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class="vector-menu-heading"> ログアウトした編集者のページ <a href="/wiki/Wikipedia:%E3%82%A6%E3%82%A3%E3%82%AD%E3%83%9A%E3%83%87%E3%82%A3%E3%82%A2%E3%81%B8%E3%82%88%E3%81%86%E3%81%93%E3%81%9D" aria-label="編集の詳細"><span>もっと詳しく</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E8%87%AA%E5%88%86%E3%81%AE%E6%8A%95%E7%A8%BF%E8%A8%98%E9%8C%B2" title="このIPアドレスからなされた編集の一覧 [y]" accesskey="y"><span>投稿記録</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%83%88%E3%83%BC%E3%82%AF%E3%83%9A%E3%83%BC%E3%82%B8" title="このIPアドレスからなされた編集についての議論 [n]" accesskey="n"><span>トーク</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="サイト"> <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="目次" 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">目次</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">非表示</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">ページ先頭</div> </a> </li> <li id="toc-歴史" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#歴史"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>歴史</span> </div> </a> <ul id="toc-歴史-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-算木の使用" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#算木の使用"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>算木の使用</span> </div> </a> <ul id="toc-算木の使用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-算木数字" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#算木数字"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>算木数字</span> </div> </a> <ul id="toc-算木数字-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-代数記号" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#代数記号"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>代数記号</span> </div> </a> <ul id="toc-代数記号-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Unicode" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Unicode"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Unicode</span> </div> </a> <button aria-controls="toc-Unicode-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>Unicodeサブセクションを切り替えます</span> </button> <ul id="toc-Unicode-sublist" class="vector-toc-list"> <li id="toc-符号位置" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#符号位置"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>符号位置</span> </div> </a> <ul id="toc-符号位置-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-易占用の算木" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#易占用の算木"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>易占用の算木</span> </div> </a> <ul id="toc-易占用の算木-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-易者のシンボル" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#易者のシンボル"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>易者のシンボル</span> </div> </a> <ul id="toc-易者のシンボル-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-家紋" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#家紋"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>家紋</span> </div> </a> <ul id="toc-家紋-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>参考文献</span> </div> </a> <ul id="toc-参考文献-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-脚注" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#脚注"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>脚注</span> </div> </a> <ul id="toc-脚注-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-関連項目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#関連項目"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>関連項目</span> </div> </a> <ul id="toc-関連項目-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部リンク" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部リンク"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>外部リンク</span> </div> </a> <ul id="toc-外部リンク-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="目次" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="目次" > <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="目次の表示・非表示を切り替え" > <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">目次の表示・非表示を切り替え</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">算木</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="特定の記事の別の言語版に移動します。利用可能な言語17件" > <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-17" 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">17の言語版</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Numeraci%C3%B3_amb_varetes" title="カタロニア語: Numeració amb varetes" lang="ca" hreflang="ca" data-title="Numeració amb varetes" data-language-autonym="Català" data-language-local-name="カタロニア語" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Counting_rods" title="英語: Counting rods" lang="en" hreflang="en" data-title="Counting rods" data-language-autonym="English" data-language-local-name="英語" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Numeraci%C3%B3n_con_varillas" title="スペイン語: Numeración con varillas" lang="es" hreflang="es" data-title="Numeración con varillas" data-language-autonym="Español" data-language-local-name="スペイン語" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Puikkolaskenta" title="フィンランド語: Puikkolaskenta" lang="fi" hreflang="fi" data-title="Puikkolaskenta" data-language-autonym="Suomi" data-language-local-name="フィンランド語" 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/Baguettes_%C3%A0_calculer" title="フランス語: Baguettes à calculer" lang="fr" hreflang="fr" data-title="Baguettes à calculer" data-language-autonym="Français" data-language-local-name="フランス語" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%95%D7%98%D7%95%D7%AA_%D7%9E%D7%A0%D7%99%D7%99%D7%94" title="ヘブライ語: מוטות מנייה" lang="he" hreflang="he" data-title="מוטות מנייה" data-language-autonym="עברית" data-language-local-name="ヘブライ語" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Tongkat_penghitung" title="インドネシア語: Tongkat penghitung" lang="id" hreflang="id" data-title="Tongkat penghitung" data-language-autonym="Bahasa Indonesia" data-language-local-name="インドネシア語" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%82%B0%EA%B0%80%EC%A7%80" title="韓国語: 산가지" lang="ko" hreflang="ko" data-title="산가지" data-language-autonym="한국어" data-language-local-name="韓国語" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Batang_pembilang" title="マレー語: Batang pembilang" lang="ms" hreflang="ms" data-title="Batang pembilang" data-language-autonym="Bahasa Melayu" data-language-local-name="マレー語" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Patyczki_liczbowe" title="ポーランド語: Patyczki liczbowe" lang="pl" hreflang="pl" data-title="Patyczki liczbowe" data-language-autonym="Polski" data-language-local-name="ポーランド語" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Sistema_num%C3%A9rico_de_varas" title="ポルトガル語: Sistema numérico de varas" lang="pt" hreflang="pt" data-title="Sistema numérico de varas" data-language-autonym="Português" data-language-local-name="ポルトガル語" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%87%D1%91%D1%82%D0%BD%D1%8B%D0%B5_%D0%BF%D0%B0%D0%BB%D0%BE%D1%87%D0%BA%D0%B8" title="ロシア語: Счётные палочки" lang="ru" hreflang="ru" data-title="Счётные палочки" data-language-autonym="Русский" data-language-local-name="ロシア語" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%B0%D1%85%D1%83%D0%BD%D0%BA%D0%BE%D0%B2%D1%96_%D0%BF%D0%B0%D0%BB%D0%B8%D1%87%D0%BA%D0%B8" title="ウクライナ語: Рахункові палички" lang="uk" hreflang="uk" data-title="Рахункові палички" data-language-autonym="Українська" data-language-local-name="ウクライナ語" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%AE%97%E7%AD%B9" title="呉語: 算筹" lang="wuu" hreflang="wuu" data-title="算筹" data-language-autonym="吴语" data-language-local-name="呉語" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%AE%97%E7%AD%B9" title="中国語: 算筹" lang="zh" hreflang="zh" data-title="算筹" data-language-autonym="中文" data-language-local-name="中国語" 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%B1%8C" title="漢文: 算籌" lang="lzh" hreflang="lzh" data-title="算籌" data-language-autonym="文言" data-language-local-name="漢文" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%AE%97%E7%B1%8C" title="広東語: 算籌" lang="yue" hreflang="yue" data-title="算籌" data-language-autonym="粵語" data-language-local-name="広東語" 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/Q583473#sitelinks-wikipedia" title="言語間リンクを編集" class="wbc-editpage">リンクを編集</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="名前空間"> <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/%E7%AE%97%E6%9C%A8" title="本文を閲覧 [c]" accesskey="c"><span>ページ</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%E3%83%8E%E3%83%BC%E3%83%88:%E7%AE%97%E6%9C%A8" rel="discussion" title="本文ページについての議論 [t]" accesskey="t"><span>ノート</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="別の言語に切り替える" > <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">日本語</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="表示"> <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/%E7%AE%97%E6%9C%A8"><span>閲覧</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit" title="このページのソースコードを編集する [e]" accesskey="e"><span>編集</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=history" title="このページの過去の版 [h]" accesskey="h"><span>履歴を表示</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" 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aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">出典: フリー百科事典『ウィキペディア（Wikipedia）』</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="ja" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Yanghui_triangle.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Yanghui_triangle.PNG/200px-Yanghui_triangle.PNG" decoding="async" width="200" height="317" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Yanghui_triangle.PNG/300px-Yanghui_triangle.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Yanghui_triangle.PNG/400px-Yanghui_triangle.PNG 2x" data-file-width="475" data-file-height="753" /></a><figcaption>朱世傑の四元玉鑑 (<a href="/wiki/1303%E5%B9%B4" title="1303年">1303年</a>) で書かれた<a href="/wiki/%E3%83%91%E3%82%B9%E3%82%AB%E3%83%AB%E3%81%AE%E4%B8%89%E8%A7%92%E5%BD%A2" title="パスカルの三角形">楊輝の三角形</a></figcaption></figure> <p><b>算木</b>（さんぎ）または<b>算籌</b>（さんちゅう）とは、中国数学や<a href="/wiki/%E5%92%8C%E7%AE%97" title="和算">和算</a>で用いられた計算用具である。縦または横に置くことで数を表した。算木に基づく算木数字も使われた。算木を用いた計算法を<a href="/wiki/%E7%B1%8C%E7%AE%97" title="籌算">籌算</a>という。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="歴史"><span id=".E6.AD.B4.E5.8F.B2"></span>歴史</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=1" title="節を編集: 歴史"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>中国では紀元前から算木が使われていた。<a href="/wiki/1954%E5%B9%B4" title="1954年">1954年</a>、<a href="/wiki/%E6%B9%96%E5%8D%97%E7%9C%81" title="湖南省">湖南省</a><a href="/wiki/%E9%95%B7%E6%B2%99" class="mw-redirect" title="長沙">長沙</a>の左家公山15号<a href="/wiki/%E6%A5%9A_(%E6%98%A5%E7%A7%8B)" title="楚 (春秋)">楚</a>墓で、<a href="/wiki/%E6%88%A6%E5%9B%BD%E6%99%82%E4%BB%A3_(%E4%B8%AD%E5%9B%BD)" title="戦国時代 (中国)">戦国時代</a>の算木が四十数本発掘された<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>。文献の記録はさらに古く、<a href="/wiki/%E8%80%81%E5%AD%90" title="老子">老子</a>には「善く数える者は籌策（ちゅうさく）を用いず」とある<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>。 </p><p><a href="/wiki/13%E4%B8%96%E7%B4%80" title="13世紀">13世紀</a>に<a href="/wiki/%E3%81%9D%E3%82%8D%E3%81%B0%E3%82%93" title="そろばん">そろばん</a>が使われるようになるまで、算木で計算を行った<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>。算木はそろばんと異なり多元の<a href="/wiki/%E4%BB%A3%E6%95%B0%E6%96%B9%E7%A8%8B%E5%BC%8F" title="代数方程式">代数方程式</a>を解くことができたが（<a href="/wiki/%E7%B1%8C%E7%AE%97#連立一次方程式" title="籌算">別項</a>参照）、中国ではそろばんの普及により解法が失われた。<a href="/wiki/%E6%B1%9F%E6%88%B8%E6%99%82%E4%BB%A3" title="江戸時代">江戸時代</a>の日本の数学者はそろばんと並んで算木を用い、数学の発展に貢献した<sup id="cite_ref-FOOTNOTE矢代(2004)_5-0" class="reference"><a href="#cite_note-FOOTNOTE矢代(2004)-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="算木の使用"><span id=".E7.AE.97.E6.9C.A8.E3.81.AE.E4.BD.BF.E7.94.A8"></span>算木の使用</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=2" title="節を編集: 算木の使用"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>算木は長さ 3 - 14<a href="/wiki/%E3%82%BB%E3%83%B3%E3%83%81%E3%83%A1%E3%83%BC%E3%83%88%E3%83%AB" title="センチメートル">cm</a> の木製または竹製の細長い直方体で、縦または横に並べて数を表し、配列を動かすことで<a href="/wiki/%E5%9B%9B%E5%89%87%E6%BC%94%E7%AE%97" class="mw-redirect" title="四則演算">四則演算</a>、<a href="/wiki/%E9%96%8B%E5%B9%B3%E6%B3%95" title="開平法">開平</a>、<a href="/wiki/%E9%96%8B%E7%AB%8B%E6%B3%95" title="開立法">開立</a>などの計算をした。1から5まではその数だけ算木を並べ、6以上は異なる向きの1本で5を表した。 </p><p><a href="/wiki/%E3%82%A2%E3%83%A9%E3%83%93%E3%82%A2%E6%95%B0%E5%AD%97" title="アラビア数字">アラビア数字</a>のように左を上位として横に並べることで数を示す<sup id="cite_ref-FOOTNOTE矢代(2004)_5-1" class="reference"><a href="#cite_note-FOOTNOTE矢代(2004)-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>。隣の桁と間違えないよう、桁によって算木の向きを変え、縦式によって奇数桁（一・百・万……の位）を、横式によって偶数桁（十・千……の位）を示した。<a href="/wiki/%E5%AD%AB%E5%AD%90%E7%AE%97%E7%B5%8C" title="孫子算経">孫子算経</a>には「一は縦、十は横、百は立ち、千は倒れる」とある<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>。 </p><p>日本では<a href="/wiki/%E7%AE%97%E7%9B%A4" title="算盤">算盤</a>（さんばん）と呼ばれる格子を書いた布の上で算木を使用した<sup id="cite_ref-FOOTNOTE矢代(2004)_5-2" class="reference"><a href="#cite_note-FOOTNOTE矢代(2004)-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>。はじめは中国と同じく縦式横式のしくみを用いていたが、江戸後期になると算木を使って計算する時に横式を用いず、一位十位百位など位にかかわらず縦式のみを扱う者が多くなった（算盤の格子によって桁がわかるために、縦横の区別がいらなかったため）。ただし、紙の上では格子はなく続けざまに算木を書くので従来どおり縦式横式で書き続けた。 </p><p>算木は2色に着色され、<a href="/wiki/%E8%B5%A4" title="赤">赤</a>の算木は<a href="/wiki/%E6%AD%A3%E3%81%AE%E6%95%B0%E3%81%A8%E8%B2%A0%E3%81%AE%E6%95%B0" title="正の数と負の数">正の数</a>を、<a href="/wiki/%E9%BB%92" title="黒">黒</a>の算木は<a href="/wiki/%E6%AD%A3%E3%81%AE%E6%95%B0%E3%81%A8%E8%B2%A0%E3%81%AE%E6%95%B0#負の数" title="正の数と負の数">負の数</a>を表した。<a href="/wiki/0" title="0">0</a> はその場所に算木を置かず空けておくことで示し、後に<a href="/wiki/%E7%A2%81%E7%9F%B3" title="碁石">碁石</a>を置いて明示するようになった。<a href="/wiki/%E4%B9%9D%E7%AB%A0%E7%AE%97%E8%A1%93" title="九章算術">九章算術</a>には、「（引き算の時）同符号は引き、異符号は加える。正を無入から引いて負とし、負を無入から引いて正とする」とある<sup id="cite_ref-wang_7-0" class="reference"><a href="#cite_note-wang-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>。この「無入」とは「0」のことである。これから、0と正負の計算を理解していたことが分かる。 </p><p>算木を利用する事で、<a href="/wiki/%E6%9C%89%E7%90%86%E6%95%B0" title="有理数">有理数</a>の四則演算ができ、また高次の方程式の解を考察する事が可能である<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>。分数の<a href="/wiki/%E7%B4%84%E5%88%86" class="mw-redirect" title="約分">約分</a>を<a href="/wiki/%E3%83%A6%E3%83%BC%E3%82%AF%E3%83%AA%E3%83%83%E3%83%89%E3%81%AE%E4%BA%92%E9%99%A4%E6%B3%95" title="ユークリッドの互除法">互除法</a>で求める事にも使われる<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>。 </p> <table class="wikitable" border="1" style="text-align:center"> <caption>正の数 </caption> <tbody><tr> <th>  </th> <th style="width:50px">0 </th> <th style="width:50px">1 </th> <th style="width:50px">2 </th> <th style="width:50px">3 </th> <th style="width:50px">4 </th> <th style="width:50px">5 </th> <th style="width:50px">6 </th> <th style="width:50px">7 </th> <th style="width:50px">8 </th> <th style="width:50px">9 </th></tr> <tr> <th style="height:50px">縦式 </th> <td>  </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/Counting_rod_v1r.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v2r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/16/Counting_rod_v2r.png" decoding="async" width="13" height="29" class="mw-file-element" data-file-width="13" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v3r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/Counting_rod_v3r.png" decoding="async" width="19" height="29" class="mw-file-element" data-file-width="19" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v4r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/3a/Counting_rod_v4r.png" decoding="async" width="25" height="29" class="mw-file-element" data-file-width="25" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v5r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/8/88/Counting_rod_v5r.png" decoding="async" width="31" height="29" class="mw-file-element" data-file-width="31" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v6r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/20/Counting_rod_v6r.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v7r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/4/49/Counting_rod_v7r.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v8r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/df/Counting_rod_v8r.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v9r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2a/Counting_rod_v9r.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td></tr> <tr> <th style="height:50px">横式 </th> <td>  </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h1r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e8/Counting_rod_h1r.png" decoding="async" width="29" height="7" class="mw-file-element" data-file-width="29" data-file-height="7" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h2r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/9/9a/Counting_rod_h2r.png" decoding="async" width="29" height="13" class="mw-file-element" data-file-width="29" data-file-height="13" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h3r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7f/Counting_rod_h3r.png" decoding="async" width="29" height="19" class="mw-file-element" data-file-width="29" data-file-height="19" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h4r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/Counting_rod_h4r.png" decoding="async" width="29" height="25" class="mw-file-element" data-file-width="29" data-file-height="25" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h5r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/73/Counting_rod_h5r.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h6r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2c/Counting_rod_h6r.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h7r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/fe/Counting_rod_h7r.png" decoding="async" width="29" height="37" class="mw-file-element" data-file-width="29" data-file-height="37" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h8r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e4/Counting_rod_h8r.png" decoding="async" width="29" height="43" class="mw-file-element" data-file-width="29" data-file-height="43" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h9r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/a/ac/Counting_rod_h9r.png" decoding="async" width="29" height="47" class="mw-file-element" data-file-width="29" data-file-height="47" /></a></span> </td></tr></tbody></table> <p><br /> </p> <table class="wikitable" border="1" style="text-align:center"> <caption>負の数 </caption> <tbody><tr> <th>  </th> <th style="width:50px">0 </th> <th style="width:50px">-1 </th> <th style="width:50px">-2 </th> <th style="width:50px">-3 </th> <th style="width:50px">-4 </th> <th style="width:50px">-5 </th> <th style="width:50px">-6 </th> <th style="width:50px">-7 </th> <th style="width:50px">-8 </th> <th style="width:50px">-9 </th></tr> <tr> <th style="height:50px">縦式 </th> <td>  </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Counting_rod_v2.png" decoding="async" width="13" height="29" class="mw-file-element" data-file-width="13" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Counting_rod_v3.png" decoding="async" width="19" height="29" class="mw-file-element" data-file-width="19" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/67/Counting_rod_v4.png" decoding="async" width="25" height="29" class="mw-file-element" data-file-width="25" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v5.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e4/Counting_rod_v5.png" decoding="async" width="31" height="29" class="mw-file-element" data-file-width="31" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v6.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d1/Counting_rod_v7.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v8.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/64/Counting_rod_v8.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v9.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7a/Counting_rod_v9.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td></tr> <tr> <th style="height:50px">横式 </th> <td>  </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Counting_rod_h1.png" decoding="async" width="29" height="7" class="mw-file-element" data-file-width="29" data-file-height="7" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/51/Counting_rod_h2.png" decoding="async" width="29" height="13" class="mw-file-element" data-file-width="29" data-file-height="13" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/6b/Counting_rod_h3.png" decoding="async" width="29" height="19" class="mw-file-element" data-file-width="29" data-file-height="19" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/ce/Counting_rod_h4.png" decoding="async" width="29" height="25" class="mw-file-element" data-file-width="29" data-file-height="25" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h5.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/74/Counting_rod_h5.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c1/Counting_rod_h6.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/5d/Counting_rod_h7.png" decoding="async" width="29" height="37" class="mw-file-element" data-file-width="29" data-file-height="37" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h8.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Counting_rod_h8.png" decoding="async" width="29" height="43" class="mw-file-element" data-file-width="29" data-file-height="43" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h9.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Counting_rod_h9.png" decoding="async" width="29" height="47" class="mw-file-element" data-file-width="29" data-file-height="47" /></a></span> </td></tr></tbody></table> <p><br /> 例： </p> <table class="wikitable" border="1" style="text-align:center"> <tbody><tr> <th style="text-align:right;height:50px">231 </th> <td style="width:50px">  </td> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v2r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/16/Counting_rod_v2r.png" decoding="async" width="13" height="29" class="mw-file-element" data-file-width="13" data-file-height="29" /></a></span> </td> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h3r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7f/Counting_rod_h3r.png" decoding="async" width="29" height="19" class="mw-file-element" data-file-width="29" data-file-height="19" /></a></span> </td> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/Counting_rod_v1r.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span> </td></tr> <tr> <th style="text-align:right;height:50px">5089 </th> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h5r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/73/Counting_rod_h5r.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td style="width:50px">  </td> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h8r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e4/Counting_rod_h8r.png" decoding="async" width="29" height="43" class="mw-file-element" data-file-width="29" data-file-height="43" /></a></span> </td> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v9r.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2a/Counting_rod_v9r.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td></tr> <tr> <th style="text-align:right;height:50px">-407 </th> <td style="width:50px">  </td> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/67/Counting_rod_v4.png" decoding="async" width="25" height="29" class="mw-file-element" data-file-width="25" data-file-height="29" /></a></span> </td> <td style="width:50px">  </td> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d1/Counting_rod_v7.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td></tr> <tr> <th style="text-align:right;height:50px">-6720 </th> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c1/Counting_rod_h6.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d1/Counting_rod_v7.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td style="width:50px"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/51/Counting_rod_h2.png" decoding="async" width="29" height="13" class="mw-file-element" data-file-width="29" data-file-height="13" /></a></span> </td> <td style="width:50px">  </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="算木数字"><span id=".E7.AE.97.E6.9C.A8.E6.95.B0.E5.AD.97"></span>算木数字</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=3" title="節を編集: 算木数字"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>算木を紙に記すときは正の数をそのまま書き、負の数は最後の桁に斜線を書いて示した。この算木数字は真の<a href="/wiki/%E4%BD%8D%E5%8F%96%E3%82%8A%E8%A8%98%E6%95%B0%E6%B3%95" title="位取り記数法">位取り記数法</a>である。横式の字の縦棒は、字の高さを揃えるため短く書いた。 </p><p>また当初「0」は空白だったが、「〇」を書くようになった。<a href="/wiki/718%E5%B9%B4" title="718年">718年</a>に<a href="/wiki/%E7%9E%BF%E6%9B%87%E6%82%89%E9%81%94" title="瞿曇悉達">瞿曇悉達</a>により<a href="/wiki/%E3%82%A2%E3%83%A9%E3%83%93%E3%82%A2%E6%95%B0%E5%AD%97" title="アラビア数字">インド数字</a>から導入されたとも<sup id="cite_ref-wang_7-1" class="reference"><a href="#cite_note-wang-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>、<a href="/wiki/%E4%B8%AD%E5%9B%BD%E8%AA%9E" title="中国語">中国語</a>で欠字を表した「<a href="/wiki/%E5%9B%9B%E8%A7%92_(%E8%A8%98%E5%8F%B7)" title="四角 (記号)">□</a>」から来ているとも<sup id="cite_ref-qian_11-0" class="reference"><a href="#cite_note-qian-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>言われる。<a href="/wiki/%E6%BC%A2%E6%95%B0%E5%AD%97#〇" title="漢数字">漢数字#〇</a>を参照すること。 </p><p><a href="/wiki/13%E4%B8%96%E7%B4%80" title="13世紀">13世紀</a>、<a href="/wiki/%E5%8D%97%E5%AE%8B" title="南宋">南宋</a>の数学者は 4、5、9の数字の画数を減らして書きやすくした<sup id="cite_ref-qian_11-1" class="reference"><a href="#cite_note-qian-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>。この新しい数字の横式は最終的に<a href="/wiki/%E8%98%87%E5%B7%9E%E5%8F%B7%E7%A2%BC" title="蘇州号碼">蘇州号碼</a>に変化した。日本では紙の上では従来の算木数字を使い続けた。 </p> <table class="wikitable" border="1" style="text-align:center"> <caption>正の数 </caption> <tbody><tr> <th>  </th> <th style="width:50px">0 </th> <th style="width:50px">1 </th> <th style="width:50px">2 </th> <th style="width:50px">3 </th> <th style="width:50px">4 </th> <th style="width:50px">5 </th> <th style="width:50px">6 </th> <th style="width:50px">7 </th> <th style="width:50px">8 </th> <th style="width:50px">9 </th></tr> <tr> <th style="height:50px">縦式 </th> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/50/Counting_rod_0.png" decoding="async" width="23" height="23" class="mw-file-element" data-file-width="23" data-file-height="23" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Counting_rod_v2.png" decoding="async" width="13" height="29" class="mw-file-element" data-file-width="13" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Counting_rod_v3.png" decoding="async" width="19" height="29" class="mw-file-element" data-file-width="19" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/67/Counting_rod_v4.png" decoding="async" width="25" height="29" class="mw-file-element" data-file-width="25" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v5.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e4/Counting_rod_v5.png" decoding="async" width="31" height="29" class="mw-file-element" data-file-width="31" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v6.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d1/Counting_rod_v7.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v8.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/64/Counting_rod_v8.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v9.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7a/Counting_rod_v9.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td></tr> <tr> <th style="height:50px">横式 </th> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/50/Counting_rod_0.png" decoding="async" width="23" height="23" class="mw-file-element" data-file-width="23" data-file-height="23" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Counting_rod_h1.png" decoding="async" width="29" height="7" class="mw-file-element" data-file-width="29" data-file-height="7" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/51/Counting_rod_h2.png" decoding="async" width="29" height="13" class="mw-file-element" data-file-width="29" data-file-height="13" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/6b/Counting_rod_h3.png" decoding="async" width="29" height="19" class="mw-file-element" data-file-width="29" data-file-height="19" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/ce/Counting_rod_h4.png" decoding="async" width="29" height="25" class="mw-file-element" data-file-width="29" data-file-height="25" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h5.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/74/Counting_rod_h5.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c1/Counting_rod_h6.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h7_num.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/3c/Counting_rod_h7_num.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h8_num.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7e/Counting_rod_h8_num.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h9_num.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e4/Counting_rod_h9_num.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td></tr></tbody></table> <p><br /> </p> <table class="wikitable" border="1" style="text-align:center"> <caption>負の数 </caption> <tbody><tr> <th>  </th> <th style="width:50px">-0 </th> <th style="width:50px">-1 </th> <th style="width:50px">-2 </th> <th style="width:50px">-3 </th> <th style="width:50px">-4 </th> <th style="width:50px">-5 </th> <th style="width:50px">-6 </th> <th style="width:50px">-7 </th> <th style="width:50px">-8 </th> <th style="width:50px">-9 </th></tr> <tr> <th style="height:50px">縦式 </th> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_-0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/37/Counting_rod_-0.png" decoding="async" width="23" height="23" class="mw-file-element" data-file-width="23" data-file-height="23" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/6f/Counting_rod_v-1.png" decoding="async" width="23" height="29" class="mw-file-element" data-file-width="23" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/64/Counting_rod_v-2.png" decoding="async" width="23" height="29" class="mw-file-element" data-file-width="23" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/3f/Counting_rod_v-3.png" decoding="async" width="25" height="29" class="mw-file-element" data-file-width="25" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/ba/Counting_rod_v-4.png" decoding="async" width="31" height="29" class="mw-file-element" data-file-width="31" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-5.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/66/Counting_rod_v-5.png" decoding="async" width="35" height="29" class="mw-file-element" data-file-width="35" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/11/Counting_rod_v-6.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/04/Counting_rod_v-7.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-8.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/72/Counting_rod_v-8.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-9.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/0d/Counting_rod_v-9.png" decoding="async" width="31" height="32" class="mw-file-element" data-file-width="31" data-file-height="32" /></a></span> </td></tr></tbody></table> <p><br /> </p> <table class="wikitable" border="1" style="text-align:center"> <caption>正の数 (南宋) </caption> <tbody><tr> <th>  </th> <th style="width:50px">0 </th> <th style="width:50px">1 </th> <th style="width:50px">2 </th> <th style="width:50px">3 </th> <th style="width:50px">4 </th> <th style="width:50px">5 </th> <th style="width:50px">6 </th> <th style="width:50px">7 </th> <th style="width:50px">8 </th> <th style="width:50px">9 </th></tr> <tr> <th style="height:50px">縦式 </th> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/50/Counting_rod_0.png" decoding="async" width="23" height="23" class="mw-file-element" data-file-width="23" data-file-height="23" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Counting_rod_v2.png" decoding="async" width="13" height="29" class="mw-file-element" data-file-width="13" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Counting_rod_v3.png" decoding="async" width="19" height="29" class="mw-file-element" data-file-width="19" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_4_song.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/10/Counting_rod_4_song.png" decoding="async" width="23" height="24" class="mw-file-element" data-file-width="23" data-file-height="24" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v5_song.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/57/Counting_rod_v5_song.png" decoding="async" width="29" height="29" class="mw-file-element" data-file-width="29" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v6.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d1/Counting_rod_v7.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v8.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/64/Counting_rod_v8.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v9_song.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d1/Counting_rod_v9_song.png" decoding="async" width="29" height="29" class="mw-file-element" data-file-width="29" data-file-height="29" /></a></span> </td></tr> <tr> <th style="height:50px">横式 </th> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/50/Counting_rod_0.png" decoding="async" width="23" height="23" class="mw-file-element" data-file-width="23" data-file-height="23" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Counting_rod_h1.png" decoding="async" width="29" height="7" class="mw-file-element" data-file-width="29" data-file-height="7" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/51/Counting_rod_h2.png" decoding="async" width="29" height="13" class="mw-file-element" data-file-width="29" data-file-height="13" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/6b/Counting_rod_h3.png" decoding="async" width="29" height="19" class="mw-file-element" data-file-width="29" data-file-height="19" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_4_song.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/10/Counting_rod_4_song.png" decoding="async" width="23" height="24" class="mw-file-element" data-file-width="23" data-file-height="24" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h5_song.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c4/Counting_rod_h5_song.png" decoding="async" width="23" height="29" class="mw-file-element" data-file-width="23" data-file-height="29" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c1/Counting_rod_h6.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h7_num.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/3c/Counting_rod_h7_num.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h8_num.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7e/Counting_rod_h8_num.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h9_song.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/f2/Counting_rod_h9_song.png" decoding="async" width="23" height="29" class="mw-file-element" data-file-width="23" data-file-height="29" /></a></span> </td></tr></tbody></table> <p><br /> 例： </p> <table class="wikitable" border="1" style="text-align:center"> <tbody><tr> <th style="text-align:right;height:50px">231 </th> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Counting_rod_v2.png" decoding="async" width="13" height="29" class="mw-file-element" data-file-width="13" data-file-height="29" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/6b/Counting_rod_h3.png" decoding="async" width="29" height="19" class="mw-file-element" data-file-width="29" data-file-height="19" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span> </td></tr> <tr> <th style="text-align:right;height:50px">5089 </th> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h5.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/74/Counting_rod_h5.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/50/Counting_rod_0.png" decoding="async" width="23" height="23" class="mw-file-element" data-file-width="23" data-file-height="23" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h8_num.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7e/Counting_rod_h8_num.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v9.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/7a/Counting_rod_v9.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td></tr> <tr> <th style="text-align:right;height:50px">-407 </th> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/67/Counting_rod_v4.png" decoding="async" width="25" height="29" class="mw-file-element" data-file-width="25" data-file-height="29" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/50/Counting_rod_0.png" decoding="async" width="23" height="23" class="mw-file-element" data-file-width="23" data-file-height="23" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/04/Counting_rod_v-7.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td></tr> <tr> <th style="text-align:right;height:50px">-6720 </th> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c1/Counting_rod_h6.png" decoding="async" width="29" height="31" class="mw-file-element" data-file-width="29" data-file-height="31" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d1/Counting_rod_v7.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/51/Counting_rod_h2.png" decoding="async" width="29" height="13" class="mw-file-element" data-file-width="29" data-file-height="13" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_-0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/37/Counting_rod_-0.png" decoding="async" width="23" height="23" class="mw-file-element" data-file-width="23" data-file-height="23" /></a></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="代数記号"><span id=".E4.BB.A3.E6.95.B0.E8.A8.98.E5.8F.B7"></span>代数記号</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=4" title="節を編集: 代数記号"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>日本では<a href="/wiki/%E9%96%A2%E5%AD%9D%E5%92%8C" title="関孝和">関孝和</a>が算木数字から傍書法という<a href="/wiki/%E4%BB%A3%E6%95%B0%E5%AD%A6" title="代数学">代数</a>記号体系を作り出した。これにより未知数を含む<a href="/wiki/%E7%AD%86%E7%AE%97" title="筆算">筆算</a>ができるようになり、<a href="/wiki/%E5%92%8C%E7%AE%97" title="和算">和算</a>を飛躍的に発展させた<sup id="cite_ref-wang_7-2" class="reference"><a href="#cite_note-wang-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>。さらに関以降、数を表すのに算木による数の表示にならんで<a href="/wiki/%E6%BC%A2%E6%95%B0%E5%AD%97" title="漢数字">漢数字</a>を位取り記数法で並べることもふえた。 </p> <table class="wikitable" border="1" style="text-align:center"> <tbody><tr> <th>西洋数学</th> <th>関</th> <th>関以降 </th></tr> <tr> <td><i>x</i> + <i>y</i> + 246 </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span>甲<span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span>乙<span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Counting_rod_v2.png" decoding="async" width="13" height="29" class="mw-file-element" data-file-width="13" data-file-height="29" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_h4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/ce/Counting_rod_h4.png" decoding="async" width="29" height="25" class="mw-file-element" data-file-width="29" data-file-height="25" /></a></span><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v6.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span>甲<span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span>乙<span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span>二四六 </td></tr> <tr> <td>5<i>x</i> - 6<i>y</i> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v5.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e4/Counting_rod_v5.png" decoding="async" width="31" height="29" class="mw-file-element" data-file-width="31" data-file-height="29" /></a></span>甲<span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/11/Counting_rod_v-6.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span>乙 </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span>五甲<span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v-1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/6f/Counting_rod_v-1.png" decoding="async" width="23" height="29" class="mw-file-element" data-file-width="23" data-file-height="29" /></a></span>六乙 </td></tr> <tr> <td>7<i>xy</i> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v7.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d1/Counting_rod_v7.png" decoding="async" width="29" height="32" class="mw-file-element" data-file-width="29" data-file-height="32" /></a></span>甲乙 </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span>七甲乙 </td></tr> <tr> <td>8<i>x</i> / <i>y</i> </td> <td>（なし） </td> <td>八乙<span class="mw-default-size" typeof="mw:File"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Counting_rod_v1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Counting_rod_v1.png" decoding="async" width="7" height="29" class="mw-file-element" data-file-width="7" data-file-height="29" /></a></span>甲 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Unicode">Unicode</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=5" title="節を編集: Unicode"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r94202605">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box metadata side-box-right" style="width:22em;" id=""> <div class="side-box-flex"> <div class="side-box-text plainlist">この項目には、一部のコンピュータや<a href="/wiki/%E3%82%A6%E3%82%A7%E3%83%96%E3%83%96%E3%83%A9%E3%82%A6%E3%82%B6" title="ウェブブラウザ">閲覧ソフト</a>で表示できない文字が含まれています<span class="noprint selfreference">（<a href="/wiki/Help:%E7%89%B9%E6%AE%8A%E6%96%87%E5%AD%97" title="Help:特殊文字">詳細</a>）</span>。</div></div> </div> <p><a href="/wiki/Unicode" title="Unicode">Unicode</a>第5.0版は<a href="/wiki/%E8%BF%BD%E5%8A%A0%E5%A4%9A%E8%A8%80%E8%AA%9E%E9%9D%A2" title="追加多言語面">追加多言語面</a> (SMP) の U+1D360-U+1D37F の範囲を算木に割り当てている。横式の 1 から 9 が U+1D360-U+1D368、縦式の 1 から 9 が U+1D369-U+1D371 である。上記の慣習とは逆に、横式が一の位 (<i>unit digits</i>)、縦式が十の位 (<i>tens digits</i>) となっている<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>。0 の算木は U+3007 （<a href="/wiki/%E6%BC%A2%E6%95%B0%E5%AD%97" title="漢数字">漢数字</a>の〇、<a href="/wiki/CJK%E3%81%AE%E8%A8%98%E5%8F%B7%E5%8F%8A%E3%81%B3%E5%8F%A5%E8%AA%AD%E7%82%B9" title="CJKの記号及び句読点">CJKの記号及び句読点</a>のブロックに属する）で、負の斜線は U+20E5 (combining reverse solidus overlay) で示す<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>。 </p> <div class="mw-heading mw-heading3"><h3 id="符号位置"><span id=".E7.AC.A6.E5.8F.B7.E4.BD.8D.E7.BD.AE"></span>符号位置</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=6" title="節を編集: 符号位置"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center;"> <tbody><tr> <th>記号</th> <th><a href="/wiki/Unicode" title="Unicode">Unicode</a></th> <th><a href="/wiki/JIS_X_0213" title="JIS X 0213">JIS X 0213</a></th> <th><a href="/wiki/%E6%96%87%E5%AD%97%E5%8F%82%E7%85%A7" title="文字参照">文字参照</a></th> <th>名称 </th></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">〇</td> <td><code>U+3007</code></td> <td><code>1-1-27</code></td> <td><code>&#x3007;</code><br /><code>&#12295;</code></td> <td>IDEOGRAPHIC NUMBER ZERO </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍠</td> <td><code>U+1D360</code></td> <td><code>-</code></td> <td><code>&#x1D360;</code><br /><code>&#119648;</code></td> <td>COUNTING ROD UNIT DIGIT ONE </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍡</td> <td><code>U+1D361</code></td> <td><code>-</code></td> <td><code>&#x1D361;</code><br /><code>&#119649;</code></td> <td>COUNTING ROD UNIT DIGIT TWO </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍢</td> <td><code>U+1D362</code></td> <td><code>-</code></td> <td><code>&#x1D362;</code><br /><code>&#119650;</code></td> <td>COUNTING ROD UNIT DIGIT THREE </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍣</td> <td><code>U+1D363</code></td> <td><code>-</code></td> <td><code>&#x1D363;</code><br /><code>&#119651;</code></td> <td>COUNTING ROD UNIT DIGIT FOUR </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍤</td> <td><code>U+1D364</code></td> <td><code>-</code></td> <td><code>&#x1D364;</code><br /><code>&#119652;</code></td> <td>COUNTING ROD UNIT DIGIT FIVE </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍥</td> <td><code>U+1D365</code></td> <td><code>-</code></td> <td><code>&#x1D365;</code><br /><code>&#119653;</code></td> <td>COUNTING ROD UNIT DIGIT SIX </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍦</td> <td><code>U+1D366</code></td> <td><code>-</code></td> <td><code>&#x1D366;</code><br /><code>&#119654;</code></td> <td>COUNTING ROD UNIT DIGIT SEVEN </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍧</td> <td><code>U+1D367</code></td> <td><code>-</code></td> <td><code>&#x1D367;</code><br /><code>&#119655;</code></td> <td>COUNTING ROD UNIT DIGIT EIGHT </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍨</td> <td><code>U+1D368</code></td> <td><code>-</code></td> <td><code>&#x1D368;</code><br /><code>&#119656;</code></td> <td>COUNTING ROD UNIT DIGIT NINE </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍩</td> <td><code>U+1D369</code></td> <td><code>-</code></td> <td><code>&#x1D369;</code><br /><code>&#119657;</code></td> <td>COUNTING ROD TENS DIGIT ONE </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍪</td> <td><code>U+1D36A</code></td> <td><code>-</code></td> <td><code>&#x1D36A;</code><br /><code>&#119658;</code></td> <td>COUNTING ROD TENS DIGIT TWO </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍫</td> <td><code>U+1D36B</code></td> <td><code>-</code></td> <td><code>&#x1D36B;</code><br /><code>&#119659;</code></td> <td>COUNTING ROD TENS DIGIT THREE </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍬</td> <td><code>U+1D36C</code></td> <td><code>-</code></td> <td><code>&#x1D36C;</code><br /><code>&#119660;</code></td> <td>COUNTING ROD TENS DIGIT FOUR </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍭</td> <td><code>U+1D36D</code></td> <td><code>-</code></td> <td><code>&#x1D36D;</code><br /><code>&#119661;</code></td> <td>COUNTING ROD TENS DIGIT FIVE </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍮</td> <td><code>U+1D36E</code></td> <td><code>-</code></td> <td><code>&#x1D36E;</code><br /><code>&#119662;</code></td> <td>COUNTING ROD TENS DIGIT SIX </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍯</td> <td><code>U+1D36F</code></td> <td><code>-</code></td> <td><code>&#x1D36F;</code><br /><code>&#119663;</code></td> <td>COUNTING ROD TENS DIGIT SEVEN </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍰</td> <td><code>U+1D370</code></td> <td><code>-</code></td> <td><code>&#x1D370;</code><br /><code>&#119664;</code></td> <td>COUNTING ROD TENS DIGIT EIGHT </td></tr> <tr> <td style="font-size:300%;line-height:100%" lang="">𝍱</td> <td><code>U+1D371</code></td> <td><code>-</code></td> <td><code>&#x1D371;</code><br /><code>&#119665;</code></td> <td>COUNTING ROD TENS DIGIT NINE </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="易占用の算木"><span id=".E6.98.93.E5.8D.A0.E7.94.A8.E3.81.AE.E7.AE.97.E6.9C.A8"></span>易占用の算木</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=7" title="節を編集: 易占用の算木"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E6%98%93#易占の成立" class="mw-redirect" title="易">易占</a>で用いられる算木は算術用のものより大型で、2 - 3寸程度。6本を組にし、出た卦を<a href="/wiki/%E5%8D%B3%E5%B8%AD" title="即席">即席</a>に記録・表示するのに用いる。角材の4面のうち連続した2面の中央に浅い彫り込みがあり、陰爻を示す。両端に<a href="/wiki/%E5%85%AB%E5%8D%A6" title="八卦">八卦</a>の漢字が書かれたものもあり、この書き込みは本筮法、中筮法で用いる。 </p> <div class="mw-heading mw-heading2"><h2 id="易者のシンボル"><span id=".E6.98.93.E8.80.85.E3.81.AE.E3.82.B7.E3.83.B3.E3.83.9C.E3.83.AB"></span>易者のシンボル</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=8" title="節を編集: 易者のシンボル"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>算木で表示した卦を意匠化したマークがしばしば易占いの商標のように用いられる。古くは恋愛を表す「<a href="/wiki/%E5%91%A8%E6%98%93%E4%B8%8B%E7%B5%8C%E4%B8%89%E5%8D%81%E5%9B%9B%E5%8D%A6%E3%81%AE%E4%B8%80%E8%A6%A7#咸" title="周易下経三十四卦の一覧">咸</a>」が、近代に入ってからは開運を表す「<a href="/wiki/%E5%91%A8%E6%98%93%E4%B8%8A%E7%B5%8C%E4%B8%89%E5%8D%81%E5%8D%A6%E3%81%AE%E4%B8%80%E8%A6%A7#泰" title="周易上経三十卦の一覧">泰</a>」が使われている。 </p> <div class="mw-heading mw-heading2"><h2 id="家紋"><span id=".E5.AE.B6.E7.B4.8B"></span>家紋</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=9" title="節を編集: 家紋"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>日本では算木の家紋が複数あり、「算木」、「丸に算木」、「丸に縦算木」、「石持ち地抜き算木」、「丸に一つ算木」、「丸に二つ算木」がある他、木の紋が複数確認できる<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-heading2"><h2 id="参考文献"><span id=".E5.8F.82.E8.80.83.E6.96.87.E7.8C.AE"></span>参考文献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=10" title="節を編集: 参考文献"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite style="font-style:normal" class="citation journal" id="CITEREF矢代(2004)">矢代淳「<a rel="nofollow" class="external text" href="http://math-info.criced.tsukuba.ac.jp/Forall/project/history/2003/sangi/doc/sangi_report.pdf">9-3 算木と天元術を用いた実践研究 : 証明のない数学による証明観の変容(9総合的な学習の時間,高等学校,日本数学教育学会第86回総会全国算数・数学教育研究(鹿児島)大会)</a>」（PDF）『日本数学教育学会誌. 臨時増刊総会特集号』第86巻、日本数学教育学会、2004年8月、469頁、<style data-mw-deduplicate="TemplateStyles:r101121245">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:var(--color-success,#3a3);margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><a href="/wiki/NAID_(%E8%AD%98%E5%88%A5%E5%AD%90)" class="mw-redirect" title="NAID (識別子)">NAID</a> <a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/naid/110008597573">110008597573</a>。</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=9-3+%E7%AE%97%E6%9C%A8%E3%81%A8%E5%A4%A9%E5%85%83%E8%A1%93%E3%82%92%E7%94%A8%E3%81%84%E3%81%9F%E5%AE%9F%E8%B7%B5%E7%A0%94%E7%A9%B6+%3A+%E8%A8%BC%E6%98%8E%E3%81%AE%E3%81%AA%E3%81%84%E6%95%B0%E5%AD%A6%E3%81%AB%E3%82%88%E3%82%8B%E8%A8%BC%E6%98%8E%E8%A6%B3%E3%81%AE%E5%A4%89%E5%AE%B9%289%E7%B7%8F%E5%90%88%E7%9A%84%E3%81%AA%E5%AD%A6%E7%BF%92%E3%81%AE%E6%99%82%E9%96%93%2C%E9%AB%98%E7%AD%89%E5%AD%A6%E6%A0%A1%2C%E6%97%A5%E6%9C%AC%E6%95%B0%E5%AD%A6%E6%95%99%E8%82%B2%E5%AD%A6%E4%BC%9A%E7%AC%AC86%E5%9B%9E%E7%B7%8F%E4%BC%9A%E5%85%A8%E5%9B%BD%E7%AE%97%E6%95%B0%E3%83%BB%E6%95%B0%E5%AD%A6%E6%95%99%E8%82%B2%E7%A0%94%E7%A9%B6%28%E9%B9%BF%E5%85%90%E5%B3%B6%29%E5%A4%A7%E4%BC%9A%29&rft.jtitle=%E6%97%A5%E6%9C%AC%E6%95%B0%E5%AD%A6%E6%95%99%E8%82%B2%E5%AD%A6%E4%BC%9A%E8%AA%8C.+%E8%87%A8%E6%99%82%E5%A2%97%E5%88%8A%E7%B7%8F%E4%BC%9A%E7%89%B9%E9%9B%86%E5%8F%B7&rft.aulast=%E7%9F%A2%E4%BB%A3%E6%B7%B3&rft.au=%E7%9F%A2%E4%BB%A3%E6%B7%B3&rft.volume=86&rft.pages=469%E9%A0%81&rft.pub=%E6%97%A5%E6%9C%AC%E6%95%B0%E5%AD%A6%E6%95%99%E8%82%B2%E5%AD%A6%E4%BC%9A&rft_dat=naid/110008597573&rft_id=http%3A%2F%2Fmath-info.criced.tsukuba.ac.jp%2FForall%2Fproject%2Fhistory%2F2003%2Fsangi%2Fdoc%2Fsangi_report.pdf&rfr_id=info:sid/ja.wikipedia.org:%E7%AE%97%E6%9C%A8"><span style="display: none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="脚注"><span id=".E8.84.9A.E6.B3.A8"></span>脚注</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AE%97%E6%9C%A8&action=edit&section=11" title="節を編集: 脚注"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="noprint" style="float:right; font-size:90%;">[<a href="/wiki/Help:%E8%84%9A%E6%B3%A8/%E8%AA%AD%E8%80%85%E5%90%91%E3%81%91" title="Help:脚注/読者向け"><span title="この欄の操作法">脚注の使い方</span></a>]</div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="citation"> <a rel="nofollow" class="external text" href="http://www.yiyangcity.gov.cn/zhuanti/nanzhu/bamboo_produce/20070716094037.htm"><i><span lang="zh">先秦時期竹林資源的利用</span></i></a><span style="display:none;">, 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href="http://mkd.lyge.cn/zhanzheng/a04/x3/040.htm"><i><span lang="zh">中国独特的計算工具</span></i></a><span style="display:none;">, <a rel="nofollow" class="external free" href="http://mkd.lyge.cn/zhanzheng/a04/x3/040.htm">http://mkd.lyge.cn/zhanzheng/a04/x3/040.htm</a></span> <span class="reference-accessdate"><span title="">2007年12月16日</span>閲覧。</span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%3Cspan+lang%3D%22zh%22%3E%E4%B8%AD%E5%9B%BD%E7%8B%AC%E7%89%B9%E7%9A%84%E8%A8%88%E7%AE%97%E5%B7%A5%E5%85%B7%3C%2Fspan%3E&rft_id=http%3A%2F%2Fmkd.lyge.cn%2Fzhanzheng%2Fa04%2Fx3%2F040.htm&rfr_id=info:sid/ja.wikipedia.org:%E7%AE%97%E6%9C%A8"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-3"><b><a href="#cite_ref-3">^</a></b> <span class="reference-text">老子: <span lang="zh">善數者不用籌策。</span></span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text"><a 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class="reference-text"><cite style="font-style:normal" class="citation" id="CITEREF王青翔1999">王青翔 (1999), <i>「算木」を超えた男</i>, 東京: 東洋書店, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101121245"><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%87%E7%8C%AE%E8%B3%87%E6%96%99/4-88595-226-3" title="特別:文献資料/4-88595-226-3">4-88595-226-3</a></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%E3%80%8C%E7%AE%97%E6%9C%A8%E3%80%8D%E3%82%92%E8%B6%85%E3%81%88%E3%81%9F%E7%94%B7&rft.aulast=%E7%8E%8B%E9%9D%92%E7%BF%94&rft.au=%E7%8E%8B%E9%9D%92%E7%BF%94&rft.date=1999&rft.place=%E6%9D%B1%E4%BA%AC&rft.pub=%E6%9D%B1%E6%B4%8B%E6%9B%B8%E5%BA%97&rft.isbn=4-88595-226-3&rfr_id=info:sid/ja.wikipedia.org:%E7%AE%97%E6%9C%A8"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-8"><b><a href="#cite_ref-8">^</a></b> <span class="reference-text"><a class="external text" href="https://zh.wikisource.org/wiki/%E4%B9%9D%E7%AB%A0%E7%AE%97%E8%A1%93">正負術曰: <span lang="zh">同名相除，異名相益，正無入負之，負無入正之。其異名相除，同名相益，正無入正之，負無入負之。</span></a></span> </li> <li id="cite_note-9"><b><a href="#cite_ref-9">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="citation journal">西森敏之「<a rel="nofollow" class="external text" href="https://www.mathsoc.jp/assets/pdf/publications/tushin/backissue/1101/nishimori.pdf">算木で3次方程式を解く</a>」（PDF）『数学通信』第11巻第1号、日本数学会、2006年5月、15-27頁、<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101121245"><a href="/wiki/ISSN" title="ISSN">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/ja/search?fq=x0:jrnl&q=n2:13421387">13421387</a>、<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101121245"><a href="/wiki/NAID_(%E8%AD%98%E5%88%A5%E5%AD%90)" class="mw-redirect" title="NAID (識別子)">NAID</a> <a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/naid/40007315668">40007315668</a>。</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%E7%AE%97%E6%9C%A8%E3%81%A73%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F%E3%82%92%E8%A7%A3%E3%81%8F&rft.jtitle=%E6%95%B0%E5%AD%A6%E9%80%9A%E4%BF%A1&rft.aulast=%E8%A5%BF%E6%A3%AE%E6%95%8F%E4%B9%8B&rft.au=%E8%A5%BF%E6%A3%AE%E6%95%8F%E4%B9%8B&rft.volume=11&rft.issue=1&rft.pages=15-27%E9%A0%81&rft.pub=%E6%97%A5%E6%9C%AC%E6%95%B0%E5%AD%A6%E4%BC%9A&rft.issn=13421387&rft_dat=naid/40007315668&rft_id=https%3A%2F%2Fwww.mathsoc.jp%2Fassets%2Fpdf%2Fpublications%2Ftushin%2Fbackissue%2F1101%2Fnishimori.pdf&rfr_id=info:sid/ja.wikipedia.org:%E7%AE%97%E6%9C%A8"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-10"><b><a href="#cite_ref-10">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="citation journal">杜威「<a rel="nofollow" class="external text" href="https://hdl.handle.net/10295/533">『九章算術』に関する研究 : 方田章を中心として</a>」『秋田大学教育文化学部研究紀要教育科学』第55巻、秋田大学教育文化学部、2000年3月、23-30頁、<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101121245"><a href="/wiki/ISSN" title="ISSN">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/ja/search?fq=x0:jrnl&q=n2:13485288">13485288</a>、<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101121245"><a href="/wiki/NAID_(%E8%AD%98%E5%88%A5%E5%AD%90)" class="mw-redirect" title="NAID (識別子)">NAID</a> <a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/naid/110000088206">110000088206</a>。</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%E3%80%8E%E4%B9%9D%E7%AB%A0%E7%AE%97%E8%A1%93%E3%80%8F%E3%81%AB%E9%96%A2%E3%81%99%E3%82%8B%E7%A0%94%E7%A9%B6+%3A+%E6%96%B9%E7%94%B0%E7%AB%A0%E3%82%92%E4%B8%AD%E5%BF%83%E3%81%A8%E3%81%97%E3%81%A6&rft.jtitle=%E7%A7%8B%E7%94%B0%E5%A4%A7%E5%AD%A6%E6%95%99%E8%82%B2%E6%96%87%E5%8C%96%E5%AD%A6%E9%83%A8%E7%A0%94%E7%A9%B6%E7%B4%80%E8%A6%81+%E6%95%99%E8%82%B2%E7%A7%91%E5%AD%A6&rft.aulast=%E6%9D%9C%E5%A8%81&rft.au=%E6%9D%9C%E5%A8%81&rft.volume=55&rft.pages=23-30%E9%A0%81&rft.pub=%E7%A7%8B%E7%94%B0%E5%A4%A7%E5%AD%A6%E6%95%99%E8%82%B2%E6%96%87%E5%8C%96%E5%AD%A6%E9%83%A8&rft.issn=13485288&rft_dat=naid/110000088206&rft_id=https%3A%2F%2Fhdl.handle.net%2F10295%2F533&rfr_id=info:sid/ja.wikipedia.org:%E7%AE%97%E6%9C%A8"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-qian-11">^ <a href="#cite_ref-qian_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-qian_11-1"><sup><i><b>b</b></i></sup></a> <span class="reference-text"><cite style="font-style:normal" class="citation" id="CITEREF銭宝琮1964">銭宝琮 (1964), <i>中国数学史</i>, 北京: 科学出版社</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%E4%B8%AD%E5%9B%BD%E6%95%B0%E5%AD%A6%E5%8F%B2&rft.aulast=%E9%8A%AD%E5%AE%9D%E7%90%AE&rft.au=%E9%8A%AD%E5%AE%9D%E7%90%AE&rft.date=1964&rft.place=%E5%8C%97%E4%BA%AC&rft.pub=%E7%A7%91%E5%AD%A6%E5%87%BA%E7%89%88%E7%A4%BE&rfr_id=info:sid/ja.wikipedia.org:%E7%AE%97%E6%9C%A8"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-12"><b><a href="#cite_ref-12">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="citation"> (PDF) <a rel="nofollow" class="external text" href="https://www.unicode.org/charts/PDF/U1D360.pdf"><i>The Unicode Standard, Version 5.0 - Electronic edition</i></a>, Unicode, Inc., (2006), p. 558<span style="display:none;">, <a rel="nofollow" class="external free" href="https://www.unicode.org/charts/PDF/U1D360.pdf">https://www.unicode.org/charts/PDF/U1D360.pdf</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Unicode+Standard%2C+Version+5.0+-+Electronic+edition&rft.date=2006&rft.pages=p.%26nbsp%3B558&rft.pub=Unicode%2C+Inc.&rft_id=https%3A%2F%2Fwww.unicode.org%2Fcharts%2FPDF%2FU1D360.pdf&rfr_id=info:sid/ja.wikipedia.org:%E7%AE%97%E6%9C%A8"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-13"><b><a href="#cite_ref-13">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="citation"> (PDF) <a rel="nofollow" class="external text" href="https://www.unicode.org/versions/Unicode5.0.0/ch15.pdf"><i>The Unicode Standard, Version 5.0 - Electronic edition</i></a>, Unicode, Inc., (2006), pp. 499-500<span style="display:none;">, <a rel="nofollow" class="external free" href="https://www.unicode.org/versions/Unicode5.0.0/ch15.pdf">https://www.unicode.org/versions/Unicode5.0.0/ch15.pdf</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Unicode+Standard%2C+Version+5.0+-+Electronic+edition&rft.date=2006&rft.pages=pp.%26nbsp%3B499-500&rft.pub=Unicode%2C+Inc.&rft_id=https%3A%2F%2Fwww.unicode.org%2Fversions%2FUnicode5.0.0%2Fch15.pdf&rfr_id=info:sid/ja.wikipedia.org:%E7%AE%97%E6%9C%A8"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-14"><b><a href="#cite_ref-14">^</a></b> <span class="reference-text"><a href="/w/index.php?title=%E5%8F%A4%E6%B2%A2%E6%81%92%E6%95%8F&action=edit&redlink=1" class="new" title="古沢恒敏 (存在しないページ)">古沢恒敏</a>編『正しい家紋帖』（<a href="/wiki/%E9%87%91%E5%9C%92%E7%A4%BE" title="金園社">金園社</a>、1995年）pp.199-200</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="関連項目"><span 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