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title="Ua lhista de redadeiras altaraçones nesta biqui. [r]" accesskey="r"><span>Redadeiras altaraçones</span></a></li><li id="n-newpages" class="mw-list-item"><a href="/wiki/Special:P%C3%A1ginas_novas"><span>Páiginas nuobas</span></a></li><li id="n-store" class="mw-list-item"><a href="//store.wikimedia.org/"><span>Loija de la Biquipédia</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Biquip%C3%A9dia:P%C3%A1igina_percipal" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Biquipédia" src="/static/images/mobile/copyright/wikipedia-wordmark-mwl.svg" style="width: 7.5em; height: 1.375em;"> <img class="mw-logo-tagline" alt="la anciclopédia lhibre" src="/static/images/mobile/copyright/wikipedia-tagline-mwl.svg" width="120" height="14" style="width: 7.5em; height: 0.875em;"> </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/Special:Pesquisar" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Percurar an Biquipédia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Percura</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 cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Percurar an Biquipédia" aria-label="Percurar an Biquipédia" autocapitalize="sentences" title="Percurar an Biquipédia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Pesquisar"> </div> <button class="cdx-button cdx-search-input__end-button">Percurar</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Ferramientas pessonales"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" 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-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Aspeto"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <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="Aspeto" > <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">Aspeto</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="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_mwl.wikipedia.org&uselang=mwl" class=""><span>Donaçones</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=Special:Criar_Cuonta&returnto=%C3%81baco" title="Ye ancorajado a criar ua cuonta i ampeçar sesson; 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[o]" accesskey="o" class=""><span>Antrar</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="Mais opções" > <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="Ferramientas pessonales" > <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">Ferramientas pessonales</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal" title="Menu do utilizador" > <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="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_mwl.wikipedia.org&uselang=mwl"><span>Donaçones</span></a></li><li id="pt-contribute" class="mw-list-item"><a href="/wiki/Special:Contribute"><span class="vector-icon mw-ui-icon-edit mw-ui-icon-wikimedia-edit"></span> <span>Contribuir</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:Criar_Cuonta&returnto=%C3%81baco" title="Ye ancorajado a criar ua cuonta i ampeçar sesson; inda assi, nun ye oubrigatório"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Criar ua cuonta</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:Antrar&returnto=%C3%81baco" title="Tu sós animado pa que te outentiques, inda que esso nun seia oubrigatório. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Antrar</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"> Páginas para editores sem sessão iniciada <a href="/wiki/Ajuda:Introduction" aria-label="Saiba mais sobre edição"><span>saber mais</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:Minha_discuss%C3%A3o" title="Discussão sobre edições feitas a partir deste endereço IP [n]" accesskey="n"><span>Cumbersa</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="Conteúdo" 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">Conteúdo</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ocultar</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">Início</div> </a> </li> <li id="toc-Custruçon_i_outelizaçon_de_l_ábaco" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Custruçon_i_outelizaçon_de_l_ábaco"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Custruçon i outelizaçon de l ábaco</span> </div> </a> <button aria-controls="toc-Custruçon_i_outelizaçon_de_l_ábaco-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Alternar a subsecção Custruçon i outelizaçon de l ábaco</span> </button> <ul id="toc-Custruçon_i_outelizaçon_de_l_ábaco-sublist" class="vector-toc-list"> <li id="toc-Eisemplo_de_cálclo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Eisemplo_de_cálclo"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Eisemplo de cálclo</span> </div> </a> <ul id="toc-Eisemplo_de_cálclo-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Stória_i_Bersones_de_l_ábaco" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Stória_i_Bersones_de_l_ábaco"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Stória i Bersones de l ábaco</span> </div> </a> <button aria-controls="toc-Stória_i_Bersones_de_l_ábaco-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Alternar a subsecção Stória i Bersones de l ábaco</span> </button> <ul id="toc-Stória_i_Bersones_de_l_ábaco-sublist" class="vector-toc-list"> <li id="toc-Ouriges" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ouriges"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Ouriges</span> </div> </a> <ul id="toc-Ouriges-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-L_ábaco_na_eidade_média" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#L_ábaco_na_eidade_média"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>L ábaco na eidade média</span> </div> </a> <button aria-controls="toc-L_ábaco_na_eidade_média-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Alternar a subsecção L ábaco na eidade média</span> </button> <ul id="toc-L_ábaco_na_eidade_média-sublist" class="vector-toc-list"> <li id="toc-Ábaco_babilónio" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábaco_babilónio"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Ábaco babilónio</span> </div> </a> <ul id="toc-Ábaco_babilónio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ábaco_eigipcio" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábaco_eigipcio"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Ábaco eigipcio</span> </div> </a> <ul id="toc-Ábaco_eigipcio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ábaco_griego" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábaco_griego"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Ábaco griego</span> </div> </a> <ul id="toc-Ábaco_griego-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ábaco_romano" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábaco_romano"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Ábaco romano</span> </div> </a> <ul id="toc-Ábaco_romano-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ábaco_andiano" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábaco_andiano"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Ábaco andiano</span> </div> </a> <ul id="toc-Ábaco_andiano-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ábaco_chinés" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábaco_chinés"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Ábaco chinés</span> </div> </a> <ul id="toc-Ábaco_chinés-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ábaco_japonés" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábaco_japonés"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Ábaco japonés</span> </div> </a> <ul id="toc-Ábaco_japonés-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ábacos_de_ls_natibos_amaricanos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábacos_de_ls_natibos_amaricanos"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Ábacos de ls natibos amaricanos</span> </div> </a> <ul id="toc-Ábacos_de_ls_natibos_amaricanos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ábaco_russo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábaco_russo"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.9</span> <span>Ábaco russo</span> </div> </a> <ul id="toc-Ábaco_russo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ábaco_scolar" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ábaco_scolar"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.10</span> <span>Ábaco scolar</span> </div> </a> <ul id="toc-Ábaco_scolar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Usos_puls_deficientes_bisuales" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Usos_puls_deficientes_bisuales"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.11</span> <span>Usos puls deficientes bisuales</span> </div> </a> <ul id="toc-Usos_puls_deficientes_bisuales-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Curjidades" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Curjidades"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Curjidades</span> </div> </a> <ul id="toc-Curjidades-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="Conteúdo" 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="Alternar o índice" > <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">Alternar o índice</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">Ábaco</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="Ir para um artigo noutra língua. Disponível em 109 línguas" > <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-109" 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">109 línguas</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/Abakus" title="Abakus — africanês" lang="af" hreflang="af" data-title="Abakus" data-language-autonym="Afrikaans" data-language-local-name="africanês" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Abaco" title="Abaco — Aragonese" lang="an" hreflang="an" data-title="Abaco" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%AF%D8%A7%D8%AF" title="معداد — Arabic" lang="ar" hreflang="ar" data-title="معداد" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%8F%E0%A6%AC%E0%A6%BE%E0%A6%95%E0%A6%BE%E0%A6%9B" title="এবাকাছ — Assamese" lang="as" hreflang="as" data-title="এবাকাছ" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" 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%81bacu" title="Ábacu — Asturian" lang="ast" hreflang="ast" data-title="Ábacu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Jakhu%C3%B1a" title="Jakhuña — Aymara" lang="ay" hreflang="ay" data-title="Jakhuña" data-language-autonym="Aymar aru" data-language-local-name="Aymara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Abak" title="Abak — Azerbaijani" lang="az" hreflang="az" data-title="Abak" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%86%D8%A4%D8%B1%D8%AA%DA%A9%D9%87" title="چؤرتکه — South Azerbaijani" lang="azb" hreflang="azb" data-title="چؤرتکه" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Abakus" title="Abakus — Central Bikol" lang="bcl" hreflang="bcl" data-title="Abakus" 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%B1%D0%B0%D0%BA" title="Абак — Belarusian" lang="be" hreflang="be" data-title="Абак" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA" title="Абак — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Абак" 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%B1%D0%B0%D0%BA_(%D1%81%D0%BC%D0%B5%D1%82%D0%B0%D0%BB%D0%BE)" title="Абак (сметало) — Bulgarian" lang="bg" hreflang="bg" data-title="Абак (сметало)" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Abakus" title="Abakus — Bislama" lang="bi" hreflang="bi" data-title="Abakus" data-language-autonym="Bislama" data-language-local-name="Bislama" class="interlanguage-link-target"><span>Bislama</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AC%E0%A6%BE%E0%A6%95%E0%A6%BE%E0%A6%B8" title="অ্যাবাকাস — bengalês" lang="bn" hreflang="bn" data-title="অ্যাবাকাস" data-language-autonym="বাংলা" data-language-local-name="bengalês" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Abakus_(ra%C4%8Dunaljka)" title="Abakus (računaljka) — Bosnian" lang="bs" hreflang="bs" data-title="Abakus (računaljka)" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BC%D0%BF%D0%B8%D0%BD" title="Сампин — Russia Buriat" lang="bxr" hreflang="bxr" data-title="Сампин" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%80bac" title="Àbac — Catalan" lang="ca" hreflang="ca" data-title="Àbac" data-language-autonym="Català" data-language-local-name="Catalan" 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/S%C3%A1ung-bu%C3%A0ng" title="Sáung-buàng — Mindong" lang="cdo" hreflang="cdo" data-title="Sáung-buàng" 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-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Po%C4%8D%C3%ADtadlo" title="Počítadlo — checo" lang="cs" hreflang="cs" data-title="Počítadlo" data-language-autonym="Čeština" data-language-local-name="checo" 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%B1%D0%B0%D0%BA" title="Абак — chuvash" lang="cv" hreflang="cv" data-title="Абак" 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/Abacws" title="Abacws — Welsh" lang="cy" hreflang="cy" data-title="Abacws" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Abacus_(regnemaskine)" title="Abacus (regnemaskine) — Danish" lang="da" hreflang="da" data-title="Abacus (regnemaskine)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Abakus_(Rechenhilfsmittel)" title="Abakus (Rechenhilfsmittel) — German" lang="de" hreflang="de" data-title="Abakus (Rechenhilfsmittel)" data-language-autonym="Deutsch" data-language-local-name="German" 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%86%CE%B2%CE%B1%CE%BA%CE%B1%CF%82" title="Άβακας — Greek" lang="el" hreflang="el" data-title="Άβακας" data-language-autonym="Ελληνικά" data-language-local-name="Greek" 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/Abacus" title="Abacus — English" lang="en" hreflang="en" data-title="Abacus" data-language-autonym="English" data-language-local-name="English" 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/Abako_(me%C4%A5anika_kalkulilo)" title="Abako (meĥanika kalkulilo) — Esperanto" lang="eo" hreflang="eo" data-title="Abako (meĥanika kalkulilo)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" 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%81baco" title="Ábaco — Spanish" lang="es" hreflang="es" data-title="Ábaco" data-language-autonym="Español" data-language-local-name="Spanish" 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/Abakus" title="Abakus — estónio" lang="et" hreflang="et" data-title="Abakus" data-language-autonym="Eesti" data-language-local-name="estónio" 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/Abako" title="Abako — Basque" lang="eu" hreflang="eu" data-title="Abako" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%86%D8%B1%D8%AA%DA%A9%D9%87" title="چرتکه — Persian" lang="fa" hreflang="fa" data-title="چرتکه" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Helmitaulu" title="Helmitaulu — Finnish" lang="fi" hreflang="fi" data-title="Helmitaulu" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Abaque_(calcul)" title="Abaque (calcul) — French" lang="fr" hreflang="fr" data-title="Abaque (calcul)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Abacas" title="Abacas — Irish" lang="ga" hreflang="ga" data-title="Abacas" data-language-autonym="Gaeilge" data-language-local-name="Irish" 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/%E7%AE%97%E7%9B%A4" title="算盤 — Gan" lang="gan" hreflang="gan" data-title="算盤" 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/Bouly%C3%A9" title="Boulyé — Guianan Creole" lang="gcr" hreflang="gcr" data-title="Boulyé" 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-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%81baco" title="Ábaco — Galician" lang="gl" hreflang="gl" data-title="Ábaco" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-glk mw-list-item"><a href="https://glk.wikipedia.org/wiki/%DA%86%DB%8A%D8%B1%D8%AA%D9%8A%DA%A9%D8%A7" title="چۊرتيکا — Gilaki" lang="glk" hreflang="glk" data-title="چۊرتيکا" data-language-autonym="گیلکی" data-language-local-name="Gilaki" class="interlanguage-link-target"><span>گیلکی</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AE%E0%AA%A3%E0%AA%95%E0%AA%BE%E0%AA%98%E0%AB%8B%E0%AA%A1%E0%AB%80" title="મણકાઘોડી — Gujarati" lang="gu" hreflang="gu" data-title="મણકાઘોડી" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%A9%D7%91%D7%95%D7%A0%D7%99%D7%99%D7%94" title="חשבונייה — Hebrew" lang="he" hreflang="he" data-title="חשבונייה" data-language-autonym="עברית" data-language-local-name="Hebrew" 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%97%E0%A4%BF%E0%A4%A8%E0%A4%A4%E0%A4%BE%E0%A4%B0%E0%A4%BE" title="गिनतारा — hindi" lang="hi" hreflang="hi" data-title="गिनतारा" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Abak" title="Abak — Croatian" lang="hr" hreflang="hr" data-title="Abak" data-language-autonym="Hrvatski" data-language-local-name="Croatian" 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/Abakusz" title="Abakusz — Hungarian" lang="hu" hreflang="hu" data-title="Abakusz" data-language-autonym="Magyar" data-language-local-name="Hungarian" 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%B1%D5%A2%D5%A1%D5%AF_(%D5%BF%D5%A1%D5%AD%D5%BF%D5%A1%D5%AF)" title="Աբակ (տախտակ) — arménio" lang="hy" hreflang="hy" data-title="Աբակ (տախտակ)" data-language-autonym="Հայերեն" data-language-local-name="arménio" 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/Abaco" title="Abaco — Interlingua" lang="ia" hreflang="ia" data-title="Abaco" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Swipoa" title="Swipoa — Indonesian" lang="id" hreflang="id" data-title="Swipoa" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Abako" title="Abako — Ido" lang="io" hreflang="io" data-title="Abako" 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/Talnagrind" title="Talnagrind — Icelandic" lang="is" hreflang="is" data-title="Talnagrind" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Abaco" title="Abaco — Italian" lang="it" hreflang="it" data-title="Abaco" data-language-autonym="Italiano" data-language-local-name="Italian" 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%82%A2%E3%83%90%E3%82%AB%E3%82%B9" title="アバカス — Japanese" lang="ja" hreflang="ja" data-title="アバカス" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Abakos" title="Abakos — Jamaican Creole English" lang="jam" hreflang="jam" data-title="Abakos" 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-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Simpoa" title="Simpoa — Javanese" lang="jv" hreflang="jv" data-title="Simpoa" data-language-autonym="Jawa" data-language-local-name="Javanese" 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%91%E1%83%90%E1%83%99%E1%83%98" title="აბაკი — Georgian" lang="ka" hreflang="ka" data-title="აბაკი" data-language-autonym="ქართული" data-language-local-name="Georgian" 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/Abakus" title="Abakus — Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Abakus" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/Abacus" title="Abacus — Kikuyu" lang="ki" hreflang="ki" data-title="Abacus" data-language-autonym="Gĩkũyũ" data-language-local-name="Kikuyu" 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%90%D0%B1%D0%B0%D0%BA" title="Абак — Kazakh" lang="kk" hreflang="kk" data-title="Абак" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%80%E1%9F%92%E1%9E%94%E1%9E%B6%E1%9E%85%E1%9F%8B%E1%9E%82%E1%9E%B7%E1%9E%8F%E1%9E%9B%E1%9F%81%E1%9E%81" title="ក្បាច់គិតលេខ — Khmer" lang="km" hreflang="km" data-title="ក្បាច់គិតលេខ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%AC%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%95%E0%B2%B8%E0%B3%8D%E2%80%8C" title="ಅಬ್ಯಾಕಸ್‌ — Kannada" lang="kn" hreflang="kn" data-title="ಅಬ್ಯಾಕಸ್‌" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" 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%A3%BC%ED%8C%90" title="주판 — Korean" lang="ko" hreflang="ko" data-title="주판" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%DA%AF%D9%90%D9%86%D8%AA%D8%A7%D8%B1%D9%95" title="گِنتارٕ — Kashmiri" lang="ks" hreflang="ks" data-title="گِنتارٕ" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="Kashmiri" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Абак (математика) — Kyrgyz" lang="ky" hreflang="ky" data-title="Абак (математика)" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Abacus" title="Abacus — Latin" lang="la" hreflang="la" data-title="Abacus" data-language-autonym="Latina" data-language-local-name="Latin" 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/Abaco" title="Abaco — Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Abaco" 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-li mw-list-item"><a href="https://li.wikipedia.org/wiki/T%C3%A8lraam" title="Tèlraam — Limburgish" lang="li" hreflang="li" data-title="Tèlraam" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%A5%E0%BA%B9%E0%BA%81%E0%BA%84%E0%BA%B4%E0%BA%94" title="ລູກຄິດ — Lao" lang="lo" hreflang="lo" data-title="ລູກຄິດ" data-language-autonym="ລາວ" data-language-local-name="Lao" 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/Abakas" title="Abakas — Lithuanian" lang="lt" hreflang="lt" data-title="Abakas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" 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/Skait%C4%ABk%C4%BCi" title="Skaitīkļi — Latvian" lang="lv" hreflang="lv" data-title="Skaitīkļi" data-language-autonym="Latviešu" data-language-local-name="Latvian" 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%A1%D0%BC%D0%B5%D1%82%D0%B0%D0%BB%D0%BA%D0%B0" title="Сметалка — macedónio" lang="mk" hreflang="mk" data-title="Сметалка" data-language-autonym="Македонски" data-language-local-name="macedónio" 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%AE%E0%B4%A3%E0%B4%BF%E0%B4%9A%E0%B5%8D%E0%B4%9A%E0%B4%9F%E0%B5%8D%E0%B4%9F%E0%B4%82" title="മണിച്ചട്ടം — Malayalam" lang="ml" hreflang="ml" data-title="മണിച്ചട്ടം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" 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%A1%D0%B0%D0%BC%D0%BF%D0%B8%D0%BD" title="Сампин — Mongolian" lang="mn" hreflang="mn" data-title="Сампин" data-language-autonym="Монгол" data-language-local-name="Mongolian" 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/Sempoa" title="Sempoa — Malay" lang="ms" hreflang="ms" data-title="Sempoa" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%85%E0%A4%AC%E0%A4%BE%E0%A4%95%E0%A4%B8" title="अबाकस — Nepali" lang="ne" hreflang="ne" data-title="अबाकस" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Abacus_(rekentuig)" title="Abacus (rekentuig) — neerlandês" lang="nl" hreflang="nl" data-title="Abacus (rekentuig)" data-language-autonym="Nederlands" data-language-local-name="neerlandês" 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/Kuleramme" title="Kuleramme — norueguês nynorsk" lang="nn" hreflang="nn" data-title="Kuleramme" data-language-autonym="Norsk nynorsk" data-language-local-name="norueguês 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/Abakus_(kuleramme)" title="Abakus (kuleramme) — norueguês bokmål" lang="nb" hreflang="nb" data-title="Abakus (kuleramme)" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%AC%E0%A9%88%E0%A8%95%E0%A8%B8" title="ਅਬੈਕਸ — Punjabi" lang="pa" hreflang="pa" data-title="ਅਬੈਕਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" 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/Abakus_(liczyd%C5%82o)" title="Abakus (liczydło) — polaco" lang="pl" hreflang="pl" data-title="Abakus (liczydło)" data-language-autonym="Polski" data-language-local-name="polaco" 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%80baco" title="Àbaco — Piedmontese" lang="pms" hreflang="pms" data-title="Àbaco" 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/%DA%AF%D9%86%D8%AA%D8%A7%D8%B1%D8%A7" title="گنتارا — Western Punjabi" lang="pnb" hreflang="pnb" data-title="گنتارا" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81baco" title="Ábaco — Portuguese" lang="pt" hreflang="pt" data-title="Ábaco" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Abac" title="Abac — Romanian" lang="ro" hreflang="ro" data-title="Abac" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA" title="Абак — Russian" lang="ru" hreflang="ru" data-title="Абак" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/%C3%80bbacu_(c%C3%A0rculu)" title="Àbbacu (càrculu) — Sicilian" lang="scn" hreflang="scn" data-title="Àbbacu (càrculu)" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A2%D8%A8%D8%A7%DA%AA%D8%B3" title="آباڪس — Sindhi" lang="sd" hreflang="sd" data-title="آباڪس" data-language-autonym="سنڌي" data-language-local-name="Sindhi" 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/Abakus_(ra%C4%8Dunanje)" title="Abakus (računanje) — Serbo-Croatian" lang="sh" hreflang="sh" data-title="Abakus (računanje)" 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-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Abacus" title="Abacus — Simple English" lang="en-simple" hreflang="en-simple" data-title="Abacus" 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/Abakus_(po%C4%8D%C3%ADtacia_tabu%C4%BEka)" title="Abakus (počítacia tabuľka) — Slovak" lang="sk" hreflang="sk" data-title="Abakus (počítacia tabuľka)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Abak" title="Abak — Slovenian" lang="sl" hreflang="sl" data-title="Abak" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" 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/Abakusi" title="Abakusi — Albanian" lang="sq" hreflang="sq" data-title="Abakusi" data-language-autonym="Shqip" data-language-local-name="Albanian" 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%B1%D0%B0%D0%BA%D1%83%D1%81_(%D1%80%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D1%9A%D0%B5)" title="Абакус (рачунање) — Serbian" lang="sr" hreflang="sr" data-title="Абакус (рачунање)" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Sipoah" title="Sipoah — Sundanese" lang="su" hreflang="su" data-title="Sipoah" 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/Abakus" title="Abakus — Swedish" lang="sv" hreflang="sv" data-title="Abakus" data-language-autonym="Svenska" data-language-local-name="Swedish" 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/Abakasi" title="Abakasi — Swahili" lang="sw" hreflang="sw" data-title="Abakasi" 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%8E%E0%AE%A3%E0%AF%8D%E0%AE%9A%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%AE%E0%AF%8D" title="எண்சட்டம் — Tamil" lang="ta" hreflang="ta" data-title="எண்சட்டம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%85%E0%B0%AC%E0%B0%BE%E0%B0%95%E0%B0%B8%E0%B1%8D" title="అబాకస్ — telugu" lang="te" hreflang="te" data-title="అబాకస్" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA" title="Абак — tajique" lang="tg" hreflang="tg" data-title="Абак" data-language-autonym="Тоҷикӣ" data-language-local-name="tajique" 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%B8%A5%E0%B8%B9%E0%B8%81%E0%B8%84%E0%B8%B4%E0%B8%94" title="ลูกคิด — Thai" lang="th" hreflang="th" data-title="ลูกคิด" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Abakus" title="Abakus — Tagalog" lang="tl" hreflang="tl" data-title="Abakus" 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/Abak%C3%BCs" title="Abaküs — Turkish" lang="tr" hreflang="tr" data-title="Abaküs" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA_(%D1%80%D0%B0%D1%85%D1%96%D0%B2%D0%BD%D0%B8%D1%86%D1%8F)" title="Абак (рахівниця) — Ukrainian" lang="uk" hreflang="uk" data-title="Абак (рахівниця)" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DA%AF%D9%86%D8%AA%D8%A7%D8%B1%D8%A7" title="گنتارا — Urdu" lang="ur" hreflang="ur" data-title="گنتارا" data-language-autonym="اردو" data-language-local-name="Urdu" 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/Abak" title="Abak — usbeque" lang="uz" hreflang="uz" data-title="Abak" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbeque" 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/B%C3%A0n_t%C3%ADnh" title="Bàn tính — Vietnamese" lang="vi" hreflang="vi" data-title="Bàn tính" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Abacus" title="Abacus — Waray" lang="war" hreflang="war" data-title="Abacus" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%AE%97%E7%9B%98" title="算盘 — Wu" lang="wuu" hreflang="wuu" data-title="算盘" 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-abacus" title="I-abacus — xosa" lang="xh" hreflang="xh" data-title="I-abacus" data-language-autonym="IsiXhosa" data-language-local-name="xosa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%AE%97%E7%9B%98" title="算盘 — Chinese" lang="zh" hreflang="zh" data-title="算盘" data-language-autonym="中文" data-language-local-name="Chinese" 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/%E7%AE%97%E7%9B%A4" title="算盤 — Literary Chinese" lang="lzh" hreflang="lzh" data-title="算盤" 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/S%C7%B9g-p%C3%B4a%E2%81%BF" title="Sǹg-pôaⁿ — Minnan" lang="nan" hreflang="nan" data-title="Sǹg-pôaⁿ" 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/%E7%AE%97%E7%9B%A4" title="算盤 — Cantonese" lang="yue" hreflang="yue" data-title="算盤" 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/Q12806#sitelinks-wikipedia" title="Eiditar lhigaçones anterlhenguísticas" class="wbc-editpage">Eiditar lhigaçones</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="Domínios"> <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 href="/wiki/%C3%81baco" title="Ber la páigina de l cuntenido [c]" accesskey="c"><span>Páigina</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Cumbersa:%C3%81baco&action=edit&redlink=1" rel="discussion" class="new" title="Cumbersa subre l cuntenido de la páigina (la páigina nun eisiste) [t]" accesskey="t"><span>Cumbersa</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Mudar a variante da língua" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Mirandés</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Besitas"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%C3%81baco"><span>Lher</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%C3%81baco&veaction=edit" title="Eiditar esta páigina [v]" accesskey="v"><span>Eiditar</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%C3%81baco&action=edit" title="Editar o código-fonte desta página [e]" accesskey="e"><span>Eiditar código-fuonte</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%C3%81baco&action=history" title="Eidiçones mais antigas desta páigina. [h]" accesskey="h"><span>Ber stórico</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Ferramentas de página"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Ferramientas" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Ferramientas</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Ferramentas</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ocultar</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Mais opções" > <div class="vector-menu-heading"> Operações </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%C3%81baco"><span>Lher</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%C3%81baco&veaction=edit" title="Eiditar esta páigina [v]" accesskey="v"><span>Eiditar</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%C3%81baco&action=edit" title="Editar o código-fonte desta página [e]" accesskey="e"><span>Eiditar código-fuonte</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%C3%81baco&action=history"><span>Ber stórico</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Geral </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:P%C3%A1ginas_afluentes/%C3%81baco" title="Todas las páiginas que se lhigan eiqui [j]" accesskey="j"><span>L que lhiga eiqui</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:Altera%C3%A7%C3%B5es_relacionadas/%C3%81baco" rel="nofollow" title="Redadeiras altaraçones an páiginas que ténen a ber cun esta [k]" accesskey="k"><span>Altaraçones relacionadas</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=mwl" title="Cargar eimaiges ó fexeiros [u]" accesskey="u"><span>Cargar fexeiro</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:P%C3%A1ginas_especiais" title="Todas las páiginas speciales [q]" accesskey="q"><span>Páiginas speciales</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%C3%81baco&oldid=102027" title="Lhigaçon pa siempre desta berson desta páigina"><span>Lhigaçon pa siempre</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%C3%81baco&action=info" title="Mais informações sobre esta página"><span>Anformaçones de la páigina</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:Citar&page=%C3%81baco&id=102027&wpFormIdentifier=titleform" title="Anformaçon subre cumo citar esta páigina"><span>Citar esta páigina</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fmwl.wikipedia.org%2Fwiki%2F%25C3%2581baco"><span>Obter URL encurtado</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fmwl.wikipedia.org%2Fwiki%2F%25C3%2581baco"><span>Descarregar código QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Amprimir/sportar </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Special:Lhibro&bookcmd=book_creator&referer=%C3%81baco"><span>Criar un lhibro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%C3%81baco&action=show-download-screen"><span>Çcargar cumo PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%C3%81baco&printable=yes" title="Berson pa ampremir desta páigina [p]" accesskey="p"><span>Berson pa ampremir</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Noutros porjetos </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Abacus" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12806" title="Lhigaçon pa l eilemiento de l repositório de dados [g]" accesskey="g"><span>Eilemiento Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Ferramentas de página"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspeto"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspeto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</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">Ourige: Biquipédia, la anciclopédia lhibre.</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="mwl" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Fexeiro:Abacus_6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/a/af/Abacus_6.png" decoding="async" width="247" height="145" class="mw-file-element" data-file-width="247" data-file-height="145" /></a><figcaption>Purmeira calculadora outelizada pul home: un ábaco a repersentar l númaro 6302715408</figcaption></figure> <p>L <b>ábaco</b> ye un antigo strumiento de <a href="/w/index.php?title=C%C3%A1lclo&action=edit&redlink=1" class="new" title="Cálclo (la páigina nun eisiste)">cálclo</a>, formado por ua moldura cun baras ó arames <a href="/w/index.php?title=Paralelismo&action=edit&redlink=1" class="new" title="Paralelismo (la páigina nun eisiste)">paralelos</a>, çpuostos ne l sentido bertical, correspundentes cada un a ua posiçon degital (ounidades, dezenas,...) i adonde stan ls eilemientos de cuntaige (fixas, bolas, cuntas,...) que puoden fazer-se correr lhibremente. Tubo ourige probablemente na <a href="/w/index.php?title=Mesopot%C3%A1mia&action=edit&redlink=1" class="new" title="Mesopotámia (la páigina nun eisiste)">Mesopotámia</a>, hai mais de 5.500 anhos. L ábaco puode ser cunsidrado cumo ua stenson de l ato natural de se cuntar culs dedos. Amprega un porcesso de cálclo cun <a href="/wiki/Sistema_decimal" class="mw-redirect" title="Sistema decimal">sistema decimal</a>, atribuindo a cada heste un múltiplo de dieç. El ye outelizado inda hoije para ansinar a las ninos las ouparaçones de <a href="/w/index.php?title=Soma&action=edit&redlink=1" class="new" title="Soma (la páigina nun eisiste)">somar</a> i <a href="/w/index.php?title=Sumir&action=edit&redlink=1" class="new" title="Sumir (la páigina nun eisiste)">sumir</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Custruçon_i_outelizaçon_de_l_ábaco"><span id="Custru.C3.A7on_i_outeliza.C3.A7on_de_l_.C3.A1baco"></span>Custruçon i outelizaçon de l ábaco</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=1" title="Eiditar cacho: Custruçon i outelizaçon de l ábaco" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=1" title="Editar código-fonte da secção: Custruçon i outelizaçon de l ábaco"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cada bara cuntén dieç bolas mobles, que puoden ser mobidas para cima i para baixo. Assi, d'acuordo cul númaro de bolas na posiçon de baixo, tenemos un balor repersentado. Puode haber bariaçones, cumo na figura al lhado, adonde se fázen <a href="/w/index.php?title=Debison&action=edit&redlink=1" class="new" title="Debison (la páigina nun eisiste)">debisones</a> na moldura i l númaro de bolas ye demudado. Bei que na figura tenemos l númaro 6302715408 (por eisemplo 8=5+3, cula parte ambaixo repersentando <a href="/w/index.php?title=M%C3%BAltiplo&action=edit&redlink=1" class="new" title="Múltiplo (la páigina nun eisiste)">múltiplos</a> de 5, neste causo 0, 5 i 10). </p><p>Strutura cun hastes metálicas dibedidas an dues partes, onde ua ten dues cuntas i la outra, cinco cuntas, que cuorren nessas baras. Ls ábacos ourientales çpónen de baras berticales dibedidas an dous, cun las cuntas subre la bara tenendo l balor cinco bezes superior als de las cuntas ambaixo. L <i><a href="/w/index.php?title=Suanpan&action=edit&redlink=1" class="new" title="Suanpan (la páigina nun eisiste)">suanpan</a></i> chinés çpone de dues cuntas arriba de la barra ó debisor i cinco ambaixo. L moderno <i><a href="/w/index.php?title=Soroban&action=edit&redlink=1" class="new" title="Soroban (la páigina nun eisiste)">soroban</a></i> japonés por outro lhado, ten ua cunta arriba i quatro ambaixo de l debisor. </p><p>Alguas baras puoden ser reserbadas pul ouperador para guardar resultados antermediários. Assi, poucas guias son neçairas, yá que l ábaco ye ousado mais cumo un refuorço de mimória anquanto l outelizador faç las cuntas de cabeça. </p> <div class="mw-heading mw-heading3"><h3 id="Eisemplo_de_cálclo"><span id="Eisemplo_de_c.C3.A1lclo"></span>Eisemplo de cálclo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=2" title="Eiditar cacho: Eisemplo de cálclo" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=2" title="Editar código-fonte da secção: Eisemplo de cálclo"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L cálclo ampeça a la squierda, ó na coluna mais alta an sou cálclo, i trabalha de la squierda para la dreita. Assi, se tubires 548 i quejires somar 637, purmeiro pon 548 na calculadora. Dende, ajunda 6 al 5. Sigue la regra ó padron 6 = 10 - 4 por remober l 5 na bara de las cientos i adicionar 1 na mesma bara (-5 + 1 = -4) dende, ajunta ua de las cuntas de miles a la bara a la squierda. Dende, passa a somar l trés al quatro, l siete al uito, i ne l ábaco aparecerá la repuosta: 1.185. </p><p>Debido a ouperar assi, de la squierda para la dreita, puode ampeçar sou cálclo assi que sabas l purmeiro númaro. Na aritmética mental ó scrita, calcula a partir de las ounidades ó de l lhado dreito de l porblema. </p> <div class="mw-heading mw-heading2"><h2 id="Stória_i_Bersones_de_l_ábaco"><span id="St.C3.B3ria_i_Bersones_de_l_.C3.A1baco"></span>Stória i Bersones de l ábaco</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=3" title="Eiditar cacho: Stória i Bersones de l ábaco" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=3" title="Editar código-fonte da secção: Stória i Bersones de l ábaco"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ouriges">Ouriges</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=4" title="Eiditar cacho: Ouriges" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=4" title="Editar código-fonte da secção: Ouriges"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L purmeiro ábaco fui quaije de certeza custruído nua piedra lhisa cubierta por arena ó pulo. Palabras i lhetras éran zenhadas na arena; númaros éran ajuntados<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> i bolas de piedra éran outelizadas para ajuda ne ls cálclos. Ls <a href="/w/index.php?title=Babil%C3%B3nia&action=edit&redlink=1" class="new" title="Babilónia (la páigina nun eisiste)">babilónios</a> outelizában este ábaco an <a href="/w/index.php?title=Seclo_XXIB_a.C&action=edit&redlink=1" class="new" title="Seclo XXIB a.C (la páigina nun eisiste)">2400 a.C.</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> La ourige de l ábaco de cuntar cun [choupas <a rel="nofollow" class="external autonumber" href="http://pt.wikipedie.org/wiki/Bast%C3%A3o_(magia)">[1]</a> ye ouscuro, mas la <a href="/wiki/%C3%8Dndia" title="Índia">Índia</a>, la <a href="/w/index.php?title=Mesopot%C3%A1mia&action=edit&redlink=1" class="new" title="Mesopotámia (la páigina nun eisiste)">Mesopotámia</a> ó l <a href="/wiki/Eigito" title="Eigito">Eigito</a> son bistos cumo probables puntos de ourige.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> La <a href="/wiki/China" title="China">China</a> zampenhou un papel amportante ne l zambolbimiento de l ábaco. </p> <div class="mw-heading mw-heading2"><h2 id="L_ábaco_na_eidade_média"><span id="L_.C3.A1baco_na_eidade_m.C3.A9dia"></span>L ábaco na eidade média</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=5" title="Eiditar cacho: L ábaco na eidade média" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=5" title="Editar código-fonte da secção: L ábaco na eidade média"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fexeiro:Rechentisch.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Rechentisch.png/250px-Rechentisch.png" decoding="async" width="250" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Rechentisch.png/375px-Rechentisch.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Rechentisch.png/500px-Rechentisch.png 2x" data-file-width="598" data-file-height="393" /></a><figcaption>Figura dun ábaco ousado na <a href="/wiki/Eidade_M%C3%A9dia" title="Eidade Média">Eidade Média</a></figcaption></figure> <p>Ls <a href="/w/index.php?title=Amp%C3%A9rio_romano&action=edit&redlink=1" class="new" title="Ampério romano (la páigina nun eisiste)">romanos</a>, na antiguidade, outelizában l ábaco para calcular, i depuis ls <a href="/wiki/China" title="China">chineses</a> i <a href="/wiki/Japon" title="Japon">japoneses</a> l aperfeiçoórun. </p><p>Dende, ua bariadade de ábacos fúrun zambolbidos; l mais popular outeliza ua cumbinaçon de dous númaros-base (2 i 5) para repersentar númaros decimales. Mas ls mais antigos ábacos ousados purmeiro na Mesopotamia i depuis na <a href="/wiki/Gr%C3%A9cia" title="Grécia">Grécia</a> i ne l Eigito por scribones usában númaros <a href="/w/index.php?title=Sistema_sexagesimal&action=edit&redlink=1" class="new" title="Sistema sexagesimal (la páigina nun eisiste)">sexagesimales</a> repersentados por fatores de 5, 2, 3 i 2 por cada númaro. </p><p>La palabra <i>ábaco</i> oureginou-se de l <a href="/w/index.php?title=Latin&action=edit&redlink=1" class="new" title="Latin (la páigina nun eisiste)">Latin</a> <i>abacus</i>, i esta bieno de l <a href="/w/index.php?title=L%C3%A9ngua_griega&action=edit&redlink=1" class="new" title="Léngua griega (la páigina nun eisiste)">griego</a> <i>abakos</i>. Esta era un deribado de la <a href="/wiki/Causo_genitibo" title="Causo genitibo">forma genitiba</a> <i>abax</i> (lhit. <i>tábua de cálclos</i>). Porque <i>abax</i> tenie tamien l sentido de <i>tábua polbilhada cun tierra ó pó, outelizada para fazer figuras giométricas</i>, alguns lhenguistas specúlan que tenga benido dua <a href="/w/index.php?title=L%C3%A9ngua_sem%C3%ADtica&action=edit&redlink=1" class="new" title="Léngua semítica (la páigina nun eisiste)">léngua semítica</a> (l <a href="/w/index.php?title=L%C3%A9ngua_p%C3%BAnica&action=edit&redlink=1" class="new" title="Léngua púnica (la páigina nun eisiste)">púnico</a> <i>abak</i>, <i>arena</i>, ó l <a href="/w/index.php?title=Heibreu&action=edit&redlink=1" class="new" title="Heibreu (la páigina nun eisiste)">heibreu</a> <i>ābāq</i> (pernunciado <i>la-bak</i>), <i>arena</i>). </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fexeiro:Gregor_Reisch,_Margarita_Philosophica,_1508_(1230x1615).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png/250px-Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png" decoding="async" width="250" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png/375px-Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png/500px-Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png 2x" data-file-width="1205" data-file-height="1591" /></a><figcaption>Figura de la çputa antre un abacista <i>bersus</i> un algorista por Griegor Reisch, Margarita Philosophica, 1508</figcaption></figure> <p>Ne l causo de l <a href="/wiki/L%C3%A9ngua_anglesa" title="Léngua anglesa">Anglés</a>, la palabra <i>abacus</i> ye outelizada zde antes de <a href="/w/index.php?title=1387&action=edit&redlink=1" class="new" title="1387 (la páigina nun eisiste)">1387</a> i fui amprestada de l Lhatin <i>abacus</i>. L plural de l anglés <i>abacus</i> ye cuntroberso, mas <i>abacuses</i><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> i <i>abaci</i><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> stan an uso. </p> <div class="mw-heading mw-heading3"><h3 id="Ábaco_babilónio"><span id=".C3.81baco_babil.C3.B3nio"></span>Ábaco babilónio</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=6" title="Eiditar cacho: Ábaco babilónio" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=6" title="Editar código-fonte da secção: Ábaco babilónio"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ls babilónios puoden tener outelizado l ábaco pa ouparaçones de adiçon i subtraçon. Inda assi, este outensílio primetibo probou ser defícel para la outelizaçon an cálclos mais cumplexos.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Alguas pessonas conhécen un carater de l abc cuneiforme babilónio que puode tener sido deribado dua repersentaçon de l ábaco.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ábaco_eigipcio"><span id=".C3.81baco_eigipcio"></span>Ábaco eigipcio</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=7" title="Eiditar cacho: Ábaco eigipcio" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=7" title="Editar código-fonte da secção: Ábaco eigipcio"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L uso de l ábaco ne l <a href="/wiki/Antigo_Eigito" title="Antigo Eigito">antigo Eigito</a> ye mencionado pul storiador griego <a href="/w/index.php?title=Crabiertotous&action=edit&redlink=1" class="new" title="Crabiertotous (la páigina nun eisiste)">Crabiertotous</a>, que scribe subre la maneira de l uso de discos (ábacos) puls eigípcios, que era ouposta na direçon quando cumparada cul método griego. Arqueologistas ancuntrórun discos antigos de bários tamanhos que se pénsan tenéren sido ousados cumo material de cálclo. Inda assi, pinturas de parede nun fúrun çcubiertas, spalhando alguas dúbedas subre la antençon de uso deste strumiento.<sup id="cite_ref-Smith1_8-0" class="reference"><a href="#cite_note-Smith1-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ábaco_griego"><span id=".C3.81baco_griego"></span>Ábaco griego</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=8" title="Eiditar cacho: Ábaco griego" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=8" title="Editar código-fonte da secção: Ábaco griego"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ua tábua ancuntrada na ilha griega de <a href="/w/index.php?title=Salamina&action=edit&redlink=1" class="new" title="Salamina (la páigina nun eisiste)">Salamina</a> an <a href="/w/index.php?title=1846&action=edit&redlink=1" class="new" title="1846 (la páigina nun eisiste)">1846</a> data de <a href="/w/index.php?title=300_a.C.&action=edit&redlink=1" class="new" title="300 a.C. (la páigina nun eisiste)">300 a.C.</a>, fazendo deste l mais bielho ábaco çcubierto até agora. Ye un ábaco de mármore de 149 cm de cumprimento, 75 cn de anchura i de 4,5 cn de spessura, ne l qual eisísten 5 grupos de marcaçones. Ne l centro de la tábua eisiste un cunjunto de 5 lhinhas paralelas eigualmente debedidas por ua lhinha bertical, tampada por un semicirclo na anterseçon de la lhinha hourizontal mais al canto i la lhinha bertical sola. Ambaixo destas lhinhas, eisiste un spácio ancho cun ua rachadura hourizontal a dibedi-los. Ambaixo desta rachadura, eisiste outro grupo de onze lhinhas paralelas, debedidas an dues seçones por ua lhinha perpendicular a eilhas, mas cul semicirclo ne l topo de la anterseçon; la terceira, sesta i nona lhinhas stan marcadas cun ua cruç adonde se crúzan cula lhinha bertical. </p> <div class="mw-heading mw-heading3"><h3 id="Ábaco_romano"><span id=".C3.81baco_romano"></span>Ábaco romano</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=9" title="Eiditar cacho: Ábaco romano" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=9" title="Editar código-fonte da secção: Ábaco romano"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fexeiro:RomanAbacusRecon.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/RomanAbacusRecon.jpg/250px-RomanAbacusRecon.jpg" decoding="async" width="250" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/b5/RomanAbacusRecon.jpg 1.5x" data-file-width="300" data-file-height="239" /></a><figcaption>Ábaco romano recustruído</figcaption></figure> <div class="hatnote"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Magnifying_glass_01.svg/17px-Magnifying_glass_01.svg.png" decoding="async" width="17" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Magnifying_glass_01.svg/26px-Magnifying_glass_01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Magnifying_glass_01.svg/34px-Magnifying_glass_01.svg.png 2x" data-file-width="663" data-file-height="659" /></span></span>Ber artigo percipal: <a href="/w/index.php?title=%C3%81baco_romano&action=edit&redlink=1" class="new" title="Ábaco romano (la páigina nun eisiste)">Ábaco romano</a></div> <p>L método normal de cálclo na Roma antiga, assi cumo na Grécia antiga, era mober bolas de cuntaige nua tábua própia pa l eifeito. Las bolas de cuntaige oureginales chamában-se <i>calculi</i>. Mais tarde, i na Ouropa mediebal, ls <i>jetones</i> ampeçórun a ser manufaturados. Lhinhas marcadas andicában ounidades, meias dezenas, dezenas, etc., cumo na <a href="/w/index.php?title=Numara%C3%A7on_romana&action=edit&redlink=1" class="new" title="Numaraçon romana (la páigina nun eisiste)">numaraçon romana</a>. L sistema de <i>cuntaige cuntrária</i> cuntinou até a la queda de Roma, assi cumo na Eidade Média i até al seclo XIX, ambora yá cun ua outelizaçon mais lhemitada.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>An adiçon a las mais outelizadas bolas de cuntaige frouxas, bários tipos dun ábaco romano fúrun ancuntrados, mostrados eiqui an recustruçon. Ten uito lhargos sulcos tenendo até 5 bolas an cada i 8 sulcos menores tenendo tanto ua cumo nanhue bola. </p><p>Ne ls sulcos menores, l sulco marcado I marca ounidades, l X dezenas i assi sucessibamente até als milhones. Las bolas ne ls sulcos menores márcan ls cincos - cinco ounidades, cinco dezenas, etc. - eissencialmente baseado na <a href="/w/index.php?title=Numara%C3%A7on_romana&action=edit&redlink=1" class="new" title="Numaraçon romana (la páigina nun eisiste)">numaraçon romana</a>. Ls sulcos mais pequeinhos a la dreita puoden tener sido outelizados para la marcaçon de las onças romanas. </p> <div class="mw-heading mw-heading3"><h3 id="Ábaco_andiano"><span id=".C3.81baco_andiano"></span>Ábaco andiano</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=10" title="Eiditar cacho: Ábaco andiano" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=10" title="Editar código-fonte da secção: Ábaco andiano"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Fuontes de l <a href="/wiki/Seclo_I" title="Seclo I">seclo I</a>, cumo la <i>Abhidharmakosa</i>, çcríben la sabedorie i l uso de l ábaco na <a href="/wiki/%C3%8Dndia" title="Índia">Índia</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Por buolta de l <a href="/w/index.php?title=Seclo_V&action=edit&redlink=1" class="new" title="Seclo V (la páigina nun eisiste)">seclo V</a>, scribones andianos stában yá a la percura de grabar ls resultados de l Ábaco.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Testos <a href="/w/index.php?title=Hinduismo&action=edit&redlink=1" class="new" title="Hinduismo (la páigina nun eisiste)">hindus</a> ousában la palabra <i>shunya</i> (zero) para andicar la coluna bazie ne l ábaco.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ábaco_chinés"><span id=".C3.81baco_chin.C3.A9s"></span>Ábaco chinés</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=11" title="Eiditar cacho: Ábaco chinés" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=11" title="Editar código-fonte da secção: Ábaco chinés"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fexeiro:Abacus_6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Abacus_6.png/220px-Abacus_6.png" decoding="async" width="220" height="129" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/a/af/Abacus_6.png 1.5x" data-file-width="247" data-file-height="145" /></a><figcaption>Suanpan (l númaro repersentado na figura ye 6.302.715.408)</figcaption></figure> <div class="hatnote"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Magnifying_glass_01.svg/17px-Magnifying_glass_01.svg.png" decoding="async" width="17" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Magnifying_glass_01.svg/26px-Magnifying_glass_01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Magnifying_glass_01.svg/34px-Magnifying_glass_01.svg.png 2x" data-file-width="663" data-file-height="659" /></span></span>Ber artigo percipal: <a href="/w/index.php?title=Suanpan&action=edit&redlink=1" class="new" title="Suanpan (la páigina nun eisiste)">Suanpan</a></div> <p>La mençon mais antiga a un <i>suanpan</i> (ábaco chinés) ye ancuntrada nun lhibro de l <a href="/wiki/Seclo_I" title="Seclo I">seclo I</a> de la <a href="/w/index.php?title=Dinastie_Han_Ouriental&action=edit&redlink=1" class="new" title="Dinastie Han Ouriental (la páigina nun eisiste)">Dinastie Han Ouriental</a>, l <i>Notas Suplementares na Arte de las Figuras</i> scrito por Xu Yue.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Inda assi, l aspeto eisato deste <i>suanpan</i> ye çcoincido. </p><p>Normalmente, un <i>suanpan</i> ten cerca de 20 cm de altura i ben an bariadas lharguras, dependendo de l fabricante. Ten normalmente mais de siete baras. Eisisten dues bolas an cada bara na parte de riba i cinco na parte de baixo, para númaros <a href="/wiki/Sistema_decimal" class="mw-redirect" title="Sistema decimal">decimales</a> i <a href="/wiki/Sistema_heixadecimal" class="mw-redirect" title="Sistema heixadecimal">heixadecimales</a>. Ábacos mais modernos ténen ua bola na parte de riba i quatro na parte de baixo. Las bolas son habitualmente redondas i feitas an madeira. Las bolas son cuntadas por séren mobidas para cima ó para baixo. Se las moberes pa l alto, cunta-les l balor; se nó, nun se les cunta l balor. L <i>suanpan</i> puode tornar a la posiçon einicial anstantaneamente por un pequeinho agitar al lhargo de l eixe hourizontal para afastar todas las pieças de l centro. </p><p>Ls <i>suanpanes</i> puoden ser outelizados para outras funçones sin ser cuntar. Al cuntrário de ls simples ábaco outelizado nas scuolas, muitas técnicas eficientes pa l <i>suanpan</i> fúrun feitas para calcular ouparaçones que outelizan la <a href="/w/index.php?title=Multiplica%C3%A7on&action=edit&redlink=1" class="new" title="Multiplicaçon (la páigina nun eisiste)">multiplicaçon</a>, la <a href="/w/index.php?title=Debison&action=edit&redlink=1" class="new" title="Debison (la páigina nun eisiste)">debison</a>, la <a href="/w/index.php?title=Adi%C3%A7on&action=edit&redlink=1" class="new" title="Adiçon (la páigina nun eisiste)">adiçon</a>, la <a href="/w/index.php?title=Subtra%C3%A7on&action=edit&redlink=1" class="new" title="Subtraçon (la páigina nun eisiste)">subtraçon</a>, la <a href="/w/index.php?title=Rai%C3%A7_quadrada&action=edit&redlink=1" class="new" title="Raiç quadrada (la páigina nun eisiste)">raiç quadrada</a> i la <a href="/w/index.php?title=Rai%C3%A7_c%C3%BAbica&action=edit&redlink=1" class="new" title="Raiç cúbica (la páigina nun eisiste)">raiç cúbica</a> a ua alta belocidade. </p><p>Ne l famoso quadro <i>Cenas al cerca de l mar ne l Festibal de Qingming</i> pintado por <a href="/w/index.php?title=Zhang_Zeduan&action=edit&redlink=1" class="new" title="Zhang Zeduan (la páigina nun eisiste)">Zhang Zeduan</a> (<a href="/w/index.php?title=1085&action=edit&redlink=1" class="new" title="1085 (la páigina nun eisiste)">1085</a>-<a href="/w/index.php?title=1145&action=edit&redlink=1" class="new" title="1145 (la páigina nun eisiste)">1145</a>) durante la <a href="/w/index.php?title=Dinastie_Song&action=edit&redlink=1" class="new" title="Dinastie Song (la páigina nun eisiste)">Dinastie Song</a> (<a href="/w/index.php?title=960&action=edit&redlink=1" class="new" title="960 (la páigina nun eisiste)">960</a>-<a href="/w/index.php?title=1297&action=edit&redlink=1" class="new" title="1297 (la páigina nun eisiste)">1297</a>), un <i>suanpan</i> ye claramente bisto al lhado dun lhibro de ancargos i de prescriçones de l doutor na secretaira dun apotecário. </p><p>La aparecenças de l ábaco romano cul <i>suanpan</i> faç parecer que un puode tener anspirado l outro, pus eisisten eibidéncias de relaçones comerciales antre l Ampério Romano i la China. Inda assi, nanhue lhigaçon direta ye passible de ser demunstrada, i la aparecença de l ábacos puode bien ser cuncidéncia, dambos deribando de la cuntaige de cinco dedos por mano. Adonde l modelo romano ten 4 mais 1 bolas por spácio decimal, l <i>suanpan</i> padron ten 5 mais 2, podendo ser outelizado cun númaros heixadecimales, al cuntrário de l romano. An beç de funcionar an cuordas cumo ls modelos chinés i japonés, l ábaco romano funciona an sulcos, probablemente fazendo ls cálclos mais defíceles. </p><p>Outra fuonte probable de l <i>suanpan</i> son las <a href="/w/index.php?title=Pir%C3%A1mide_num%C3%A9rica&action=edit&redlink=1" class="new" title="Pirámide numérica (la páigina nun eisiste)">pirámides numéricas</a> chinesas, que ouperában cul sistema decimal mas nun ancluian l cunceito de zero. L zero fui probablemente antroduzido als chineses na <a href="/w/index.php?title=Dinastie_Tang&action=edit&redlink=1" class="new" title="Dinastie Tang (la páigina nun eisiste)">Dinastie Tang</a> (<a href="/w/index.php?title=618&action=edit&redlink=1" class="new" title="618 (la páigina nun eisiste)">618</a>-<a href="/w/index.php?title=907&action=edit&redlink=1" class="new" title="907 (la páigina nun eisiste)">907</a>), quando las biaiges ne l <a href="/wiki/Ouceano_%C3%8Dndico" title="Ouceano Índico">Ouceano Índico</a> i ne l <a href="/wiki/M%C3%A9dio_Ouriente" title="Médio Ouriente">Médio Ouriente</a> tenerien dado cuntato direto cula <a href="/wiki/%C3%8Dndia" title="Índia">Índia</a> i l <a href="/wiki/Eislan" title="Eislan">Eislan</a>, premetindo-les saber l cunceito de zero i de l <a href="/w/index.php?title=Punto_decimal&action=edit&redlink=1" class="new" title="Punto decimal (la páigina nun eisiste)">punto decimal</a> de mercantes i matemáticos andianos i eislámicos. </p><p>L <i>suanpan</i> migrou de la China para la <a href="/w/index.php?title=Coreia&action=edit&redlink=1" class="new" title="Coreia (la páigina nun eisiste)">Coreia</a> an cerca de l anho <a href="/w/index.php?title=1400&action=edit&redlink=1" class="new" title="1400 (la páigina nun eisiste)">1400</a>. Ls coreanos chaman-le <i>jupan</i> (주판), <i>supan</i> (수판) or <i>jusan</i> (주산).<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ábaco_japonés"><span id=".C3.81baco_japon.C3.A9s"></span>Ábaco japonés</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=12" title="Eiditar cacho: Ábaco japonés" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=12" title="Editar código-fonte da secção: Ábaco japonés"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fexeiro:Soroban.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Soroban.JPG/400px-Soroban.JPG" decoding="async" width="400" height="117" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Soroban.JPG/600px-Soroban.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/7/72/Soroban.JPG 2x" data-file-width="629" data-file-height="184" /></a><figcaption>Soroban japonés</figcaption></figure> <div class="hatnote"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Magnifying_glass_01.svg/17px-Magnifying_glass_01.svg.png" decoding="async" width="17" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Magnifying_glass_01.svg/26px-Magnifying_glass_01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Magnifying_glass_01.svg/34px-Magnifying_glass_01.svg.png 2x" data-file-width="663" data-file-height="659" /></span></span>Ber artigo percipal: <a href="/w/index.php?title=Soroban&action=edit&redlink=1" class="new" title="Soroban (la páigina nun eisiste)">Soroban</a></div> <p>Un <i>soroban</i> (算盤, そろばん, lhit. <i>tábua de cuntar</i>) ye ua berson demudada puls japoneses de l <i>suanpan</i>. Ye planeado de l <i>suanpan</i>, amportado pa l <a href="/wiki/Japon" title="Japon">Japon</a> antes de l <a href="/w/index.php?title=Seclo_XVI&action=edit&redlink=1" class="new" title="Seclo XVI (la páigina nun eisiste)">seclo XVI</a>.]].<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Inda assi, la eidade de trasmisson eisata i l meio son anciertos porque nun eisisten registros specíficos.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Cumo l <i>suanpan</i>, l <i>soroban</i> inda hoije ye outelizado ne l Japon. </p><p>La Coreia ten tamien l sou própio, l <i>supan</i> (수판), que ye basicamente l <i>soroban</i> antes de tomar la sue atul forma ne ls anhos 30. L <i>soroban</i> moderno tamien ten este nome.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ábacos_de_ls_natibos_amaricanos"><span id=".C3.81bacos_de_ls_natibos_amaricanos"></span>Ábacos de ls natibos amaricanos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=13" title="Eiditar cacho: Ábacos de ls natibos amaricanos" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=13" title="Editar código-fonte da secção: Ábacos de ls natibos amaricanos"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fexeiro:Quipu.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Quipu.png/100px-Quipu.png" decoding="async" width="100" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Quipu.png/150px-Quipu.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Quipu.png/200px-Quipu.png 2x" data-file-width="299" data-file-height="449" /></a><figcaption>Repersentaçon dun <i>quipu</i> Anca</figcaption></figure> <p>Alguas fuontes fálan l uso dun ábaco chamado <i>nepohualtzintzin</i> na antiga cultura azteca. Este ábaco mesoamaricano outeliza un sistema de base 20 cun 5 númaros. </p><p>L <i>quipu</i> de ls Ancas era un sistema de cuordas atadas ousado para grabar dados numéricos, cumo baras de registro abançadas - mas nun éran ousadas para fazer cálclos. Ls cálclos éran feitos outelizando ua <i>yupana</i> (<a href="/w/index.php?title=L%C3%A9ngua_quechua&action=edit&redlink=1" class="new" title="Léngua quechua (la páigina nun eisiste)">quechua</a> para <i>tábua de cuntar</i>), que staba inda an uso depuis de la cunquista de l Peru. L percípio de trabalho dua <i>yupana</i> ye çcoincido, mas, an <a href="/w/index.php?title=2001&action=edit&redlink=1" class="new" title="2001 (la páigina nun eisiste)">2001</a>, ua splicaçon pa la base matemática deste strumiento fui perpuosta. Por cumparaçon a la forma de bárias <i>yupanas</i>, ls ambestigadores çcubrírun que ls cálclos éran baseados na <a href="/w/index.php?title=Sequ%C3%A9ncia_Fibonnaci&action=edit&redlink=1" class="new" title="Sequéncia Fibonnaci (la páigina nun eisiste)">sequéncia Fibonnaci</a>, outelizando 1,1,2,3,5 i múltiplos de 10, 20 i 40 pa ls defrentes campos de l strumiento. Outelizar la sequéncia Fibonnaci farie quedar l númaro de bolas nun campo ne l mínemo. </p> <div class="mw-heading mw-heading3"><h3 id="Ábaco_russo"><span id=".C3.81baco_russo"></span>Ábaco russo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=14" title="Eiditar cacho: Ábaco russo" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=14" title="Editar código-fonte da secção: Ábaco russo"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fexeiro:Schoty_abacus.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Schoty_abacus.jpg/220px-Schoty_abacus.jpg" decoding="async" width="220" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Schoty_abacus.jpg/330px-Schoty_abacus.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Schoty_abacus.jpg/440px-Schoty_abacus.jpg 2x" data-file-width="919" data-file-height="1064" /></a><figcaption>Ábaco russo.</figcaption></figure> <p>L ábaco russo, l <i>schoty</i> (счёты), normalmente ten solo un lhado cumprido, cun 10 bolas an cada filo (fuora un que ten 4 bolas, para fraçones de quartos de rublo). Este questuma star de l lhado de l outelizador. (Modelos mais bielhos ténen outra cuorda cun 4 bolas, para quartos de kopeks, que éran eimitidos até <a href="/w/index.php?title=1916&action=edit&redlink=1" class="new" title="1916 (la páigina nun eisiste)">1916</a>. L ábaco russo ye normalmente outelizado na bertical, cun ls filos de la squierda para la dreita al modo de l lhibro. Las bolas son normalmente curbadas para se mobéren pa l outro lhado ne l centro, an orde para mantener las bolas an cada un de l lhados. Ye clareficado quando las bolas se dében mober para la dreita. Durante la manipulaçon, las bolas son mobidas pa la dreita. Para mais fácele bisualizaçon, las dues bolas de l meio de cada cuorda (a 5ª i a 6ª; ne l causo de la cuorda eicepçon, a 3ª i a 4ª) questúman star cun quelores defrentes de las outras uito. Cumo tal, la bola mais a la squierda de la cuorda de ls miles (i de l milhones, se eisistir) questuma tamien star pintada de maneira defrente. </p><p>L ábaco russo staba an uso an todos ls sotos i mercados de toda la antiga <a href="/wiki/Ounion_Sobi%C3%A9tica" title="Ounion Sobiética">Ounion Sobiética</a>, i l uso de l ábaco era ansinado an todas las scuolas até als anhos 90. Hoije ye bisto cumo algo arcaico i fui sustituído pula calculadora. Na scuola, l uso de la calculadora ye ansinado zde ls anhos 90. </p> <div class="mw-heading mw-heading3"><h3 id="Ábaco_scolar"><span id=".C3.81baco_scolar"></span>Ábaco scolar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=15" title="Eiditar cacho: Ábaco scolar" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=15" title="Editar código-fonte da secção: Ábaco scolar"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fexeiro:Kugleramme.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Kugleramme.jpg/150px-Kugleramme.jpg" decoding="async" width="150" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Kugleramme.jpg/225px-Kugleramme.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Kugleramme.jpg/300px-Kugleramme.jpg 2x" data-file-width="1675" data-file-height="1793" /></a><figcaption>Ábaco scolar outelizado nua scuola purmária dinamarquesa, de l seclo XX.</figcaption></figure> <p>An to l mundo, ls ábacos ténen sido outelizados ne l <a href="/w/index.php?title=Ansino_pr%C3%A9-scolar&action=edit&redlink=1" class="new" title="Ansino pré-scolar (la páigina nun eisiste)">ansino pré-scolar</a> i <a href="/w/index.php?title=Ansino_purm%C3%A1rio&action=edit&redlink=1" class="new" title="Ansino purmário (la páigina nun eisiste)">purmário</a> cumo ua ajuda al ansino de l <a href="/w/index.php?title=Sistema_num%C3%A9rico&action=edit&redlink=1" class="new" title="Sistema numérico (la páigina nun eisiste)">sistema numérico</a> i de la <a href="/wiki/Aritm%C3%A9tica" title="Aritmética">aritmética</a>. Ne ls países oucidentales, ua tábua cun bolas parecida al ábaco russo mas cun filos mais dreitos i un praino bertical ten sido quemun (ber eimaige). </p><p>L tipo de ábaco eiqui amostrado ye normalmente outelizado para repersentar númaros sin l uso de l lhugar de la orde de ls númaros. Cada bola i cada filo ten eisatamente l mesmo balor i, outelizado desta maneira, puode ser outelizado para repersentar númaros arriba de 100. </p><p>La bantaige eiducacional mais seneficante an outelizar un ábaco, al robés de bolas ó outro material de cuntaige, quando se pratica la cuntaige ó la adiçon simples, ye que esso dá als studantes ua eideia de ls grupos de 10 que son la base de l nuosso sistema numérico. Mesmo que ls adultos tómen esta base de 10 cumo garantida, ye na rialidade defícel de daprender. Muitas ninos de 6 anhos cunsíguen cuntar até 100 de seguida cun solamente ua pequeinha cuncéncia de ls padrones ambolbidos. </p> <div class="mw-heading mw-heading3"><h3 id="Usos_puls_deficientes_bisuales">Usos puls deficientes bisuales</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=16" title="Eiditar cacho: Usos puls deficientes bisuales" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=16" title="Editar código-fonte da secção: Usos puls deficientes bisuales"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Un ábaco adatado, ambentado por Heilen Keller i chamado de <i>Cranmer</i>, ye inda outelizado por <a href="/w/index.php?title=Deficiente_bisual&action=edit&redlink=1" class="new" title="Deficiente bisual (la páigina nun eisiste)">deficientes bisuales</a>. Un cacho de fabrico suabe ó borraixa ye puosto detrás de las bolas para nun mobéren sien querer. Esto mantén las bolas ne l sítio quando ls outelizadores las sínten ó manipúlan. Eilhas outelízan un ábaco para fazer las funçones matemáticas multeplicaçon, debison, adiçon, subtraçon, raíç quadrada i raíç cúbica. </p><p>Ambora alunos deficientes bisuales téngan beneficiado de calculadoras falantes, l uso de l ábaco ye inda ansinado a estes alunos an eidades mais nuobas, tanto an scuolas públicas cumo an scuolas pribadas de ansino special. L ábaco ansina cumpeténcias matemáticas que nunca poderán ser sustituídas por ua calculadora falante i ye ua ferramienta de ansino anportante para studantes deficientes bisuales. Ls studantes deficientes bisuales tamien cumpletan trabalhos de matemática outelizando un scritor de Braille i de código Nemeth (ua espece de código Braille pa la matemática), mas las multeplicaçones anchas i las debisones puoden ser lhongas i defíceles. L ábaco dá a studantes deficientes bisuales i bisualmente lhemitados ua ferramienta para resulber porblemas matemáticos que eiguala la belocidade de ls sous colegas sin porblemas bisuales outelizando papel i lhápeç. Muitas pessonas áchan esta ua máquina útele durante la sue bida. </p> <div class="mw-heading mw-heading2"><h2 id="Curjidades">Curjidades</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%81baco&veaction=edit&section=17" title="Eiditar cacho: Curjidades" class="mw-editsection-visualeditor"><span>eiditar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C3%81baco&action=edit&section=17" title="Editar código-fonte da secção: Curjidades"><span>eiditar código-fuonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Fui amostrado que alunos chineses cunsíguen fazer cuntas cumplexas cun un ábaco, mais debrebe que un <a href="/w/index.php?title=Oucidente&action=edit&redlink=1" class="new" title="Oucidente (la páigina nun eisiste)">oucidental</a> eiquipado cun ua moderna <a href="/wiki/Calculadora" title="Calculadora">calculadora</a> eiletrónica. Ambora la calculadora apersente la repuosta quaije anstantaneamente, ls alunos cunsíguen acabar l cálclo antes mesmo de sou cumpetidor acabar de screbir ls <a href="/wiki/N%C3%BAmaro" title="Númaro">númaros</a> na botoneira de la calculadora. </p> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://search.eb.com/eb/article-9003215"><i>Abacus</i></a>. <i><a href="/w/index.php?title=Ancyclop%C3%A6die_Britannica&action=edit&redlink=1" class="new" title="Ancyclopædie Britannica (la páigina nun eisiste)">Ancyclopædie Britannica</a></i>, <a href="/w/index.php?title=3_de_Febreiro&action=edit&redlink=1" class="new" title="3 de Febreiro (la páigina nun eisiste)">3 de Febreiro</a> de <a href="/w/index.php?title=2007&action=edit&redlink=1" class="new" title="2007 (la páigina nun eisiste)">2007</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Reilly, páigina 825</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Smith, page 159</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Oxford English Dictionary, 1989</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Merrian-Webster's 2003</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Carrucio, páigina 14</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">Crump, páigina 188</span> </li> <li id="cite_note-Smith1-8"><span class="mw-cite-backlink"><a href="#cite_ref-Smith1_8-0">↑</a></span> <span class="reference-text">Smith, page 160</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text">Pullan, páigina 18</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text">Stearnes, páigina 44</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="#cite_ref-11">↑</a></span> <span class="reference-text">Körner, páigina 232</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text">Mollin, page 3</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text">Peng Yoke Ho, páigina 71</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><a href="#cite_ref-14">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external free" href="http://anc.daun.net/dic100/cuntents.de">http://anc.daun.net/dic100/cuntents.de</a> l?query1=b19j3727a</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text"><span class="citation"> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080321023312/http://shuzan-gakko.com/rekishi/4nihon.html"><i>Archive copy</i></a>, arquivado do <a rel="nofollow" class="external text" href="http://shuzan-gakko.com/rekishi/4nihon.html">original</a> em 2008-03-21<span class="printonly">, <a rel="nofollow" class="external free" href="https://web.archive.org/web/20080321023312/http://shuzan-gakko.com/rekishi/4nihon.html">https://web.archive.org/web/20080321023312/http://shuzan-gakko.com/rekishi/4nihon.html</a></span><span class="reference-accessdate">, visitado em 2013-05-03</span></span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Archive+copy&rft_id=https%3A%2F%2Fweb.archive.org%2Fweb%2F20080321023312%2Fhttp%3A%2F%2Fshuzan-gakko.com%2Frekishi%2F4nihon.html&rfr_id=info:sid/en.wikipedia.org:%C3%81baco"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><a href="#cite_ref-16">↑</a></span> <span class="reference-text"><span class="citation"> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080227081832/http://www.tux.org/%7Ebagleyd/takashikojima2.pdf"><i>Archive copy</i></a>, arquivado do <a rel="nofollow" class="external text" href="http://www.tux.org/%7Ebagleyd/takashikojima2.pdf">original</a> em 2008-02-27<span class="printonly">, <a rel="nofollow" class="external free" href="https://web.archive.org/web/20080227081832/http://www.tux.org/%7Ebagleyd/takashikojima2.pdf">https://web.archive.org/web/20080227081832/http://www.tux.org/%7Ebagleyd/takashikojima2.pdf</a></span><span class="reference-accessdate">, visitado em 2009-06-14</span></span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Archive+copy&rft_id=https%3A%2F%2Fweb.archive.org%2Fweb%2F20080227081832%2Fhttp%3A%2F%2Fwww.tux.org%2F%257Ebagleyd%2Ftakashikojima2.pdf&rfr_id=info:sid/en.wikipedia.org:%C3%81baco"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><a href="#cite_ref-17">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external free" href="http://www.e.ryerson.ca/~eilf/abacus/story.html">http://www.e.ryerson.ca/~eilf/abacus/story.html</a><sup><a href="/w/index.php?title=Biquip%C3%A9dia:Lhiga%C3%A7on_einatiba&action=edit&redlink=1" class="new" title="Biquipédia:Lhigaçon einatiba (la páigina nun eisiste)"><i>[lhigaçon einatiba]</i></a></sup></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><a href="#cite_ref-18">↑</a></span> <span class="reference-text">Esta palabra ye mui outelizado ne l sítio coreano <a rel="nofollow" class="external free" href="http://www.supan.net">http://www.supan.net</a>, que nun solo dá liçones an cumo outelizar l ábaco mas tamien l soroban.</span> </li> </ol>    </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="">Sacado an "<a dir="ltr" href="https://mwl.wikipedia.org/w/index.php?title=Ábaco&oldid=102027">https://mwl.wikipedia.org/w/index.php?title=Ábaco&oldid=102027</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" 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