CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="nl" dir="ltr"> <head> <meta charset="UTF-8"> <title>Brahmagupta - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )nlwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":[",\t.",".\t,"],"wgDigitTransformTable":["",""], "wgDefaultDateFormat":"dmy","wgMonthNames":["","januari","februari","maart","april","mei","juni","juli","augustus","september","oktober","november","december"],"wgRequestId":"79f1993a-e41e-49d9-9bc8-2eb104a9ea85","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Brahmagupta","wgTitle":"Brahmagupta","wgCurRevisionId":66629841,"wgRevisionId":66629841,"wgArticleId":769100,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Wikipedia:Pagina's die ISBN magische links gebruiken","Indiaas astronoom","Indiaas wiskundige","Geschiedenis van Madhya Pradesh","Getaltheoreticus"],"wgPageViewLanguage":"nl","wgPageContentLanguage":"nl","wgPageContentModel":"wikitext","wgRelevantPageName":"Brahmagupta","wgRelevantArticleId":769100,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia", "wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"nl","pageLanguageDir":"ltr","pageVariantFallbacks":"nl"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":10000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q202943","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles" :"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","ext.scribunto.logs","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.Direct-link-to-Commons","ext.gadget.ProtectionTemplates","ext.gadget.InterProjectLinks","ext.gadget.hoofdbetekenis-titelwijziging","ext.gadget.switcher","ext.gadget.OpenStreetMapFrame","ext.gadget.subpages","ext.urlShortener.toolbar", "ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=nl&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=nl&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=nl&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Brahmagupta - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//nl.m.wikipedia.org/wiki/Brahmagupta"> <link rel="alternate" type="application/x-wiki" title="Bewerken" href="/w/index.php?title=Brahmagupta&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (nl)"> <link rel="EditURI" type="application/rsd+xml" href="//nl.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://nl.wikipedia.org/wiki/Brahmagupta"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.nl"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom-feed" href="/w/index.php?title=Speciaal:RecenteWijzigingen&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Brahmagupta rootpage-Brahmagupta skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Naar inhoud springen</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Hoofdmenu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Hoofdmenu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Hoofdmenu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">verbergen</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigatie </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Hoofdpagina" title="Naar de hoofdpagina gaan [z]" accesskey="z"><span>Hoofdpagina</span></a></li><li id="n-zoekartikel" class="mw-list-item"><a href="/wiki/Portaal:Navigatie"><span>Vind een artikel</span></a></li><li id="n-today" class="mw-list-item"><a href="/wiki/24_november"><span>Vandaag</span></a></li><li id="n-Etalage" class="mw-list-item"><a href="/wiki/Wikipedia:Etalage"><span>Etalage</span></a></li><li id="n-categories" class="mw-list-item"><a href="/wiki/Categorie:Alles"><span>Categorieën</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Speciaal:RecenteWijzigingen" title="Een lijst met recente wijzigingen in deze wiki. [r]" accesskey="r"><span>Recente wijzigingen</span></a></li><li id="n-newpages" class="mw-list-item"><a href="/wiki/Speciaal:NieuwePaginas"><span>Nieuwe artikelen</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Speciaal:Willekeurig" title="Een willekeurige pagina bekijken [x]" accesskey="x"><span>Willekeurige pagina</span></a></li> </ul> </div> </div> <div id="p-navigation2" class="vector-menu mw-portlet mw-portlet-navigation2" > <div class="vector-menu-heading"> Informatie </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-portal" class="mw-list-item"><a href="/wiki/Portaal:Gebruikersportaal" title="Informatie over het project: wat u kunt doen, waar u dingen kunt vinden"><span>Gebruikersportaal</span></a></li><li id="n-Snelcursus" class="mw-list-item"><a href="/wiki/Wikipedia:Snelcursus"><span>Snelcursus</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Portaal:Hulp_en_beheer" title="Hulpinformatie over deze wiki"><span>Hulp en contact</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Hoofdpagina" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="de vrije encyclopedie" src="/static/images/mobile/copyright/wikipedia-tagline-nl.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Speciaal:Zoeken" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Doorzoek Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Zoeken</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Doorzoek Wikipedia" aria-label="Doorzoek Wikipedia" autocapitalize="sentences" title="Doorzoek Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Speciaal:Zoeken"> </div> <button class="cdx-button cdx-search-input__end-button">Zoeken</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Persoonlijke hulpmiddelen"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Uiterlijk"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="De lettergrootte, breedte en kleur van de pagina wijzigen" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Uiterlijk" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Uiterlijk</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_nl.wikipedia.org&uselang=nl" class=""><span>Doneren</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciaal:GebruikerAanmaken&returnto=Brahmagupta" title="Registreer u vooral en meld u aan. Dit is echter niet verplicht." class=""><span>Account aanmaken</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciaal:Aanmelden&returnto=Brahmagupta" title="U wordt van harte uitgenodigd om aan te melden, maar dit is niet verplicht [o]" accesskey="o" class=""><span>Aanmelden</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Meer opties" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Persoonlijke hulpmiddelen" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Persoonlijke hulpmiddelen</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Gebruikersmenu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_nl.wikipedia.org&uselang=nl"><span>Doneren</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speciaal:GebruikerAanmaken&returnto=Brahmagupta" title="Registreer u vooral en meld u aan. Dit is echter niet verplicht."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Account aanmaken</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speciaal:Aanmelden&returnto=Brahmagupta" title="U wordt van harte uitgenodigd om aan te melden, maar dit is niet verplicht [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Aanmelden</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pagina's voor uitgelogde redacteuren <a href="/wiki/Help:Inleiding" aria-label="Meer leren over bewerken"><span>meer lezen</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speciaal:MijnBijdragen" title="Bijdragen IP-adres [y]" accesskey="y"><span>Bijdragen</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speciaal:MijnOverleg" title="Overlegpagina van de anonieme gebruiker van dit IP-adres [n]" accesskey="n"><span>Overleg</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Inhoud" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Inhoud</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">verbergen</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Top</div> </a> </li> <li id="toc-Leven" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Leven"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Leven</span> </div> </a> <ul id="toc-Leven-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wiskunde" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Wiskunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Wiskunde</span> </div> </a> <button aria-controls="toc-Wiskunde-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>Wiskunde-subkopje inklappen</span> </button> <ul id="toc-Wiskunde-sublist" class="vector-toc-list"> <li id="toc-Het_getal_nul" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Het_getal_nul"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Het getal nul</span> </div> </a> <ul id="toc-Het_getal_nul-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vergelijkingen" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vergelijkingen"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Vergelijkingen</span> </div> </a> <ul id="toc-Vergelijkingen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Toepassing_in_de_sterrenkunde" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Toepassing_in_de_sterrenkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Toepassing in de sterrenkunde</span> </div> </a> <ul id="toc-Toepassing_in_de_sterrenkunde-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Berekening_van_oppervlakken" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Berekening_van_oppervlakken"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Berekening van oppervlakken</span> </div> </a> <ul id="toc-Berekening_van_oppervlakken-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Pi</span> </div> </a> <ul id="toc-Pi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Meetkunde" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Meetkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Meetkunde</span> </div> </a> <button aria-controls="toc-Meetkunde-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>Meetkunde-subkopje inklappen</span> </button> <ul id="toc-Meetkunde-sublist" class="vector-toc-list"> <li id="toc-Formule_van_Brahmagupta" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formule_van_Brahmagupta"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Formule van Brahmagupta</span> </div> </a> <ul id="toc-Formule_van_Brahmagupta-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Astronomie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Astronomie"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Astronomie</span> </div> </a> <ul id="toc-Astronomie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voetnoten" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voetnoten"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Voetnoten</span> </div> </a> <ul id="toc-Voetnoten-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Literatuur" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Literatuur"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Literatuur</span> </div> </a> <ul id="toc-Literatuur-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Websites" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Websites"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Websites</span> </div> </a> <ul id="toc-Websites-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="Inhoud" 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="Inhoudsopgave omschakelen" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Inhoudsopgave omschakelen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Brahmagupta</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ga naar een artikel in een andere taal. Beschikbaar in 112 talen" > <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-112" 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">112 talen</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/Brahmagupta" title="Brahmagupta – Afrikaans" lang="af" hreflang="af" data-title="Brahmagupta" 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/Brahmagupta" title="Brahmagupta – Zwitserduits" lang="gsw" hreflang="gsw" data-title="Brahmagupta" data-language-autonym="Alemannisch" data-language-local-name="Zwitserduits" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Aragonees" lang="an" hreflang="an" data-title="Brahmagupta" data-language-autonym="Aragonés" data-language-local-name="Aragonees" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%B1%D8%A7%D9%87%D9%85%D8%A7%D8%BA%D9%88%D8%A8%D8%AA%D8%A7" title="براهماغوبتا – Arabisch" lang="ar" hreflang="ar" data-title="براهماغوبتا" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A8%D8%B1%D8%A7%D9%87%D9%85%D8%A7%D8%AC%D9%88%D8%A8%D8%AA%D8%A7" title="براهماجوبتا – Egyptisch Arabisch" lang="arz" hreflang="arz" data-title="براهماجوبتا" data-language-autonym="مصرى" data-language-local-name="Egyptisch Arabisch" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A7%8D%E0%A7%B0%E0%A6%B9%E0%A7%8D%E0%A6%AE%E0%A6%97%E0%A7%81%E0%A6%AA%E0%A7%8D%E0%A6%A4" title="ব্ৰহ্মগুপ্ত – Assamees" lang="as" hreflang="as" data-title="ব্ৰহ্মগুপ্ত" data-language-autonym="অসমীয়া" data-language-local-name="Assamees" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Asturisch" lang="ast" hreflang="ast" data-title="Brahmagupta" data-language-autonym="Asturianu" data-language-local-name="Asturisch" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Brahmaqupta" title="Brahmaqupta – Azerbeidzjaans" lang="az" hreflang="az" data-title="Brahmaqupta" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A8%D8%B1%D9%87%D9%85%D8%A7%D9%82%D9%88%D9%BE%D8%AA%D8%A7" title="برهماقوپتا – South Azerbaijani" lang="azb" hreflang="azb" data-title="برهماقوپتا" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта – Basjkiers" lang="ba" hreflang="ba" data-title="Брахмагупта" data-language-autonym="Башҡортса" data-language-local-name="Basjkiers" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Beiers" lang="bar" hreflang="bar" data-title="Brahmagupta" data-language-autonym="Boarisch" data-language-local-name="Beiers" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Samogitisch" lang="sgs" hreflang="sgs" data-title="Brahmagupta" data-language-autonym="Žemaitėška" data-language-local-name="Samogitisch" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта – Belarussisch" lang="be" hreflang="be" data-title="Брахмагупта" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" 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%91%D1%80%D0%B0%D0%B3%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брагмагупта – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Брагмагупта" 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%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта – Bulgaars" lang="bg" hreflang="bg" data-title="Брахмагупта" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%97%E0%A5%81%E0%A4%AA%E0%A5%8D%E0%A4%A4" title="ब्रह्मगुप्त – Bhojpuri" lang="bh" hreflang="bh" data-title="ब्रह्मगुप्त" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Bislama" lang="bi" hreflang="bi" data-title="Brahmagupta" data-language-autonym="Bislama" data-language-local-name="Bislama" class="interlanguage-link-target"><span>Bislama</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%8D%E0%A6%B0%E0%A6%B9%E0%A7%8D%E0%A6%AE%E0%A6%97%E0%A7%81%E0%A6%AA%E0%A7%8D%E0%A6%A4" title="ব্রহ্মগুপ্ত – Bengaals" lang="bn" hreflang="bn" data-title="ব্রহ্মগুপ্ত" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Bretons" lang="br" hreflang="br" data-title="Brahmagupta" data-language-autonym="Brezhoneg" data-language-local-name="Bretons" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Bosnisch" lang="bs" hreflang="bs" data-title="Brahmagupta" data-language-autonym="Bosanski" data-language-local-name="Bosnisch" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-btm mw-list-item"><a href="https://btm.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Batak Mandailing" lang="btm" hreflang="btm" data-title="Brahmagupta" data-language-autonym="Batak Mandailing" data-language-local-name="Batak Mandailing" class="interlanguage-link-target"><span>Batak Mandailing</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Catalaans" lang="ca" hreflang="ca" data-title="Brahmagupta" data-language-autonym="Català" data-language-local-name="Catalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%D8%B1%D8%A7%DA%BE%D9%85%D8%A7%DA%AF%D9%88%D9%BE%D8%AA%D8%A7" title="براھماگوپتا – Soranî" lang="ckb" hreflang="ckb" data-title="براھماگوپتا" data-language-autonym="کوردی" data-language-local-name="Soranî" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Corsicaans" lang="co" hreflang="co" data-title="Brahmagupta" data-language-autonym="Corsu" data-language-local-name="Corsicaans" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Tsjechisch" lang="cs" hreflang="cs" data-title="Brahmagupta" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Welsh" lang="cy" hreflang="cy" data-title="Brahmagupta" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Deens" lang="da" hreflang="da" data-title="Brahmagupta" data-language-autonym="Dansk" data-language-local-name="Deens" 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/Brahmagupta" title="Brahmagupta – Duits" lang="de" hreflang="de" data-title="Brahmagupta" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%92%CF%81%CE%B1%CF%87%CE%BC%CE%B1%CE%B3%CE%BA%CE%BF%CF%8D%CF%80%CF%84%CE%B1" title="Βραχμαγκούπτα – Grieks" lang="el" hreflang="el" data-title="Βραχμαγκούπτα" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Engels" lang="en" hreflang="en" data-title="Brahmagupta" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Esperanto" lang="eo" hreflang="eo" data-title="Brahmagupta" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Spaans" lang="es" hreflang="es" data-title="Brahmagupta" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Estisch" lang="et" hreflang="et" data-title="Brahmagupta" data-language-autonym="Eesti" data-language-local-name="Estisch" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Baskisch" lang="eu" hreflang="eu" data-title="Brahmagupta" data-language-autonym="Euskara" data-language-local-name="Baskisch" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D8%B1%D9%87%D9%85%D8%A7%DA%AF%D9%88%D9%BE%D8%AA%D8%A7" title="برهماگوپتا – Perzisch" lang="fa" hreflang="fa" data-title="برهماگوپتا" data-language-autonym="فارسی" data-language-local-name="Perzisch" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Fins" lang="fi" hreflang="fi" data-title="Brahmagupta" data-language-autonym="Suomi" data-language-local-name="Fins" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Frans" lang="fr" hreflang="fr" data-title="Brahmagupta" data-language-autonym="Français" data-language-local-name="Frans" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Galicisch" lang="gl" hreflang="gl" data-title="Brahmagupta" data-language-autonym="Galego" data-language-local-name="Galicisch" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Guaraní" lang="gn" hreflang="gn" data-title="Brahmagupta" data-language-autonym="Avañe'ẽ" data-language-local-name="Guaraní" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AC%E0%AB%8D%E0%AA%B0%E0%AA%B9%E0%AB%8D%E0%AA%AE%E0%AA%97%E0%AB%81%E0%AA%AA%E0%AB%8D%E0%AA%A4" title="બ્રહ્મગુપ્ત – Gujarati" lang="gu" hreflang="gu" data-title="બ્રહ્મગુપ્ત" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%91%D7%A8%D7%90%D7%94%D7%9E%D7%92%D7%95%D7%A4%D7%98%D7%94" title="בראהמגופטה – Hebreeuws" lang="he" hreflang="he" data-title="בראהמגופטה" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%97%E0%A5%81%E0%A4%AA%E0%A5%8D%E0%A4%A4" title="ब्रह्मगुप्त – Hindi" lang="hi" hreflang="hi" data-title="ब्रह्मगुप्त" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Fijisch Hindi" lang="hif" hreflang="hif" data-title="Brahmagupta" data-language-autonym="Fiji Hindi" data-language-local-name="Fijisch Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Kroatisch" lang="hr" hreflang="hr" data-title="Brahmagupta" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Hongaars" lang="hu" hreflang="hu" data-title="Brahmagupta" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D6%80%D5%A1%D5%B0%D5%B4%D5%A1%D5%A3%D5%B8%D6%82%D5%BA%D5%BF%D5%A1" title="Բրահմագուպտա – Armeens" lang="hy" hreflang="hy" data-title="Բրահմագուպտա" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Interlingua" lang="ia" hreflang="ia" data-title="Brahmagupta" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Indonesisch" lang="id" hreflang="id" data-title="Brahmagupta" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Iloko" lang="ilo" hreflang="ilo" data-title="Brahmagupta" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Ido" lang="io" hreflang="io" data-title="Brahmagupta" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – IJslands" lang="is" hreflang="is" data-title="Brahmagupta" data-language-autonym="Íslenska" data-language-local-name="IJslands" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Italiaans" lang="it" hreflang="it" data-title="Brahmagupta" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%96%E3%83%A9%E3%83%95%E3%83%9E%E3%82%B0%E3%83%97%E3%82%BF" title="ブラフマグプタ – Japans" lang="ja" hreflang="ja" data-title="ブラフマグプタ" data-language-autonym="日本語" data-language-local-name="Japans" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%91%E1%83%A0%E1%83%90%E1%83%B0%E1%83%9B%E1%83%90%E1%83%92%E1%83%A3%E1%83%A4%E1%83%97%E1%83%90" title="ბრაჰმაგუფთა – Georgisch" lang="ka" hreflang="ka" data-title="ბრაჰმაგუფთა" data-language-autonym="ქართული" data-language-local-name="Georgisch" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта – Kazachs" lang="kk" hreflang="kk" data-title="Брахмагупта" data-language-autonym="Қазақша" data-language-local-name="Kazachs" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AC%E0%B3%8D%E0%B2%B0%E0%B2%B9%E0%B3%8D%E0%B2%AE%E0%B2%97%E0%B3%81%E0%B2%AA%E0%B3%8D%E0%B2%A4" title="ಬ್ರಹ್ಮಗುಪ್ತ – Kannada" lang="kn" hreflang="kn" data-title="ಬ್ರಹ್ಮಗುಪ್ತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B8%8C%EB%9D%BC%EB%A7%88%EA%B5%BD%ED%83%80" title="브라마굽타 – Koreaans" lang="ko" hreflang="ko" data-title="브라마굽타" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Koerdisch" lang="ku" hreflang="ku" data-title="Brahmagupta" data-language-autonym="Kurdî" data-language-local-name="Koerdisch" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Cornish" lang="kw" hreflang="kw" data-title="Brahmagupta" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Brachmacottus" title="Brachmacottus – Latijn" lang="la" hreflang="la" data-title="Brachmacottus" data-language-autonym="Latina" data-language-local-name="Latijn" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Luxemburgs" lang="lb" hreflang="lb" data-title="Brahmagupta" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxemburgs" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Lombardisch" lang="lmo" hreflang="lmo" data-title="Brahmagupta" data-language-autonym="Lombard" data-language-local-name="Lombardisch" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Litouws" lang="lt" hreflang="lt" data-title="Brahmagupta" data-language-autonym="Lietuvių" data-language-local-name="Litouws" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Lets" lang="lv" hreflang="lv" data-title="Brahmagupta" data-language-autonym="Latviešu" data-language-local-name="Lets" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%97%E0%A5%81%E0%A4%AA%E0%A5%8D%E0%A4%A4" title="ब्रह्मगुप्त – Maithili" lang="mai" hreflang="mai" data-title="ब्रह्मगुप्त" data-language-autonym="मैथिली" data-language-local-name="Maithili" class="interlanguage-link-target"><span>मैथिली</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Malagassisch" lang="mg" hreflang="mg" data-title="Brahmagupta" data-language-autonym="Malagasy" data-language-local-name="Malagassisch" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B5%8D%E0%B4%B0%E0%B4%B9%E0%B5%8D%E0%B4%AE%E0%B4%97%E0%B5%81%E0%B4%AA%E0%B5%8D%E0%B4%A4%E0%B5%BB" title="ബ്രഹ്മഗുപ്തൻ – Malayalam" lang="ml" hreflang="ml" data-title="ബ്രഹ്മഗുപ്തൻ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%97%E0%A5%81%E0%A4%AA%E0%A5%8D%E0%A4%A4" title="ब्रह्मगुप्त – Marathi" lang="mr" hreflang="mr" data-title="ब्रह्मगुप्त" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Maleis" lang="ms" hreflang="ms" data-title="Brahmagupta" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%97%E1%80%BC%E1%80%9F%E1%80%B9%E1%80%99%E1%80%AC%E1%80%82%E1%80%AF%E1%80%95%E1%80%B9%E1%80%95%E1%80%90%E1%80%B9%E1%80%90" title="ဗြဟ္မာဂုပ္ပတ္တ – Birmaans" lang="my" hreflang="my" data-title="ဗြဟ္မာဂုပ္ပတ္တ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Birmaans" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Nedersaksisch" lang="nds" hreflang="nds" data-title="Brahmagupta" data-language-autonym="Plattdüütsch" data-language-local-name="Nedersaksisch" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%97%E0%A5%81%E0%A4%AA%E0%A5%8D%E0%A4%A4" title="ब्रह्मगुप्त – Nepalees" lang="ne" hreflang="ne" data-title="ब्रह्मगुप्त" data-language-autonym="नेपाली" data-language-local-name="Nepalees" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%97%E0%A5%81%E0%A4%AA%E0%A5%8D%E0%A4%A4" title="ब्रह्मगुप्त – Newari" lang="new" hreflang="new" data-title="ब्रह्मगुप्त" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Brahmagupta" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Brahmagupta" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Occitaans" lang="oc" hreflang="oc" data-title="Brahmagupta" data-language-autonym="Occitan" data-language-local-name="Occitaans" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AC%E0%A9%8D%E0%A8%B0%E0%A8%B9%E0%A8%AE%E0%A8%97%E0%A9%81%E0%A8%AA%E0%A8%A4" title="ਬ੍ਰਹਮਗੁਪਤ – Punjabi" lang="pa" hreflang="pa" data-title="ਬ੍ਰਹਮਗੁਪਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Pools" lang="pl" hreflang="pl" data-title="Brahmagupta" data-language-autonym="Polski" data-language-local-name="Pools" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Piëmontees" lang="pms" hreflang="pms" data-title="Brahmagupta" data-language-autonym="Piemontèis" data-language-local-name="Piëmontees" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A8%D8%B1%DB%81%D9%85%D8%A7_%DA%AF%D9%BE%D8%AA%D8%A7" title="برہما گپتا – Western Punjabi" lang="pnb" hreflang="pnb" data-title="برہما گپتا" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Portugees" lang="pt" hreflang="pt" data-title="Brahmagupta" data-language-autonym="Português" data-language-local-name="Portugees" 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/Brahmagupta" title="Brahmagupta – Roemeens" lang="ro" hreflang="ro" data-title="Brahmagupta" data-language-autonym="Română" data-language-local-name="Roemeens" 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%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта – Russisch" lang="ru" hreflang="ru" data-title="Брахмагупта" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D0%B3%D0%BC%D0%B0%D2%91%D1%83%D0%BF%D1%82%D0%B0" title="Брагмаґупта – Roetheens" lang="rue" hreflang="rue" data-title="Брагмаґупта" data-language-autonym="Русиньскый" data-language-local-name="Roetheens" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%AC%E0%A5%8D%E0%A4%B0%E0%A4%B9%E0%A5%8D%E0%A4%AE%E0%A4%97%E0%A5%81%E0%A4%AA%E0%A5%8D%E0%A4%A4%E0%A4%83" title="ब्रह्मगुप्तः – Sanskriet" lang="sa" hreflang="sa" data-title="ब्रह्मगुप्तः" data-language-autonym="संस्कृतम्" data-language-local-name="Sanskriet" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта – Jakoets" lang="sah" hreflang="sah" data-title="Брахмагупта" data-language-autonym="Саха тыла" data-language-local-name="Jakoets" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%B5%E1%B1%A8%E1%B1%9A%E1%B1%A2%E1%B1%A6%E1%B1%9A%E1%B1%9C%E1%B1%A9%E1%B1%AF%E1%B1%9B%E1%B1%9A" title="ᱵᱨᱚᱢᱦᱚᱜᱩᱯᱛᱚ – Santali" lang="sat" hreflang="sat" data-title="ᱵᱨᱚᱢᱦᱚᱜᱩᱯᱛᱚ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="Santali" class="interlanguage-link-target"><span>ᱥᱟᱱᱛᱟᱲᱤ</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A8%D8%B1%DA%BE%D9%85_%DA%AF%D9%BE%D8%AA" title="برھم گپت – Sindhi" lang="sd" hreflang="sd" data-title="برھم گپت" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Bramagupta" title="Bramagupta – Servo-Kroatisch" lang="sh" hreflang="sh" data-title="Bramagupta" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Servo-Kroatisch" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Simple English" lang="en-simple" hreflang="en-simple" data-title="Brahmagupta" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Sloveens" lang="sl" hreflang="sl" data-title="Brahmagupta" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Albanees" lang="sq" hreflang="sq" data-title="Brahmagupta" data-language-autonym="Shqip" data-language-local-name="Albanees" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брамагупта – Servisch" lang="sr" hreflang="sr" data-title="Брамагупта" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Zweeds" lang="sv" hreflang="sv" data-title="Brahmagupta" data-language-autonym="Svenska" data-language-local-name="Zweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Swahili" lang="sw" hreflang="sw" data-title="Brahmagupta" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%BF%E0%AE%B0%E0%AE%AE%E0%AF%8D%E0%AE%AE%E0%AE%95%E0%AF%81%E0%AE%AA%E0%AF%8D%E0%AE%A4%E0%AE%B0%E0%AF%8D" title="பிரம்மகுப்தர் – Tamil" lang="ta" hreflang="ta" data-title="பிரம்மகுப்தர்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tcy mw-list-item"><a href="https://tcy.wikipedia.org/wiki/%E0%B2%AC%E0%B3%8D%E0%B2%B0%E0%B2%B9%E0%B3%8D%E0%B2%AE%E0%B2%97%E0%B3%81%E0%B2%AA%E0%B3%8D%E0%B2%A4" title="ಬ್ರಹ್ಮಗುಪ್ತ – Tulu" lang="tcy" hreflang="tcy" data-title="ಬ್ರಹ್ಮಗುಪ್ತ" data-language-autonym="ತುಳು" data-language-local-name="Tulu" class="interlanguage-link-target"><span>ತುಳು</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AC%E0%B1%8D%E0%B0%B0%E0%B0%B9%E0%B1%8D%E0%B0%AE%E0%B0%97%E0%B1%81%E0%B0%AA%E0%B1%8D%E0%B0%A4%E0%B1%81%E0%B0%A1%E0%B1%81" title="బ్రహ్మగుప్తుడు – Telugu" lang="te" hreflang="te" data-title="బ్రహ్మగుప్తుడు" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D2%B3%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Браҳмагупта – Tadzjieks" lang="tg" hreflang="tg" data-title="Браҳмагупта" data-language-autonym="Тоҷикӣ" data-language-local-name="Tadzjieks" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Turks" lang="tr" hreflang="tr" data-title="Brahmagupta" data-language-autonym="Türkçe" data-language-local-name="Turks" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Tataars" lang="tt" hreflang="tt" data-title="Brahmagupta" data-language-autonym="Татарча / tatarça" data-language-local-name="Tataars" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tyv mw-list-item"><a href="https://tyv.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта – Toevaans" lang="tyv" hreflang="tyv" data-title="Брахмагупта" data-language-autonym="Тыва дыл" data-language-local-name="Toevaans" class="interlanguage-link-target"><span>Тыва дыл</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брамагупта – Oekraïens" lang="uk" hreflang="uk" data-title="Брамагупта" data-language-autonym="Українська" data-language-local-name="Oekraïens" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%D8%B1%DB%81%D9%85%D8%A7_%DA%AF%D9%BE%D8%AA%D8%A7" title="برہما گپتا – Urdu" lang="ur" hreflang="ur" data-title="برہما گپتا" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Braxmagupta" title="Braxmagupta – Oezbeeks" lang="uz" hreflang="uz" data-title="Braxmagupta" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Vietnamees" lang="vi" hreflang="vi" data-title="Brahmagupta" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Waray" lang="war" hreflang="war" data-title="Brahmagupta" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%A9%86%E7%BE%85%E6%91%A9%E7%AC%88%E5%A4%9A" title="婆羅摩笈多 – Wuyu" lang="wuu" hreflang="wuu" data-title="婆羅摩笈多" data-language-autonym="吴语" data-language-local-name="Wuyu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%91%D7%A8%D7%90%D7%94%D7%9E%D7%90%D7%92%D7%95%D7%A4%D7%98%D7%90" title="בראהמאגופטא – Jiddisch" lang="yi" hreflang="yi" data-title="בראהמאגופטא" data-language-autonym="ייִדיש" data-language-local-name="Jiddisch" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A9%86%E7%BE%85%E6%91%A9%E7%AC%88%E5%A4%9A" title="婆羅摩笈多 – Chinees" lang="zh" hreflang="zh" data-title="婆羅摩笈多" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Minnanyu" lang="nan" hreflang="nan" data-title="Brahmagupta" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnanyu" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%A9%86%E7%BE%85%E6%91%A9%E7%AC%88%E5%A4%9A" title="婆羅摩笈多 – Kantonees" lang="yue" hreflang="yue" data-title="婆羅摩笈多" data-language-autonym="粵語" data-language-local-name="Kantonees" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q202943#sitelinks-wikipedia" title="Taalkoppelingen bewerken" class="wbc-editpage">Koppelingen bewerken</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Naamruimten"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Brahmagupta" title="Inhoudspagina bekijken [c]" accesskey="c"><span>Artikel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Overleg:Brahmagupta" rel="discussion" title="Overleg over deze pagina [t]" accesskey="t"><span>Overleg</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Taalvariant wijzigen" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Nederlands</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Weergaven"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Brahmagupta"><span>Lezen</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Brahmagupta&veaction=edit" title="Deze pagina bewerken [v]" accesskey="v"><span>Bewerken</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Brahmagupta&action=edit" title="Broncode van deze pagina bewerken [e]" accesskey="e"><span>Brontekst bewerken</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Brahmagupta&action=history" title="Eerdere versies van deze pagina [h]" accesskey="h"><span>Geschiedenis weergeven</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Paginahulpmiddelen"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Hulpmiddelen" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Hulpmiddelen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Hulpmiddelen</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">verbergen</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Meer opties" > <div class="vector-menu-heading"> Handelingen </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Brahmagupta"><span>Lezen</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Brahmagupta&veaction=edit" title="Deze pagina bewerken [v]" accesskey="v"><span>Bewerken</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Brahmagupta&action=edit" title="Broncode van deze pagina bewerken [e]" accesskey="e"><span>Brontekst bewerken</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Brahmagupta&action=history"><span>Geschiedenis weergeven</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Algemeen </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciaal:VerwijzingenNaarHier/Brahmagupta" title="Lijst met alle pagina's die naar deze pagina verwijzen [j]" accesskey="j"><span>Links naar deze pagina</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciaal:RecenteWijzigingenGelinkt/Brahmagupta" rel="nofollow" title="Recente wijzigingen in pagina's waar deze pagina naar verwijst [k]" accesskey="k"><span>Gerelateerde wijzigingen</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=nl" title="Bestanden uploaden [u]" accesskey="u"><span>Bestand uploaden</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speciaal:SpecialePaginas" title="Lijst met alle speciale pagina's [q]" accesskey="q"><span>Speciale pagina's</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Brahmagupta&oldid=66629841" title="Permanente koppeling naar deze versie van deze pagina"><span>Permanente koppeling</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Brahmagupta&action=info" title="Meer informatie over deze pagina"><span>Paginagegevens</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speciaal:Citeren&page=Brahmagupta&id=66629841&wpFormIdentifier=titleform" title="Informatie over hoe u deze pagina kunt citeren"><span>Deze pagina citeren</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciaal:UrlShortener&url=https%3A%2F%2Fnl.wikipedia.org%2Fwiki%2FBrahmagupta"><span>Verkorte URL verkrijgen</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciaal:QrCode&url=https%3A%2F%2Fnl.wikipedia.org%2Fwiki%2FBrahmagupta"><span>QR-code downloaden</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Afdrukken/exporteren </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speciaal:Boek&bookcmd=book_creator&referer=Brahmagupta"><span>Boek aanmaken</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciaal:DownloadAsPdf&page=Brahmagupta&action=show-download-screen"><span>Downloaden als PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Brahmagupta&printable=yes" title="Printvriendelijke versie van deze pagina [p]" accesskey="p"><span>Afdrukversie</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In andere projecten </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Brahmagupta" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q202943" title="Koppeling naar item in verbonden gegevensrepository [g]" accesskey="g"><span>Wikidata-item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Paginahulpmiddelen"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Uiterlijk"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Uiterlijk</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">verbergen</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Uit Wikipedia, de vrije encyclopedie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nl" dir="ltr"><p><b>Brahmagupta</b>, <span lang="hi" style="font-style:normal;" title="Hindi">ब्रह्मगुप्त</span>, Bhillamala, het huidige <a href="/wiki/Bhinmal" title="Bhinmal">Bhinmal</a> <a href="/wiki/598" title="598">598</a> – <a href="/wiki/668" title="668">668</a>, was een <a href="/wiki/Indiase_wiskunde" title="Indiase wiskunde">Indiase wiskundige</a> en <a href="/wiki/Astronomie" title="Astronomie">astronoom</a>. Hij wordt gezien als de bedenker van het getal <a href="/wiki/0_(getal)" title="0 (getal)">nul</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Leven">Leven</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=1" title="Bewerk dit kopje: Leven" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=1" title="De broncode bewerken van de sectie: Leven"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Brahmagupta leefde eerst in Bhillamala in het noordwesten van India in het <a href="/wiki/Harsha_(keizer)" title="Harsha (keizer)">Harsha</a>-rijk. Daarom wordt hij ook vaak <i>Bhillamalacarya</i>, de leraar uit Bhillamala, genoemd. Later was hij het hoofd van het sterrenkundig observatorium in <a href="/wiki/Ujjain_(stad)" title="Ujjain (stad)">Ujjain</a> in <a href="/wiki/Malwa" title="Malwa">Malwa</a>. Daar schreef hij een boek over wiskunde en astronomie, de <i><a href="/wiki/Brahmasphuta-siddhanta" title="Brahmasphuta-siddhanta">Brahmasphuta-siddhanta</a></i> in <a href="/wiki/628" title="628">628</a>, en een praktisch werk <i>Khandakhadyaka</i> in 665. Van deze twee boeken is de <i>Brahmasphuta-siddhanta</i>, Gecorrigeerd werk van Brahma, ongetwijfeld de bekendste. </p> <div class="mw-heading mw-heading2"><h2 id="Wiskunde">Wiskunde</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=2" title="Bewerk dit kopje: Wiskunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=2" title="De broncode bewerken van de sectie: Wiskunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Het_getal_nul">Het getal nul</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=3" title="Bewerk dit kopje: Het getal nul" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=3" title="De broncode bewerken van de sectie: Het getal nul"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Brahmagupta gebruikte een belangrijk begrip in de wiskunde, namelijk het getal <a href="/wiki/0_(getal)" title="0 (getal)">nul</a>. De <i>Brahmasphuta-siddhanta</i> is de oudst bekende tekst die nul als een echt <a href="/wiki/Getal_(wiskunde)" title="Getal (wiskunde)">getal</a> beschouwt, dus niet als een plaatsvervangend cijfer dat een ander getal representeert, zoals de <a href="/wiki/Babyloni%C3%AB" title="Babylonië">Babyloniërs</a>, of als een symbool dat een 'gebrek aan een hoeveelheid' uitdrukt, zoals <a href="/wiki/Claudius_Ptolemaeus" title="Claudius Ptolemaeus">Ptolemaeus</a> en de <a href="/wiki/Oude_Rome" title="Oude Rome">Romeinen</a> deden. </p><p>In hoofdstuk 18 van de <i>Brahmasphuta Siddhanta</i> beschrijft Brahmagupta rekenkundige <a href="/wiki/Operatie_(wiskunde)" title="Operatie (wiskunde)">bewerkingen</a> op <a href="/wiki/Negatief_getal" title="Negatief getal">negatieve getallen</a>, als eerste <a href="/wiki/Optellen" title="Optellen">optellen</a> en <a href="/wiki/Aftrekken_(wiskunde)" title="Aftrekken (wiskunde)">aftrekken</a>: </p> <div class="hatnote" style="margin-bottom:0.5em; padding:0.5em 0 0.5em 1.6em; font-size:95%;" role="note"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/15px-1rightarrow_blue.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/23px-1rightarrow_blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/30px-1rightarrow_blue.svg.png 2x" data-file-width="480" data-file-height="480" /></span></span> <i>Zie <a href="/wiki/Brahmasphuta-siddhanta" title="Brahmasphuta-siddhanta">Brahmasphuta-siddhanta</a> voor het hoofdartikel over dit onderwerp.</i></div> <blockquote><p>18.30. De <a href="/wiki/Optellen" title="Optellen">som</a> van twee positieve getallen is positief, de som van twee negatieve getallen negatief; de som van een positief en een negatief getal is hun verschil; als zij gelijk zijn is de som nul. De som van een negatief getal en nul is negatief, die van een positief getal en nul positief, de som van twee nullen is nul. <br /> </p><p>[...] <br /> </p><p> 18.32. Een negatief getal minus nul is negatief, een positief getal minus nul is positief; nul minus nul is nul; Wanneer men een positief getal aftrekt van een negatief getal of een negatief getal van een positief getal, dan moet het worden opgeteld.</p></blockquote> <p>Hij schrijft daarna over <a href="/wiki/Vermenigvuldigen" title="Vermenigvuldigen">vermenigvuldigen</a>: </p> <blockquote><p>18.33. Het product van een negatief en een positief getal is een negatief getal, het product van twee negatieve getallen is positief, en het product van twee positieve getallen is positief.</p></blockquote> <p>Brahmagupta poneert regels voor het <a href="/wiki/Rekenkunde" class="mw-redirect" title="Rekenkunde">rekenkundige</a> gebruik van het getal 0 en van <a href="/wiki/Negatief_getal" title="Negatief getal">negatieve getallen</a>. Zijn regels zijn nagenoeg gelijk aan de moderne regels. Het belangrijke verschil zit in het definiëren van <a href="/wiki/Delen_door_nul" title="Delen door nul">delen door nul</a>. In de moderne rekenkunde wordt dit niet gedefinieerd. Brahmagupta deed dit wel en stelde dat nul gedeeld door nul gelijk is aan nul en hij liet zich niet uit over de vraag of <i>a</i>/0 voor <i>a</i>≠0 gedefinieerd is. </p> <blockquote><p>18.34. Een positief getal gedeeld door een positief getal of een negatief getal gedeeld door een negatief getal is positief; een <b>nul gedeeld door nul is nul</b>; een positief getal gedeeld door een negatief getal is negatief; een negatief getal gedeeld door een positief getal is negatief.<br /> 18.35. Een negatief of een positief getal gedeeld door nul heeft deze nul als deler; nul gedeeld door een negatief of een positief getal heeft dit negatieve en positieve getal als een deler. Het <a href="/wiki/Kwadraat" title="Kwadraat">kwadraat</a> van een negatief of positief getal is positief; Het kwadraat van nul is nul. Dat waarvan het kwadraat het kwadraat is is, is de <a href="/wiki/Vierkantswortel" title="Vierkantswortel">vierkantswortel</a>.</p></blockquote> <div class="mw-heading mw-heading3"><h3 id="Vergelijkingen">Vergelijkingen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=4" title="Bewerk dit kopje: Vergelijkingen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=4" title="De broncode bewerken van de sectie: Vergelijkingen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ruim vier hoofdstukken van <i>Brahmasphuta-siddhanta</i> zijn volledig gewijd aan wiskunde, terwijl het twaalfde hoofdstuk, <i>Ganita</i>, <a href="/wiki/Rekenkundige_rij" title="Rekenkundige rij">rekenkundige rijen</a> en <a href="/wiki/Meetkunde" title="Meetkunde">meetkunde</a> behandelt. Het achttiende hoofdstuk, de <i>Kuttaka</i>, wordt in verband gebracht met de methode van <a href="/wiki/Aryabhata" title="Aryabhata">Aryabhata</a> voor het oplossen van de <a href="/wiki/Onbepaalde_vergelijking" title="Onbepaalde vergelijking">onbepaalde vergelijking</a> van de vorm ax + by = c. Brahmagupta ontdekte de oplossing voor <a href="/wiki/Kwadratische_vergelijking" class="mw-redirect" title="Kwadratische vergelijking">tweedegraads</a> onbepaalde vergelijkingen (vergelijking in de vorm Nx<sup>2</sup> + 1 = y<sup>2</sup>). </p> <div class="mw-heading mw-heading3"><h3 id="Toepassing_in_de_sterrenkunde">Toepassing in de sterrenkunde</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=5" title="Bewerk dit kopje: Toepassing in de sterrenkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=5" title="De broncode bewerken van de sectie: Toepassing in de sterrenkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Brahmagupta was ook de eerste die <a href="/wiki/Algebra" title="Algebra">algebra</a> gebruikte om astronomische vraagstukken op te lossen. Door de <i>Brahmasphuta-siddhanta</i> kreeg de Arabische wereld kennis van de Indiase wiskunde en astronomie. De sterrenkundige <a href="/wiki/Kankah" title="Kankah">Kankah</a> gebruikte de <i>Brahmasphuta-siddhanta</i> om het <a href="/wiki/Hindoe%C3%AFsme" title="Hindoeïsme">Hindoeïstische</a> systeem van rekenkundige astronomie uit te leggen aan <a href="/wiki/Kalief" title="Kalief">kalief</a> <a href="/wiki/Al-Mansoer_(kalief)" title="Al-Mansoer (kalief)">Al-Mansoer</a> (712-775) van het <a href="/wiki/Abbasiden" class="mw-redirect" title="Abbasiden">Abbasidenrijk</a>. <a href="/wiki/Mohammed_al-Fazari" title="Mohammed al-Fazari">Al-Fazari</a> vertaalde vervolgens, op verzoek van de kalief, de <i>Brahmasphuta-siddhanta</i> in het <a href="/wiki/Arabisch" title="Arabisch">Arabisch</a> onder de titel <i>Sindhind</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Berekening_van_oppervlakken">Berekening van oppervlakken</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=6" title="Bewerk dit kopje: Berekening van oppervlakken" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=6" title="De broncode bewerken van de sectie: Berekening van oppervlakken"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Brahmagupta rekende ook de formule uit om het oppervlak van een <a href="/wiki/Vierhoek#koordenvierhoek" title="Vierhoek">koordenvierhoek</a> te berekenen. Hiervan is de formule van <a href="/wiki/Heron_van_Alexandri%C3%AB" title="Heron van Alexandrië">Heron van Alexandrië</a> afgeleid. Hij trachtte ook een vierkant te maken <a href="/wiki/Kwadratuur_van_de_cirkel" title="Kwadratuur van de cirkel">met exact dezelfde oppervlakte</a> als een gegeven cirkel. Hierbij ging hij ervan uit dat <a href="/wiki/Pi_(wiskunde)" title="Pi (wiskunde)">pi</a> zou <a href="/wiki/Convergentie_(wiskunde)" title="Convergentie (wiskunde)">convergeren</a> naar de <a href="/wiki/Vierkantswortel" title="Vierkantswortel">vierkantswortel</a> van 10. <a rel="nofollow" class="external autonumber" href="https://web.archive.org/web/20070317200330/http://www.joshgott.com/gottliebmath/pi/history.html">[1]</a> </p> <div class="mw-heading mw-heading3"><h3 id="Pi">Pi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=7" title="Bewerk dit kopje: Pi" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=7" title="De broncode bewerken van de sectie: Pi"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In hoofdstuk 12 vers 40 geeft hij een waarde voor <a href="/wiki/Pi_(wiskunde)" title="Pi (wiskunde)">pi</a>. </p> <blockquote><p>12.40. De diameter en het kwadraat van de radius [elk] vermenigvuldigd met 3 zijn [respectievelijk] de praktische omtrek en de oppervlakte van een cirkel. De accurate [waardes] zijn de vierkantswortels van de kwadraten [van de omtrek en de oppervlakte] vermenigvuldigd met tien.</p></blockquote> <p>Brahmagupta gebruikt dus 3 als een "praktische" waarde voor pi, en √10 (3,16227766) als een "accurate" waarde voor pi. </p> <div class="mw-heading mw-heading2"><h2 id="Meetkunde">Meetkunde</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=8" title="Bewerk dit kopje: Meetkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=8" title="De broncode bewerken van de sectie: Meetkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Formule_van_Brahmagupta">Formule van Brahmagupta</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=9" title="Bewerk dit kopje: Formule van Brahmagupta" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=9" title="De broncode bewerken van de sectie: Formule van Brahmagupta"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Brahmaguptas_formula.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Brahmaguptas_formula.svg/260px-Brahmaguptas_formula.svg.png" decoding="async" width="260" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Brahmaguptas_formula.svg/390px-Brahmaguptas_formula.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Brahmaguptas_formula.svg/520px-Brahmaguptas_formula.svg.png 2x" data-file-width="281" data-file-height="276" /></a><figcaption><a href="/wiki/Vierhoek" title="Vierhoek">Vierhoek</a> in een <a href="/wiki/Ingeschreven_cirkel" title="Ingeschreven cirkel">ingeschreven cirkel</a></figcaption></figure> <div class="hatnote" style="margin-bottom:0.5em; padding:0.5em 0 0.5em 1.6em; font-size:95%;" role="note"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/15px-1rightarrow_blue.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/23px-1rightarrow_blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/30px-1rightarrow_blue.svg.png 2x" data-file-width="480" data-file-height="480" /></span></span> <i>Zie <a href="/wiki/Formule_van_Brahmagupta" title="Formule van Brahmagupta">formule van Brahmagupta</a> voor het hoofdartikel over dit onderwerp.</i></div> <p>Brahmagupta's beroemdste resultaat in de meetkunde is zijn <a href="/wiki/Formule_van_Brahmagupta" title="Formule van Brahmagupta">formule</a> voor <a href="/wiki/Koordenvierhoek" title="Koordenvierhoek">koordenvierhoeken</a>. Gegeven de lengtes van de <a href="/wiki/Zijde_(meetkunde)" title="Zijde (meetkunde)">zijden</a> van een <a href="/wiki/Koordenvierhoek" title="Koordenvierhoek">koordenvierhoek</a> gaf Brahmagupta een benadering en een exacte formule voor de oppervlakte van het figuur, </p> <blockquote><p>12,21. De benaderde oppervlakte is het product van de helften van de sommen van de zijden en de tegenoverelkaarliggende zijden van een driehoek en een vierhoek. De nauwkeurige [oppervlakte] is de vierkantswortel van het product van de helften van de sommen van de zijden verminderd met [elke] zijde van de vierhoek.<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></p></blockquote> <p>Dus gegeven de lengten <i>p</i>, <i>q</i>, <i>r</i> en <i>s</i> van een cyclische vierhoek, is de oppervlakte bij benadering gelijk aan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\tfrac {p+r}{2}})({\tfrac {q+s}{2}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mi>p</mi> <mo>+</mo> <mi>r</mi> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mi>q</mi> <mo>+</mo> <mi>s</mi> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\tfrac {p+r}{2}})({\tfrac {q+s}{2}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af81c547b4631ee1ff0023d5587c2e3521243d6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.944ex; height:3.676ex;" alt="{\displaystyle ({\tfrac {p+r}{2}})({\tfrac {q+s}{2}})}"></span> terwijl, als <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t={\tfrac {p+q+r+s}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mi>p</mi> <mo>+</mo> <mi>q</mi> <mo>+</mo> <mi>r</mi> <mo>+</mo> <mi>s</mi> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t={\tfrac {p+q+r+s}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5238fda96ae8ff4cbd3904ec99e73ab9ff29d6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:11.706ex; height:3.676ex;" alt="{\displaystyle t={\tfrac {p+q+r+s}{2}}}"></span>, de exacte oppervlakte gelijk is aan </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {(t-p)(t-q)(t-r)(t-s)}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <mi>s</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {(t-p)(t-q)(t-r)(t-s)}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e404c450b20ca0223f194aed8a4d6be6120e1e5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:29.306ex; height:4.843ex;" alt="{\displaystyle {\sqrt {(t-p)(t-q)(t-r)(t-s)}}.}"></span></dd></dl> <p>Hoewel Brahmagupta niet expliciet stelt dat deze vierhoeken cyclisch zijn, blijkt uit zijn regels dat dit het geval is.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> De <a href="/wiki/Formule_van_Heron" title="Formule van Heron">formule van Heron</a> is een speciaal geval van deze formule en kan worden afgeleid door een van de zijden gelijk te zetten aan nul. </p> <div class="mw-heading mw-heading2"><h2 id="Astronomie">Astronomie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=10" title="Bewerk dit kopje: Astronomie" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=10" title="De broncode bewerken van de sectie: Astronomie"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De <a href="/wiki/Arabieren" title="Arabieren">Arabieren</a> leerden de Indiaanse astronomie uit <i>Brahmasphuta-siddhanta</i>.<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> de beroemde <a href="/wiki/Kalifaat_van_de_Abbasiden" title="Kalifaat van de Abbasiden">Abassijnse</a> kalief <a href="/wiki/Al-Mansoer_(kalief)" title="Al-Mansoer (kalief)">Al-Mansoer</a> (712–775) stichtte <a href="/wiki/Baghdad" class="mw-redirect" title="Baghdad">Baghdad</a>, en maakte deze stad vervolgens tot een centrum van wetenschap. De kalief nodigde in <a href="/wiki/770" title="770">770</a> een geleerde uit <a href="/wiki/Ujjain_(stad)" title="Ujjain (stad)">Ujjain (stad)</a>, <a href="/wiki/Kankah" title="Kankah">Kankah</a> geheten, uit om het Hindoe systeem van rekenkundige astronomie uit te leggen. Kankah deed dit aan de hand van de <i>Brahmasphutasiddhanta</i> blijkbaar tot tevredenheid van de kalief, want op diens verzoek vertaalde <a href="/wiki/Mohammed_al-Fazari" title="Mohammed al-Fazari">Mohammed al-Fazari</a> vervolgens Brahmagupta's werk in het <a href="/wiki/Arabische_taal" class="mw-redirect" title="Arabische taal">Arabisch</a>. </p><p>In hoofdstuk zeven van de <i>Brahmasphuta-siddhanta</i>, getiteld <i>Wassende maan</i>, weerlegt Brahmagupta het idee, geuit in diverse religieuze geschriften, dat de <a href="/wiki/Maan" title="Maan">maan</a> verder van de <a href="/wiki/Aarde_(planeet)" title="Aarde (planeet)">aarde</a> staat dan de <a href="/wiki/Zon" title="Zon">zon</a>. Hij doet dat door te wijzen op het feit dat de maan verlicht wordt door de zon. </p> <blockquote><p>7.1. Als de maan boven de zon zou staan, hoe wordt dan de wassende en de krimpende maan verklaard? De dichtstbijzijnde helft van de maan zou altijd verlicht zijn.<br /> </p><p>7.2. Op dezelfde manier dat de geziene helft van een pot die in de zon staat helder is, en de ongeziene helft donker, zo geldt dit ook voor [de helderheid] van de maan onder de zon.<br /> </p><p> 7.3. De helderheid neemt toe in de richting van de zon. Aan het eind van de wassende maan is de dichtstbijzijnde helft helder en de verste helft donker. De mate van de opheffing van de 'hoornen' [van de wassende maan] kan worden berekend. [...]<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></p></blockquote> <p>Op basis van zijn conclusie dat de maan dichter bij de aarde staat dan bij de zon, legt Brahmagupta uit dat de mate waarin de maan verlicht wordt, afhangt van de relatieve posities van de zon en de maan en dat de mate kan worden berekend uit de grootte van de <a href="/wiki/Hoek_(meetkunde)" title="Hoek (meetkunde)">hoek</a> tussen de zon en de maan.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Verder heeft Brahmagupta in de astronomie belangrijke bijdragen geleverd aan methoden om de positie van de hemellichamen in de tijd te berekenen (<a href="/wiki/Efemeriden" title="Efemeriden">efemeriden</a>), verklaringen voor het wassen en krimpen van hemellichamen en de <a href="/wiki/Conjunctie_(astronomie)" title="Conjunctie (astronomie)">conjunctie</a> van planeten. Ook ontwikkelde hij een methode om <a href="/wiki/Zonsverduistering" title="Zonsverduistering">zons</a> en <a href="/wiki/Maansverduistering" title="Maansverduistering">maansverduisteringen</a> te berekenen.<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> Brahmagupta uitte verder kritiek op de visie van de <a href="/wiki/Purana" class="mw-redirect" title="Purana">purana</a>'s dat de aarde <a href="/wiki/Platte_Aarde" title="Platte Aarde">plat</a> of hol was. Hij nam waar dat aarde en hemel bolvormig waren. </p> <div class="mw-heading mw-heading2"><h2 id="Voetnoten">Voetnoten</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=11" title="Bewerk dit kopje: Voetnoten" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=11" title="De broncode bewerken van de sectie: Voetnoten"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r67679320">.mw-parser-output .taalaanduiding{font-family:sans-serif;font-size:85%;cursor:help;color:var(--color-subtle,#555)}.mw-parser-output .taalaanduiding span{border-bottom:1px dotted var(--color-subtle,#555)}</style><span class="taalaanduiding" title="Taal: Engels">(<span>en</span>) </span> <span style="font-variant:small-caps;">Kim Plofker</span>, 2007, citaat hoofdstuk 12</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r67679320"><span class="taalaanduiding" title="Taal: Engels">(<span>en</span>) </span> <span style="font-variant:small-caps;">Kim Plofker</span>, 2007, pag 424, Brahmagupta stelt niet expliciet dat hij figuren iningeschreven cirkels bespreekt, maar dit wordt geïmpliceerd door deze regels voor de berekening van hun omtrek</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130702204751/http://www-groups.dcs.st-and.ac.uk/~history/Projects/Pearce/Chapters/Ch8_3.html">Brahmagupta, en zijn invloed op de Arabieren</a>. Retrieved 23 December 2007.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><span class="citation" id="CITEREFPlofker_420"><span style="font-variant:small-caps;">Plofker, Kim</span>. <cite><i>The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook</i></cite>, pp. 420.</span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><span style="font-variant:small-caps;">Plofker</span>, 2007, blz 419-20, "Brahmagupta bespreekt de verlichting van de maan door de zon, waarbij het idee weerlegt dat in oudere geschriften wordt beschreven: namelijk, dat de maan verder van de aarde staat dan de zon. In feite, zoals hij uitlegt, staat de maan dichterbij omdat de grootte van het verlichte gedeelte van de maan afhangt van de relatieve posities van de maan en de zon; dit kan worden berekend door gebruik te maken van grootte van de <a href="/wiki/Hoek_(meetkunde)" title="Hoek (meetkunde)">hoek</a> α tussen de zon en de maan.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><span style="font-variant:small-caps;">Dick Teresi</span>, <i>Lost Discoveries: The Ancient Roots of Modern Science</i>, Simon and Schuster, 2002, blz. 135, <a href="/wiki/Speciaal:Boekbronnen/074324379X" class="internal mw-magiclink-isbn">ISBN 0-7432-4379-X</a></span> </li> </ol></div></div> <style data-mw-deduplicate="TemplateStyles:r67837862">.mw-parser-output .navigatie{position:relative;clear:both;overflow:auto;margin:1em auto -0.5em;padding:2px;background-color:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);text-align:center;font-size:87%}.mw-parser-output .navigatie-bewerken{margin-left:0.5em}.mw-parser-output .navigatie-bewerken .mw-ui-icon::before{background-size:0.9em}.mw-parser-output .navigatie-afb-links,.mw-parser-output .navigatie-afb-rechts{position:absolute}.mw-parser-output .navigatie-afb-rechts{right:2px}.mw-parser-output .navigatie-afb-groot{float:right;padding-left:0.5em}.mw-parser-output .navigatie-titel{background-color:#ddeef8;padding:2px 5.5em;font-weight:bold}.mw-parser-output .navigatie-inhoud{padding:0.5em}.mw-parser-output .navigatie-inhoud p:first-child{margin:0}.mw-parser-output .navigatie div[style*="background-color"],.mw-parser-output .navigatie div[style*="background"]{color:inherit}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navigatie-titel{background-color:var(--background-color-interactive,#eaecf0)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navigatie-titel{background-color:var(--background-color-interactive,#eaecf0)!important}}</style><div class="navigatie mw-collapsible mw-collapsed" role="navigation" aria-labelledby="Bibliografische informatie" data-collapsetext="Inklappen" data-expandtext="Uitklappen"><div id="Bibliografische_informatie" class="navigatie-titel"><a href="/wiki/Wikipedia:Bibliografische_informatie" title="Wikipedia:Bibliografische informatie">Bibliografische informatie</a></div><div class="navigatie-inhoud mw-collapsible-content plainlist ta-left"><ul style="column-width:36em"><li><b><a href="/wiki/Biblioteca_Nacional_de_Espa%C3%B1a" title="Biblioteca Nacional de España">Biblioteca Nacional de España</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX1211622">XX1211622</a></span></li><li><b><a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">Bibliothèque nationale de France</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12982384t">cb12982384t</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb12982384t">(data)</a></span></li><li><b><a href="/wiki/Cat%C3%A0leg_d%27autoritats_de_noms_i_t%C3%ADtols_de_Catalunya" title="Catàleg d'autoritats de noms i títols de Catalunya">Catàleg d'autoritats de noms i títols de Catalunya</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058508864306706">981058508864306706</a></span></li><li><b><a href="/wiki/CiNii" title="CiNii">CiNii</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA16111474?l=en">DA16111474</a></span></li><li><b><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">Gemeinsame Normdatei</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/120322420">120322420</a></span></li><li><b><a href="/wiki/International_Standard_Name_Identifier" title="International Standard Name Identifier">International Standard Name Identifier</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="http://isni.org/isni/0000000062992448">0000 0000 6299 2448</a></span></li><li><b><a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">Library of Congress Control Number</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/names/n87151821">n87151821</a></span></li><li><b><a href="/wiki/Nationale_bibliotheek_van_Australi%C3%AB" title="Nationale bibliotheek van Australië">Nationale bibliotheek van Australië</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35725455">35725455</a></span></li><li><b><a href="/wiki/Nationale_Bibliotheek_van_Isra%C3%ABl" title="Nationale Bibliotheek van Israël">Nationale Bibliotheek van Israël</a>:</b> <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=987007274771605171">987007274771605171</a></span></li><li><b><a href="https://www.wikidata.org/wiki/Property:P1006" class="extiw" title="d:Property:P1006">Nederlandse Thesaurus van Auteursnamen</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p072897678">072897678</a></span></li><li><b><a href="/wiki/R%C3%89RO" title="RÉRO">Réseau des bibliothèques de Suisse occidentale</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="http://data.rero.ch/02-A010056612">02-A010056612</a></span></li><li><b><a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">Système universitaire de documentation</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/11215591X">11215591X</a></span></li><li><b><a href="/wiki/Trove" title="Trove">Trove</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/1059630">1059630</a></span></li><li><b><a href="/wiki/Virtual_International_Authority_File" title="Virtual International Authority File">Virtual International Authority File</a>:</b> <span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/39509380">39509380</a></span></li><li><b></b> <b><a href="/wiki/WorldCat" title="WorldCat">WorldCat</a></b> (via VIAF): <a rel="nofollow" class="external text" href="https://www.worldcat.org/identities/containsVIAFID/39509380">39509380</a></li></ul></div></div> <div class="mw-heading mw-heading2"><h2 id="Literatuur">Literatuur</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=12" title="Bewerk dit kopje: Literatuur" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=12" title="De broncode bewerken van de sectie: Literatuur"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation" id="CITEREFPlofker2007"><span style="font-variant:small-caps;">Plofker, Kim</span> (2007). <cite><i><a rel="nofollow" class="external text" href="https://archive.org/details/mathematicsofegy0000unse">The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook</a></i></cite>. Princeton University Press, "Mathematics in India". <span class="ISBN"><a href="/wiki/Speciaal:Boekbronnen/9780691114859" title="Speciaal:Boekbronnen/9780691114859">ISBN 9780691114859</a></span>.</span></li> <li><span class="citation" id="CITEREFBoyer1991"><span style="font-variant:small-caps;"><a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer"> Boyer, Carl B.</a></span> (1991). <cite><i><a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema00boye">A History of Mathematics</a></i></cite>, Second Edition. John Wiley & Sons, Inc. <span class="ISBN"><a href="/wiki/Speciaal:Boekbronnen/0471543977" title="Speciaal:Boekbronnen/0471543977">ISBN 0471543977</a></span>.</span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Websites">Websites</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=13" title="Bewerk dit kopje: Websites" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=13" title="De broncode bewerken van de sectie: Websites"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.cut-the-knot.org/Curriculum/Geometry/Brahmagupta.shtml">Brahmagupta's theorie</a></li> <li><a rel="nofollow" class="external text" href="http://www.cut-the-knot.org/Curriculum/Geometry/Brahmagupta2.shtml">Brahmagupta's theorie II</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20180825043927/https://www.cut-the-knot.org/pythagoras/herons.shtml#Brahmagupta">Brahmagupta's formule</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Overgenomen van "<a dir="ltr" href="https://nl.wikipedia.org/w/index.php?title=Brahmagupta&oldid=66629841">https://nl.wikipedia.org/w/index.php?title=Brahmagupta&oldid=66629841</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categorie:Alles" title="Categorie:Alles">Categorieën</a>: <ul><li><a href="/wiki/Categorie:Indiaas_astronoom" title="Categorie:Indiaas astronoom">Indiaas astronoom</a></li><li><a href="/wiki/Categorie:Indiaas_wiskundige" title="Categorie:Indiaas wiskundige">Indiaas wiskundige</a></li><li><a href="/wiki/Categorie:Geschiedenis_van_Madhya_Pradesh" title="Categorie:Geschiedenis van Madhya Pradesh">Geschiedenis van Madhya Pradesh</a></li><li><a href="/wiki/Categorie:Getaltheoreticus" title="Categorie:Getaltheoreticus">Getaltheoreticus</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Verborgen categorie: <ul><li><a href="/wiki/Categorie:Wikipedia:Pagina%27s_die_ISBN_magische_links_gebruiken" title="Categorie:Wikipedia:Pagina's die ISBN magische links gebruiken">Wikipedia:Pagina's die ISBN magische links gebruiken</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Deze pagina is voor het laatst bewerkt op 23 dec 2023 om 01:44.</li> <li id="footer-info-copyright">De tekst is beschikbaar onder de licentie <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.nl">Creative Commons Naamsvermelding/Gelijk delen</a>, er kunnen aanvullende voorwaarden van toepassing zijn. Zie de <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use/nl">gebruiksvoorwaarden</a> voor meer informatie.<br /> Wikipedia® is een geregistreerd handelsmerk van de <a rel="nofollow" class="external text" href="https://www.wikimediafoundation.org">Wikimedia Foundation, Inc.</a>, een organisatie zonder winstoogmerk.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacybeleid</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia">Over Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Algemeen_voorbehoud">Disclaimers</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Gedragscode</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Ontwikkelaars</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/nl.wikipedia.org">Statistieken</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookieverklaring</a></li> <li id="footer-places-mobileview"><a href="//nl.m.wikipedia.org/w/index.php?title=Brahmagupta&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobiele weergave</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-f69cdc8f6-2ms4s","wgBackendResponseTime":173,"wgPageParseReport":{"limitreport":{"cputime":"0.236","walltime":"0.365","ppvisitednodes":{"value":1726,"limit":1000000},"postexpandincludesize":{"value":10126,"limit":2097152},"templateargumentsize":{"value":1296,"limit":2097152},"expansiondepth":{"value":11,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":5705,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 259.466 1 -total"," 56.20% 145.826 1 Sjabloon:Lang"," 17.02% 44.166 1 Sjabloon:Bibliografische_informatie"," 15.53% 40.287 1 Sjabloon:References"," 12.15% 31.534 3 Sjabloon:Citeer_boek"," 4.51% 11.694 2 Sjabloon:En"," 2.97% 7.698 1 Sjabloon:Taalaanduiding"," 2.16% 5.608 3 Sjabloon:Sfnref"," 2.08% 5.392 2 Sjabloon:Zie_hoofdartikel"," 1.64% 4.254 7 Sjabloon:Aut"]},"scribunto":{"limitreport-timeusage":{"value":"0.135","limit":"10.000"},"limitreport-memusage":{"value":9605948,"limit":52428800},"limitreport-logs":"hi\n"},"cachereport":{"origin":"mw-web.eqiad.main-869fdccf5d-7fs2w","timestamp":"20241118113739","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Brahmagupta","url":"https:\/\/nl.wikipedia.org\/wiki\/Brahmagupta","sameAs":"http:\/\/www.wikidata.org\/entity\/Q202943","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q202943","author":{"@type":"Organization","name":"Bijdragers aan Wikimedia-projecten"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2007-02-04T17:16:43Z","dateModified":"2023-12-23T00:44:50Z","headline":"Indiaas wiskundige en astronoom (598-670)"}</script> </body> </html>