীয় জ্যামিতি — бенгальский" lang="bn" hreflang="bn" data-title="ইউক্লিডীয় জ্যামিতি" data-language-autonym="বাংলা" data-language-local-name="бенгальский" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Geometria_euclidiana" title="Geometria euclidiana — каталанский" lang="ca" hreflang="ca" data-title="Geometria euclidiana" data-language-autonym="Català" data-language-local-name="каталанский" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%DB%95%D9%86%D8%AF%D8%A7%D8%B2%DB%95%DB%8C_%D8%A6%DB%8C%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C" title="ئەندازەی ئیقلیدسی — центральнокурдский" lang="ckb" hreflang="ckb" data-title="ئەندازەی ئیقلیدسی" data-language-autonym="کوردی" data-language-local-name="центральнокурдский" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Eukleidovsk%C3%A1_geometrie" title="Eukleidovská geometrie — чешский" lang="cs" hreflang="cs" data-title="Eukleidovská geometrie" data-language-autonym="Čeština" data-language-local-name="чешский" 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%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D0%B9%C4%95" title="Евклид геометрийĕ — чувашский" lang="cv" hreflang="cv" data-title="Евклид геометрийĕ" data-language-autonym="Чӑвашла" data-language-local-name="чувашский" 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/Geometreg_Euclidaidd" title="Geometreg Euclidaidd — валлийский" lang="cy" hreflang="cy" data-title="Geometreg Euclidaidd" data-language-autonym="Cymraeg" data-language-local-name="валлийский" 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/Euklidisk_geometri" title="Euklidisk geometri — датский" lang="da" hreflang="da" data-title="Euklidisk geometri" data-language-autonym="Dansk" data-language-local-name="датский" 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/Euklidische_Geometrie" title="Euklidische Geometrie — немецкий" lang="de" hreflang="de" data-title="Euklidische Geometrie" data-language-autonym="Deutsch" data-language-local-name="немецкий" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B5%CE%B9%CE%B1_%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1" title="Ευκλείδεια γεωμετρία — греческий" lang="el" hreflang="el" data-title="Ευκλείδεια γεωμετρία" data-language-autonym="Ελληνικά" data-language-local-name="греческий" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Euclidean_geometry" title="Euclidean geometry — английский" lang="en" hreflang="en" data-title="Euclidean geometry" data-language-autonym="English" data-language-local-name="английский" 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/E%C5%ADklida_geometrio" title="Eŭklida geometrio — эсперанто" lang="eo" hreflang="eo" data-title="Eŭklida geometrio" 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/Geometr%C3%ADa_euclidiana" title="Geometría euclidiana — испанский" lang="es" hreflang="es" data-title="Geometría euclidiana" data-language-autonym="Español" data-language-local-name="испанский" 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/Eukleidese_geomeetria" title="Eukleidese geomeetria — эстонский" lang="et" hreflang="et" data-title="Eukleidese geomeetria" data-language-autonym="Eesti" data-language-local-name="эстонский" 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/Geometria_euklidear" title="Geometria euklidear — баскский" lang="eu" hreflang="eu" data-title="Geometria euklidear" data-language-autonym="Euskara" data-language-local-name="баскский" 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/%D9%87%D9%86%D8%AF%D8%B3%D9%87_%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C" title="هندسه اقلیدسی — персидский" lang="fa" hreflang="fa" data-title="هندسه اقلیدسی" data-language-autonym="فارسی" data-language-local-name="персидский" 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/Euklidinen_geometria" title="Euklidinen geometria — финский" lang="fi" hreflang="fi" data-title="Euklidinen geometria" data-language-autonym="Suomi" data-language-local-name="финский" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr badge-Q17437798 badge-goodarticle mw-list-item" title="яҡшы мәҡәлә"><a href="https://fr.wikipedia.org/wiki/G%C3%A9om%C3%A9trie_euclidienne" title="Géométrie euclidienne — французский" lang="fr" hreflang="fr" data-title="Géométrie euclidienne" data-language-autonym="Français" data-language-local-name="французский" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Xeometr%C3%ADa_euclidiana" title="Xeometría euclidiana — галисийский" lang="gl" hreflang="gl" data-title="Xeometría euclidiana" data-language-autonym="Galego" data-language-local-name="галисийский" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AF%E0%AB%81%E0%AA%95%E0%AB%8D%E0%AA%B2%E0%AA%BF%E0%AA%A1%E0%AA%BF%E0%AA%AF%E0%AA%A8_%E0%AA%AD%E0%AB%82%E0%AA%AE%E0%AA%BF%E0%AA%A4%E0%AA%BF" title="યુક્લિડિયન ભૂમિતિ — гуджарати" lang="gu" hreflang="gu" data-title="યુક્લિડિયન ભૂમિતિ" data-language-autonym="ગુજરાતી" data-language-local-name="гуджарати" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Euclid_K%C3%AD-h%C3%B2" title="Euclid Kí-hò — хакка" lang="hak" hreflang="hak" data-title="Euclid Kí-hò" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="хакка" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94_%D7%90%D7%95%D7%A7%D7%9C%D7%99%D7%93%D7%99%D7%AA" title="גאומטריה אוקלידית — иврит" lang="he" hreflang="he" data-title="גאומטריה אוקלידית" data-language-autonym="עברית" data-language-local-name="иврит" 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%AF%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%BF%E0%A4%A1%E0%A5%80%E0%A4%AF_%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="यूक्लिडीय ज्यामिति — хинди" lang="hi" hreflang="hi" data-title="यूक्लिडीय ज्यामिति" data-language-autonym="हिन्दी" data-language-local-name="хинди" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Euklidska_geometrija" title="Euklidska geometrija — хорватский" lang="hr" hreflang="hr" data-title="Euklidska geometrija" data-language-autonym="Hrvatski" data-language-local-name="хорватский" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Euklideszi_geometria" title="Euklideszi geometria — венгерский" lang="hu" hreflang="hu" data-title="Euklideszi geometria" data-language-autonym="Magyar" data-language-local-name="венгерский" 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/%D4%B7%D5%BE%D5%AF%D5%AC%D5%AB%D5%A4%D5%A5%D5%BD%D5%B5%D5%A1%D5%B6_%D5%A5%D6%80%D5%AF%D6%80%D5%A1%D5%B9%D5%A1%D6%83%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Էվկլիդեսյան երկրաչափություն — армянский" lang="hy" hreflang="hy" data-title="Էվկլիդեսյան երկրաչափություն" data-language-autonym="Հայերեն" data-language-local-name="армянский" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Geometri_Euklides" title="Geometri Euklides — индонезийский" lang="id" hreflang="id" data-title="Geometri Euklides" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезийский" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Geometria_euclidea" title="Geometria euclidea — итальянский" lang="it" hreflang="it" data-title="Geometria euclidea" data-language-autonym="Italiano" data-language-local-name="итальянский" 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/%E3%83%A6%E3%83%BC%E3%82%AF%E3%83%AA%E3%83%83%E3%83%89%E5%B9%BE%E4%BD%95%E5%AD%A6" title="ユークリッド幾何学 — японский" lang="ja" hreflang="ja" data-title="ユークリッド幾何学" data-language-autonym="日本語" data-language-local-name="японский" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/euklidi_tamcmaci" title="euklidi tamcmaci — ложбан" lang="jbo" hreflang="jbo" data-title="euklidi tamcmaci" data-language-autonym="La .lojban." data-language-local-name="ложбан" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/Euclidean_Geometry" title="Euclidean Geometry — кикуйю" lang="ki" hreflang="ki" data-title="Euclidean Geometry" data-language-autonym="Gĩkũyũ" data-language-local-name="кикуйю" class="interlanguage-link-target"><span>Gĩkũyũ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D1%82%D1%96%D0%BA_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Евклидтік геометрия — казахский" lang="kk" hreflang="kk" data-title="Евклидтік геометрия" data-language-autonym="Қазақша" data-language-local-name="казахский" 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%AF%E0%B3%82%E0%B2%95%E0%B3%8D%E0%B2%B2%E0%B2%BF%E0%B2%A1%E0%B3%80%E0%B2%AF_%E0%B2%9C%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%AE%E0%B2%BF%E0%B2%A4%E0%B2%BF" title="ಯೂಕ್ಲಿಡೀಯ ಜ್ಯಾಮಿತಿ — каннада" lang="kn" hreflang="kn" data-title="ಯೂಕ್ಲಿಡೀಯ ಜ್ಯಾಮಿತಿ" 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/%EC%9C%A0%ED%81%B4%EB%A6%AC%EB%93%9C_%EA%B8%B0%ED%95%98%ED%95%99" title="유클리드 기하학 — корейский" lang="ko" hreflang="ko" data-title="유클리드 기하학" data-language-autonym="한국어" data-language-local-name="корейский" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Евклид геометриясы — киргизский" lang="ky" hreflang="ky" data-title="Евклид геометриясы" data-language-autonym="Кыргызча" data-language-local-name="киргизский" 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/Geometria_Euclidea" title="Geometria Euclidea — латинский" lang="la" hreflang="la" data-title="Geometria Euclidea" data-language-autonym="Latina" data-language-local-name="латинский" 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/Jeometria_euclidal" title="Jeometria euclidal — Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Jeometria euclidal" 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-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Euklidin%C4%97_geometrija" title="Euklidinė geometrija — литовский" lang="lt" hreflang="lt" data-title="Euklidinė geometrija" data-language-autonym="Lietuvių" data-language-local-name="литовский" 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/Eikl%C4%ABda_%C4%A3eometrija" title="Eiklīda ģeometrija — латышский" lang="lv" hreflang="lv" data-title="Eiklīda ģeometrija" data-language-autonym="Latviešu" data-language-local-name="латышский" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Евклидова геометрија — македонский" lang="mk" hreflang="mk" data-title="Евклидова геометрија" data-language-autonym="Македонски" data-language-local-name="македонский" 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%AF%E0%B5%82%E0%B4%95%E0%B5%8D%E0%B4%B2%E0%B4%BF%E0%B4%A1%E0%B4%BF%E0%B4%AF%E0%B5%BB_%E0%B4%9C%E0%B5%8D%E0%B4%AF%E0%B4%BE%E0%B4%AE%E0%B4%BF%E0%B4%A4%E0%B4%BF" title="യൂക്ലിഡിയൻ ജ്യാമിതി — малаялам" lang="ml" hreflang="ml" data-title="യൂക്ലിഡിയൻ ജ്യാമിതി" data-language-autonym="മലയാളം" data-language-local-name="малаялам" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%B8%D0%B9%D0%BD_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80" title="Евклидийн геометр — монгольский" lang="mn" hreflang="mn" data-title="Евклидийн геометр" data-language-autonym="Монгол" data-language-local-name="монгольский" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Geometri_Euclid" title="Geometri Euclid — малайский" lang="ms" hreflang="ms" data-title="Geometri Euclid" data-language-autonym="Bahasa Melayu" data-language-local-name="малайский" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Euclidische_meetkunde" title="Euclidische meetkunde — нидерландский" lang="nl" hreflang="nl" data-title="Euclidische meetkunde" data-language-autonym="Nederlands" data-language-local-name="нидерландский" 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/Euklidsk_geometri" title="Euklidsk geometri — нюнорск" lang="nn" hreflang="nn" data-title="Euklidsk geometri" data-language-autonym="Norsk nynorsk" data-language-local-name="нюнорск" 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/Euklidsk_geometri" title="Euklidsk geometri — норвежский букмол" lang="nb" hreflang="nb" data-title="Euklidsk geometri" data-language-autonym="Norsk bokmål" data-language-local-name="норвежский букмол" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Geometria_euclidiana" title="Geometria euclidiana — окситанский" lang="oc" hreflang="oc" data-title="Geometria euclidiana" data-language-autonym="Occitan" data-language-local-name="окситанский" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Geometria_euklidesowa" title="Geometria euklidesowa — польский" lang="pl" hreflang="pl" data-title="Geometria euklidesowa" data-language-autonym="Polski" data-language-local-name="польский" 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/Geometr%C3%ACa_euclid%C3%A9a" title="Geometrìa euclidéa — Piedmontese" lang="pms" hreflang="pms" data-title="Geometrìa euclidéa" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Geometria_euclidiana" title="Geometria euclidiana — португальский" lang="pt" hreflang="pt" data-title="Geometria euclidiana" data-language-autonym="Português" data-language-local-name="португальский" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Geometrie_euclidian%C4%83" title="Geometrie euclidiană — румынский" lang="ro" hreflang="ro" data-title="Geometrie euclidiană" data-language-autonym="Română" data-language-local-name="румынский" 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%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Евклидова геометрия — русский" lang="ru" hreflang="ru" data-title="Евклидова геометрия" data-language-autonym="Русский" data-language-local-name="русский" 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%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D1%81%D0%BA%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Евклидовска геометрия — русинский" lang="rue" hreflang="rue" data-title="Евклидовска геометрия" data-language-autonym="Русиньскый" data-language-local-name="русинский" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Giomitr%C3%ACa_euclidea" title="Giomitrìa euclidea — сицилийский" lang="scn" hreflang="scn" data-title="Giomitrìa euclidea" data-language-autonym="Sicilianu" data-language-local-name="сицилийский" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Euklidova_geometrija" title="Euklidova geometrija — сербскохорватский" lang="sh" hreflang="sh" data-title="Euklidova geometrija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="сербскохорватский" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%BA%E0%B7%96%E0%B6%9A%E0%B7%8A%E0%B6%BD%E0%B7%92%E0%B6%A9%E0%B7%92%E0%B6%BA%E0%B7%8F%E0%B6%B1%E0%B7%94_%E0%B6%A2%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%B8%E0%B7%92%E0%B6%AD%E0%B7%92%E0%B6%BA" title="යූක්ලිඩියානු ජ්‍යාමිතිය — сингальский" lang="si" hreflang="si" data-title="යූක්ලිඩියානු ජ්‍යාමිතිය" data-language-autonym="සිංහල" data-language-local-name="сингальский" 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/Euclidean_geometry" title="Euclidean geometry — Simple English" lang="en-simple" hreflang="en-simple" data-title="Euclidean geometry" 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/Euklidovsk%C3%A1_geometria" title="Euklidovská geometria — словацкий" lang="sk" hreflang="sk" data-title="Euklidovská geometria" data-language-autonym="Slovenčina" data-language-local-name="словацкий" 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/Evklidska_geometrija" title="Evklidska geometrija — словенский" lang="sl" hreflang="sl" data-title="Evklidska geometrija" data-language-autonym="Slovenščina" data-language-local-name="словенский" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Gjeometria_euklidiane" title="Gjeometria euklidiane — албанский" lang="sq" hreflang="sq" data-title="Gjeometria euklidiane" data-language-autonym="Shqip" data-language-local-name="албанский" 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%95%D1%83%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Еуклидова геометрија — сербский" lang="sr" hreflang="sr" data-title="Еуклидова геометрија" data-language-autonym="Српски / srpski" data-language-local-name="сербский" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Euklidisk_geometri" title="Euklidisk geometri — шведский" lang="sv" hreflang="sv" data-title="Euklidisk geometri" data-language-autonym="Svenska" data-language-local-name="шведский" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AF%E0%AF%82%E0%AE%95%E0%AF%8D%E0%AE%B3%E0%AF%80%E0%AE%9F%E0%AF%8D_%E0%AE%B5%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="யூக்ளீட் வடிவியல் — тамильский" lang="ta" hreflang="ta" data-title="யூக்ளீட் வடிவியல்" data-language-autonym="தமிழ்" data-language-local-name="тамильский" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D2%B2%D0%B0%D0%BD%D0%B4%D0%B0%D1%81%D0%B0%D0%B8_%D1%83%D2%9B%D0%BB%D0%B8%D0%B4%D1%83%D1%81%D3%A3" title="Ҳандасаи уқлидусӣ — таджикский" lang="tg" hreflang="tg" data-title="Ҳандасаи уқлидусӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="таджикский" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%A3%E0%B8%82%E0%B8%B2%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B9%81%E0%B8%9A%E0%B8%9A%E0%B8%A2%E0%B8%B8%E0%B8%84%E0%B8%A5%E0%B8%B4%E0%B8%94" title="เรขาคณิตแบบยุคลิด — тайский" lang="th" hreflang="th" data-title="เรขาคณิตแบบยุคลิด" data-language-autonym="ไทย" data-language-local-name="тайский" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%96klid_geometrisi" title="Öklid geometrisi — турецкий" lang="tr" hreflang="tr" data-title="Öklid geometrisi" data-language-autonym="Türkçe" data-language-local-name="турецкий" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D1%87%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Евклидча геометрия — татарский" lang="tt" hreflang="tt" data-title="Евклидча геометрия" data-language-autonym="Татарча / tatarça" data-language-local-name="татарский" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D1%96%D0%B4%D0%BE%D0%B2%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F" title="Евклідова геометрія — украинский" lang="uk" hreflang="uk" data-title="Евклідова геометрія" data-language-autonym="Українська" data-language-local-name="украинский" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Yevklid_geometriyasi" title="Yevklid geometriyasi — узбекский" lang="uz" hreflang="uz" data-title="Yevklid geometriyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="узбекский" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%ACnh_h%E1%BB%8Dc_Euclid" title="Hình học Euclid — вьетнамский" lang="vi" hreflang="vi" data-title="Hình học Euclid" data-language-autonym="Tiếng Việt" data-language-local-name="вьетнамский" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="欧几里得几何 — у" lang="wuu" hreflang="wuu" data-title="欧几里得几何" data-language-autonym="吴语" data-language-local-name="у" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%9C%E2%B4%B0%E2%B5%8F%E2%B5%A3%E2%B4%B3%E2%B4%B3%E2%B5%89%E2%B5%9C_%E2%B5%9C%E2%B5%93%E2%B4%BD%E2%B5%8D%E2%B5%89%E2%B4%B7%E2%B5%9C" title="ⵜⴰⵏⵣⴳⴳⵉⵜ ⵜⵓⴽⵍⵉⴷⵜ — тамазигхтский" lang="zgh" hreflang="zgh" data-title="ⵜⴰⵏⵣⴳⴳⵉⵜ ⵜⵓⴽⵍⵉⴷⵜ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="тамазигхтский" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="欧几里得几何 — китайский" lang="zh" hreflang="zh" data-title="欧几里得几何" data-language-autonym="中文" data-language-local-name="китайский" 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/%E6%AD%90%E6%B0%8F%E5%B9%BE%E4%BD%95" title="歐氏幾何 — Literary Chinese" lang="lzh" hreflang="lzh" data-title="歐氏幾何" 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-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%AD%90%E5%B9%BE%E9%87%8C%E5%BE%97%E5%B9%BE%E4%BD%95" title="歐幾里得幾何 — кантонский" lang="yue" hreflang="yue" data-title="歐幾里得幾何" data-language-autonym="粵語" data-language-local-name="кантонский" 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/Q162886#sitelinks-wikipedia" title="Башҡа телдәргә һылтанмаларҙы төҙәтеү" class="wbc-editpage">Һылтанмаларҙы төҙәтергә</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="Исем арауыҡтары"> <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 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cellspacing="2" class="infobox ts-Универсальная_карточка"> <tbody><tr><td colspan="2" class="infobox-above ts-Универсальная_карточка-above">Евклид геометрияһы</td></tr> <tr><td colspan="2" class="infobox-image ts-Универсальная_карточка-image"><span data-wikidata-claim-id="Q162886$2D0CB278-EDE4-46A2-B1A8-39253D493A84" class="wikidata-claim" data-wikidata-property-id="P18"><span class="wikidata-snak wikidata-main-snak"><span typeof="mw:File/Frameless"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Dodecahedron.gif" class="mw-file-description"><img alt="Рәсем" src="//upload.wikimedia.org/wikipedia/commons/7/73/Dodecahedron.gif" decoding="async" width="256" height="256" class="mw-file-element" data-file-width="256" data-file-height="256" /></a></span></span></span></td></tr> <tr><th class="infobox-label ts-Универсальная_карточка-label">Кем хөрмәтенә аталған</th><td class="infobox-text"> <span data-wikidata-claim-id="q162886$99039bd1-470d-276a-9cca-19cd7cd036e1" class="wikidata-claim" data-wikidata-property-id="P138"><span class="wikidata-snak wikidata-main-snak"><a href="/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид">Евклид</a></span></span></td></tr> <tr><th class="infobox-label ts-Универсальная_карточка-label">Башланыу датаһы</th><td class="infobox-text"> <span data-wikidata-claim-id="Q162886$7dfd16c9-417a-41e1-b041-5c3bc4f2d6f3" class="wikidata-claim" data-wikidata-property-id="P580"><span class="wikidata-snak wikidata-main-snak"><a href="/w/index.php?title=%D0%91._%D1%8D._%D1%82._III_%D0%B1%D1%8B%D1%83%D0%B0%D1%82&action=edit&redlink=1" class="new" title="Б. э. т. III быуат (был бит юҡ)">Б. э. т. III быуат</a></span></span></td></tr> <tr><th class="infobox-label ts-Универсальная_карточка-label">Вики-проект</th><td class="infobox-text"> <span data-wikidata-claim-id="Q162886$AF6C5A8C-073A-47EF-A1A1-347AC8F2179A" class="wikidata-claim" data-wikidata-property-id="P6104"><span class="wikidata-snak wikidata-main-snak"><span class="plainlinks"><a class="external text" href="https://ru.wikipedia.org/w/index.php?title=%D0%9F%D1%80%D0%BE%D0%B5%D0%BA%D1%82%3A%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0&action=edit&editintro=T:Нет_статьи/editintro&preload=T:Нет_статьи/preload&preloadparams%5B%5D=Q8487137&preloadparams%5B%5D=%D0%9F%D1%80%D0%BE%D0%B5%D0%BA%D1%82%3A%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0&preloadparams%5B%5D=Универсальная+карточка"><span style="color:var(--color-link-red, #d73333); text-decoration:inherit; text-decoration-color:var(--color-link-red, #d73333);">Проект:Математика</span></a></span><sup><a href="https://www.wikidata.org/wiki/Q8487137" class="extiw" title="d:Q8487137">[d]</a></sup></span></span></td></tr> <tr><td colspan="2" class="infobox-below ts-Универсальная_карточка-below"><span data-wikidata-claim-id="Q162886$f1ac68f8-4d15-665e-15fd-9c682189df85" class="wikidata-claim" data-wikidata-property-id="P373"><span class="wikidata-snak wikidata-main-snak"><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/Category:Euclidean_geometry" title="commons:Category:Euclidean geometry"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> <a href="https://commons.wikimedia.org/wiki/Category:Euclidean_geometry" class="extiw" title="commons:Category:Euclidean geometry">Евклид геометрияһы Викимилектә</a></span></span></td></tr> </tbody></table> <p><b>Евкли́д геоме́трияһы</b> (йәки <b>элементар геометрия</b>) — башлап <a href="/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид">Евклидтың</a> <a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B1%D0%B0%D1%88%D0%BB%D0%B0%D0%BD%D2%93%D1%8B%D1%81%D1%82%D0%B0%D1%80%D1%8B&action=edit&redlink=1" class="new" title="Евклид башланғыстары (был бит юҡ)">«Башланғыстар»</a> китабында яҙылған (<a href="/w/index.php?title=%D0%91._%D1%8D._%D1%82%D0%B8%D0%BA%D0%BB%D0%B5%D0%BC_III_%D0%B1%D1%8B%D1%83%D0%B0%D1%82&action=edit&redlink=1" class="new" title="Б. э. тиклем III быуат (был бит юҡ)">б. э. тиклем III быуат</a>) <a href="/w/index.php?title=%D0%90%D0%BA%D1%81%D0%B8%D0%BE%D0%BC%D0%B0%D0%BB%D0%B0%D1%80_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0%D2%BB%D1%8B&action=edit&redlink=1" class="new" title="Аксиомалар системаһы (был бит юҡ)">аксиомалар системаһына</a> нигеҙләнгән геометрик <a href="/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F" title="Теория">теория</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Төп_мәғлүмәттәр"><span id=".D0.A2.D3.A9.D0.BF_.D0.BC.D3.99.D2.93.D0.BB.D2.AF.D0.BC.D3.99.D1.82.D1.82.D3.99.D1.80"></span>Төп мәғлүмәттәр</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B&veaction=edit&section=1" title="Төп мәғлүмәттәр бүлеген мөхәррирләргә" class="mw-editsection-visualeditor"><span>үҙгәртергә</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B&action=edit&section=1" title="Төп мәғлүмәттәр бүлегенең сығанаҡ кодын мөхәррирләү"><span>сығанаҡты үҙгәртеү</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Элементар геометрия</b> — башлыса күсеш <a href="/wiki/%D0%A2%D3%A9%D1%80%D0%BA%D3%A9%D0%BC_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Төркөм (математика)">төркөмө</a> (<a href="/w/index.php?title=%D0%98%D0%B7%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&redlink=1" class="new" title="Изометрия (математика) (был бит юҡ)">изометриялар</a>) һәм <a href="/wiki/%D0%9E%D2%A1%D1%88%D0%B0%D1%88%D0%BB%D1%8B%D2%A1" title="Оҡшашлыҡ">оҡшашлыҡ</a> <a href="/wiki/%D0%A2%D3%A9%D1%80%D0%BA%D3%A9%D0%BC_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Төркөм (математика)"> төркөмө</a> менән билдәләнгән геометрия. Әммә элементар геометрия йөкмәткеһе күрһәтелгән үҙгәртеүҙәр менән генә бөтмәй. Элементар геометрияға шулай уҡ <a href="/w/index.php?title=%D0%98%D0%BD%D0%B2%D0%B5%D1%80%D1%81%D0%B8%D1%8F_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)&action=edit&redlink=1" class="new" title="Инверсия (геометрия) (был бит юҡ)">инверсия</a> үҙгәртеүен, <a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B8%D0%BA_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F&action=edit&redlink=1" class="new" title="Сферик геометрия (был бит юҡ)">сферик геометрия</a> мәсьәләләрен, <a href="/w/index.php?title=%D0%A6%D0%B8%D1%80%D0%BA%D1%83%D0%BB%D1%8C_%D2%BB%D3%99%D0%BC_%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BA%D0%B0_%D1%8F%D1%80%D2%99%D0%B0%D0%BC%D1%8B%D0%BD%D0%B4%D0%B0_%D1%82%D3%A9%D2%99%D3%A9%D2%AF&action=edit&redlink=1" class="new" title="Циркуль һәм линейка ярҙамында төҙөү (был бит юҡ)">геометрик төҙөүҙәр</a> элементтарын, геометрик дәүмәлдәрҙе үлсәү теорияһын һәм башҡа мәсьәләләрҙе индерәләр. </p><p>Элементар геометрияны йыш ҡына <b>Евклид геометрияһы</b> тип атайҙар, сөнки ул, етерлек ҡәтғи булмаһа ла, тәү башлап һәм систематик рәүештә <a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D1%82%D1%8B%D2%A3_%D0%91%D0%B0%D1%88%D0%BB%D0%B0%D0%BD%D2%93%D1%8B%D1%81%D1%82%D0%B0%D1%80%D1%8B&action=edit&redlink=1" class="new" title="Евклидтың Башланғыстары (был бит юҡ)">Евклидтың «Башланғыстар»ында</a> яҙылған. Элементар геометрияның беренсе ҡәтғи аксиоматикаһы <a href="/w/index.php?title=%D0%93%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82,_%D0%94%D0%B0%D0%B2%D0%B8%D0%B4&action=edit&redlink=1" class="new" title="Гильберт, Давид (был бит юҡ)">Гильберт</a> тарафынан бирелгән. Элементар геометрия дөйөм урта белем биреү мәктәбендә өйрәнелә. </p> <div class="mw-heading mw-heading2"><h2 id="Аксиоматика"><span id=".D0.90.D0.BA.D1.81.D0.B8.D0.BE.D0.BC.D0.B0.D1.82.D0.B8.D0.BA.D0.B0"></span>Аксиоматика</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B&veaction=edit&section=2" title="Аксиоматика бүлеген мөхәррирләргә" class="mw-editsection-visualeditor"><span>үҙгәртергә</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B&action=edit&section=2" title="Аксиоматика бүлегенең сығанаҡ кодын мөхәррирләү"><span>сығанаҡты үҙгәртеү</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Элементар геометрияны аксиоматикалаштырыу мәсьәләһе <a href="/wiki/%D0%90%D0%BA%D1%81%D0%B8%D0%BE%D0%BC%D0%B0" title="Аксиома">аксиомалар</a> системаһын, Евклид геометрияһының бөтә раҫлауҙары был аксиомаларҙан, һыҙмаларҙың күргәҙмәлелегенән тыш, логик һығымта яһау юлы менән сығырлыҡ итеп төҙөүҙә тора. </p><p><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D1%82%D1%8B%D2%A3_%D0%91%D0%B0%D1%88%D0%BB%D0%B0%D0%BD%D2%93%D1%8B%D1%81%D1%82%D0%B0%D1%80%D1%8B&action=edit&redlink=1" class="new" title="Евклидтың Башланғыстары (был бит юҡ)">Евклидтың «Башланғыстар»ында</a> шундай аксиомалар системаһы була: </p> <ol><li>Теләһә ниндәй нөктәнән теләһә ниндәй нөктәгә тиклем тура һыҙыҡ үткәреп була.</li> <li>Сикләнгән тура һыҙыҡты тура һыҙыҡҡа тиклем өҙлөкһөҙ дауам итеп була.</li> <li>Һәр үҙәктән теләһә ниндәй радиус менән түңәрәк ҡамарға мөмкин.</li> <li>Бөтә тура мөйөштәр ҙә үҙ-ара тигеҙ.</li> <li>Әгәр ике тура һыҙыҡты киҫкән тура һыҙыҡ ике тура мөйөштән бәләкәйерәк эске бер яҡлы мөйөштәр барлыҡҡа килтерһә, сикһеҙ дауам ителгән был ике тура һыҙыҡ, мөйөштәре ике тура мөйөштән бәләкәйерәк булған яҡтан осрашалар.</li></ol> <p>Был система, бер математик икенсеһен аңлау өсөн етерлек була, ләкин иҫбатлауҙарҙа аңғармаҫтан икенсе раҫлауҙар ҡулланыла. </p><p>Айырып әйткәндә, <a href="/w/index.php?title=%D0%9F%D0%B0%D1%88%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0%D2%BB%D1%8B&action=edit&redlink=1" class="new" title="Паша теоремаһы (был бит юҡ)">Паша теоремаһы</a>. Шулай уҡ был аксиомалар системаһынан бирелгән яҡтары <a href="/w/index.php?title=%D3%A8%D1%81%D0%BC%D3%A9%D0%B9%D3%A9%D1%88_%D1%82%D0%B8%D0%B3%D0%B5%D2%99%D2%BB%D0%B5%D2%99%D0%BB%D0%B5%D0%B3%D0%B5&action=edit&redlink=1" class="new" title="Өсмөйөш тигеҙһеҙлеге (был бит юҡ)">өсмөйөш тигеҙһеҙлеген</a> ҡәнәғәтләндергән өсмөйөштөң булыуы килеп сыҡмай <span class="noprint"><sup><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%A1%D1%8B%D2%93%D0%B0%D0%BD%D0%B0%D2%A1%D1%82%D0%B0%D1%80%D2%93%D0%B0_%D2%BB%D1%8B%D0%BB%D1%82%D0%B0%D0%BD%D0%BC%D0%B0%D0%BB%D0%B0%D1%80" title="Википедия:Сығанаҡтарға һылтанмалар">[<i>сығанаҡ 3206  көн күрһәтелмәгән</i>]</a></sup></span>. </p><p><a href="/wiki/1899_%D0%B9%D1%8B%D0%BB" title="1899 йыл">1899 йылда</a> <a href="/w/index.php?title=%D0%93%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82,_%D0%94%D0%B0%D0%B2%D0%B8%D0%B4&action=edit&redlink=1" class="new" title="Гильберт, Давид (был бит юҡ)">Гильберт</a> беренсе етерлек ҡәтғи <a href="/w/index.php?title=%D0%93%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82_%D0%B0%D0%BA%D1%81%D0%B8%D0%BE%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D2%BB%D1%8B&action=edit&redlink=1" class="new" title="Гильберт аксиоматикаһы (был бит юҡ)">Евклид геометрияһы аксиоматикаһын</a> тәҡдим итә. Евклид геометрияһы аксиоматикаһын Гильбертҡа тиклем <a href="/w/index.php?title=%D0%9F%D0%B0%D1%88,_%D0%9C%D0%BE%D1%80%D0%B8%D1%86&action=edit&redlink=1" class="new" title="Паш, Мориц (был бит юҡ)">Паш</a>, <a href="/w/index.php?title=%D0%A8%D1%83%D1%80,_%D0%A4%D1%80%D0%B5%D0%B4%D0%B5%D1%80%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Шур, Фредерик (был бит юҡ)">Шур</a><sup><a href="https://en.wikipedia.org/wiki/Friedrich_Schur" class="extiw" title="en:Friedrich Schur"><span style="font-style:normal; font-weight:normal;" title="Friedrich Schur — инглиз телендә мәҡәлә версияһы">[en]</span></a></sup>, <a href="/w/index.php?title=%D0%9F%D0%B5%D0%B0%D0%BD%D0%BE,_%D0%94%D0%B6%D1%83%D0%B7%D0%B5%D0%BF%D0%BF%D0%B5&action=edit&redlink=1" class="new" title="Пеано, Джузеппе (был бит юҡ)">Пеано</a>, <a href="/w/index.php?title=%D0%92%D0%B5%D1%80%D0%BE%D0%BD%D0%B5%D0%B7%D0%B5,_%D0%94%D0%B6%D1%83%D0%B7%D0%B5%D0%BF%D0%BF%D0%B5&action=edit&redlink=1" class="new" title="Веронезе, Джузеппе (был бит юҡ)">Веронезе</a> яҡшыртырға маташып ҡарай, әммә Гильберттың ҡарашы, төшөнсәләрҙе һайлауҙа консерваторлығына ҡарамай, уңышлыраҡ булып сыға. Башҡа хәҙерге заман аксиоматикалары ла бар, иң билдәлеләре: </p> <ul><li><a href="/w/index.php?title=%D0%90%D0%BB%D0%B5%D0%BA%D1%81%D0%B0%D0%BD%D0%B4%D1%80%D0%BE%D0%B2_%D0%B0%D0%BA%D1%81%D0%B8%D0%BE%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D2%BB%D1%8B&action=edit&redlink=1" class="new" title="Александров аксиоматикаһы (был бит юҡ)">Александров аксиоматикаһы</a></li> <li><a href="/w/index.php?title=%D0%91%D0%B8%D1%80%D0%B3%D0%BE%D1%84_%D0%B0%D0%BA%D1%81%D0%B8%D0%BE%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D2%BB%D1%8B&action=edit&redlink=1" class="new" title="Биргоф аксиоматикаһы (был бит юҡ)">Биргоф аксиоматикаһы</a>, барлығы 4 аксиоманан тора, ләкин ысын һандарҙы әҙер төшөнсә кеүек ҡуллана.</li> <li><a href="/w/index.php?title=%D0%A2%D0%B0%D1%80%D1%81%D0%BA%D0%B8%D0%B9_%D0%B0%D0%BA%D1%81%D0%B8%D0%BE%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D2%BB%D1%8B&action=edit&redlink=1" class="new" title="Тарский аксиоматикаһы (был бит юҡ)">Тарский аксиоматикаһы</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Тамғалауҙар_системалары"><span id=".D0.A2.D0.B0.D0.BC.D2.93.D0.B0.D0.BB.D0.B0.D1.83.D2.99.D0.B0.D1.80_.D1.81.D0.B8.D1.81.D1.82.D0.B5.D0.BC.D0.B0.D0.BB.D0.B0.D1.80.D1.8B"></span>Тамғалауҙар системалары</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B&veaction=edit&section=3" title="Тамғалауҙар системалары бүлеген мөхәррирләргә" class="mw-editsection-visualeditor"><span>үҙгәртергә</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B&action=edit&section=3" title="Тамғалауҙар системалары бүлегенең сығанаҡ кодын мөхәррирләү"><span>сығанаҡты үҙгәртеү</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Бер нисә көнәркәшле тамғалауҙар системаһы бар. </p> <ul><li>Нөктәләр ғәҙәттә ҙур латин хәрефтәре <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A,B,C,\dots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> <mo>,</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A,B,C,\dots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e52a4e31e9f1ae344fa5536be4835405050aa17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.098ex; height:2.509ex;" alt="{\displaystyle A,B,C,\dots }"></span> менән тамғаланалар.</li> <li>Тура һыҙыҡтар ғәҙәттә бәләкәй латин хәрефтәре <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a,b,c,\dots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>,</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a,b,c,\dots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/948b9e9c25a46ba3515e07facbbee84dd8db5bcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.059ex; height:2.509ex;" alt="{\displaystyle a,b,c,\dots }"></span> менән тамғаланалар.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> һәм <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> нөктәләре араһындағы алыҫлыҡ ғәҙәттә <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle PQ}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PQ}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56648d25dcb487300d460480dec33d3c713fe4ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.584ex; height:2.509ex;" alt="{\displaystyle PQ}"></span> йәки <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |PQ|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>P</mi> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |PQ|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bce9b5b9a3507edea5dd51e5fe92e446776e4c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.877ex; height:2.843ex;" alt="{\displaystyle |PQ|}"></span> тип тамғалана.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> һәм <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> нөктәләре араһындағы киҫек ғәҙәттә <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [PQ]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>P</mi> <mi>Q</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [PQ]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1103707481b5a55fd636cb13fdd707c6822b80c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.877ex; height:2.843ex;" alt="{\displaystyle [PQ]}"></span> йәки <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {PQ}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {PQ}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ad2cb75b43d5d9406bd87afc2da2bcbc9eb8241" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.699ex; height:3.343ex;" alt="{\displaystyle {\overline {PQ}}}"></span> тип тамғалана.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> нөктәһенән <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> нөктәһе аша нур ғәҙәттә <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [PQ)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>P</mi> <mi>Q</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [PQ)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a41c60f98565a706e803b7080ec86d83270ced8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.135ex; height:2.843ex;" alt="{\displaystyle [PQ)}"></span> йәки <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {PQ}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo>→</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {PQ}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/675febeea8e91072fb11994af206714d0bc598a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-top: -0.4ex; width:3.714ex; height:4.176ex;" alt="{\displaystyle {\overrightarrow {PQ}}}"></span> тип тамғалана.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> һәм <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> нөктәләре аша тура һыҙыҡ ғәҙәттә <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (PQ)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>P</mi> <mi>Q</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (PQ)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e08b8df5668d3213b657afdee5a8d3ce4c93c67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.393ex; height:2.843ex;" alt="{\displaystyle (PQ)}"></span> йәки <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overleftrightarrow {PQ}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo>↔</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overleftrightarrow {PQ}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8d29d32aa56c1fd24dfbe0a97d77c8e6337862f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.714ex; height:4.009ex;" alt="{\displaystyle {\overleftrightarrow {PQ}}}"></span> тип тамғалана.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> һәм <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> нөктәләре түбәләре булған өсмөйөш ғәҙәттә <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \triangle PQR}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">△</mi> <mi>P</mi> <mi>Q</mi> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \triangle PQR}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe141632c5c249fa78ca2eb47ab8aa2e758a36a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.414ex; height:2.509ex;" alt="{\displaystyle \triangle PQR}"></span> йәки <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [PQR]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>P</mi> <mi>Q</mi> <mi>R</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [PQR]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d915f5adaf1949c3ef0e3cbfe636b12e1f7212bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.641ex; height:2.843ex;" alt="{\displaystyle [PQR]}"></span> тип тамғалана.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> фигураһының майҙаны ғәҙәттә <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S(F)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">(</mo> <mi>F</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S(F)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/455b465d726e4142c0b74fbf7f5d04cacf14c86d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.049ex; height:2.843ex;" alt="{\displaystyle S(F)}"></span> йәки <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |F|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |F|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3187e21284738d96caaf9b9bfc0505b0c95f75ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.034ex; height:2.843ex;" alt="{\displaystyle |F|}"></span> тип тамғалана.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [OP)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>O</mi> <mi>P</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [OP)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1802c709858b9b534333848dfe02938cb932eae5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.07ex; height:2.843ex;" alt="{\displaystyle [OP)}"></span> һәм <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [OQ)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>O</mi> <mi>Q</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [OQ)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b8aaa299c3f5827c705d9db9405219c16ba8d03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.163ex; height:2.843ex;" alt="{\displaystyle [OQ)}"></span> нурҙары менән яһалған мөйөш ғәҙәттә <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \angle POQ}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∠</mi> <mi>P</mi> <mi>O</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle POQ}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37a2778ff6b6faa0cfd2dad6ac6d63769fd2eb39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.035ex; height:2.509ex;" alt="{\displaystyle \angle POQ}"></span> тип тамғалана.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \angle POQ}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∠</mi> <mi>P</mi> <mi>O</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle POQ}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37a2778ff6b6faa0cfd2dad6ac6d63769fd2eb39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.035ex; height:2.509ex;" alt="{\displaystyle \angle POQ}"></span> мөйөшөнөң дәүмәле ғәҙәттә <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \measuredangle POQ}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>∡</mi> <mi>P</mi> <mi>O</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \measuredangle POQ}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ffa810696bce7e05a7c9808539fb4f5827dee9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.035ex; height:2.509ex;" alt="{\displaystyle \measuredangle POQ}"></span> тип тамғалана. <ul><li>Шуның менән бергә, мөйөштөң дәүмәле, ҡыҫҡартып яҙыу өсөн бәләкәй грек хәрефе <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ,\beta ,\gamma ,\dots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>,</mo> <mi>γ</mi> <mo>,</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ,\beta ,\gamma ,\dots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103d7baac0c8cc902585f063b564b3395e76dad7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.907ex; height:2.676ex;" alt="{\displaystyle \alpha ,\beta ,\gamma ,\dots }"></span> менән тамғалана.</li></ul></li></ul> <div class="mw-heading mw-heading2"><h2 id="Шулай_уҡ_ҡарағыҙ"><span id=".D0.A8.D1.83.D0.BB.D0.B0.D0.B9_.D1.83.D2.A1_.D2.A1.D0.B0.D1.80.D0.B0.D2.93.D1.8B.D2.99"></span>Шулай уҡ ҡарағыҙ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B&veaction=edit&section=4" title="Шулай уҡ ҡарағыҙ бүлеген мөхәррирләргә" class="mw-editsection-visualeditor"><span>үҙгәртергә</span></a><span class="mw-editsection-divider"> | </span><a 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булмаған геометрия (был бит юҡ)">Евклид булмаған геометрия</a></li> <li><a href="/wiki/%D0%90%D0%BD%D0%B0%D0%BB%D0%B8%D1%82%D0%B8%D0%BA_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Аналитик геометрия">Аналитик геометрия</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Әҙәбиәт"><span id=".D3.98.D2.99.D3.99.D0.B1.D0.B8.D3.99.D1.82"></span>Әҙәбиәт</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B&veaction=edit&section=5" title="Әҙәбиәт бүлеген мөхәррирләргә" class="mw-editsection-visualeditor"><span>үҙгәртергә</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B&action=edit&section=5" title="Әҙәбиәт бүлегенең сығанаҡ кодын мөхәррирләү"><span>сығанаҡты үҙгәртеү</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Давид Гильберт</i> <a rel="nofollow" class="external text" href="http://ilib.mccme.ru/djvu/geometry/osn_geom.htm">Основания геометрии.</a> <small><span style="white-space: nowrap;"> 2011 йыл 28 июль <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110728164722/http://ilib.mccme.ru/djvu/geometry/osn_geom.htm">архивланған</a>.</span></small> Перевод с немецкого под редакцией А. В. Васильева. — Ленинград: «Сеятель», 1923—152 с.</li> <li><i>Адамар Ж. </i> Элементарная геометрия. — Ч. 1. — <span style="border-bottom:1px dotted gray; cursor:default" title="Москва">М</span>.: Учпедгиз, 1948; Ч. 2. — <span style="border-bottom:1px dotted gray; cursor:default" title="Москва">М</span>.: Учпедгиз, 1951.</li> <li>Математический энциклопедический словарь, — <span style="border-bottom:1px dotted gray; cursor:default" title="Москва">М</span>.: «Советская энциклопедия», 1988</li> <li><a rel="nofollow" class="external text" href="http://isgeom.narod.ru/index.html">Обухова А. И., История элементарной геометрии</a></li> <li><span class="citation" id="CITEREFБСЭ">Евклидова геометрия // <a href="/wiki/%D0%91%D0%BE%D0%BB%D1%8C%D1%88%D0%B0%D1%8F_%D1%81%D0%BE%D0%B2%D0%B5%D1%82%D1%81%D0%BA%D0%B0%D1%8F_%D1%8D%D0%BD%D1%86%D0%B8%D0%BA%D0%BB%D0%BE%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F#Третье_издание" class="mw-redirect" title="Большая советская энциклопедия">Большая советская энциклопедия</a> : <span style="white-space: nowrap;">[в 30 т.]</span> / гл. ред. <span style="white-space: nowrap;"> <a href="/w/index.php?title=%D0%9F%D1%80%D0%BE%D1%85%D0%BE%D1%80%D0%BE%D0%B2,_%D0%90%D0%BB%D0%B5%D0%BA%D1%81%D0%B0%D0%BD%D0%B4%D1%80_%D0%9C%D0%B8%D1%85%D0%B0%D0%B9%D0%BB%D0%BE%D0%B2%D0%B8%D1%87&action=edit&redlink=1" class="new" title="Прохоров, Александр Михайлович (был бит юҡ)">А. М. Прохоров</a></span>. — 3-е изд. — <span style="border-bottom:1px dotted gray; cursor:default" title="Москва">М</span>. : Советская энциклопедия, 1969—1978.</span></li></ul> <p><br /> <a href="/w/index.php?title=%D2%A0%D0%B0%D0%BB%D1%8B%D0%BF:%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%B1%D2%AF%D0%BB%D0%B5%D0%BA%D1%82%D3%99%D1%80%D0%B5&action=edit&redlink=1" class="new" title="Ҡалып:Математика бүлектәре (был бит юҡ)">Ҡалып:Математика бүлектәре</a> </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">«<a dir="ltr" href="https://ba.wikipedia.org/w/index.php?title=Евклид_геометрияһы&oldid=1179895">https://ba.wikipedia.org/w/index.php?title=Евклид_геометрияһы&oldid=1179895</a>» битенән алынған</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D0%9C%D0%B0%D1%85%D1%81%D1%83%D1%81:%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%8F%D0%BB%D0%B0%D1%80" title="Махсус:Категориялар">Категория</a>: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%8F:%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D2%BB%D1%8B" title="Категория:Евклид геометрияһы">Евклид геометрияһы</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Йәшерелгән категория: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%8F:%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%A1%D1%82%D0%B0%D1%82%D1%8C%D0%B8_%D1%81%D0%BE_%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B0%D0%BC%D0%B8_%D0%BD%D0%B0_%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%8B_%D0%92%D0%B8%D0%BA%D0%B8%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85_%D0%B1%D0%B5%D0%B7_%D1%80%D1%83%D1%81%D1%81%D0%BA%D0%BE%D0%B9_%D0%BF%D0%BE%D0%B4%D0%BF%D0%B8%D1%81%D0%B8" title="Категория:Википедия:Статьи со ссылками на элементы Викиданных без русской подписи">Википедия:Статьи со ссылками на элементы Викиданных без русской подписи</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"> Был бит һуңғы тапҡыр 00:12 5 октябрь 2022 үҙгәртелгән.</li> <li id="footer-info-copyright">Текст <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License</a> буйынса рөхсәт ителгән; өҫтәмә шарттар ҡулланылыуы мөмкин. 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