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vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Mga nilalaman</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">itago</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">Simula</div> </a> </li> <li id="toc-Buhay_at_karera" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Buhay_at_karera"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Buhay at karera</span> </div> </a> <ul id="toc-Buhay_at_karera-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mga_gawa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mga_gawa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Mga gawa</span> </div> </a> <ul id="toc-Mga_gawa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pagtanggap" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pagtanggap"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Pagtanggap</span> </div> </a> <ul id="toc-Pagtanggap-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mathematika" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mathematika"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Mathematika</span> </div> </a> <button aria-controls="toc-Mathematika-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>Ipakita/Itago ang subseksyon na Mathematika</span> </button> <ul id="toc-Mathematika-sublist" class="vector-toc-list"> <li id="toc-Alhebra" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Alhebra"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Alhebra</span> </div> </a> <ul id="toc-Alhebra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aritmetika" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aritmetika"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Aritmetika</span> </div> </a> <ul id="toc-Aritmetika-sublist" class="vector-toc-list"> <li id="toc-Sero" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Sero"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Sero</span> </div> </a> <ul id="toc-Sero-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Heometriya" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriya"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Heometriya</span> </div> </a> <ul id="toc-Heometriya-sublist" class="vector-toc-list"> <li id="toc-Pormula_ni_Brahmagupta" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Pormula_ni_Brahmagupta"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.1</span> <span>Pormula ni Brahmagupta</span> </div> </a> <ul id="toc-Pormula_ni_Brahmagupta-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mga_tatsulok" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mga_tatsulok"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Mga tatsulok</span> </div> </a> <ul id="toc-Mga_tatsulok-sublist" class="vector-toc-list"> <li id="toc-Teorama_ni_Brahmagupta" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Teorama_ni_Brahmagupta"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.1</span> <span>Teorama ni Brahmagupta</span> </div> </a> <ul id="toc-Teorama_ni_Brahmagupta-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pi" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Pi"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.2</span> <span>Pi</span> </div> </a> <ul id="toc-Pi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Maagang_konsepto_ng_grabidad" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Maagang_konsepto_ng_grabidad"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Maagang konsepto ng grabidad</span> </div> </a> <ul id="toc-Maagang_konsepto_ng_grabidad-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Astronomiya" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Astronomiya"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Astronomiya</span> </div> </a> <ul id="toc-Astronomiya-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mga_sanggunian" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mga_sanggunian"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Mga sanggunian</span> </div> </a> <button aria-controls="toc-Mga_sanggunian-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>Ipakita/Itago ang subseksyon na Mga sanggunian</span> </button> <ul id="toc-Mga_sanggunian-sublist" class="vector-toc-list"> <li id="toc-Mga_pananda" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mga_pananda"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Mga pananda</span> </div> </a> <ul id="toc-Mga_pananda-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mga_pagsipi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mga_pagsipi"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Mga pagsipi</span> </div> </a> <ul id="toc-Mga_pagsipi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliograpiya" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliograpiya"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Bibliograpiya</span> </div> </a> <ul id="toc-Bibliograpiya-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Karagdagang_pagbabasa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Karagdagang_pagbabasa"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Karagdagang pagbabasa</span> </div> </a> <ul id="toc-Karagdagang_pagbabasa-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="Mga nilalaman" 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="Itago/Ipakita ang talaan ng mga nilalaman" > <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">Itago/Ipakita ang talaan ng mga nilalaman</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="Pumunta sa isang artikulo na nakasulat sa ibang wika. Mayroon ito sa 113 (na) wika" > <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-113" 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">113 wika</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 – Alemannic" lang="gsw" hreflang="gsw" data-title="Brahmagupta" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" 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 – Aragonese" lang="an" hreflang="an" data-title="Brahmagupta" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%B1%D8%A7%D9%87%D9%85%D8%A7%D8%BA%D9%88%D8%A8%D8%AA%D8%A7" title="براهماغوبتا – Arabic" lang="ar" hreflang="ar" data-title="براهماغوبتا" data-language-autonym="العربية" data-language-local-name="Arabic" 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 – Egyptian Arabic" lang="arz" hreflang="arz" data-title="براهماجوبتا" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" 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 – Assamese" lang="as" hreflang="as" data-title="ব্ৰহ্মগুপ্ত" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Asturian" lang="ast" hreflang="ast" data-title="Brahmagupta" data-language-autonym="Asturianu" data-language-local-name="Asturian" 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 – Azerbaijani" lang="az" hreflang="az" data-title="Brahmaqupta" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%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 – Bashkir" lang="ba" hreflang="ba" data-title="Брахмагупта" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" 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 – Bavarian" lang="bar" hreflang="bar" data-title="Brahmagupta" data-language-autonym="Boarisch" data-language-local-name="Bavarian" 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 – Samogitian" lang="sgs" hreflang="sgs" data-title="Brahmagupta" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" 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 – Belarusian" lang="be" hreflang="be" data-title="Брахмагупта" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%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 – Bulgarian" lang="bg" hreflang="bg" data-title="Брахмагупта" data-language-autonym="Български" data-language-local-name="Bulgarian" 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 – Bangla" lang="bn" hreflang="bn" data-title="ব্রহ্মগুপ্ত" data-language-autonym="বাংলা" data-language-local-name="Bangla" 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 – Breton" lang="br" hreflang="br" data-title="Brahmagupta" data-language-autonym="Brezhoneg" data-language-local-name="Breton" 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 – Bosnian" lang="bs" hreflang="bs" data-title="Brahmagupta" data-language-autonym="Bosanski" data-language-local-name="Bosnian" 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 – Catalan" lang="ca" hreflang="ca" data-title="Brahmagupta" data-language-autonym="Català" data-language-local-name="Catalan" 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 – Central Kurdish" lang="ckb" hreflang="ckb" data-title="براھماگوپتا" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" 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 – Corsican" lang="co" hreflang="co" data-title="Brahmagupta" data-language-autonym="Corsu" data-language-local-name="Corsican" 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 – Czech" lang="cs" hreflang="cs" data-title="Brahmagupta" data-language-autonym="Čeština" data-language-local-name="Czech" 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 – Danish" lang="da" hreflang="da" data-title="Brahmagupta" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – German" lang="de" hreflang="de" data-title="Brahmagupta" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%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 – Greek" lang="el" hreflang="el" data-title="Βραχμαγκούπτα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – English" lang="en" hreflang="en" data-title="Brahmagupta" data-language-autonym="English" data-language-local-name="English" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/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 – Spanish" lang="es" hreflang="es" data-title="Brahmagupta" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Estonian" lang="et" hreflang="et" data-title="Brahmagupta" data-language-autonym="Eesti" data-language-local-name="Estonian" 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 – Basque" lang="eu" hreflang="eu" data-title="Brahmagupta" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D8%B1%D9%87%D9%85%D8%A7%DA%AF%D9%88%D9%BE%D8%AA%D8%A7" title="برهماگوپتا – Persian" lang="fa" hreflang="fa" data-title="برهماگوپتا" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Finnish" lang="fi" hreflang="fi" data-title="Brahmagupta" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – French" lang="fr" hreflang="fr" data-title="Brahmagupta" data-language-autonym="Français" data-language-local-name="French" 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 – Galician" lang="gl" hreflang="gl" data-title="Brahmagupta" data-language-autonym="Galego" data-language-local-name="Galician" 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 – Guarani" lang="gn" hreflang="gn" data-title="Brahmagupta" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" 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 – Hebrew" lang="he" hreflang="he" data-title="בראהמגופטה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%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 – Fiji Hindi" lang="hif" hreflang="hif" data-title="Brahmagupta" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji 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 – Croatian" lang="hr" hreflang="hr" data-title="Brahmagupta" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Hungarian" lang="hu" hreflang="hu" data-title="Brahmagupta" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%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 – Armenian" lang="hy" hreflang="hy" data-title="Բրահմագուպտա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" 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 – Indonesian" lang="id" hreflang="id" data-title="Brahmagupta" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-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 – Icelandic" lang="is" hreflang="is" data-title="Brahmagupta" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Italian" lang="it" hreflang="it" data-title="Brahmagupta" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%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 – Japanese" lang="ja" hreflang="ja" data-title="ブラフマグプタ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-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 – Georgian" lang="ka" hreflang="ka" data-title="ბრაჰმაგუფთა" data-language-autonym="ქართული" data-language-local-name="Georgian" 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 – Kazakh" lang="kk" hreflang="kk" data-title="Брахмагупта" data-language-autonym="Қазақша" data-language-local-name="Kazakh" 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 – Korean" lang="ko" hreflang="ko" data-title="브라마굽타" data-language-autonym="한국어" data-language-local-name="Korean" 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 – Kurdish" lang="ku" hreflang="ku" data-title="Brahmagupta" data-language-autonym="Kurdî" data-language-local-name="Kurdish" 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 – Latin" lang="la" hreflang="la" data-title="Brachmacottus" data-language-autonym="Latina" data-language-local-name="Latin" 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 – Luxembourgish" lang="lb" hreflang="lb" data-title="Brahmagupta" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" 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 – Lombard" lang="lmo" hreflang="lmo" data-title="Brahmagupta" data-language-autonym="Lombard" data-language-local-name="Lombard" 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 – Lithuanian" lang="lt" hreflang="lt" data-title="Brahmagupta" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Latvian" lang="lv" hreflang="lv" data-title="Brahmagupta" data-language-autonym="Latviešu" data-language-local-name="Latvian" 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 – Malagasy" lang="mg" hreflang="mg" data-title="Brahmagupta" data-language-autonym="Malagasy" data-language-local-name="Malagasy" 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 – Malay" lang="ms" hreflang="ms" data-title="Brahmagupta" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-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 – Burmese" lang="my" hreflang="my" data-title="ဗြဟ္မာဂုပ္ပတ္တ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" 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 – Low German" lang="nds" hreflang="nds" data-title="Brahmagupta" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" 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 – Nepali" lang="ne" hreflang="ne" data-title="ब्रह्मगुप्त" data-language-autonym="नेपाली" data-language-local-name="Nepali" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Dutch" lang="nl" hreflang="nl" data-title="Brahmagupta" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Brahmagupta" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian 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 – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Brahmagupta" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Occitan" lang="oc" hreflang="oc" data-title="Brahmagupta" data-language-autonym="Occitan" data-language-local-name="Occitan" 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 – Polish" lang="pl" hreflang="pl" data-title="Brahmagupta" data-language-autonym="Polski" data-language-local-name="Polish" 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 – Piedmontese" lang="pms" hreflang="pms" data-title="Brahmagupta" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%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 – Portuguese" lang="pt" hreflang="pt" data-title="Brahmagupta" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Romanian" lang="ro" hreflang="ro" data-title="Brahmagupta" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D1%85%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брахмагупта – Russian" lang="ru" hreflang="ru" data-title="Брахмагупта" data-language-autonym="Русский" data-language-local-name="Russian" 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 – Rusyn" lang="rue" hreflang="rue" data-title="Брагмаґупта" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" 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 – Sanskrit" lang="sa" hreflang="sa" data-title="ब्रह्मगुप्तः" data-language-autonym="संस्कृतम्" data-language-local-name="Sanskrit" 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 – Yakut" lang="sah" hreflang="sah" data-title="Брахмагупта" data-language-autonym="Саха тыла" data-language-local-name="Yakut" 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 – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Bramagupta" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/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 – Slovenian" lang="sl" hreflang="sl" data-title="Brahmagupta" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Albanian" lang="sq" hreflang="sq" data-title="Brahmagupta" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D1%80%D0%B0%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Брамагупта – Serbian" lang="sr" hreflang="sr" data-title="Брамагупта" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Swedish" lang="sv" hreflang="sv" data-title="Brahmagupta" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/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 – Tajik" lang="tg" hreflang="tg" data-title="Браҳмагупта" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" 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 – Turkish" lang="tr" hreflang="tr" data-title="Brahmagupta" data-language-autonym="Türkçe" data-language-local-name="Turkish" 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 – Tatar" lang="tt" hreflang="tt" data-title="Brahmagupta" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" 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 – Tuvinian" lang="tyv" hreflang="tyv" data-title="Брахмагупта" data-language-autonym="Тыва дыл" data-language-local-name="Tuvinian" 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 – Ukrainian" lang="uk" hreflang="uk" data-title="Брамагупта" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%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 – Uzbek" lang="uz" hreflang="uz" data-title="Braxmagupta" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" 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 – Vietnamese" lang="vi" hreflang="vi" data-title="Brahmagupta" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/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 – Wu" lang="wuu" hreflang="wuu" data-title="婆羅摩笈多" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-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 – Yiddish" lang="yi" hreflang="yi" data-title="בראהמאגופטא" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" 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 – Chinese" lang="zh" hreflang="zh" data-title="婆羅摩笈多" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Brahmagupta" title="Brahmagupta – Minnan" lang="nan" hreflang="nan" data-title="Brahmagupta" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%A9%86%E7%BE%85%E6%91%A9%E7%AC%88%E5%A4%9A" title="婆羅摩笈多 – Cantonese" lang="yue" hreflang="yue" data-title="婆羅摩笈多" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q202943#sitelinks-wikipedia" title="Baguhin ang link sa ibang wika" class="wbc-editpage">baguhin ang mga link</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="Namespace"> <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 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class="mw-content-ltr mw-parser-output" lang="tl" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r1971697">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}body.skin-minerva .mw-parser-output .infobox-header,body.skin-minerva .mw-parser-output .infobox-subheader,body.skin-minerva .mw-parser-output .infobox-above,body.skin-minerva .mw-parser-output .infobox-title,body.skin-minerva .mw-parser-output .infobox-image,body.skin-minerva .mw-parser-output .infobox-full-data,body.skin-minerva .mw-parser-output .infobox-below{text-align:center}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn" style="display:inline">Brahmagupta</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/Talaksan:Hindu_astronomer,_19th-century_illustration.jpg" class="mw-file-description" title="Hindu_astronomer,_19th-century_illustration"><img alt="Hindu_astronomer,_19th-century_illustration" src="//upload.wikimedia.org/wikipedia/commons/b/b5/Hindu_astronomer%2C_19th-century_illustration.jpg" decoding="async" width="300" height="454" class="mw-file-element" data-file-width="300" data-file-height="454" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Kapanganakan</th><td class="infobox-data"><abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 598 CE</span><br /><div style="display:inline" class="birthplace">Bhillamala, Gurjaradesa, kaharian ng Chavda <br /> (makabagong-panahong Bhinmal, <a href="/wiki/Rajasthan" title="Rajasthan">Rajasthan</a>, <a href="/wiki/Indya" class="mw-redirect" title="Indya">Indya</a>)</div></td></tr><tr><th scope="row" class="infobox-label">Kamatayan</th><td class="infobox-data"><abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 668 CE</span> (edad c. 69–70)<br /><div style="display:inline" class="deathplace">Ujjain, Imperyong Chalukya <br /> (makabagong-panahong <a href="/wiki/Madhya_Pradesh" title="Madhya Pradesh">Madhya Pradesh</a>, <a href="/wiki/Indya" class="mw-redirect" title="Indya">Indya</a>)</div></td></tr><tr><th scope="row" class="infobox-label">Kilala sa</th><td class="infobox-data"><div class="plainlist"><ul><li>Patakaran para sa pakalkula na may <a href="/wiki/Sero" class="mw-redirect" title="Sero">Sero</a></li><li>Makabagong <a href="/wiki/Sistemang_pamilang" class="mw-redirect" title="Sistemang pamilang">sistemang pamilang</a></li><li>Teorema ni Brahmagupta</li><li>Identidad ni Brahmagupta</li><li>Problema ni Brahmagupta</li><li>Identidad ni Brahmagupta–Fibonacci</li><li>Pormulang interpolasyon ni Brahmagupta</li><li>Pormula ni Brahmagupta</li></ul></div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1971697"><b>Karera sa agham</b></td></tr><tr><th scope="row" class="infobox-label">Larangan</th><td class="infobox-data category"><a href="/wiki/Astronomiya" title="Astronomiya">Astronomiya</a>, <a href="/wiki/Matematika" title="Matematika">matematika</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p>Ang <b>Brahmagupta</b> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 598</span> – <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 668 <a href="/wiki/Common_Era" class="mw-redirect" title="Common Era">CE</a></span>) ay isang <a href="/wiki/Matematiko" title="Matematiko">matematiko</a> at <a href="/wiki/Astronomo" title="Astronomo">astronomo</a> mula sa <a href="/wiki/Indiya" title="Indiya">Indiya</a>. Siya ang may-akda ng dalawang maagang gawa sa <a href="/wiki/Matematika" title="Matematika">matematika</a> at <a href="/wiki/Astronomiya" title="Astronomiya">astronomiya</a>: ang <i>Brāhmasphuṭasiddhānta</i> (BSS, "tama na itinatag ang doktrina ng <a href="/wiki/Brahma" title="Brahma">Brahma</a>", na may petsang 628), isang teoretikal na <a href="/wiki/Sanaysay" title="Sanaysay">sanaysay</a>, at ang <i>Khandakhadyaka</i> ("nakakain sa kagat", na may petsang 665), isang mas praktikal na teksto. </p><p>Noong 628 CE, unang inilarawan ni Brahmagupta ang <a href="/wiki/Grabedad" title="Grabedad">grabidad</a> bilang isang puwersang atraksyon, at ginamit ang terminong "gurutvākarṣaṇam (गुरुत्वाकर्षणम्)" sa <a href="/wiki/Sanskrito" class="mw-redirect" title="Sanskrito">Sanskrito</a> upang ilarawan ito.<sup id="cite_ref-Oxford_1-0" class="reference"><a href="#cite_note-Oxford-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Sen_2-0" class="reference"><a href="#cite_note-Sen-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Binigay din sa kanya ang kredito sa unang malinaw na paglalarawan ng <a href="/wiki/Kwadratikong_pormula" title="Kwadratikong pormula">pormulng kuwadratiko</a> (ang solusyon ng ekwasyong kuwadratiko) sa kanyang pangunahing gawa, ang <i>Brāhma-sphuṭa-siddhānta</i>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Buhay_at_karera">Buhay at karera</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=1" title="Baguhin seksiyon: Buhay at karera" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=1" title="Edit section's source code: Buhay at karera"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si Brahmagupta, ayon sa kanyang sariling pahayag, ay isinilang noong 598 CE. Ipinanganak sa <i>Bhillamāla</i> sa Gurjaradesa<sup id="cite_ref-Sachau2013_3-0" class="reference"><a href="#cite_note-Sachau2013-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> (modernong-panahong Bhinmal sa <a href="/wiki/Rajasthan" title="Rajasthan">Rajasthan</a>, Indiya) sa panahon ng paghahari ng pinuno ng dinastiyang Chavda na si Vyagrahamukha. Anak siya ni Jishnugupta at <a href="/wiki/Hindu" class="mw-redirect" title="Hindu">Hindu</a> ang <a href="/wiki/Relihiyon" title="Relihiyon">relihiyon</a>, partikular, isang Shaivite.<sup id="cite_ref-Bhattacharyya_4-0" class="reference"><a href="#cite_note-Bhattacharyya-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Nanirahan at nagtrabaho siya doon para sa isang magandang bahagi ng kanyang buhay. Tinawag siya ni Prithudaka Svamin, isang komentarista sa kalaunan, bilang <i>Bhillamalacharya</i>, ang guro mula sa Bhillamala.<sup id="cite_ref-FOOTNOTEGupta2008_5-0" class="reference"><a href="#cite_note-FOOTNOTEGupta2008-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Ang Bhillamala ay ang kabisera ng Gurjaradesa, ang pangalawang pinakamalaking kaharian ng Kanlurang Indiya, na binubuo ng timog <a href="/wiki/Rajasthan" title="Rajasthan">Rajasthan</a> at hilagang <a href="/wiki/Gujarat" title="Gujarat">Gujarat</a> sa modernong-panahong Indiya. Ito rin ang sentro ng pag-aaral para sa matematika at astronomiya. Naging astronomo siya ng paaralang <i>Brahmapaksha</i>, isa sa apat na pangunahing paaralan ng astronomiyang Indiyano sa panahong ito. Pinag-aralan niya ang limang tradisyonal na mga <i>Siddhanta</i> sa astronomiya ng Indiya gayundin ang mga gawa ng iba pang mga astronomo kabilang sina Aryabhata I, Latadeva, Pradyumna, Varahamihira, Simha, Srisena, Vijayanandin at Vishnuchandra.<sup id="cite_ref-FOOTNOTEGupta2008_5-1" class="reference"><a href="#cite_note-FOOTNOTEGupta2008-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Noong taong 628, sa edad na 30, binuo niya ang <i>Brāhmasphuṭasiddhānta</i> ("pinahusay na sanaysay ng Brahma") na pinaniniwalaang isang binagong bersyon ng natanggap na <i>Siddhanta</i> ng paaralang <i>Brahmapaksha</i> ng astronomiya. Sinasabi ng mga iskolar na isinama niya ang napakaraming orihinalidad sa kanyang rebisyon, na nagdagdag ng malaking halaga ng bagong materyal. Binubuo ang aklat ng 24 na mga kabanata na may 1008 na mga taludtod sa <i>ārya meter</i>. Ang isang magandang panukala dito ay astronomiya, subalit naglalaman din ito ng mga pangunahing kabanata sa matematika, kabilang ang <a href="/wiki/Alhebra" title="Alhebra">alhebra</a>, <a href="/wiki/Heometriya" title="Heometriya">heometriya</a>, <a href="/wiki/Trigonometriya" title="Trigonometriya">trigonometriya</a> at algoritmiya, na pinaniniwalaang naglalaman ng mga bagong pananaw dahil mismo kay Brahmagupta.<sup id="cite_ref-FOOTNOTEGupta2008_5-2" class="reference"><a href="#cite_note-FOOTNOTEGupta2008-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEBhattacharyya2011_6-0" class="reference"><a href="#cite_note-FOOTNOTEBhattacharyya2011-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEBoseSenSubbarayappa1971_7-0" class="reference"><a href="#cite_note-FOOTNOTEBoseSenSubbarayappa1971-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Nang maglaon, lumipat si Brahmagupta sa Ujjaini, Avanti,<sup id="cite_ref-FOOTNOTEGupta2008_5-3" class="reference"><a href="#cite_note-FOOTNOTEGupta2008-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> isang pangunahing sentro ng astronomiya sa gitnang Indiya. Sa edad na 67, binuo niya ang kanyang susunod na kilalang akda na <i>Khanda-khādyaka</i>, isang praktikal na manwal ng astronomiya ng Indiya sa kategoryang <i>karana</i> na nilalayong gamitin ng mga mag-aaral.<sup id="cite_ref-FOOTNOTEGupta2008_5-4" class="reference"><a href="#cite_note-FOOTNOTEGupta2008-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Namatay si Brahmagupta noong 668 CE, at ipinapalagay na namatay siya sa Ujjain. </p> <div class="mw-heading mw-heading2"><h2 id="Mga_gawa">Mga gawa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=2" title="Baguhin seksiyon: Mga gawa" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=2" title="Edit section's source code: Mga gawa"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Binubuo ni Brahmagupta ang mga sumusunod na sanaysay: </p> <ul><li><i>Brāhmasphuṭasiddhānta</i>,<sup id="cite_ref-:0_8-0" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> binubuo noong 628 CE.</li> <li><i>Khaṇḍakhādyaka</i>,<sup id="cite_ref-:0_8-1" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> binubuo noong 665 CE.</li> <li><i>Grahaṇārkajñāna</i>,<sup id="cite_ref-:0_8-2" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> (na inilarawan sa isang manuskrito)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Pagtanggap">Pagtanggap</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=3" title="Baguhin seksiyon: Pagtanggap" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=3" title="Edit section's source code: Pagtanggap"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang mga pagsulong sa matematika ni Brahmagupta ay isinagawa pa ni Bhāskara II, isang angkan na inapo sa Ujjain, na inilarawan si Brahmagupta bilang <i>ganaka-chakra-chudamani</i> (ang hiyas ng pangkat ng mga matematiko). Nagsulat si Prithudaka Svamin ng mga komentaryo sa parehong kanyang mga gawa, na gumagawa ng mahihirap na talata sa mas simpleng wika at nagdagdag ng mga ilustrasyon. Nagsulat sina Lalla at Bhattotpala noong ika-8 at ika-9 na dantaon ng mga komentaryo sa <i>Khanda-khadyaka</i>.<sup id="cite_ref-FOOTNOTEBhattacharyya2011_6-1" class="reference"><a href="#cite_note-FOOTNOTEBhattacharyya2011-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Patuloy na naisulat ang karagdagang mga komentaryo noong ika-12 dantaon.<sup id="cite_ref-FOOTNOTEGupta2008_5-5" class="reference"><a href="#cite_note-FOOTNOTEGupta2008-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Ilang dekada pagkatapos ng kamatayan ni Brahmagupta, sumailalim ang <a href="/wiki/Sindh" title="Sindh">Sindh</a> sa <a href="/wiki/Kalipato" title="Kalipato">Kalipatong</a> <a href="/wiki/Arabe" class="mw-redirect" title="Arabe">Arabe</a> noong 712 CE. Ipinadala ang mga ekspedisyon sa <i>Gurjaradesa</i> ("<i>Al-Baylaman</i> sa <i>Jurz</i>", ayon sa mga Arabong <a href="/wiki/Historyador" class="mw-redirect" title="Historyador">historyador</a>). Tila nalipol ang kaharian ng Bhillamala subalit tinanggihan ng Ujjain ang mga pag-atake. Tumanggap ang hukuman ni <a href="/wiki/Kalipa" class="mw-redirect" title="Kalipa">Kalipa</a> Al-Mansur (754–775) ng isang embahada mula sa Sindh, kabilang ang isang astrologo na tinatawag na Kanaka, na nagdala (maaaring naisaulo) ng mga astronomikal na teksto, kabilang ang mga gawa mula kay Brahmagupta. Isinalin ang mga teksto ni Brahmagupta sa <a href="/wiki/Wikang_Arabe" title="Wikang Arabe">Arabe</a> ni Muḥammad ibn Ibrāhīm al-Fazārī, isang astronomo sa korte ni Al-Mansur, sa ilalim ng mga pangalang <i>Sindhind</i> at <i>Arakhand</i>. Ang isang agarang resulta ay ang pagkalat ng sistemang desimal na ginamit sa mga teksto. Sumulat ang matematikong si <a href="/wiki/Muhammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB" title="Muhammad ibn Mūsā al-Khwārizmī">Al-Khwarizmi</a> (800–850 CE) ng isang teksto na tinatawag na <i>al-Jam wal-tafriq bi hisal-al-Hind</i> (<a href="/wiki/Pagdaragdag" title="Pagdaragdag">Pagdaragdag</a> at <a href="/wiki/Pagbabawas" title="Pagbabawas">Pagbabawas</a> sa <a href="/wiki/Aritmetika" title="Aritmetika">Aritmetikong</a> Indiyano), na isinalin sa <a href="/wiki/Latin" class="mw-redirect" title="Latin">Latin</a> noong ika-13 danton bilang <i>Algorithmi de numero indorum</i>. Sa pamamagitan ng mga tekstong ito, kumalat sa buong mundo ang sistemang desimal na numero at ang mga algoritmo ni Brahmagupta para sa aritmetika. Nagsulat din si Al-Khwarizmi ng sarili niyang bersyon ng <i>Sindhind</i>, iginuhit ang bersyon ni Al-Fazari at isinasama ang mga elementong <a href="/wiki/Ptolomeo" title="Ptolomeo">Ptolemaiko</a>. Malawakang kumalat ang materyal na astronomiko ng Indiya sa loob ng maraming siglo, kahit na nakapasok sa mga <a href="/wiki/Medyebal" class="mw-redirect" title="Medyebal">medyebal</a> na tekstong Latin.<sup id="cite_ref-FOOTNOTEAvari2013_9-0" class="reference"><a href="#cite_note-FOOTNOTEAvari2013-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-YoungLatham2006_10-0" class="reference"><a href="#cite_note-YoungLatham2006-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-van_Bladel_11-0" class="reference"><a href="#cite_note-van_Bladel-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Tinawag ng mananalaysay ng <a href="/wiki/Agham" title="Agham">agham</a> na si George Sarton si Brahmagupta na "isa sa mga pinakadakilang siyentipiko sa kanyang lahi at pinakadakila sa kanyang panahon."<sup id="cite_ref-FOOTNOTEGupta2008_5-6" class="reference"><a href="#cite_note-FOOTNOTEGupta2008-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematika">Mathematika</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=4" title="Baguhin seksiyon: Mathematika" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=4" title="Edit section's source code: Mathematika"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Alhebra">Alhebra</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=5" title="Baguhin seksiyon: Alhebra" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=5" title="Edit section's source code: Alhebra"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Ibinigay ni Brahmagupta ang solusyon ng pangkalahatang <a href="/wiki/Linyar_na_ekwasyon" title="Linyar na ekwasyon">linyar na ekwasyon</a> sa ika-labingwalong kabanata ng <i>Brahmasphuṭasiddhānta</i>,</p><blockquote><p>Ang pagkakaiba sa pagitan ng <i>rupas</i>, kapag binaligtd at hinati sa pagkakaiba ng [<a href="/wiki/Koepisyente" title="Koepisyente">koepisiyente</a>] ng [mga di-alam], ay ang hindi alam sa <a href="/wiki/Ekwasyon" title="Ekwasyon">ekwasyon</a>. Ang <i>rupas</i> ay [ibawas sa gilid] sa ibaba ng kung saan ang parisukat at ang hindi alam ay dapat ibawas.</p></blockquote><p>na isang solusyon para sa ekwasyong <span class="texhtml"><i>bx</i> + <i>c</i> = <i>dx</i> + <i>e</i></span> kung saan <i>ang rupas</i> ay tumutukoy sa mga di-nagbabagong <span class="texhtml"><i>c</i></span> at <span class="texhtml"><i>e</i></span>. Ang ibinigay na solusyon ay katumbas ng <span class="texhtml"><i>x</i> = <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;"><i>e</i> − <i>c</i></span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;"><i>b</i> − <i>d</i></span></span></span>. Nagbigay pa siya ng dalawang katumbas na solusyon sa pangkalahatang ekwasyong kuwadratiko:</p><blockquote><p>18.44. Bawasan ng gitnang [bilang] ang <a href="/wiki/Pariugat" title="Pariugat">pariugat</a> ng <i>rupas</i> na pinarami ng apat na beses ng parisukat at nadagdagan ng parisukat ng gitnang [bilang]; hatiin ang natitira sa dalawang beses sa parisukat. [Ang resulta ay] ang gitnang [bilang]. 18.45. Anuman ang pariugat ng <i>rupas</i> na pinarami ng parisukat [at] nadagdagan ng parisukat ng kalahati ng hindi alam, nabawasan na sa kalahati ng hindi alam [at] <a href="/wiki/Paghahati" title="Paghahati">hatiin</a> [ang natitira] sa parisukat nito. [Ang resulta ay] hindi alam. </p></blockquote><p>na, ayon sa pagkakabanggit, mga solusyon para sa ekwasyon na <span class="texhtml"><i>ax</i><sup>2</sup> + <i>bx</i> = <i>c</i></span> katumbas ng, </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 x={\frac {\pm {\sqrt {4ac+b^{2}}}-b}{2a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>4</mn> <mi>a</mi> <mi>c</mi> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>−</mo> <mi>b</mi> </mrow> <mrow> <mn>2</mn> <mi>a</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x={\frac {\pm {\sqrt {4ac+b^{2}}}-b}{2a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03d2ad8a48c479728b906394ebbc56d3686b4ef1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.525ex; height:6.176ex;" alt="{\displaystyle x={\frac {\pm {\sqrt {4ac+b^{2}}}-b}{2a}}}"></span></dd></dl> <p>at </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 x={\frac {\pm {\sqrt {ac+{\tfrac {b^{2}}{4}}}}-{\tfrac {b}{2}}}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>a</mi> <mi>c</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>4</mn> </mfrac> </mstyle> </mrow> </msqrt> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>b</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> </mrow> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x={\frac {\pm {\sqrt {ac+{\tfrac {b^{2}}{4}}}}-{\tfrac {b}{2}}}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/181ef89d7eba9dffdc920992a5af1c6df46882fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.345ex; height:7.676ex;" alt="{\displaystyle x={\frac {\pm {\sqrt {ac+{\tfrac {b^{2}}{4}}}}-{\tfrac {b}{2}}}{a}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Aritmetika">Aritmetika</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=6" title="Baguhin seksiyon: Aritmetika" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=6" title="Edit section's source code: Aritmetika"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Ang apat na pangunahing operasyon (<a href="/wiki/Pagdaragdag" title="Pagdaragdag">pagdaragdag</a>, <a href="/wiki/Pagbabawas" title="Pagbabawas">pagbabawas</a>, <a href="/wiki/Pagpaparami" title="Pagpaparami">pagpaparami</a>, at <a href="/wiki/Paghahati" title="Paghahati">paghahati</a>) ay kilala sa maraming <a href="/wiki/Kalinangan" class="mw-redirect" title="Kalinangan">kalinangan</a> bago si Brahmagupta. Ang kasalukuyang sistemang ito ay batay sa <a href="/wiki/Sistemang_pamilang" class="mw-redirect" title="Sistemang pamilang">sistemang pamilang</a> na Hindu–Arabe at unang lumitaw sa <i>Brāhmasphuṭasiddhānta</i>. Inilalarawan ng Brahmagupta ang pagpaparami sa sumusunod na paraan:</p><blockquote><p>Inuulit ang multiplikando tulad ng tali ng baka, kung gaano kadalas mayroong mga integrante na bahagi sa multiplikador at inuulit ang pagpaparami nito sa pamamagitan nila at ang mga produkto ay dinadagdag ng magkasama. Multiplikasyon ito. O inuulit ng maraming beses ang multiplikando hanggang mayroong bahagi sa multiplikador.<sup id="cite_ref-Brahmagupta18172_12-0" class="reference"><a href="#cite_note-Brahmagupta18172-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading4"><h4 id="Sero">Sero</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=7" title="Baguhin seksiyon: Sero" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=7" title="Edit section's source code: Sero"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Ang <i>Brahmasphuṭasiddhānta</i> ni Brahmagupta ay ang unang aklat na nagbibigay ng mga panuntunan para sa mga manipulasyon sa aritmetika na nalalapat sa <a href="/wiki/0_(bilang)" title="0 (bilang)">sero</a> at sa mga negatibong numero.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Ang <i>Brāhmasphuṭasiddhānta</i> ay ang pinakaunang kilalang teksto na tinatrato ang sero bilang isang numero sa sarili nito, sa halip na isang pamalit na tambilang na kumakatawan sa isa pang numero tulad ng ginawa ng mga <a href="/wiki/Babilonya" title="Babilonya">taga-Babilonya</a> o bilang isang simbolo para sa kakulangan ng dami tulad ng ginawa ni <a href="/wiki/Ptolomeo" title="Ptolomeo">Ptolomeo</a> at ng <a href="/wiki/Sinaunang_Roma" title="Sinaunang Roma">mga Romano</a>. Sa ika-labingwalong kabanata ng kanyang <i>Brāhmasphuṭasiddhānta</i>, inilalarawan ni Brahmagupta ang mga operasyon sa mga negatibong numero. Una niyang inilalarawan ang pagdaragdag at pagbabawas,</p><blockquote><p>18.30. [Ang kabuuan] ng dalawang positibo ay positibo, ng dalawang negatibong negatibo; ng isang positibo at isang negatibo [ang kabuuan] ay ang kanilang pagkakaiba; kung sila ay pantay ito ay sero. Ang kabuuan ng negatibo at sero ay negatibo, [na] ng positibo at sero na positibo, [at iyon] ng dalawang sero na sero. </p><p> [...] </p><p> 18.32. Ang negatibong binawasan ng sero ay negatibo, ang isang positibong [binawasan ng sero] ay positibo; ang sero [binawasan ng sero] ay sero. Kapag ang isang positibo ay ibawas mula sa isang negatibo o isang negatibo mula sa isang positibo, pagkatapos ito ay dapat idagdag.</p></blockquote><p>Nagpatuloy siya sa paglalarawan ng pagpaparami,</p><blockquote><p>18.33. Ang produkto ng isang negatibo at isang positibo ay negatibo, ng dalawang negatibong positibo, at ng mga positibong positibo; ang produkto ng sero at negatibo, ng sero at positibo, o ng dalawang sero ay sero.</p></blockquote><p>Subalit ang kanyang paglalarawan ng <a href="/wiki/Paghahati_sa_sero" title="Paghahati sa sero">paghahati sa pamamagitan ng sero</a> ay naiiba sa ating modernong pag-unawa:</p><blockquote><p>18.34. Ang positibong hinati sa positibo o negatibong hinati sa negatibo ay positibo; ang sero na hinati sa sero ay sero; ang positibong hinati sa negatibo ay negatibo; ang negatibong hinati sa positibo ay negatibo [din]. 18.35. Ang isang negatibo o isang positibong hinati sa sero ay mayroong [sero] na iyon bilang panghati nito, o sero na hinati sa isang negatibo o isang positibo [may negatibo o positibong iyon bilang panghati nito]. Ang parisukat ng isang negatibo o positibo ay positibo; [ang parisukat] ng sero ay sero. Yaong kung saan [ang parisukat] ay ang parisukat ay [nito] parisukat na ugat [o pariugat].</p></blockquote><p>Dito sinabi ni Brahmagupta na <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;">0</span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">0</span></span> = 0 at para sa tanong ng <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;"><span class="texhtml"><i>a</i></span></span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">0</span></span> kung saan <span class="texhtml"><i>a</i></span> ≠ 0 hindi niya pinasyahan ito. Ang kanyang mga alituntunin para sa <a href="/wiki/Aritmetika" title="Aritmetika">aritmetika</a> sa mga negatibong numero at sero ay medyo malapit sa makabagong pag-unawa, maliban na sa modernong matematika dibisyon sa pamamagitan ng sero ay naiwang hindi natukoy. </p><div class="mw-heading mw-heading3"><h3 id="Heometriya">Heometriya</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=8" title="Baguhin seksiyon: Heometriya" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=8" title="Edit section's source code: Heometriya"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Pormula_ni_Brahmagupta">Pormula ni Brahmagupta</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=9" title="Baguhin seksiyon: Pormula ni Brahmagupta" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=9" title="Edit section's source code: Pormula ni Brahmagupta"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Brahmaguptas_formula.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Brahmaguptas_formula.svg/200px-Brahmaguptas_formula.svg.png" decoding="async" width="200" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Brahmaguptas_formula.svg/300px-Brahmaguptas_formula.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Brahmaguptas_formula.svg/400px-Brahmaguptas_formula.svg.png 2x" data-file-width="281" data-file-height="276" /></a><figcaption> Diagrama para sa reperensya</figcaption></figure><p> Ang pinakatanyag na resulta ni Brahmagupta sa <a href="/wiki/Heometriya" title="Heometriya">heometriya</a> ay ang kanyang <a href="/wiki/Pormula" title="Pormula">pormula</a> para sa kuwadilaterong sikliko. Dahil sa haba ng mga gilid ng anumang kuwadilaterong sikliko, nagbigay si Brahmagupta ng tinatayang at eksaktong pormula para sa lugar ng pigura,</p><blockquote><p>12.21. Ang tinatayang lugar ay ang produkto ng mga kalahati ng mga kabuuan ng mga gilid at magkasalungat na gilid ng isang <a href="/wiki/Tatsulok" title="Tatsulok">tatsulok</a> at isang kuwadralatero. Ang tumpak na [sukat] ay ang pariugat mula sa produkto ng mga kalahati ng mga kabuuan ng mga gilid na pinaliit ng [bawat] gilid ng kuwadralatero.</p></blockquote><p>Kung ibinigay ang mga haba <span class="texhtml"><i>p</i></span>, <span class="texhtml"><i>q</i></span>, <span class="texhtml"><i>r</i></span> at <span class="texhtml"><i>s</i></span> ng isang kuwadralatero sikliko, ang tinatayang sukat ay <span class="texhtml"><span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;"><i>p</i> + <i>r</i></span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">2</span></span> · <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;"><i>q</i> + <i>s</i></span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">2</span></span></span> habang, hinahayaan ang <span class="texhtml"><i>t</i> = <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;"><i>p</i> + <i>q</i> + <i>r</i> + <i>s</i></span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">2</span></span></span>. ang eksakstong sukat ay </p><dl><dd><span class="texhtml"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">(<i>t</i> − <i>p</i>)(<i>t</i> − <i>q</i>)(<i>t</i> − <i>r</i>)(<i>t</i> − <i>s</i>)</span></span></span>.</dd></dl> <p>Bagaman hindi tahasang sinabi ni Brahmagupta na sikliko ang mga kuwadralatero, maliwanag sa kanyang mga tuntunin na ito ang kaso. Ang <a href="/wiki/Pormula_ni_Heron" title="Pormula ni Heron">pormula ni Heron</a> ay isang espesyal na kaso ng pormula na ito at maaari itong makuha sa pamamagitan ng pagtatakda ng isa sa mga panig na katumbas ng sero. </p> <div class="mw-heading mw-heading3"><h3 id="Mga_tatsulok">Mga tatsulok</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=10" title="Baguhin seksiyon: Mga tatsulok" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=10" title="Edit section's source code: Mga tatsulok"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Inilaan ni Brahmagupta ang isang malaking bahagi ng kanyang gawa sa heometriya. Nagbibigay ang isang teorama ng mga haba ng dalawang piraso na ang base ng <a href="/wiki/Tatsulok" title="Tatsulok">tatsulok</a> ay nahahati sa <a href="/wiki/Altitud" title="Altitud">altitud</a> nito:</p><blockquote><p>12.22. Ang base ay nabawasan at nadagdagan ng pagkakaiba sa pagitan ng mga parisukat ng mga gilid na hinati ng base; kapag hinati sa dalawa sila ang tunay na mga piraso [o segmente]. Ang [altitud] na patayo ay ang pariugat mula sa parisukat ng isang gilid na pinaliit ng parisukat ng piraso nito.</p></blockquote><p>Kaya ang haba ng dalawang segmente ay <span class="texhtml"><span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;">1</span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">2</span></span>(<i>b</i> ± <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;"><i>c</i><sup>2</sup> − <i>a</i><sup>2</sup></span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;"><i>b</i></span></span>)</span> </p><div class="mw-heading mw-heading4"><h4 id="Teorama_ni_Brahmagupta">Teorama ni Brahmagupta</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=11" title="Baguhin seksiyon: Teorama ni Brahmagupta" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=11" title="Edit section's source code: Teorama ni Brahmagupta"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Brahmaguptra%27s_theorem.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Brahmaguptra%27s_theorem.svg/220px-Brahmaguptra%27s_theorem.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Brahmaguptra%27s_theorem.svg/330px-Brahmaguptra%27s_theorem.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Brahmaguptra%27s_theorem.svg/440px-Brahmaguptra%27s_theorem.svg.png 2x" data-file-width="234" data-file-height="234" /></a><figcaption> Ang teorama ni Brahmagupta ay nagsasaad na <i>AF</i> = <i>FD</i> .</figcaption></figure><p> Patuloy ni Brahmagupta,</p><blockquote><p>12.23. Ang pariugat ng kabuuan ng dalawang produkto ng mga gilid at magkasalungat na gilid ng isang hindi pantay na kuwadralatero ay ang dayagonal. Ang parisukat ng diyagonal ay pinaliit ng parisukat ng kalahati ng kabuuan ng base at tuktok; ang pariugat ay ang [altitud] na patayo.</p></blockquote><p>Kaya, sa isang "hindi pantay" na kuwadralaterong sikliko (iyon ay, isang <a href="/wiki/Trapesoid" title="Trapesoid">trapesoid</a> na isosseles), ang haba ng bawat diyagonal ay <span class="texhtml"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;"><i>pr</i> + <i>qs</i></span></span></span>. </p><div class="mw-heading mw-heading4"><h4 id="Pi">Pi</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=12" title="Baguhin seksiyon: Pi" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=12" title="Edit section's source code: Pi"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Sa taludtod 40, nagbibigay siya ng mga halaga ng <a href="/wiki/Pi" title="Pi"><span class="texhtml">π</span></a>,</p><blockquote><p>12.40. Ang diyametero at ang parisukat ng <a href="/wiki/Radius" title="Radius">radyo</a> [bawat isa] na pinarami ng 3 ay [ayon sa pagkakabanggit] ang praktikal na <a href="/wiki/Sirkumperensya" class="mw-redirect" title="Sirkumperensya">sirkumperensya</a> at ang lugar [ng isang <a href="/wiki/Bilog" title="Bilog">bilog</a>]. Ang tumpak na [mga halaga] ay ang mga pariguat mula sa mga parisukat ng dalawang iyon na pinarami ng sampu.</p></blockquote><p>Kaya ginagamit ni Brahmagupta ang 3 bilang isang "praktikal" na halaga ng <span class="texhtml">π</span>, at <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 {10}}\approx 3.1622\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>10</mn> </msqrt> </mrow> <mo>≈</mo> <mn>3.1622</mn> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {10}}\approx 3.1622\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe870be5e2ba25351bc672992ac4441f951708b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.929ex; height:2.843ex;" alt="{\displaystyle {\sqrt {10}}\approx 3.1622\ldots }"></span> bilang isang "tumpak" na halaga ng <span class="texhtml">π</span>, na may kamalian na mas mababa sa 1%. </p><div class="mw-heading mw-heading2"><h2 id="Maagang_konsepto_ng_grabidad">Maagang konsepto ng grabidad</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=13" title="Baguhin seksiyon: Maagang konsepto ng grabidad" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=13" title="Edit section's source code: Maagang konsepto ng grabidad"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Unang inilarawan ni Brahmagupta noong 628 ang <a href="/wiki/Grabidad" class="mw-redirect" title="Grabidad">grabidad</a> bilang isang puwersang atraksyon, gamit ang katawagang "<a href="https://en.wiktionary.org/wiki/%E0%A4%97%E0%A5%81%E0%A4%B0%E0%A5%81%E0%A4%A4%E0%A5%8D%E0%A4%B5%E0%A4%BE%E0%A4%95%E0%A4%B0%E0%A5%8D%E0%A4%B7%E0%A4%A3%E0%A4%AE%E0%A5%8D" class="extiw" title="wiktionary:गुरुत्वाकर्षणम्">gurutvākarṣaṇam (गुरुत्वाकर्षणम्)</a>" upang ilarawan ito:<sup id="cite_ref-Oxford_1-1" class="reference"><a href="#cite_note-Oxford-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Sen_2-1" class="reference"><a href="#cite_note-Sen-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <blockquote><p>Ang lupa sa lahat ng panig nito ay pareho; lahat ng tao sa lupa ay tumayo nang tuwid, at lahat ng mabibigat na bagay ay nahuhulog sa lupa sa pamamagitan ng batas ng kalikasan, dahil likas na katangian ng mundo ang umakit at panatilihin ang mga bagay, dahil likas na katangian ng tubig ang dumaloy ... Kung nais ng isang bagay na mas malalim kaysa sa lupa, hayaang subukan ito. Ang lupa ay ang tanging <i>mababang</i> bagay, at ang mga <a href="/wiki/Buto_ng_halaman" title="Buto ng halaman">buto</a> ay palaging bumabalik dito, sa anumang direksyon maaari mong itapon ang mga ito, at hindi kailanman tumaas mula sa lupa.<sup id="cite_ref-Alberuni_14-0" class="reference"><a href="#cite_note-Alberuni-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Astronomiya">Astronomiya</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=14" title="Baguhin seksiyon: Astronomiya" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=14" title="Edit section's source code: Astronomiya"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Itinuro ni Brahmagupta ang maraming <a href="/wiki/Kritisismo" class="mw-redirect" title="Kritisismo">kritisismo</a> sa gawain ng mga karibal na astronomo, at nagpapakita ang kanyang <i>Brāhmasphuṭasiddhānta</i> ng isa sa mga pinakaunang paghahati sa mga matematikong Indiyano. Pangunahing tungkol ang dibisyon sa aplikasyon ng matematika sa pisikal na mundo, sa halip na tungkol sa matematika mismo. Sa kaso ni Brahmagupta, ang mga hindi pagkakasundo ay nagmula sa pagpili ng mga astronomikal na parametro at teorya.<sup id="cite_ref-Plofker_418-419_17-0" class="reference"><a href="#cite_note-Plofker_418-419-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Lumilitaw ang mga kritika sa mga karibal na <a href="/wiki/Teorya" title="Teorya">teorya</a> sa buong unang sampung astronomikal na kabanata at ganap na nakatuon ang ikalabing-isang kabanata sa pagpuna sa mga teoryang ito, bagama't walang mga pagpuna na lumilitaw sa ikalabindalawa at ikalabinwalong kabanata.<sup id="cite_ref-Plofker_418-419_17-1" class="reference"><a href="#cite_note-Plofker_418-419-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mga_sanggunian">Mga sanggunian</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=15" title="Baguhin seksiyon: Mga sanggunian" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=15" title="Edit section's source code: Mga sanggunian"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Mga_pananda">Mga pananda</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=16" title="Baguhin seksiyon: Mga pananda" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=16" title="Edit section's source code: Mga pananda"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r2121818">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-16"><span class="mw-cite-backlink"><a href="#cite_ref-16">↑</a></span> <span class="reference-text">Ang pinagmulan ng sipi ay sa <i>Al-Biruni's India</i> (c. 1030).<sup id="cite_ref-Alberuni_14-1" class="reference"><a href="#cite_note-Alberuni-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Mga_pagsipi">Mga pagsipi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=17" title="Baguhin seksiyon: Mga pagsipi" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=17" title="Edit section's source code: Mga pagsipi"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2121818"><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-Oxford-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Oxford_1-0">1.0</a></sup> <sup><a href="#cite_ref-Oxford_1-1">1.1</a></sup></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r2132731">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFPickover2008" class="citation book cs1 cs1-prop-foreign-lang-source">Pickover, Clifford (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=SQXcpvjcJBUC&pg=PA105"><i>Archimedes to Hawking: Laws of Science and the Great Minds Behind Them</i></a> (sa wikang Ingles). Oxford University Press. p. 105. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/978-0-19-979268-9" title="Natatangi:Mga pinagmulang aklat/978-0-19-979268-9"><bdi>978-0-19-979268-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Archimedes+to+Hawking%3A+Laws+of+Science+and+the+Great+Minds+Behind+Them&rft.pages=105&rft.pub=Oxford+University+Press&rft.date=2008&rft.isbn=978-0-19-979268-9&rft.aulast=Pickover&rft.aufirst=Clifford&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DSQXcpvjcJBUC%26pg%3DPA105&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-Sen-2"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Sen_2-0">2.0</a></sup> <sup><a href="#cite_ref-Sen_2-1">2.1</a></sup></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFSen2005" class="citation book cs1 cs1-prop-foreign-lang-source">Sen, Amartya (2005). <i>The Argumentative Indian</i> (sa wikang Ingles). Allen Lane. p. 29. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/978-0-7139-9687-6" title="Natatangi:Mga pinagmulang aklat/978-0-7139-9687-6"><bdi>978-0-7139-9687-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Argumentative+Indian&rft.pages=29&rft.pub=Allen+Lane&rft.date=2005&rft.isbn=978-0-7139-9687-6&rft.aulast=Sen&rft.aufirst=Amartya&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-Sachau2013-3"><span class="mw-cite-backlink"><a href="#cite_ref-Sachau2013_3-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFSachau1910" class="citation cs2 cs1-prop-foreign-lang-source">Sachau, Edward C. (1910), <a rel="nofollow" class="external text" href="https://archive.org/details/alberunisindiaac01biru/page/152/mode/2up"><i>Alberuni's India, Volume I</i></a> (sa wikang Ingles), London: Kegan Paul, Trench and Trubner, p. 153, <q><i>Brahma-siddhānta</i>, so-called from Brahman, composed by Brahmagupta, the son of Jishnu, from the town of Bhillamāla between Multān and Anhilwāra, 16 <i>yojana</i> from the latter place (?)</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Alberuni%27s+India%2C+Volume+I&rft.place=London&rft.pages=153&rft.pub=Kegan+Paul%2C+Trench+and+Trubner&rft.date=1910&rft.aulast=Sachau&rft.aufirst=Edward+C.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Falberunisindiaac01biru%2Fpage%2F152%2Fmode%2F2up&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Citation" title="Padron:Citation">citation</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-Bhattacharyya-4"><span class="mw-cite-backlink"><a href="#cite_ref-Bhattacharyya_4-0">↑</a></span> <span class="reference-text"><a href="#CITEREFBhattacharyya2011">Bhattacharyya 2011</a>: "Brahmagupta, one of the most celebrated mathematicians of the East, indeed of the world, was born in the year 598 CE, in the town of Bhillamala during the reign of King Vyaghramukh of the Chapa Dynasty." (sa Ingles)</span> </li> <li id="cite_note-FOOTNOTEGupta2008-5"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-FOOTNOTEGupta2008_5-0">5.0</a></sup> <sup><a href="#cite_ref-FOOTNOTEGupta2008_5-1">5.1</a></sup> <sup><a href="#cite_ref-FOOTNOTEGupta2008_5-2">5.2</a></sup> <sup><a href="#cite_ref-FOOTNOTEGupta2008_5-3">5.3</a></sup> <sup><a href="#cite_ref-FOOTNOTEGupta2008_5-4">5.4</a></sup> <sup><a href="#cite_ref-FOOTNOTEGupta2008_5-5">5.5</a></sup> <sup><a href="#cite_ref-FOOTNOTEGupta2008_5-6">5.6</a></sup></span> <span class="reference-text"><a href="#CITEREFGupta2008">Gupta 2008</a>.</span> </li> <li id="cite_note-FOOTNOTEBhattacharyya2011-6"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-FOOTNOTEBhattacharyya2011_6-0">6.0</a></sup> <sup><a href="#cite_ref-FOOTNOTEBhattacharyya2011_6-1">6.1</a></sup></span> <span class="reference-text"><a href="#CITEREFBhattacharyya2011">Bhattacharyya 2011</a>.</span> </li> <li id="cite_note-FOOTNOTEBoseSenSubbarayappa1971-7"><span class="mw-cite-backlink"><a href="#cite_ref-FOOTNOTEBoseSenSubbarayappa1971_7-0">↑</a></span> <span class="reference-text"><a href="#CITEREFBoseSenSubbarayappa1971">Bose, Sen & Subbarayappa 1971</a>.</span> </li> <li id="cite_note-:0-8"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:0_8-0">8.0</a></sup> <sup><a href="#cite_ref-:0_8-1">8.1</a></sup> <sup><a href="#cite_ref-:0_8-2">8.2</a></sup></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFPingree1970–1994" class="citation book cs1 cs1-prop-foreign-lang-source">Pingree, David E. (1970–1994). <a rel="nofollow" class="external text" href="http://archive.org/details/PingreeCESS"><i>Pingree's Census of the Exact Sciences in Sanskrit</i></a> (sa wikang Ingles). APS. pp. A4, 256 ff., A5, 239–240 et passim.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Pingree%27s+Census+of+the+Exact+Sciences+in+Sanskrit&rft.pages=A4%2C+256+ff.%2C+A5%2C+239-240+et+passim&rft.pub=APS&rft.date=1970%2F1994&rft.aulast=Pingree&rft.aufirst=David+E.&rft_id=http%3A%2F%2Farchive.org%2Fdetails%2FPingreeCESS&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-FOOTNOTEAvari2013-9"><span class="mw-cite-backlink"><a href="#cite_ref-FOOTNOTEAvari2013_9-0">↑</a></span> <span class="reference-text"><a href="#CITEREFAvari2013">Avari 2013</a>.</span> </li> <li id="cite_note-YoungLatham2006-10"><span class="mw-cite-backlink"><a href="#cite_ref-YoungLatham2006_10-0">↑</a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFYoungLathamSerjeant2006" class="citation cs2 cs1-prop-foreign-lang-source">Young, M. J. L.; Latham, J. D.; Serjeant, R. B. (2 Nobyembre 2006), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=cJuDafHpk3oC&pg=PA302"><i>Religion, Learning and Science in the 'Abbasid Period</i></a> (sa wikang Ingles), Cambridge University Press, pp. 302–303, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/978-0-521-02887-5" title="Natatangi:Mga pinagmulang aklat/978-0-521-02887-5"><bdi>978-0-521-02887-5</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Religion%2C+Learning+and+Science+in+the+%27Abbasid+Period&rft.pages=302-303&rft.pub=Cambridge+University+Press&rft.date=2006-11-02&rft.isbn=978-0-521-02887-5&rft.aulast=Young&rft.aufirst=M.+J.+L.&rft.au=Latham%2C+J.+D.&rft.au=Serjeant%2C+R.+B.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DcJuDafHpk3oC%26pg%3DPA302&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Citation" title="Padron:Citation">citation</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-van_Bladel-11"><span class="mw-cite-backlink"><a href="#cite_ref-van_Bladel_11-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFvan_Bladel2014" class="citation cs2 cs1-prop-foreign-lang-source">van Bladel, Kevin (28 Nobyembre 2014), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7nSjBQAAQBAJ&pg=PA260">"Eighth Century Indian Astronomy in the Two Cities of Peace"</a>, sa Asad Q. Ahmed; Benham Sadeghi; Robert G. Hoyland (mga pat.), <i>Islamic Cultures, Islamic Contexts: Essays in Honor of Professor Patricia Crone</i> (sa wikang Ingles), BRILL, pp. 257–294, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/978-90-04-28171-4" title="Natatangi:Mga pinagmulang aklat/978-90-04-28171-4"><bdi>978-90-04-28171-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Eighth+Century+Indian+Astronomy+in+the+Two+Cities+of+Peace&rft.btitle=Islamic+Cultures%2C+Islamic+Contexts%3A+Essays+in+Honor+of+Professor+Patricia+Crone&rft.pages=257-294&rft.pub=BRILL&rft.date=2014-11-28&rft.isbn=978-90-04-28171-4&rft.aulast=van+Bladel&rft.aufirst=Kevin&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7nSjBQAAQBAJ%26pg%3DPA260&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Citation" title="Padron:Citation">citation</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-Brahmagupta18172-12"><span class="mw-cite-backlink"><a href="#cite_ref-Brahmagupta18172_12-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFBrahmaguptaBhāskara_II1817" class="citation book cs1 cs1-prop-foreign-lang-source">Brahmagupta; Bhāskara II (1817). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ebZIAAAAcAAJ&pg=PA319"><i>Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara</i></a> (sa wikang Ingles). Sinalin ni Henry Thomas Colebrooke. John Murray. p. 319.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Algebra%2C+with+Arithmetic+and+Mensuration%2C+from+the+Sanscrit+of+Brahmegupta+and+Bh%C3%A1scara&rft.pages=319&rft.pub=John+Murray&rft.date=1817&rft.au=Brahmagupta&rft.au=Bh%C4%81skara+II&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DebZIAAAAcAAJ%26pg%3DPA319&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFKaplan1999" class="citation book cs1 cs1-prop-foreign-lang-source">Kaplan, Robert (1999). <i>The Nothing That Is: A Natural History of Zero</i> (sa wikang Ingles). London: Allen Lane/The Penguin Press. pp. 68–75. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000tnti.book.....K">2000tnti.book.....K</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Nothing+That+Is%3A+A+Natural+History+of+Zero&rft.place=London&rft.pages=68-75&rft.pub=Allen+Lane%2FThe+Penguin+Press&rft.date=1999&rft_id=info%3Abibcode%2F2000tnti.book.....K&rft.aulast=Kaplan&rft.aufirst=Robert&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-Alberuni-14"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Alberuni_14-0">14.0</a></sup> <sup><a href="#cite_ref-Alberuni_14-1">14.1</a></sup></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="http://www.columbia.edu/cu/lweb/digital/collections/cul/texts/ldpd_5949073_001/pages/ldpd_5949073_001_00000328.html?toggle=image&menu=maximize&top=&left="><i>Alberuni's India</i></a> (sa wikang Ingles). London: Kegan Paul, Trench, Trübner & Co., 1910. Electronic reproduction. Vol. 1 and 2. New York: Columbia University Libraries, 2006. p. 272<span class="reference-accessdate">. Nakuha noong <span class="nowrap">3 Hunyo</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Alberuni%27s+India&rft.pages=272&rft.pub=London%3A+Kegan+Paul%2C+Trench%2C+Tr%C3%BCbner+%26+Co.%2C+1910.+Electronic+reproduction.+Vol.+1+and+2.+New+York%3A+Columbia+University+Libraries%2C+2006&rft_id=http%3A%2F%2Fwww.columbia.edu%2Fcu%2Flweb%2Fdigital%2Fcollections%2Fcul%2Ftexts%2Fldpd_5949073_001%2Fpages%2Fldpd_5949073_001_00000328.html%3Ftoggle%3Dimage%26menu%3Dmaximize%26top%3D%26left%3D&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite class="citation book cs1 cs1-prop-script cs1-prop-foreign-lang-source"><i>Kitāb al-Jawharatayn al-'atīqatayn al-mā'i'atayn min al-ṣafrā' wa-al-bayḍā': al-dhahab wa-al-fiḍḍah</i> <bdi lang="ar">كتاب الجوهرتين العتيقتين المائعتين من الصفراء والبيضاء : الذهب والفضة</bdi> (sa wikang Arabe). Cairo: Maṭba'at Dār al-Kutub wa-al-Wathā'iq al-Qawmīyah bi-al-Qāhirah. 2004. pp. 43–44, 87. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/607846741">607846741</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Kit%C4%81b+al-Jawharatayn+al-%27at%C4%ABqatayn+al-m%C4%81%27i%27atayn+min+al-%E1%B9%A3afr%C4%81%27+wa-al-bay%E1%B8%8D%C4%81%27%3A+al-dhahab+wa-al-fi%E1%B8%8D%E1%B8%8Dah+%D9%83%D8%AA%D8%A7%D8%A8+%D8%A7%D9%84%D8%AC%D9%88%D9%87%D8%B1%D8%AA%D9%8A%D9%86+%D8%A7%D9%84%D8%B9%D8%AA%D9%8A%D9%82%D8%AA%D9%8A%D9%86+%D8%A7%D9%84%D9%85%D8%A7%D8%A6%D8%B9%D8%AA%D9%8A%D9%86+%D9%85%D9%86+%D8%A7%D9%84%D8%B5%D9%81%D8%B1%D8%A7%D8%A1+%D9%88%D8%A7%D9%84%D8%A8%D9%8A%D8%B6%D8%A7%D8%A1+%3A+%D8%A7%D9%84%D8%B0%D9%87%D8%A8+%D9%88%D8%A7%D9%84%D9%81%D8%B6%D8%A9&rft.place=Cairo&rft.pages=43-44%2C+87&rft.pub=Ma%E1%B9%ADba%27at+D%C4%81r+al-Kutub+wa-al-Wath%C4%81%27iq+al-Qawm%C4%AByah+bi-al-Q%C4%81hirah&rft.date=2004&rft_id=info%3Aoclcnum%2F607846741&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-Plofker_418-419-17"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Plofker_418-419_17-0">16.0</a></sup> <sup><a href="#cite_ref-Plofker_418-419_17-1">16.1</a></sup></span> <span class="reference-text"><a href="#CITEREFPlofker2007">Plofker (2007</a>, pp. 418–419)</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Bibliograpiya">Bibliograpiya</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=18" title="Baguhin seksiyon: Bibliograpiya" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=18" title="Edit section's source code: Bibliograpiya"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFAvari2013" class="citation cs2 cs1-prop-foreign-lang-source">Avari, Burjor (2013), <i>Islamic Civilization in South Asia: A history of Muslim power and presence in the Indian subcontinent</i> (sa wikang Ingles), Routledge, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/978-0-415-58061-8" title="Natatangi:Mga pinagmulang aklat/978-0-415-58061-8"><bdi>978-0-415-58061-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Islamic+Civilization+in+South+Asia%3A+A+history+of+Muslim+power+and+presence+in+the+Indian+subcontinent&rft.pub=Routledge&rft.date=2013&rft.isbn=978-0-415-58061-8&rft.aulast=Avari&rft.aufirst=Burjor&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Citation" title="Padron:Citation">citation</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFBoseSenSubbarayappa1971" class="citation cs2 cs1-prop-foreign-lang-source">Bose, D. M.; Sen, S. N.; Subbarayappa, B. V. (1971), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151208075132/http://www.dli.gov.in/scripts/FullindexDefault.htm?path1=%2Fdata_copy%2Fupload%2F0080%2F243&first=114&last=1168&barcode=1040010080238"><i>A Concise History of Science in India</i></a> (sa wikang Ingles), New Delhi: Indian National Academy of Science, pp. 95–97, inarkibo mula sa <a rel="nofollow" class="external text" href="http://www.dli.gov.in/scripts/FullindexDefault.htm?path1=/data_copy/upload/0080/243&first=114&last=1168&barcode=1040010080238">orihinal</a> noong Disyembre 8, 2015</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Concise+History+of+Science+in+India&rft.place=New+Delhi&rft.pages=95-97&rft.pub=Indian+National+Academy+of+Science&rft.date=1971&rft.aulast=Bose&rft.aufirst=D.+M.&rft.au=Sen%2C+S.+N.&rft.au=Subbarayappa%2C+B.+V.&rft_id=http%3A%2F%2Fwww.dli.gov.in%2Fscripts%2FFullindexDefault.htm%3Fpath1%3D%2Fdata_copy%2Fupload%2F0080%2F243%26first%3D114%26last%3D1168%26barcode%3D1040010080238&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Citation" title="Padron:Citation">citation</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFBhattacharyya2011" class="citation cs2 cs1-prop-foreign-lang-source">Bhattacharyya, R. K. (2011), "Brahmagupta: The Ancient Indian Mathematician", sa B. S. Yadav; Man Mohan (mga pat.), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nwrw0Lv1vXIC"><i>Ancient Indian Leaps into Mathematics</i></a> (sa wikang Ingles), Springer Science & Business Media, pp. 185–192, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/978-0-8176-4695-0" title="Natatangi:Mga pinagmulang aklat/978-0-8176-4695-0"><bdi>978-0-8176-4695-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Brahmagupta%3A+The+Ancient+Indian+Mathematician&rft.btitle=Ancient+Indian+Leaps+into+Mathematics&rft.pages=185-192&rft.pub=Springer+Science+%26+Business+Media&rft.date=2011&rft.isbn=978-0-8176-4695-0&rft.aulast=Bhattacharyya&rft.aufirst=R.+K.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dnwrw0Lv1vXIC&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Citation" title="Padron:Citation">citation</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFGupta2008" class="citation cs2">Gupta, Radha Charan (2008), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=raKRY3KQspsC&pg=PA162">"Brahmagupta"</a>, sa Selin, Helaine (pat.), <i>Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures</i>, Springer, pp. 162–163, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/978-1-4020-4559-2" title="Natatangi:Mga pinagmulang aklat/978-1-4020-4559-2"><bdi>978-1-4020-4559-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Brahmagupta&rft.btitle=Encyclopaedia+of+the+History+of+Science%2C+Technology%2C+and+Medicine+in+Non-Western+Cultures&rft.pages=162-163&rft.pub=Springer&rft.date=2008&rft.isbn=978-1-4020-4559-2&rft.aulast=Gupta&rft.aufirst=Radha+Charan&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DraKRY3KQspsC%26pg%3DPA162&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Citation" title="Padron:Citation">citation</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFPlofker2007" class="citation cs2 cs1-prop-foreign-lang-source">Plofker, Kim (2007), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3ullzl036UEC">"Mathematics in India"</a>, sa Victor Katz (pat.), <i>The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook</i> (sa wikang Ingles), Princeton University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/978-0-691-11485-9" title="Natatangi:Mga pinagmulang aklat/978-0-691-11485-9"><bdi>978-0-691-11485-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Mathematics+in+India&rft.btitle=The+Mathematics+of+Egypt%2C+Mesopotamia%2C+China%2C+India%2C+and+Islam%3A+A+Sourcebook&rft.pub=Princeton+University+Press&rft.date=2007&rft.isbn=978-0-691-11485-9&rft.aulast=Plofker&rft.aufirst=Kim&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D3ullzl036UEC&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Citation" title="Padron:Citation">citation</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Karagdagang_pagbabasa">Karagdagang pagbabasa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmagupta&veaction=edit&section=19" title="Baguhin seksiyon: Karagdagang pagbabasa" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brahmagupta&action=edit&section=19" title="Edit section's source code: Karagdagang pagbabasa"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFSetsuro_Ikeyama2003" class="citation book cs1 cs1-prop-foreign-lang-source">Setsuro Ikeyama (2003). <i>Brāhmasphuṭasiddhānta (Chapter 21) of Brahmagupta with Commentary of Pṛthūdhakasvāmin, critically edited with English translation and notes</i> (sa wikang Ingles). INSA.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Br%C4%81hmasphu%E1%B9%ADasiddh%C4%81nta+%28Chapter+21%29+of+Brahmagupta+with+Commentary+of+P%E1%B9%9Bth%C5%ABdhakasv%C4%81min%2C+critically+edited+with+English+translation+and+notes&rft.pub=INSA&rft.date=2003&rft.au=Setsuro+Ikeyama&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFDavid_Pingree" class="citation book cs1 cs1-prop-foreign-lang-source">David Pingree. <i>Census of the Exact Sciences in Sanskrit (CESS)</i> (sa wikang Ingles). American Philosophical Society. A4, p. 254.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Census+of+the+Exact+Sciences+in+Sanskrit+%28CESS%29&rft.pages=A4%2C+p.+254&rft.pub=American+Philosophical+Society&rft.au=David+Pingree&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFShashi_S._Sharma" class="citation book cs1 cs1-prop-foreign-lang-source">Shashi S. Sharma. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=g9ykYZlzV1oC"><i>Mathematics & Astronomers of Ancient India</i></a> (sa wikang Ingles). Pitambar Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/9788120914216" title="Natatangi:Mga pinagmulang aklat/9788120914216"><bdi>9788120914216</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+%26+Astronomers+of+Ancient+India&rft.pub=Pitambar+Publishing&rft.isbn=9788120914216&rft.au=Shashi+S.+Sharma&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dg9ykYZlzV1oC&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ABrahmagupta" class="Z3988"></span></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="">Kinuha sa "<a dir="ltr" href="https://tl.wikipedia.org/w/index.php?title=Brahmagupta&oldid=2139126">https://tl.wikipedia.org/w/index.php?title=Brahmagupta&oldid=2139126</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Natatangi:Mga_kategorya" title="Natatangi:Mga kategorya">Kategorya</a>: <ul><li><a href="/wiki/Kategorya:Mga_matematikong_Indiano" title="Kategorya:Mga matematikong Indiano">Mga matematikong Indiano</a></li><li><a href="/wiki/Kategorya:Ipinanganak_noong_598" title="Kategorya:Ipinanganak noong 598">Ipinanganak noong 598</a></li><li><a href="/wiki/Kategorya:Mga_siyentipiko_mula_sa_India" title="Kategorya:Mga siyentipiko mula sa India">Mga siyentipiko mula sa India</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Nakatagong kategorya: <ul><li><a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">CS1 maint: date auto-translated</a></li><li><a href="/wiki/Kategorya:Sangguniang_CS1_sa_wikang_Ingles_(en)" title="Kategorya:Sangguniang CS1 sa wikang Ingles (en)">Sangguniang CS1 sa wikang Ingles (en)</a></li><li><a href="/wiki/Kategorya:CS1_na_gumagamit_ng_sulat_ng_wikang_Arabe_(ar)" title="Kategorya:CS1 na gumagamit ng sulat ng wikang Arabe (ar)">CS1 na gumagamit ng sulat ng wikang Arabe (ar)</a></li><li><a href="/wiki/Kategorya:Sangguniang_CS1_sa_wikang_Arabe_(ar)" title="Kategorya:Sangguniang CS1 sa wikang Arabe (ar)">Sangguniang CS1 sa wikang Arabe (ar)</a></li><li><a href="/wiki/Kategorya:Articles_with_hCards" title="Kategorya:Articles with hCards">Articles with hCards</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"> Huling pagbabago: 15:51, 25 Nobyembre 2024.</li> <li id="footer-info-copyright">Magagamit ang teksto sa ilalim ng <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Lisensyang Creative Commons Attribution/Share-Alike</a>; maaaring mailapat ang karagdagang termino. 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