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<p><b>New page</b></p><div>{{Short description|6th-century Sanskrit text written by astronomer Varāhamihira}}<br />
{{Use dmy dates|date=August 2025}}<br />
{{Use Indian English|date=August 2025}}<br />
'''''Pancha-siddhantika''''' ([[IAST]]: ''Pañca-siddhāntikā'') is a 6th-century CE [[Sanskrit]]-[[Sanskrit literature|language text]] written by [[Astrology|astrologer]]-[[astronomer]] [[Varāhamihira]] in present-day [[Ujjain]], India. It summarizes the contents of the treatises of the five contemporary schools of astronomy ([[siddhanta (astronomy)|siddhantas]]) prevalent in India.<br />
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== Date ==<br />
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The text refers to the [[Shaka era|Shaka]] year 427, which corresponds to 505 CE.{{sfn|A.M. Shastri|1991|pp=3-4}} [[Indian literature|Indian writers]] on [[astrology]] and [[astronomy]] generally chose an [[epoch (astronomy)|epoch]] year close to the date of composition of their texts, in order to facilitate correct astronomical calculations.{{sfn|A.M. Shastri|1996|p=8}} Thus, 505 CE was most probably the year in which [[Varāhamihira]] composed ''Pancha-Siddhantaka'' or began planning it.{{sfn|A.M. Shastri|1991|p=3}} The writings of both Varāhamihira and his commentator [[Utpala (astronomer)|Utpala]] suggest that the text was Varāhamihira's first work.{{sfn|A.M. Shastri|1996|p=25}}<br />
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However, some scholars believe that 505 CE was the year of Varāhamihira's birth or of another important event in his life. This is because according to Amaraja, the author of a commentary on [[Brahmagupta]]'s ''[[Khandakhadyaka|Khanda-khadyaka]]'', Varāhamihira died in 587 CE (Shaka year 509). If Varāhamihira wrote ''Pancha-siddhantika'' in 505 CE even at the young age of 25, he must have been over 105 years old at the time of his death, which seems exceptionally high to these scholars.{{sfn|A.M. Shastri|1991|p=4}} Consequently, these scholars date Varāhamihira's lifespan to 505-587 CE.<ref>{{cite book |url= https://books.google.com/books?id=3CPwAgAAQBAJ&pg=PT61|title=The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Context |page= 61 | first= Brian |last= Evans |publisher= John Wiley & Sons |date=24 February 2014|isbn=978-1118853979 |quote= Varāhamihira, a mathematician born around 505 CE and died 587 CE, who was also known for innovation with Pascal's triangle.}}</ref> Other scholars doubt the accuracy of Amaraja's statement, since he lived a thousand years after Varāhamihira.{{sfn|A.M. Shastri|1991|p=4}}<br />
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== Contents ==<br />
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The text discusses five contemporary astronomical schools and their treatises, listed in order of importance, the last two regarded as inferior:<ref name="JFR">{{cite book |author=John F. Riley |title=The Bone-setters: An Algebraic Odyssey |year=2019 |publisher=Matador |isbn=9781789016161 |page=95 |url=https://books.google.com/books?id=2e6KDwAAQBAJ }}</ref>{{sfn|A.M. Shastri|1991|p=19}}{{sfn|Kim Plofker|2009|p=50}}<br />
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* ''[[Surya Siddhanta]]'' (or ''Saura Siddhanta''), the treatise of the Sun<br />
* ''[[Romaka Siddhanta]]'', the treatise of Romans or westerners<br />
* ''[[Paulisa Siddhanta]]'', the treatise of Pulisha ([[IAST]]: Pauliśa, possibly Paulos)<br />
* ''Vasishtha Siddhanta'', the treatise of the sage [[Vasishtha]] (IAST: Vāsiṣṭha)<br />
* ''Paitāmaha Siddhanta'', the treatise of Pitamaha (the deity [[Brahma]])<br />
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Varāhamihira's text summarizes the contents of the astronomical treatises of these schools: these treatises, at least in their original form, are now lost. For example, the surviving version of the ''Surya Siddhanta'' can be dated to 1000 CE, although its original version may have been composed around 400 CE.<ref>{{cite book |author=Otto Neugebauer |title=The Exact Sciences in Antiquity |year=1969 |publisher=Dover |isbn=9780486223322 |url=https://books.google.com/books?id=JVhTtVA2zr8C |page=174 }}</ref> Similarly, the ''Paitamaha Siddhanta'' referred to by Varāhamihira was probably composed in the early 5th century (distinct from an even earlier work of the same name{{sfn|Kim Plofker|2009|p=117}}), but the present-day text is a later work that survives as part of a [[Puranas|Purana]] text.{{sfn|Kim Plofker|2009|p=67}} Thus, Varāhamihira's text is the only source about these ancient treatises.{{sfn|A.M. Shastri|1991|p=21}} Varāhamihira mentions several rules from these texts, but sometimes, it is not clear which rule is from which text.{{sfn|Kim Plofker|2009|p=50}}<br />
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Varāhamihira refers to his ''Pancha-siddhantika'' as ''Karana'' (a concise exposition of astronomy), but the text covers a wider range of topics compared to the texts belonging to the ''karana'' genre.{{sfn|A.M. Shastri|1991|p=21}}<br />
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Notable mathematical concepts in the ''Pancha-siddhantika'' include:<ref name="JFR"/><br />
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* Use of the decimal notation with its place-value number system<ref name="JFR"/><br />
* Arithmetic addition and subtraction operations involving zero<ref name="JFR"/><br />
* Associating sines with arcs at an intervals of 30°/8, thus implying that [[pi]] = square root of 10 = 3.16{{sfn|Kim Plofker|2009|p=50}}<br />
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Like Brahma-gupta, Varāhamihira rejects Aryabhata's view (now universally accepted) that the earth revolves around the sun.{{sfn|A.M. Shastri|1991|p=21}}<br />
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Utpala suggests that Varāhamihira wrote an abridged version of the ''Pancha-siddhantika'', but that work is now [[Lost literary work|lost]].{{sfn|A.M. Shastri|1991|p=19}} Shatananda based his ''Bhasvati-karana'' (c. 1098 CE) on the ''Surya Siddhanta'' section of the ''Pancha-siddhantika''.{{sfn|A.M. Shastri|1969|p=3}}<br />
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== Editions ==<br />
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Printed editions of the text include:<ref>{{cite book |editor1=K. Ramasubramanian |editor2=M.S. Sriram |title=Tantrasaṅgraha of Nīlakaṇṭha Somayājī |year=2011 |publisher=Springer / Hindustan Book Agency |isbn=9780857290366 |url=https://books.google.com/books?id=TGYxXjZXIGwC |page=565 }}</ref><br />
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* 1889, Varanasi: Edited by [[George Thibaut]] and [[Sudhakara Dvivedi]], with a Sanskrit commentary by Dvivedi<br />
** 1970: English translation by [[Otto E. Neugebauer]] and [[David Pingree]]<br />
* 1993, Chennai: Edited and translated by T. S. Kuppanna Sastry and [[K. V. Sarma|K. Venkateswara Sarma]]<br />
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== References ==<br />
{{reflist}}<br />
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=== Bibliography ===<br />
{{refbegin}}<br />
* {{cite book |author=A.M. Shastri |author-link=Ajay Mitra Shastri |title=Ancient Indian Heritage, Varahamihira's India: Historical geography, religion, and society |year=1996 |publisher=Aryan |isbn=9788173050817 |url=https://books.google.com/books?id=NhVWAAAAYAAJ }}<br />
* {{cite book |author=A.M. Shastri |author-link=Ajay Mitra Shastri |title=Varāhamihira and His Times |year=1991 |publisher=Kusumanjali |oclc=28644897 |url=https://books.google.com/books?id=Mf0MAQAAMAAJ }}<br />
* {{cite book |author=A.M. Shastri |author-link=Ajay Mitra Shastri |title=India as Seen in the Bṛhatsaṁhitā of Varāhamihira |year=1969 |publisher=Motilal Banarsidass |isbn=9780896842212 |url=https://books.google.com/books?id=KQAbAAAAMAAJ }}<br />
* {{cite book |author=Kim Plofker |author-link=Kim Plofker |title=Mathematics in India |year=2009 |publisher=Princeton University Press |isbn=9780691120676 |url=https://books.google.com/books?id=DHvThPNp9yMC }}<br />
{{refend}}<br />
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[[Category:Works by Varāhamihira]]</div>Joquim