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<span>Mathematics</span> </div> </a> <button aria-controls="toc-Mathematics-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>Toggle Mathematics subsection</span> </button> <ul id="toc-Mathematics-sublist" class="vector-toc-list"> <li id="toc-Translation_of_Piero_della_Francesca's_work" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Translation_of_Piero_della_Francesca's_work"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Translation of Piero della Francesca's work</span> </div> </a> <ul id="toc-Translation_of_Piero_della_Francesca's_work-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Impact_on_accounting_and_business" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Impact_on_accounting_and_business"> <div 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class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <button aria-controls="toc-References-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>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span 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Available in 59 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-59" 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">59 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Afrikaans" lang="af" hreflang="af" data-title="Luca Pacioli" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Alemannic" lang="gsw" hreflang="gsw" data-title="Luca Pacioli" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%84%D9%88%D9%83%D8%A7_%D8%A8%D8%A7%D8%AA%D8%B4%D9%88%D9%84%D9%8A" title="لوكا باتشولي – Arabic" lang="ar" hreflang="ar" data-title="لوكا باتشولي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Luka_Pa%C3%A7oli" title="Luka Paçoli – Azerbaijani" lang="az" hreflang="az" data-title="Luka Paçoli" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B2%E0%A7%81%E0%A6%95%E0%A6%BE_%E0%A6%AA%E0%A6%BE%E0%A6%9A%E0%A6%BF%E0%A6%93%E0%A6%B2%E0%A6%BF" title="লুকা পাচিওলি – Bangla" lang="bn" hreflang="bn" data-title="লুকা পাচিওলি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9B%D1%83%D0%BA%D0%B0_%D0%9F%D0%B0%D1%87%D0%BE%D0%BB%D1%96" title="Лука Пачолі – Belarusian" lang="be" hreflang="be" data-title="Лука Пачолі" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9B%D1%8E%D0%BA%D0%B0_%D0%9F%D0%B0%D1%87%D0%BE%D0%BB%D1%96" title="Люка Пачолі – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Люка Пачолі" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9B%D1%83%D0%BA%D0%B0_%D0%9F%D0%B0%D1%87%D0%BE%D0%BB%D0%B8" title="Лука Пачоли – Bulgarian" lang="bg" hreflang="bg" data-title="Лука Пачоли" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Catalan" lang="ca" hreflang="ca" data-title="Luca Pacioli" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Czech" lang="cs" hreflang="cs" data-title="Luca Pacioli" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Danish" lang="da" hreflang="da" data-title="Luca Pacioli" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – German" lang="de" hreflang="de" data-title="Luca Pacioli" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Estonian" lang="et" hreflang="et" data-title="Luca Pacioli" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%BF%CF%8D%CE%BA%CE%B1_%CE%A0%CE%B1%CF%84%CF%83%CE%B9%CF%8C%CE%BB%CE%B9" title="Λούκα Πατσιόλι – Greek" lang="el" hreflang="el" data-title="Λούκα Πατσιόλι" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Spanish" lang="es" hreflang="es" data-title="Luca Pacioli" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Esperanto" lang="eo" hreflang="eo" data-title="Luca Pacioli" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Basque" lang="eu" hreflang="eu" data-title="Luca Pacioli" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%84%D9%88%DA%A9%D8%A7_%D9%BE%D8%A7%DA%86%DB%8C%D9%88%D9%84%DB%8C" title="لوکا پاچیولی – Persian" lang="fa" hreflang="fa" data-title="لوکا پاچیولی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – French" lang="fr" hreflang="fr" data-title="Luca Pacioli" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A3%A8%EC%B9%B4_%ED%8C%8C%EC%B9%98%EC%98%AC%EB%A6%AC" title="루카 파치올리 – Korean" lang="ko" hreflang="ko" data-title="루카 파치올리" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Hausa" lang="ha" hreflang="ha" data-title="Luca Pacioli" data-language-autonym="Hausa" data-language-local-name="Hausa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BC%D5%B8%D6%82%D5%AF%D5%A1_%D5%8A%D5%A1%D5%B9%D5%B8%D5%AC%D5%AB" title="Լուկա Պաչոլի – Armenian" lang="hy" hreflang="hy" data-title="Լուկա Պաչոլի" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Croatian" lang="hr" hreflang="hr" data-title="Luca Pacioli" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Indonesian" lang="id" hreflang="id" data-title="Luca Pacioli" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Interlingua" lang="ia" hreflang="ia" data-title="Luca Pacioli" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Italian" lang="it" hreflang="it" data-title="Luca Pacioli" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9C%D7%95%D7%A7%D7%94_%D7%A4%D7%90%D7%A6%27%D7%95%D7%9C%D7%99" title="לוקה פאצ'ולי – Hebrew" lang="he" hreflang="he" data-title="לוקה פאצ'ולי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B2%E0%B3%8D%E0%B2%AF%E0%B3%82%E0%B2%95%E0%B2%BE_%E0%B2%AA%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%B8%E0%B2%BF%E0%B2%AF%E0%B3%8B%E0%B2%B2%E0%B2%BF" title="ಲ್ಯೂಕಾ ಪ್ಯಾಸಿಯೋಲಿ – Kannada" lang="kn" hreflang="kn" data-title="ಲ್ಯೂಕಾ ಪ್ಯಾಸಿಯೋಲಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Haitian Creole" lang="ht" hreflang="ht" data-title="Luca Pacioli" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Lucas_Pacioli" title="Lucas Pacioli – Latin" lang="la" hreflang="la" data-title="Lucas Pacioli" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Luka_Pa%C4%8Doli" title="Luka Pačoli – Latvian" lang="lv" hreflang="lv" data-title="Luka Pačoli" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Lithuanian" lang="lt" hreflang="lt" data-title="Luca Pacioli" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Hungarian" lang="hu" hreflang="hu" data-title="Luca Pacioli" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B2%E0%B5%82%E0%B4%95%E0%B5%8D%E0%B4%95%E0%B4%BE_%E0%B4%AA%E0%B4%B8%E0%B4%BF%E0%B4%AF%E0%B5%8B%E0%B4%B3%E0%B4%BF" title="ലൂക്കാ പസിയോളി – Malayalam" lang="ml" hreflang="ml" data-title="ലൂക്കാ പസിയോളി" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%84%D9%88%D9%83%D8%A7_%D8%A8%D8%A7%D8%AA%D8%B4%D9%88%D9%84%D9%89" title="لوكا باتشولى – Egyptian Arabic" lang="arz" hreflang="arz" data-title="لوكا باتشولى" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Malay" lang="ms" hreflang="ms" data-title="Luca Pacioli" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Dutch" lang="nl" hreflang="nl" data-title="Luca Pacioli" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%AB%E3%82%AB%E3%83%BB%E3%83%91%E3%83%81%E3%83%A7%E3%83%BC%E3%83%AA" title="ルカ・パチョーリ – Japanese" lang="ja" hreflang="ja" data-title="ルカ・パチョーリ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Luca Pacioli" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Piedmontese" lang="pms" hreflang="pms" data-title="Luca Pacioli" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Polish" lang="pl" hreflang="pl" data-title="Luca Pacioli" data-language-autonym="Polski" data-language-local-name="Polish" 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/Luca_Pacioli" title="Luca Pacioli – Portuguese" lang="pt" hreflang="pt" data-title="Luca Pacioli" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Romanian" lang="ro" hreflang="ro" data-title="Luca Pacioli" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%B0%D1%87%D0%BE%D0%BB%D0%B8,_%D0%9B%D1%83%D0%BA%D0%B0" title="Пачоли, Лука – Russian" lang="ru" hreflang="ru" data-title="Пачоли, Лука" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Slovak" lang="sk" hreflang="sk" data-title="Luca Pacioli" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Slovenian" lang="sl" hreflang="sl" data-title="Luca Pacioli" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%84%D9%88%D9%88%DA%A9%D8%A7_%D9%BE%D8%A7%DA%86%DB%86%D9%84%DB%8C" title="لووکا پاچۆلی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="لووکا پاچۆلی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9B%D1%83%D0%BA%D0%B0_%D0%9F%D0%B0%D1%87%D0%BE%D0%BB%D0%B8" title="Лука Пачоли – Serbian" lang="sr" hreflang="sr" data-title="Лука Пачоли" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Luca Pacioli" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Sundanese" lang="su" hreflang="su" data-title="Luca Pacioli" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Finnish" lang="fi" hreflang="fi" data-title="Luca Pacioli" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Swedish" lang="sv" hreflang="sv" data-title="Luca Pacioli" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B2%E0%AF%82%E0%AE%95%E0%AE%BE_%E0%AE%AA%E0%AE%9A%E0%AE%BF%E0%AE%AF%E0%AF%8B%E0%AE%B2%E0%AE%BF" title="லூகா பசியோலி – Tamil" lang="ta" hreflang="ta" data-title="லூகா பசியோலி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Turkish" lang="tr" hreflang="tr" data-title="Luca Pacioli" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9B%D1%83%D0%BA%D0%B0_%D0%9F%D0%B0%D1%87%D0%BE%D0%BB%D1%96" title="Лука Пачолі – Ukrainian" lang="uk" hreflang="uk" data-title="Лука Пачолі" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Luca_Pacioli" title="Luca Pacioli – Vietnamese" lang="vi" hreflang="vi" data-title="Luca Pacioli" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8D%A2%E5%8D%A1%C2%B7%E5%B8%95%E8%A5%BF%E5%A5%A5%E5%88%A9" title="卢卡·帕西奥利 – Wu" lang="wuu" hreflang="wuu" data-title="卢卡·帕西奥利" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%9B%A7%E5%8D%A1%C2%B7%E5%B8%95%E8%A5%BF%E5%A5%A7%E5%88%A9" title="盧卡·帕西奧利 – Cantonese" lang="yue" hreflang="yue" data-title="盧卡·帕西奧利" 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searchaux" style="display:none">15th c. Italian Friar Minor, mathematician and economic theorist</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Luca_Pacioni" title="Luca Pacioni">Luca Pacioni</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Luca Pacioli, <a href="/wiki/Order_of_Friars_Minor" title="Order of Friars Minor">O.F.M.</a></div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Pacioli.jpg" class="mw-file-description"><img alt="Portrait of Friar Luca Pacioli" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pacioli.jpg/220px-Pacioli.jpg" decoding="async" width="220" height="183" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pacioli.jpg/330px-Pacioli.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pacioli.jpg/440px-Pacioli.jpg 2x" data-file-width="1500" data-file-height="1250" /></a></span><div class="infobox-caption"><i><a href="/wiki/Portrait_of_Luca_Pacioli" title="Portrait of Luca Pacioli">Portrait of Luca Pacioli</a></i>, traditionally attributed to <a href="/wiki/Jacopo_de%27_Barbari" title="Jacopo de' Barbari">Jacopo de' Barbari</a>, 1495<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></div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><abbr title="circa">c.</abbr> 1447<sup id="cite_ref-Treccani_2-0" class="reference"><a href="#cite_note-Treccani-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><br /><div style="display:inline" class="birthplace"><a href="/wiki/Sansepolcro" title="Sansepolcro">Sansepolcro</a>, <a href="/wiki/Republic_of_Florence" title="Republic of Florence">Republic of Florence</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">19 June 1517<span style="display:none">(1517-06-19)</span> (aged 69–70)<br /><div style="display:inline" class="deathplace">Sansepolcro, Republic of Florence</div></td></tr><tr><th scope="row" class="infobox-label">Citizenship</th><td class="infobox-data category">Florentine</td></tr><tr><th scope="row" class="infobox-label">Occupation(s)</th><td class="infobox-data role">Friar, mathematician, writer</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><i><a href="/wiki/Summa_de_arithmetica" title="Summa de arithmetica">Summa de arithmetica</a></i>,<br /><i><a href="/wiki/Divina_proportione" title="Divina proportione">Divina proportione</a></i>,<br /><a href="/wiki/Double-entry_bookkeeping_system" class="mw-redirect" title="Double-entry bookkeeping system">double-entry bookkeeping</a></td></tr></tbody></table> <p><b>Luca Bartolomeo de Pacioli, <a href="/wiki/Order_of_Friars_Minor" title="Order of Friars Minor">O.F.M.</a></b> (sometimes <i>Paccioli</i> or <i>Paciolo</i>; <abbr title="circa">c.</abbr> 1447 – 19 June 1517)<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> was an Italian <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, <a href="/wiki/Order_of_Friars_Minor" title="Order of Friars Minor">Franciscan friar</a>, collaborator with <a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a>, and an early contributor to the field now known as <a href="/wiki/Accounting" title="Accounting">accounting</a>. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the <a href="/wiki/Double-entry_bookkeeping_system" class="mw-redirect" title="Double-entry bookkeeping system">double-entry system of book-keeping</a> on the continent<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="The previous citation coudn't be found anywhere other than other books/articles that just copy-pasted the wikipedia reference, without adding new information like citing a new edition of the book, of informing the correct ISBN. Nor author's names, title, ISBN or publisher's name could be found so as to provide a hint to the existence of the book "Accounting Concepts & Theories", written by Diwan and Jaswith, published by Morre and with an ISBN starting by 94452. This citation seems to be widespread in minor works about the subject and seems to have done quite a lot of "damage", since I assume their authors didn't check the source and just copy-pasted an empty citation. (August 2024)">citation needed</span></a></i>]</sup>. He was also called <b>Luca di Borgo</b> after his birthplace, <a href="/wiki/Sansepolcro" title="Sansepolcro">Borgo Sansepolcro</a>, <a href="/wiki/Tuscany" title="Tuscany">Tuscany</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Life">Life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luca_Pacioli&action=edit&section=1" title="Edit section: Life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Luca_Pacioli_in_the_Summa.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Luca_Pacioli_in_the_Summa.jpg/220px-Luca_Pacioli_in_the_Summa.jpg" decoding="async" width="220" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Luca_Pacioli_in_the_Summa.jpg/330px-Luca_Pacioli_in_the_Summa.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c8/Luca_Pacioli_in_the_Summa.jpg 2x" data-file-width="396" data-file-height="459" /></a><figcaption>A woodcut of Pacioli which appears throughout the <i><a href="/wiki/Summa_de_arithmetica" title="Summa de arithmetica">Summa de arithmetica</a></i><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>Luca Pacioli was born between 1446 and 1448 in the Tuscan town of <a href="/wiki/Sansepolcro" title="Sansepolcro">Sansepolcro</a> where he received an <a href="/wiki/Abacus_school" title="Abacus school">abbaco education</a>. This was education in the vernacular (<i>i.e.</i>, the local tongue) rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli; however, Luca Pacioli was said to have lived with the Befolci family as a child in his birth town Sansepolcro.<sup id="cite_ref-bio_5-0" class="reference"><a href="#cite_note-bio-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> He moved to <a href="/wiki/Venice" title="Venice">Venice</a> around 1464, where he continued his own education while working as a tutor to the three sons of a merchant. It was during this period that he wrote his first book, a treatise on arithmetic for the boys he was tutoring. Between 1472 and 1475, he became a <a href="/wiki/Franciscan" class="mw-redirect" title="Franciscan">Franciscan</a> friar.<sup id="cite_ref-bio_5-1" class="reference"><a href="#cite_note-bio-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Thus, he could be referred to as Fra ('Friar') Luca. </p><p>In 1475, he started teaching in Perugia as a private teacher before becoming first chair in mathematics in 1477. During this time, he wrote a comprehensive textbook in the vernacular for his students. He continued to work as a private tutor of <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> and was instructed to stop teaching at this level in Sansepolcro in 1491. In 1494, his first book, <span title="Latin-language text"><i lang="la"><a href="/wiki/Summa_de_arithmetica" title="Summa de arithmetica">Summa de arithmetica, geometria, Proportioni et proportionalita</a></i></span>, was published in Venice. In 1497, he accepted an invitation from Duke <a href="/wiki/Ludovico_Sforza" title="Ludovico Sforza">Ludovico Sforza</a> to work in <a href="/wiki/Milan" title="Milan">Milan</a>. There he met, taught mathematics to, collaborated, and lived with <a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a>. In 1499, Pacioli and Leonardo were forced to flee Milan when <a href="/wiki/Louis_XII_of_France" class="mw-redirect" title="Louis XII of France">Louis XII of France</a> seized the city and drove out their patron. Their paths appear to have finally separated around 1506. Pacioli died at about the age of 70 on 19 June 1517, most likely in Sansepolcro, where it is thought that he had spent much of his final years.<sup id="cite_ref-bio_5-2" class="reference"><a href="#cite_note-bio-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematics">Mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luca_Pacioli&action=edit&section=2" title="Edit section: Mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:De_divina_proportione_-_Vigintisex_Basium_Planum_Vacuum.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/De_divina_proportione_-_Vigintisex_Basium_Planum_Vacuum.jpg/220px-De_divina_proportione_-_Vigintisex_Basium_Planum_Vacuum.jpg" decoding="async" width="220" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/De_divina_proportione_-_Vigintisex_Basium_Planum_Vacuum.jpg/330px-De_divina_proportione_-_Vigintisex_Basium_Planum_Vacuum.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/12/De_divina_proportione_-_Vigintisex_Basium_Planum_Vacuum.jpg/440px-De_divina_proportione_-_Vigintisex_Basium_Planum_Vacuum.jpg 2x" data-file-width="1235" data-file-height="1338" /></a><figcaption>The first printed illustration of a <a href="/wiki/Rhombicuboctahedron" title="Rhombicuboctahedron">rhombicuboctahedron</a>, by <a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a>, published in <i><a href="/wiki/Divina_proportione" title="Divina proportione">Divina proportione</a></i></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pacioli_De_Divina_Proportione_Head_Equilateral_Triangle_1509.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Pacioli_De_Divina_Proportione_Head_Equilateral_Triangle_1509.jpg/220px-Pacioli_De_Divina_Proportione_Head_Equilateral_Triangle_1509.jpg" decoding="async" width="220" height="365" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Pacioli_De_Divina_Proportione_Head_Equilateral_Triangle_1509.jpg/330px-Pacioli_De_Divina_Proportione_Head_Equilateral_Triangle_1509.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/d/d7/Pacioli_De_Divina_Proportione_Head_Equilateral_Triangle_1509.jpg 2x" data-file-width="429" data-file-height="712" /></a><figcaption>Woodcut illustrating the proportions of the human face from the second part of <i>Divina proportione</i>, which covers the Vitruvian system</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Mathematics_and_art" title="Mathematics and art">Mathematics and art</a></div> <p>Pacioli published several works on <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>, including: </p> <ul><li><span title="Latin-language text"><i lang="la">Tractatus mathematicus ad discipulos perusinos</i></span> (Ms. Vatican Library, Lat. 3129), a nearly 600-page textbook dedicated to his students at the University of Perugia where Pacioli taught from 1477 to 1480. The manuscript was written between December 1477 and 29 April 1478. It contains 16 sections on merchant arithmetic, such as barter, exchange, profit, mixing metals, and algebra, though 25 pages from the chapter on algebra are missing. A modern transcription was published by Calzoni and Cavazzoni (1996) along with a partial translation of the chapter on partitioning problems.<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></li> <li><span title="Latin-language text"><i lang="la"><a href="/wiki/Summa_de_arithmetica" title="Summa de arithmetica">Summa de arithmetica, geometria. Proportioni et proportionalita</a></i></span> (<a href="/wiki/Venice" title="Venice">Venice</a> 1494), a textbook for use in the schools of Northern Italy. It was a synthesis of the mathematical knowledge of his time and contained the first printed work on algebra written in the vernacular (<i>i.e.</i>, the spoken language of the day). It is also notable for including one of the first published descriptions of the bookkeeping method that Venetian merchants used during the Italian Renaissance, known as the <a href="/wiki/Double-entry_accounting_system" class="mw-redirect" title="Double-entry accounting system">double-entry accounting system</a>. The system he published included most of the accounting cycle as we know it today. He described the use of journals and ledgers and warned that a person should not go to sleep at night until the debits equalled the credits.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> His ledger had accounts for assets (including receivables and inventories), liabilities, capital, income, and expenses – the account categories that are reported on an organization's <a href="/wiki/Balance_sheet" title="Balance sheet">balance sheet</a> and <a href="/wiki/Income_statement" title="Income statement">income statement</a>, respectively. He demonstrated year-end closing entries and proposed that a <a href="/wiki/Trial_balance" title="Trial balance">trial balance</a> be used to prove a balanced ledger. Additionally, his treatise touches on a wide range of related topics from <a href="/wiki/Accounting_ethics" title="Accounting ethics">accounting ethics</a> to <a href="/wiki/Cost_accounting" title="Cost accounting">cost accounting</a>. He introduced the <a href="/wiki/Rule_of_72" title="Rule of 72">Rule of 72</a>, using an approximation of 100*ln 2 more than 100 years before <a href="/wiki/John_Napier" title="John Napier">Napier</a> and <a href="/wiki/Henry_Briggs_(mathematician)" title="Henry Briggs (mathematician)">Briggs</a>.<sup id="cite_ref-paccioliLog_8-0" class="reference"><a href="#cite_note-paccioliLog-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Its exercises were largely copied without credit from <a href="/wiki/Piero_della_Francesca" title="Piero della Francesca">Piero della Francesca</a>'s earlier book, <i>Trattato d'abaco</i>.<sup id="cite_ref-davis_9-0" class="reference"><a href="#cite_note-davis-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li><span title="Latin-language text"><i lang="la">De viribus quantitatis</i></span> (Ms. Università degli Studi di Bologna, 1496–1508), a treatise on mathematics and magic. Written between 1496 and 1508, it contains the first reference to card tricks as well as guidance on how to juggle, eat fire, and make coins dance. It is the first work to note that Leonardo was left-handed. <i>De viribus quantitatis</i> is divided into three sections: Mathematical problems, puzzles, and tricks, along with a collection of proverbs and verses. The book has been described as the "Foundation of modern magic and numerical puzzles," but it was never published and sat in the archives of the University of Bologna, where it was seen by only a small number of scholars during the Middle Ages. The book was rediscovered after <a href="/wiki/David_Singmaster" title="David Singmaster">David Singmaster</a>, a mathematician, came across a reference to it in a 19th-century manuscript. An English translation was published for the first time in 2007.<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></li> <li><i>Geometry</i> (1509), a Latin translation of <a href="/wiki/Euclid" title="Euclid">Euclid</a>'s <a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements"><i>Elements</i></a>.</li> <li><i><a href="/wiki/Divina_proportione" title="Divina proportione">Divina proportione</a></i> (written in Milan in 1496–1498, published in Venice in 1509). Two versions of the original manuscript are extant, one in the Biblioteca Ambrosiana in Milan, the other in the Bibliothèque Publique et Universitaire in Geneva. The subject was mathematical and artistic proportion, especially the mathematics of the <a href="/wiki/Golden_ratio" title="Golden ratio">golden ratio</a> and its application in <a href="/wiki/Architecture" title="Architecture">architecture</a>. It incorporates without credit a translation of the entire book <i><a href="/wiki/De_quinque_corporibus_regularibus" title="De quinque corporibus regularibus">De quinque corporibus regularibus</a></i> by <a href="/wiki/Piero_della_Francesca" title="Piero della Francesca">Piero della Francesca</a>.<sup id="cite_ref-davis_9-1" class="reference"><a href="#cite_note-davis-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a> drew the illustrations of the regular solids in <i>Divina proportione</i> while he lived with and took mathematics lessons from Pacioli. Leonardo's drawings are probably the first illustrations of skeletal solids, which allowed an easy distinction between front and back. The work also discusses the use of perspective by painters such as <a href="/wiki/Piero_della_Francesca" title="Piero della Francesca">Piero della Francesca</a>, <a href="/wiki/Melozzo_da_Forl%C3%AC" title="Melozzo da Forlì">Melozzo da Forlì</a>, and <a href="/wiki/Marco_Palmezzano" title="Marco Palmezzano">Marco Palmezzano</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Translation_of_Piero_della_Francesca's_work"><span id="Translation_of_Piero_della_Francesca.27s_work"></span>Translation of Piero della Francesca's work</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luca_Pacioli&action=edit&section=3" title="Edit section: Translation of Piero della Francesca's work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The majority of the second volume of <span title="Latin-language text"><i lang="la">Summa de arithmetica, geometria. Proportioni et proportionalita</i></span> was a slightly rewritten version of one of <a href="/wiki/Piero_della_Francesca" title="Piero della Francesca">Piero della Francesca</a>'s works. The third volume of Pacioli's <i>Divina proportione</i> was an Italian translation of <a href="/wiki/Piero_della_Francesca" title="Piero della Francesca">Piero della Francesca</a>'s Latin book <i><a href="/wiki/De_quinque_corporibus_regularibus" title="De quinque corporibus regularibus">De quinque corporibus regularibus</a></i>. In neither case did Pacioli include an attribution to Piero. He was severely criticized for this and accused of plagiarism by sixteenth-century art historian and biographer <a href="/wiki/Giorgio_Vasari" title="Giorgio Vasari">Giorgio Vasari</a>. R. Emmett Taylor (1889–1956) said that Pacioli may have had nothing to do with the translated volume <i>Divina proportione</i>, and that it may just have been appended to his work. However, no such defense can be presented concerning the inclusion of Piero della Francesca's material in Pacioli's Summa. </p> <div class="mw-heading mw-heading2"><h2 id="Impact_on_accounting_and_business">Impact on accounting and business</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luca_Pacioli&action=edit&section=4" title="Edit section: Impact on accounting and business"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pacioli dramatically affected the practice of accounting by describing the double-entry accounting method used in parts of Italy. This revolutionized how businesses oversaw their operations, enabling improved efficiency and profitability. The <i>Summa'</i>s section on accounting was used internationally as an accounting textbook up to the mid-16th century. The essentials of double-entry accounting have for the most part remained unchanged for over 500 years. "Accounting practitioners in public accounting, industry, and not-for-profit organizations, as well as investors, lending institutions, business firms, and all other users for financial information are indebted to Luca Pacioli for his monumental role in the development of accounting."<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/ICAEW" class="mw-redirect" title="ICAEW">ICAEW</a> Library's rare book collection at <a href="/wiki/Chartered_Accountants%27_Hall" title="Chartered Accountants' Hall">Chartered Accountants' Hall</a> holds the complete published works of Luca Pacioli. Sections of two of Pacioli's books, 'Summa de arithmetica' and 'Divina proportione' can be viewed online using Turning the Pages, an interactive tool developed by the British Library.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Chess">Chess</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luca_Pacioli&action=edit&section=5" title="Edit section: Chess"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Luca Pacioli also wrote an unpublished treatise on <a href="/wiki/Chess" title="Chess">chess</a>, <i><a href="/wiki/De_ludo_scachorum" title="De ludo scachorum">De ludo scachorum</a></i> (<i>On the Game of Chess</i>). Long thought to have been lost, a surviving <a href="/wiki/Manuscript" title="Manuscript">manuscript</a> was rediscovered in 2006, in the 22,000-volume library of Count Guglielmo Coronini-Cronberg in <a href="/wiki/Gorizia" title="Gorizia">Gorizia</a>. A facsimile edition of the book was published in Pacioli's home town of Sansepolcro in 2008. Based on Leonardo da Vinci's long association with the author and his having illustrated <i>Divina proportione</i>, some scholars speculate that Leonardo either drew the <a href="/wiki/Chess_problem" title="Chess problem">chess problems</a> that appear in the manuscript or at least designed the chess pieces used in the problems.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luca_Pacioli&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/List_of_Catholic_churchmen-scientists" class="mw-redirect" title="List of Catholic churchmen-scientists">List of Roman Catholic scientist-clerics</a></li> <li><a href="/wiki/Della_mercatura_e_del_mercante_perfetto" title="Della mercatura e del mercante perfetto">Della mercatura e del mercante perfetto</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luca_Pacioli&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Footnotes</b> </p> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">The <a href="/wiki/Metropolitan_Museum_of_Art" title="Metropolitan Museum of Art">Metropolitan Museum of Art</a> in <a href="/wiki/New_York_City" title="New York City">New York City</a> claims that the "M" logo it uses to decorate souvenir items (which the museum calls "the Renaissance M") is from an illustration originally in the <i><a href="/wiki/Divina_proportione" title="Divina proportione">Divina proportione</a></i>. <i>See</i> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://store.metmuseum.org/magnets+bookmarks/renaissance-m-bookmark/invt/10086668">"Renaissance 'M' bookmark"</a>. <i>The Met Store (Metropolitan Museum of Art shopping catalog)</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Met+Store+%28Metropolitan+Museum+of+Art+shopping+catalog%29&rft.atitle=Renaissance+%27M%27+bookmark&rft_id=http%3A%2F%2Fstore.metmuseum.org%2Fmagnets%2Bbookmarks%2Frenaissance-m-bookmark%2Finvt%2F10086668&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span>.</span> </li> </ol></div></div> <p><b>Citations</b> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.ritrattopacioli.it/texting.htm">"The Enigma of Luca Pacioli's Portrait"</a>. <i>RitrattoPacioli</i><span class="reference-accessdate">. Retrieved <span class="nowrap">30 January</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=RitrattoPacioli&rft.atitle=The+Enigma+of+Luca+Pacioli%27s+Portrait&rft_id=http%3A%2F%2Fwww.ritrattopacioli.it%2Ftexting.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-Treccani-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Treccani_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDi_Teodoro2014" class="citation encyclopaedia cs1 cs1-prop-foreign-lang-source">Di Teodoro, Francesco Paolo (2014). <a rel="nofollow" class="external text" href="http://www.treccani.it/enciclopedia/luca-pacioli_%28Dizionario-Biografico%29/">"Pacioli, Luca"</a>. <i>Dizionario Biografico degli Italiani</i> (in Italian). Vol. 80. Treccani<span class="reference-accessdate">. Retrieved <span class="nowrap">30 January</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Pacioli%2C+Luca&rft.btitle=Dizionario+Biografico+degli+Italiani&rft.pub=Treccani&rft.date=2014&rft.aulast=Di+Teodoro&rft.aufirst=Francesco+Paolo&rft_id=http%3A%2F%2Fwww.treccani.it%2Fenciclopedia%2Fluca-pacioli_%2528Dizionario-Biografico%2529%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTarquini2016" class="citation book cs1">Tarquini, Luca (23 December 2016). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Sj6RDgAAQBAJ&pg=PA40"><i>il Falco e il Topo Manualetto di Gestione Aziendale</i></a>. Lulu.com. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781326893934" title="Special:BookSources/9781326893934"><bdi>9781326893934</bdi></a> – via Google Books.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=il+Falco+e+il+Topo+Manualetto+di+Gestione+Aziendale&rft.pub=Lulu.com&rft.date=2016-12-23&rft.isbn=9781326893934&rft.aulast=Tarquini&rft.aufirst=Luca&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DSj6RDgAAQBAJ%26pg%3DPA40&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMacKinnon1993" class="citation journal cs1">MacKinnon, Nick (1993). "The Portrait of Fra Luca Pacioli". <i><a href="/wiki/The_Mathematical_Gazette" title="The Mathematical Gazette">The Mathematical Gazette</a></i>. <b>77</b> (479): 132, 160. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F3619717">10.2307/3619717</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/3619717">3619717</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:195006163">195006163</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Mathematical+Gazette&rft.atitle=The+Portrait+of+Fra+Luca+Pacioli&rft.volume=77&rft.issue=479&rft.pages=132%2C+160&rft.date=1993&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A195006163%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F3619717%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F3619717&rft.aulast=MacKinnon&rft.aufirst=Nick&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-bio-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-bio_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-bio_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-bio_5-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www-groups.dcs.st-and.ac.uk/history/Biographies/Pacioli.html">"Pacioli biography"</a>. <i>www-groups.dcs.st-and.ac.uk</i><span class="reference-accessdate">. Retrieved <span class="nowrap">24 March</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www-groups.dcs.st-and.ac.uk&rft.atitle=Pacioli+biography&rft_id=http%3A%2F%2Fwww-groups.dcs.st-and.ac.uk%2Fhistory%2FBiographies%2FPacioli.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Heeffer, 2010</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChiappettaLarson1995" class="citation book cs1">Chiappetta, Barbara; Larson, Kermit D. (15 November 1995). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3ydxTif500YC&q=%22Luca%20Pacioli%22%20bed%20night"><i>Fundamental Accounting Principles: Student Learning Tools</i></a>. <a href="/wiki/McGraw-Hill_Higher_Education" class="mw-redirect" title="McGraw-Hill Higher Education">McGraw-Hill Higher Education</a>. p. 209. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780256207484" title="Special:BookSources/9780256207484"><bdi>9780256207484</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">10 November</span> 2023</span> – via Google Books.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamental+Accounting+Principles%3A+Student+Learning+Tools&rft.pages=209&rft.pub=McGraw-Hill+Higher+Education&rft.date=1995-11-15&rft.isbn=9780256207484&rft.aulast=Chiappetta&rft.aufirst=Barbara&rft.au=Larson%2C+Kermit+D.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D3ydxTif500YC%26q%3D%2522Luca%2520Pacioli%2522%2520bed%2520night&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-paccioliLog-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-paccioliLog_8-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Extras/Pacioli_logarithm.html">St-and.ac.uk</a> A Napierian logarithm before Napier, John J O'Connor and Edmund F Robertson</span> </li> <li id="cite_note-davis-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-davis_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-davis_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavis1977" class="citation book cs1 cs1-prop-foreign-lang-source">Davis, Margaret Daly (1977). <i>Piero Della Francesca's Mathematical Treatises: The Trattato D'abaco and Libellus de Quinque Corporibus Regularibus</i> (in English and Italian). Longo Editore. p. 64.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Piero+Della+Francesca%27s+Mathematical+Treatises%3A+The+Trattato+D%27abaco+and+Libellus+de+Quinque+Corporibus+Regularibus&rft.pages=64&rft.pub=Longo+Editore&rft.date=1977&rft.aulast=Davis&rft.aufirst=Margaret+Daly&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcDonald2007" class="citation news cs1">McDonald, Lucy (10 April 2007). <a rel="nofollow" class="external text" href="https://www.theguardian.com/italy/story/0,,2053433,00.html">"And that's renaissance magic ..."</a> <i><a href="/wiki/The_Guardian" title="The Guardian">The Guardian</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">30 January</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Guardian&rft.atitle=And+that%27s+renaissance+magic+...&rft.date=2007-04-10&rft.aulast=McDonald&rft.aufirst=Lucy&rft_id=https%3A%2F%2Fwww.theguardian.com%2Fitaly%2Fstory%2F0%2C%2C2053433%2C00.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmith2018" class="citation ssrn cs1">Smith, L. Murphy (2018). "Luca Pacioli: The Father of Accounting". <a href="/wiki/SSRN_(identifier)" class="mw-redirect" title="SSRN (identifier)">SSRN</a> <a rel="nofollow" class="external text" href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2320658">2320658</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=Social+Science+Research+Network&rft.atitle=Luca+Pacioli%3A+The+Father+of+Accounting&rft.date=2018&rft_id=https%3A%2F%2Fpapers.ssrn.com%2Fsol3%2Fpapers.cfm%3Fabstract_id%3D2320658%23id-name%3DSSRN&rft.aulast=Smith&rft.aufirst=L.+Murphy&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.icaew.com/library/library-collection/historical-accounting-literature/turning-the-pages">"Turning the Pages: ICAEW's collection of rare books"</a>. <i>ICAEW.com</i>. ICAEW<span class="reference-accessdate">. Retrieved <span class="nowrap">22 June</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ICAEW.com&rft.atitle=Turning+the+Pages%3A+ICAEW%27s+collection+of+rare+books&rft_id=https%3A%2F%2Fwww.icaew.com%2Flibrary%2Flibrary-collection%2Fhistorical-accounting-literature%2Fturning-the-pages&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080509143211/http://www.timesonline.co.uk/tol/life_and_style/court_and_social/article3523718.ece">Times Online: Renaissance chess master and the Da Vinci decode mystery</a></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.iht.com/articles/ap/2008/03/14/europe/EU-GEN-Italy-Da-Vinci-Chess-Code.php">"International Herald Tribune: Experts link Leonardo da Vinci to chess puzzles in long-lost Renaissance treatise"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=International+Herald+Tribune%3A+Experts+link+Leonardo+da+Vinci+to+chess+puzzles+in+long-lost+Renaissance+treatise&rft_id=http%3A%2F%2Fwww.iht.com%2Farticles%2Fap%2F2008%2F03%2F14%2Feurope%2FEU-GEN-Italy-Da-Vinci-Chess-Code.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.winnipegfreepress.com/life/story/4150848p-4739893c.html">"Winnipeg Free Press: Chess"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Winnipeg+Free+Press%3A+Chess&rft_id=http%3A%2F%2Fwww.winnipegfreepress.com%2Flife%2Fstory%2F4150848p-4739893c.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://usatoday30.usatoday.com/tech/science/discoveries/2008-03-14-leondardo-chess-puzzles_N.htm">"Experts link Leonardo da Vinci to chess puzzles - USATODAY.com"</a>. <i>usatoday30.usatoday.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=usatoday30.usatoday.com&rft.atitle=Experts+link+Leonardo+da+Vinci+to+chess+puzzles+-+USATODAY.com&rft_id=https%3A%2F%2Fusatoday30.usatoday.com%2Ftech%2Fscience%2Fdiscoveries%2F2008-03-14-leondardo-chess-puzzles_N.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luca_Pacioli&action=edit&section=8" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBambach2003" class="citation web cs1">Bambach, Carmen (2003). <a rel="nofollow" class="external text" href="http://www.metmuseum.org/special/Leonardo_Master_Draftsman/draftsman_left_essay.asp">"Leonardo, Left-Handed Draftsman and Writer"</a>. New York: Metropolitan Museum of Art<span class="reference-accessdate">. Retrieved <span class="nowrap">2 September</span> 2006</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Leonardo%2C+Left-Handed+Draftsman+and+Writer&rft.pub=New+York%3A+Metropolitan+Museum+of+Art&rft.date=2003&rft.aulast=Bambach&rft.aufirst=Carmen&rft_id=http%3A%2F%2Fwww.metmuseum.org%2Fspecial%2FLeonardo_Master_Draftsman%2Fdraftsman_left_essay.asp&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></li> <li>Calzoni, Giuseppe and Gianfranco Cavazzoni (eds.) (1996) <i>Tractatus Mathematicus ad Discipulos Perusinos</i>, Città di Castello, Perugia.</li> <li>Galassi, Giuseppe. <a rel="nofollow" class="external text" href="https://archive.today/20121211103236/http://clio.lib.olemiss.edu/u?/aah,525">"Pacioli, Luca (c. 1445-c.1517)."</a> In <i>History of Accounting: an International Encyclopedia,</i> edited by <a href="/wiki/Michael_Chatfield" title="Michael Chatfield">Michael Chatfield</a> and <a href="/wiki/Richard_Vangermeersch" title="Richard Vangermeersch">Richard Vangermeersch</a>. New York: Garland Publishing, 1996. pp. 445–447.</li> <li>Gleeson-White, Jane, "Double Entry: How the Merchants of Venice Created Modern Finance," New York: Norton, 2012.</li> <li>Heeffer, Albrecht, "Algebraic partitioning problems from Luca Paccioli's Perugia manuscript (Vat. Lat. 3129)" in <i>Sources and Commentaries in Exact Sciences</i>, (2010), 11, pp. 3–52.</li> <li>Pacioli, Luca. <i>De divina proportione</i> (English: <i>On the Divine Proportion</i>), (Antonio Capella) Venice: <a href="/wiki/Paganino_Paganini" title="Paganino Paganini">Paganino Paganini</a> (1509).</li> <li>Taylor, Emmet, R. <i>No Royal Road: Luca Paccioli and his Times</i> (1942)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Pacioli.html">"Luca Pacioli"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Luca+Pacioli&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FPacioli.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALuca+Pacioli" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.newadvent.org/cathen/11383b.htm">Lucas Paccioli</a> - <a href="/wiki/Catholic_Encyclopedia" title="Catholic Encyclopedia">Catholic Encyclopedia</a> article</li> <li><i>Libellus de quinque corporibus regularibus</i>, corredato della versione volgare di Luca Paccioli [facsimile del Codice Vat. Urb. Lat. 632]; eds. Cecil Grayson,... Marisa Dalai Emiliani, Carlo Maccagni. Firenze, Giunti, 1995. 3 vol. (68 ff., XLIV-213, XXII-223 pp.). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/88-09-01020-5" title="Special:BookSources/88-09-01020-5">88-09-01020-5</a></li> <li>Varisco, Alessio, <i>Borgo Sansepolcro. Città di cavalieri e pellegrini</i> Pessano con Bornago, Mimep-Docete (2012).</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Luca_Pacioli&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.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:var(--background-color-interactive-subtle,#f8f9fa);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 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href="https://commons.wikimedia.org/wiki/Category:Luca_Pacioli" class="extiw" title="commons:Category:Luca Pacioli">Luca Pacioli</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://archive.org/search.php?query=%28%28subject%3A%22Pacioli%2C%20Luca%22%20OR%20subject%3A%22Luca%20Pacioli%22%20OR%20creator%3A%22Pacioli%2C%20Luca%22%20OR%20creator%3A%22Luca%20Pacioli%22%20OR%20creator%3A%22Pacioli%2C%20L%2E%22%20OR%20title%3A%22Luca%20Pacioli%22%20OR%20description%3A%22Pacioli%2C%20Luca%22%20OR%20description%3A%22Luca%20Pacioli%22%29%20OR%20%28%221440s-1517%22%20AND%20Pacioli%29%29%20AND%20%28-mediatype:software%29">Works by or about Luca Pacioli</a> at the <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a></li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=126888">Luca Pacioli</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="http://www.ritrattopacioli.it/texting.htm">The Enigma of Luca Paccioli's Portrait</a></li> <li><a rel="nofollow" class="external text" href="https://issuu.com/s.c.williams-library/docs/de_divina_proportione">Full text of <i>De divina proportione</i></a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120120141459/http://www.pacioli-institute.org/">Luca Paccioli's economic research programme</a></li> <li><a rel="nofollow" class="external text" href="http://bdh.bne.es/bnesearch/detalle/1811636"><i>Diuina proportione</i></a>, Venice, 1509, digitized at <a href="/w/index.php?title=Biblioteca_Digital_Hisp%C3%A1nica&action=edit&redlink=1" class="new" title="Biblioteca Digital Hispánica (page does not exist)">Biblioteca Digital Hispánica</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://es.wikipedia.org/wiki/Biblioteca_Digital_Hisp%C3%A1nica" class="extiw" title="es:Biblioteca Digital Hispánica">es</a>]</span>, <a href="/wiki/Biblioteca_Nacional_de_Espa%C3%B1a" title="Biblioteca Nacional de España">Biblioteca Nacional de España</a></li> <li>Lauwers, Luc & Willekens, Marleen: <i>Five Hundred Years of Bookkeeping: A Portrait of Luca Pacioli</i> (Tijdschrift voor Economie en Management, <a href="/wiki/Katholieke_Universiteit_Leuven" class="mw-redirect" title="Katholieke Universiteit Leuven">Katholieke Universiteit Leuven</a>, 1994, vol. XXXIX issue 3 pp. 289–304) <a rel="nofollow" class="external text" href="https://lirias.kuleuven.be/bitstream/123456789/119065/1/TEM1994-3_289-304p.pdf">pdf</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output 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href="/wiki/Template:Mathematics_and_art" title="Template:Mathematics and art"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Mathematics_and_art" title="Template talk:Mathematics and art"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Mathematics_and_art" title="Special:EditPage/Template:Mathematics and art"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Mathematics_and_art" style="font-size:114%;margin:0 4em"><a href="/wiki/Mathematics_and_art" title="Mathematics and art">Mathematics and art</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algorithm" title="Algorithm">Algorithm</a></li> <li><a href="/wiki/Catenary" title="Catenary">Catenary</a></li> <li><a href="/wiki/Fractal" title="Fractal">Fractal</a></li> <li><a href="/wiki/Golden_ratio" title="Golden ratio">Golden ratio</a></li> <li><a href="/wiki/Hyperboloid_structure" title="Hyperboloid structure">Hyperboloid structure</a></li> <li><a href="/wiki/Minimal_surface" title="Minimal surface">Minimal surface</a></li> <li><a href="/wiki/Paraboloid" title="Paraboloid">Paraboloid</a></li> <li><a href="/wiki/Perspective_(graphical)" title="Perspective (graphical)">Perspective</a> <ul><li><a href="/wiki/Camera_lucida" title="Camera lucida">Camera lucida</a></li> <li><a href="/wiki/Camera_obscura" title="Camera obscura">Camera obscura</a></li></ul></li> <li><a href="/wiki/Plastic_ratio" title="Plastic ratio">Plastic ratio</a></li> <li><a href="/wiki/Projective_geometry" title="Projective geometry">Projective geometry</a></li> <li>Proportion <ul><li><a href="/wiki/Proportion_(architecture)" title="Proportion (architecture)">Architecture</a></li> <li><a href="/wiki/Body_proportions" title="Body proportions">Human</a></li></ul></li> <li><a href="/wiki/Symmetry" title="Symmetry">Symmetry</a></li> <li><a href="/wiki/Tessellation" title="Tessellation">Tessellation</a></li> <li><a href="/wiki/Wallpaper_group" title="Wallpaper group">Wallpaper group</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="9" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:FWF_Samuel_Monnier_(vertical_detail).jpg" class="mw-file-description" title="Fibonacci word: detail of artwork by Samuel Monnier, 2009"><img alt="Fibonacci word: detail of artwork by Samuel Monnier, 2009" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/FWF_Samuel_Monnier_%28vertical_detail%29.jpg/75px-FWF_Samuel_Monnier_%28vertical_detail%29.jpg" decoding="async" width="75" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/FWF_Samuel_Monnier_%28vertical_detail%29.jpg/113px-FWF_Samuel_Monnier_%28vertical_detail%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/FWF_Samuel_Monnier_%28vertical_detail%29.jpg/150px-FWF_Samuel_Monnier_%28vertical_detail%29.jpg 2x" data-file-width="281" data-file-height="700" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Forms</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algorithmic_art" title="Algorithmic art">Algorithmic art</a></li> <li><a href="/wiki/Anamorphosis" title="Anamorphosis">Anamorphic art</a></li> <li><a href="/wiki/Mathematics_and_architecture" title="Mathematics and architecture">Architecture</a> <ul><li><a href="/wiki/Geodesic_dome" title="Geodesic dome">Geodesic dome</a></li> <li><a href="/wiki/Pyramid" title="Pyramid">Pyramid</a></li> <li><a href="/wiki/Vastu_shastra" title="Vastu shastra">Vastu shastra</a></li></ul></li> <li><a href="/wiki/Computer_art" title="Computer art">Computer art</a></li> <li><a href="/wiki/Mathematics_and_fiber_arts" title="Mathematics and fiber arts">Fiber arts</a></li> <li><a href="/wiki/Fourth_dimension_in_art" title="Fourth dimension in art">4D art</a></li> <li><a href="/wiki/Fractal_art" title="Fractal art">Fractal art</a></li> <li><a href="/wiki/Islamic_geometric_patterns" title="Islamic geometric patterns">Islamic geometric patterns</a> <ul><li><a href="/wiki/Girih" title="Girih">Girih</a></li> <li><a href="/wiki/Jali" title="Jali">Jali</a></li> <li><a href="/wiki/Muqarnas" title="Muqarnas">Muqarnas</a></li> <li><a href="/wiki/Zellij" title="Zellij">Zellij</a></li></ul></li> <li><a href="/wiki/Knot" title="Knot">Knotting</a> <ul><li><a href="/wiki/Celtic_knot" title="Celtic knot">Celtic knot</a></li> <li><a href="/wiki/Croatian_interlace" title="Croatian interlace">Croatian interlace</a></li> <li><a href="/wiki/Interlace_(art)" title="Interlace (art)">Interlace</a></li></ul></li> <li><a href="/wiki/Music_and_mathematics" title="Music and mathematics">Music</a></li> <li><a href="/wiki/Origami" title="Origami">Origami</a> <ul><li><a href="/wiki/Mathematics_of_paper_folding" title="Mathematics of paper folding">Mathematics</a></li></ul></li> <li><a href="/wiki/Mathematical_sculpture" title="Mathematical sculpture">Sculpture</a></li> <li><a href="/wiki/String_art" title="String art">String art</a></li> <li><a href="/wiki/Tessellation" title="Tessellation">Tiling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Artworks</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_works_designed_with_the_golden_ratio" title="List of works designed with the golden ratio">List of works designed with the golden ratio</a></li> <li><i><a href="/wiki/Continuum_(sculpture)" title="Continuum (sculpture)">Continuum</a></i></li> <li><i><a href="/wiki/Mathemalchemy" title="Mathemalchemy">Mathemalchemy</a></i></li> <li><i><a href="/wiki/Mathematica:_A_World_of_Numbers..._and_Beyond" title="Mathematica: A World of Numbers... and Beyond">Mathematica: A World of Numbers... and Beyond</a></i></li> <li><i><a href="/wiki/Octacube_(sculpture)" title="Octacube (sculpture)">Octacube</a></i></li> <li><i><a href="/wiki/Pi_(art_project)" title="Pi (art project)">Pi</a></i></li> <li><i><a href="/wiki/Pi_in_the_Sky" title="Pi in the Sky">Pi in the Sky</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mathematics_and_architecture" title="Mathematics and architecture">Buildings</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cathedral_of_Saint_Mary_of_the_Assumption_(San_Francisco)" title="Cathedral of Saint Mary of the Assumption (San Francisco)">Cathedral of Saint Mary of the Assumption</a></li> <li><a href="/wiki/Hagia_Sophia" title="Hagia Sophia">Hagia Sophia</a></li> <li><a href="/wiki/Pantheon,_Rome" title="Pantheon, Rome">Pantheon</a></li> <li><a href="/wiki/Parthenon" title="Parthenon">Parthenon</a></li> <li><a href="/wiki/Great_Pyramid_of_Giza" title="Great Pyramid of Giza">Pyramid of Khufu</a></li> <li><a href="/wiki/Sagrada_Fam%C3%ADlia" title="Sagrada Família">Sagrada Família</a></li> <li><a href="/wiki/Sydney_Opera_House" title="Sydney Opera House">Sydney Opera House</a></li> <li><a href="/wiki/Taj_Mahal" title="Taj Mahal">Taj Mahal</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_mathematical_artists" title="List of mathematical artists">Artists</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Renaissance</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Paolo_Uccello" title="Paolo Uccello">Paolo Uccello</a></li> <li><a href="/wiki/Piero_della_Francesca" title="Piero della Francesca">Piero della Francesca</a></li> <li><a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a> <ul><li><i><a href="/wiki/Vitruvian_Man" title="Vitruvian Man">Vitruvian Man</a></i></li></ul></li> <li><a href="/wiki/Albrecht_D%C3%BCrer" title="Albrecht Dürer">Albrecht Dürer</a></li> <li><a href="/wiki/Parmigianino" title="Parmigianino">Parmigianino</a> <ul><li><i><a href="/wiki/Self-portrait_in_a_Convex_Mirror" title="Self-portrait in a Convex Mirror">Self-portrait in a Convex Mirror</a></i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">19th–20th<br />Century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/William_Blake" title="William Blake">William Blake</a> <ul><li><i><a href="/wiki/The_Ancient_of_Days" title="The Ancient of Days">The Ancient of Days</a></i></li> <li><i><a href="/wiki/Newton_(Blake)" title="Newton (Blake)">Newton</a></i></li></ul></li> <li><a href="/wiki/Jean_Metzinger" title="Jean Metzinger">Jean Metzinger</a> <ul><li><i><a href="/wiki/Dancer_in_a_Caf%C3%A9" title="Dancer in a Café">Danseuse au café</a></i></li> <li><i><a href="/wiki/L%27Oiseau_bleu_(Metzinger)" class="mw-redirect" title="L'Oiseau bleu (Metzinger)">L'Oiseau bleu</a></i></li></ul></li> <li><a href="/wiki/Giorgio_de_Chirico" title="Giorgio de Chirico">Giorgio de Chirico</a></li> <li><a href="/wiki/Man_Ray" title="Man Ray">Man Ray</a></li> <li><a href="/wiki/M._C._Escher" title="M. C. Escher">M. C. Escher</a> <ul><li><i><a href="/wiki/Circle_Limit_III" title="Circle Limit III">Circle Limit III</a></i></li> <li><i><a href="/wiki/Print_Gallery_(M._C._Escher)" title="Print Gallery (M. C. Escher)">Print Gallery</a></i></li> <li><i><a href="/wiki/Relativity_(M._C._Escher)" title="Relativity (M. C. Escher)">Relativity</a></i></li> <li><i><a href="/wiki/Reptiles_(M._C._Escher)" title="Reptiles (M. C. Escher)">Reptiles</a></i></li> <li><i><a href="/wiki/Waterfall_(M._C._Escher)" title="Waterfall (M. C. Escher)">Waterfall</a></i></li></ul></li> <li><a href="/wiki/Ren%C3%A9_Magritte" title="René Magritte">René Magritte</a> <ul><li><i><a href="/wiki/The_Human_Condition_(Magritte)" title="The Human Condition (Magritte)">La condition humaine</a></i></li></ul></li> <li><a href="/wiki/Salvador_Dal%C3%AD" title="Salvador Dalí">Salvador Dalí</a> <ul><li><i><a href="/wiki/Crucifixion_(Corpus_Hypercubus)" title="Crucifixion (Corpus Hypercubus)">Crucifixion</a></i></li> <li><i><a href="/wiki/The_Swallow%27s_Tail" title="The Swallow's Tail">The Swallow's Tail</a></i></li></ul></li> <li><a href="/wiki/Crockett_Johnson" title="Crockett Johnson">Crockett Johnson</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Contemporary</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Max_Bill" title="Max Bill">Max Bill</a></li> <li><a href="/wiki/Martin_Demaine" title="Martin Demaine">Martin</a> and <a href="/wiki/Erik_Demaine" title="Erik Demaine">Erik Demaine</a></li> <li><a href="/wiki/Scott_Draves" title="Scott Draves">Scott Draves</a></li> <li><a href="/wiki/Jan_Dibbets" title="Jan Dibbets">Jan Dibbets</a></li> <li><a href="/wiki/John_Ernest" title="John Ernest">John Ernest</a></li> <li><a href="/wiki/Helaman_Ferguson" title="Helaman Ferguson">Helaman Ferguson</a></li> <li><a href="/wiki/Peter_Forakis" title="Peter Forakis">Peter Forakis</a></li> <li><a href="/wiki/Susan_Goldstine" title="Susan Goldstine">Susan Goldstine</a></li> <li><a href="/wiki/Bathsheba_Grossman" title="Bathsheba Grossman">Bathsheba Grossman</a></li> <li><a href="/wiki/George_W._Hart" title="George W. Hart">George W. Hart</a></li> <li><a href="/wiki/Desmond_Paul_Henry" title="Desmond Paul Henry">Desmond Paul Henry</a></li> <li><a href="/wiki/Anthony_Hill_(artist)" title="Anthony Hill (artist)">Anthony Hill</a></li> <li><a href="/wiki/Charles_Jencks" title="Charles Jencks">Charles Jencks</a> <ul><li><i><a href="/wiki/Garden_of_Cosmic_Speculation" title="Garden of Cosmic Speculation">Garden of Cosmic Speculation</a></i></li></ul></li> <li><a href="/wiki/Andy_Lomas" title="Andy Lomas">Andy Lomas</a></li> <li><a href="/wiki/Robert_Longhurst" title="Robert Longhurst">Robert Longhurst</a></li> <li><a href="/wiki/Jeanette_McLeod" title="Jeanette McLeod">Jeanette McLeod</a></li> <li><a href="/wiki/Hamid_Naderi_Yeganeh" title="Hamid Naderi Yeganeh">Hamid Naderi Yeganeh</a></li> <li><a href="/wiki/Istv%C3%A1n_Orosz" title="István Orosz">István Orosz</a></li> <li><a href="/wiki/Hinke_Osinga" title="Hinke Osinga">Hinke Osinga</a></li> <li><a href="/wiki/Antoine_Pevsner" title="Antoine Pevsner">Antoine Pevsner</a></li> <li><a href="/wiki/Tony_Robbin" title="Tony Robbin">Tony Robbin</a></li> <li><a href="/wiki/Alba_Rojo_Cama" title="Alba Rojo Cama">Alba Rojo Cama</a></li> <li><a href="/wiki/Reza_Sarhangi" class="mw-redirect" title="Reza Sarhangi">Reza Sarhangi</a></li> <li><a href="/wiki/Oliver_Sin" title="Oliver Sin">Oliver Sin</a></li> <li><a href="/wiki/Hiroshi_Sugimoto" title="Hiroshi Sugimoto">Hiroshi Sugimoto</a></li> <li><a href="/wiki/Daina_Taimi%C5%86a" title="Daina Taimiņa">Daina Taimiņa</a></li> <li><a href="/wiki/Roman_Verostko" title="Roman Verostko">Roman Verostko</a></li> <li><a href="/wiki/Margaret_Wertheim" title="Margaret Wertheim">Margaret Wertheim</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theorists</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Ancient</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Polykleitos" title="Polykleitos">Polykleitos</a> <ul><li><i>Canon</i></li></ul></li> <li><a href="/wiki/Vitruvius" title="Vitruvius">Vitruvius</a> <ul><li><i><a href="/wiki/De_architectura" title="De architectura">De architectura</a></i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Renaissance</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Filippo_Brunelleschi" title="Filippo Brunelleschi">Filippo Brunelleschi</a></li> <li><a href="/wiki/Leon_Battista_Alberti" title="Leon Battista Alberti">Leon Battista Alberti</a> <ul><li><i><a href="/wiki/De_pictura" title="De pictura">De pictura</a></i></li> <li><i><a href="/wiki/De_re_aedificatoria" title="De re aedificatoria">De re aedificatoria</a></i></li></ul></li> <li><a href="/wiki/Piero_della_Francesca" title="Piero della Francesca">Piero della Francesca</a> <ul><li><i><a href="/wiki/De_prospectiva_pingendi" title="De prospectiva pingendi">De prospectiva pingendi</a></i></li></ul></li> <li><a class="mw-selflink selflink">Luca Pacioli</a> <ul><li><i><a href="/wiki/Divina_proportione" title="Divina proportione">De divina proportione</a></i></li></ul></li> <li><a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a> <ul><li><i><a href="/wiki/A_Treatise_on_Painting" title="A Treatise on Painting">A Treatise on Painting</a></i></li></ul></li> <li><a href="/wiki/Albrecht_D%C3%BCrer" title="Albrecht Dürer">Albrecht Dürer</a> <ul><li><i>Vier Bücher von Menschlicher Proportion</i></li></ul></li> <li><a href="/wiki/Sebastiano_Serlio" title="Sebastiano Serlio">Sebastiano Serlio</a> <ul><li><i>Regole generali d'architettura</i></li></ul></li> <li><a href="/wiki/Andrea_Palladio" title="Andrea Palladio">Andrea Palladio</a> <ul><li><i><a href="/wiki/I_quattro_libri_dell%27architettura" title="I quattro libri dell'architettura">I quattro libri dell'architettura</a></i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Romantic</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Samuel_Colman" title="Samuel Colman">Samuel Colman</a> <ul><li><i>Nature's Harmonic Unity</i></li></ul></li> <li><a href="/wiki/Frederik_Macody_Lund" title="Frederik Macody Lund">Frederik Macody Lund</a> <ul><li><i>Ad Quadratum</i></li></ul></li> <li><a href="/wiki/Jay_Hambidge" title="Jay Hambidge">Jay Hambidge</a> <ul><li><i>The Greek Vase</i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modern</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Owen_Jones_(architect)" title="Owen Jones (architect)">Owen Jones</a> <ul><li><i><a href="/wiki/Owen_Jones_(architect)#The_Grammar_of_Ornament" title="Owen Jones (architect)">The Grammar of Ornament</a></i></li></ul></li> <li><a href="/wiki/Ernest_Hanbury_Hankin" title="Ernest Hanbury Hankin">Ernest Hanbury Hankin</a> <ul><li><i>The Drawing of Geometric Patterns in Saracenic Art</i></li></ul></li> <li><a href="/wiki/G._H._Hardy" title="G. H. Hardy">G. H. Hardy</a> <ul><li><i><a href="/wiki/A_Mathematician%27s_Apology" title="A Mathematician's Apology">A Mathematician's Apology</a></i></li></ul></li> <li><a href="/wiki/George_David_Birkhoff" title="George David Birkhoff">George David Birkhoff</a> <ul><li><i>Aesthetic Measure</i></li></ul></li> <li><a href="/wiki/Douglas_Hofstadter" title="Douglas Hofstadter">Douglas Hofstadter</a> <ul><li><i><a href="/wiki/G%C3%B6del,_Escher,_Bach" title="Gödel, Escher, Bach">Gödel, Escher, Bach</a></i></li></ul></li> <li><a href="/wiki/Nikos_Salingaros" title="Nikos Salingaros">Nikos Salingaros</a> <ul><li><i>The 'Life' of a Carpet</i></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Publications</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Journal_of_Mathematics_and_the_Arts" title="Journal of Mathematics and the Arts">Journal of Mathematics and the Arts</a></i></li> <li><i><a href="/wiki/Lumen_Naturae" title="Lumen Naturae">Lumen Naturae</a></i></li> <li><i><a href="/wiki/Making_Mathematics_with_Needlework" title="Making Mathematics with Needlework">Making Mathematics with Needlework</a></i></li> <li><i><a href="/wiki/Rhythm_of_Structure" title="Rhythm of Structure">Rhythm of Structure</a></i></li> <li><i><a href="/wiki/Viewpoints:_Mathematical_Perspective_and_Fractal_Geometry_in_Art" title="Viewpoints: Mathematical Perspective and Fractal Geometry in Art">Viewpoints: Mathematical Perspective and Fractal Geometry in Art</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Organizations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ars_Mathematica_(organization)" title="Ars Mathematica (organization)">Ars Mathematica</a></li> <li><a href="/wiki/The_Bridges_Organization" title="The Bridges Organization">The Bridges Organization</a></li> <li><a href="/wiki/European_Society_for_Mathematics_and_the_Arts" title="European Society for Mathematics and the Arts">European Society for Mathematics and the Arts</a></li> <li><a href="/wiki/Goudreau_Museum_of_Mathematics_in_Art_and_Science" title="Goudreau Museum of Mathematics in Art and Science">Goudreau Museum of Mathematics in Art and Science</a></li> <li><a href="/wiki/Institute_For_Figuring" title="Institute For Figuring">Institute For Figuring</a></li> <li><a href="/wiki/Mathemalchemy" title="Mathemalchemy">Mathemalchemy</a></li> <li><a href="/wiki/National_Museum_of_Mathematics" title="National Museum of Mathematics">National Museum of Mathematics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Droste_effect" title="Droste effect">Droste effect</a></li> <li><a href="/wiki/Mathematical_beauty" title="Mathematical beauty">Mathematical beauty</a></li> <li><a href="/wiki/Patterns_in_nature" title="Patterns in nature">Patterns in nature</a></li> <li><a href="/wiki/Sacred_geometry" title="Sacred geometry">Sacred geometry</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a 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srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/0000000121355781">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/87677562">VIAF</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/26164187925718202898">2</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/305555260">3</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/262034442">4</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/172263698">5</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/210838030">6</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/88350474">7</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/61550382">8</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/149145542429196640013">9</a></span></li></ul></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/1839841/">FAST</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/118738968">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n81089368">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11918350c">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11918350c">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00451982">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Pacioli, Luca"><a rel="nofollow" class="external text" href="https://opac.sbn.it/nome/CFIV065966">Italy</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35685326">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=jn20010601048&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX848274">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.bnportugal.gov.pt/aut/catbnp/74573">Portugal</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.bnportugal.gov.pt/aut/catbnp/722131">2</a></span></li></ul></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p072681020">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90288951">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000138328&P_CON_LNG=ENG">Latvia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://katalog.nsk.hr/F/?func=direct&doc_number=000146529&local_base=nsk10">Croatia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://lod.nl.go.kr/resource/KAC201109400">Korea</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/0xbdftpj2d1jxfh">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810694149505606">Poland</a></span></li><li><span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8034&url_prefix=https://opac.vatlib.it/auth/detail/&id=495/53496">Vatican</a></span><ul><li><span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8034&url_prefix=https://opac.vatlib.it/auth/detail/&id=495/53497">2</a></span></li></ul></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007266095405171">Israel</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058513857106706">Catalonia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://opac.kbr.be/LIBRARY/doc/AUTHORITY/14174958">Belgium</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA01503594?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=126888">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:pacioli.luca">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/307399">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Artists</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.getty.edu/vow/ULANFullDisplay?find=&role=&nation=&subjectid=500263335">ULAN</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://rkd.nl/en/explore/artists/424661">RKD Artists</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://www.uni-stuttgart.de/hi/gnt/dsi2/index.php?table_name=dsi&function=details&where_field=id&where_value=12989">Scientific illustrators</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/1041940">Trove</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="PACIOLI, Luca"><a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/luca-pacioli_(Dizionario-Biografico)">Italian People</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd118738968.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/118738968">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/027055108">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6tf036p">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img 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