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'''''Bijaganita''''' ([[IAST]]: ''{{IAST|Bījagaṇita}}'') was Indian mathematician [[Bhāskara II]]'s treatise on [[algebra]]. It is the second volume of his main work ''[[Siddhānta Shiromani]],'' [[Sanskrit]] for "Crown of treatises,"{{sfn|Plofker|2009|p=71}} alongside ''[[Lilāvati]]'', ''Grahaganita'' and ''Golādhyāya''.{{sfn|Poulose|1991|p=79}}<ref>[http://www.britannica.com/EBchecked/topic/1238540/bija-ganita Bijaganita] [[Britannica.com]]</ref><br />
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== Contents ==<br />
The book is divided into six parts, mainly indeterminate equations, quadratic equations, simple equations, surds. The contents are:<br />
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* Introduction<br />
* On Simple Equations<br />
* On Quadratic Equations<br />
* On Equations involving indeterminate Questions of the 1st Degree<br />
* On Equations involving indeterminate Questions of the 2nd Degree<br />
* On Equations involving Rectangles<br />
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In Bijaganita Bhāskara II refined [[Jayadeva]]'s way of generalization of Brahmagupta's approach to solving indeterminate quadratic equations, including Pell's equation which is known as [[chakravala method]] or cyclic method. Bijaganita is the first text to recognize that a positive number has two square roots<br />
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==Translations==<br />
The translations or editions of the Bijaganita into English include:<br />
* 1817. [[Henry Thomas Colebrooke]], [https://archive.org/stream/algebrawitharith00brahuoft ''Algebra, with Arithmetic and mensuration, from the Sanscrit of Brahmegupta and Bháscara'']<br />
* 1813. [https://archive.org/details/bijaganitaoralge00bhasrich Ata Allah ibn Ahmad Nadir Rashidi; Samuel Davis]<br />
* 1813. [https://archive.org/details/bijaganitaoralge00bhas Strachey, Edward, Sir, 1812–1901]<br />
* [https://web.archive.org/web/20091010194326/http://www.bprim.org/publication.php Bhaskaracharya's Bijaganita and its English and Marathi Translation by Prof. S. K. Abhyankar] <br />
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Two notable Scholars from Varanasi [[Sudhakar Dwivedi]] and [[Bapudeva Sastri]] studied Bijaganita in the nineteenth century.<br />
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==See also==<br />
* [[Indian mathematics]]<br />
* [[Timeline of algebra and geometry]]<br />
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== References ==<br />
{{Reflist}}<br />
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== Bibliography ==<br />
* {{citation|title=Mathematics in India|title-link= Mathematics in India |publisher=Princeton University Press|first=Kim|last=Plofker|isbn=9780691120676|year=2009}}<br />
* {{citation|title=Scientific heritage of India, mathematics|first=K. G.|last=Poulose|volume=Volume 22 of Ravivarma Samskr̥ta granthāvali|publisher=Govt. Sanskrit College (Tripunithura, India)|editor=K. G. Poulose|year=1991}}<br />
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==External links==<br />
*[https://web.archive.org/web/20121007161147/http://mlbd.com/BookDecription.aspx?id=7652 Hindi translation by Durga Prasad]<br />
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{{Indian mathematics}}<br />
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[[Category:Indian mathematics]]<br />
[[Category:Social history of India]]<br />
[[Category:History of science and technology in India]]<br />
[[Category:History of algebra]]<br />
[[Category:12th-century books]]</div>2603:7081:1501:BF70:C527:DEE7:5B3:6B0Ehttps://en.bharatpedia.org/w/index.php?title=Siddh%C4%81nta_Shiromani&diff=152816Siddhānta Shiromani2021-03-28T21:58:12Z<p>2603:7081:1501:BF70:C527:DEE7:5B3:6B0E: linked to Bijaganita page</p>
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'''''Siddhānta Śiromaṇi''''' ([[Sanskrit]]: सिद्धान्त शिरोमणि for "Crown of treatises"{{sfn|Plofker|2009|p=71}}) is the major treatise of Indian mathematician [[Bhāskara II]]. He wrote the ''Siddhānta Śiromaṇi'' in 1150 when he was 36 years old. The work is composed in Sanskrit Language in 1450 verses.<ref>{{cite web|title=khagol Maandal|url=http://www.khagolmandal.com/index.php?option=com_content&do_pdf=1&id=45&limitstart=1}}</ref><br />
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==Parts==<br />
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===Līlāvatī===<br />
{{Main|Līlāvatī}}<br />
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The name of the book comes from his daughter, Līlāvatī. It is the first volume of the ''Siddhānta Śiromaṇi''. The book contains thirteen chapters, 278 verses, mainly [[arithmetic]] and [[measurement]].<br />
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===Bījagaṇita===<br />
{{Main|Bijaganita}}<br />
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It is the second volume of ''Siddhānta Śiromaṇi''. It is divided into six parts, contains 213 verses and is devoted to [[algebra]].<br />
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=== ''Gaṇitādhyāya'' and ''Golādhyāya'' ===<br />
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''Gaṇitādhyāya'' and ''Golādhyāya'' of ''Siddhānta Śiromaṇi'' are devoted to astronomy. All put together there are about 900 verses.<ref>{{cite web|title=BHASKAR’S ASTRONOMY|url=http://www.khagolmandal.com/index.php?option=com_content&do_pdf=1&id=45&limitstart=2}}</ref> (''Gaṇitādhyāya'' has 451 and ''Golādhyāya'' has 501 verses).<br />
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==References==<br />
{{Reflist}}<br />
==External links ==<br />
* [https://archive.org/details/SiddhantaSiromaniSanskrit Scan of reprint] [https://archive.org/stream/siddhntairomai00bhskuoft#page/n3/mode/2up A 1917 edition]<br />
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{{Indian mathematics}}<br />
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{{DEFAULTSORT:Siddhanta Shiromani}}<br />
[[Category:Indian mathematics]]<br />
[[Category:Social history of India]]<br />
[[Category:Science and technology in India]]<br />
[[Category:History of algebra]]<br />
[[Category:1150s books]]<br />
[[Category:Indian astronomy texts]]</div>2603:7081:1501:BF70:C527:DEE7:5B3:6B0E