https://indianpedia.org/index.php?action=history&feed=atom&title=Br%C4%81hmasphu%E1%B9%ADasiddh%C4%81ntaBrāhmasphuṭasiddhānta - Revision history2026-08-01T16:33:27ZRevision history for this page on the wikiMediaWiki 1.45.4https://indianpedia.org/index.php?title=Br%C4%81hmasphu%E1%B9%ADasiddh%C4%81nta&diff=110285&oldid=prev>Amahoney at 15:40, 26 April 20212021-04-26T15:40:41Z<p></p>
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The '''''Brāhmasphuṭasiddhānta''''' ("Correctly Established [[siddhanta|Doctrine]] of [[Brahma]]", abbreviated BSS)<br />
is the main work of [[Brahmagupta]], written c. 628.<ref>{{cite web|title=Brahmagupta {{!}} Indian astronomer|url=https://www.britannica.com/biography/Brahmagupta|website=Encyclopedia Britannica|language=en}}</ref> This text of mathematical astronomy contains significant mathematical content, including a good understanding of the role of [[0 (number)|zero]], rules for manipulating both [[negative and positive numbers]], a method for computing [[square root]]s, methods of solving [[linear equation|linear]] and [[quadratic equation]]s, and rules for summing [[series (mathematics)|series]], [[Brahmagupta's identity]], and [[Brahmagupta’s theorem]].<br />
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The book was written completely in verse and does not contain any kind of mathematical notation. Nevertheless, it contained the first clear description of the [[quadratic formula]] (the solution of the quadratic equation).<ref name=Bradley>Bradley, Michael. ''The Birth of Mathematics: Ancient Times to 1300'', p. 86 (Infobase Publishing 2006).</ref><ref>Mackenzie, Dana. ''[https://books.google.com/books?id=2QYSAAAAQBAJ&printsec=frontcover#v=onepage&q=Brahmagupta&f=false The Universe in Zero Words: The Story of Mathematics as Told through Equations]'', p. 61 (Princeton University Press, 2012).</ref><br />
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==''Brāhmasphuṭasiddhānta'' rules for numbers==<br />
'''''Brāhmasphuṭasiddhānta''''' is one of the first books to provide concrete ideas on [[positive number]]s, [[negative number]]s, and zero. He wrote the following rules:<ref>[[Henry Thomas Colebrooke]]. ''Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara'', London 1817, p. 339 ([https://archive.org/details/algebrawitharith00brahuoft online])</ref><br />
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* The [[addition|sum]] of two positive quantities is positive<br />
* The sum of two negative quantities is negative<br />
* The sum of zero and a negative number is negative<br />
* The sum of zero and a positive number is positive<br />
* The sum of zero and zero is zero<br />
* The sum of a positive and a negative is their difference; or, if they are equal, zero<br />
* In [[subtraction]], the less is to be taken from the greater, positive from positive<br />
* In subtraction, the less is to be taken from the greater, negative from negative<br />
* When the greater however, is subtracted from the less, the difference is [[additive inverse|reversed]]<br />
* When positive is to be subtracted from negative, and negative from positive, they must be added together<br />
* The [[multiplication|product]] of a negative quantity and a positive quantity is negative<br />
* The product of two negative quantities is positive<br />
* The product of two positive quantities is positive<br />
* Positive [[division (mathematics)|divided]] by positive or negative by negative is positive<br />
* Positive divided by negative is negative. Negative divided by positive is negative<br />
* Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator<br />
* A positive or negative number when [[Division by zero|divided by zero]] is a [[fraction (mathematics)|fraction]] with the zero as denominator<br />
* [[indeterminate form|Zero divided by zero]] is zero<br />
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The last two of these rules are notable as the earliest attempt to define division by zero, even though they are not compatible with modern number theory (division by zero is undefined for a [[field (mathematics)|field]]).<ref name="Kaplan">{{cite book<br />
| last = Kaplan | first = Robert | title = The Nothing that is: A Natural History of Zero<br />
| url = https://archive.org/details/nothingthatisnat00kapl | url-access = registration | publisher = Oxford University Press | year = 1999 | location = New York<br />
| pages = [https://archive.org/details/nothingthatisnat00kapl/page/68 68–75] | isbn = 0-19-514237-3}}<br />
</ref><br />
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==References==<br />
{{reflist}}<br />
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==External links==<br />
{{wikisourcelang|sa|ब्रह्मस्फुटसिद्धान्त}}<br />
* [http://gretil.sub.uni-goettingen.de/gretil/1_sanskr/6_sastra/8_jyot/brsphutu.htm ''Brahmasphutasiddhanta''] at [[GRETIL]] (mathematical chapters: 12, 18-20, 21.17-23)<br />
* {{MacTutor|id=Brahmagupta|title=Brahmagupta}}<br />
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{{Indian mathematics}}<br />
{{Indian astronomy}}<br />
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[[Category:Indian mathematics]]<br />
[[Category:Mathematics manuscripts]]<br />
[[Category:Sanskrit texts]]<br />
[[Category:7th-century manuscripts]]<br />
[[Category:History of algebra]]<br />
[[Category:Treatises]]<br />
[[Category:Indian astronomy texts]]<br />
[[Category:Brahmagupta]]</div>>Amahoney