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Pancha-siddhantika

January 01, 1970

Pancha-siddhantika (IAST: Pañca-siddhāntikā) is a 6th-century CE Sanskrit-language text written by astrologer-astronomer Varāhamihira in present-day Ujjain, India. It summarizes the contents of the treatises of the five contemporary schools of astronomy (siddhantas) prevalent in India.

Date edit

The text refers to the Shaka year 427, which corresponds to 505 CE.[1] Indian writers on astrology and astronomy generally chose an epoch year close to the date of composition of their texts, in order to facilitate correct astronomical calculations.[2] Thus, 505 CE was most probably the year in which Varāhamihira composed Pancha-Siddhantaka or began planning it.[3] The writings of both Varāhamihira and his commentator Utpala suggest that the text was Varāhamihira's first work.[4]

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 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.[5] Consequently, these scholars date Varāhamihira's lifespan to 505-587 CE.[6] Other scholars doubt the accuracy of Amaraja's statement, since he lived a thousand years after Varāhamihira.[5]

Contents edit

The text discusses five contemporary astronomical schools and their treatises, listed in order of importance, the last two regarded as inferior:[7][8][9]

  • Surya Siddhanta (or Saura Siddhanta), the treatise of the Sun
  • Romaka Siddhanta, the treatise of Romans or westerners
  • Paulisa Siddhanta, the treatise of Pulisha (IAST: Pauliśa, possibly Paulos)
  • Vasishtha Siddhanta, the treatise of the sage Vasishtha (IAST: Vāsiṣṭha)
  • Paitāmaha Siddhanta, the treatise of Pitamaha (the deity Brahma)

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.[10] 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[11]), but the present-day text is a later work that survives as part of a Purana text.[12] Thus, Varāhamihira's text is the only source about these ancient treatises.[13] Varāhamihira mentions several rules from these texts, but sometimes, it is not clear which rule is from which text.[9]

Varāhamihira refers to his Pancha-siddhantika as Karana (a concise exposition of astronomy), but the text covers a wider range of topics that appear in the texts belonging to the karana genre.[13]

Notable mathematical concepts in the Pancha-siddhantika include:[7]

  • Use of the decimal notation with its place-value number system[7]
  • Arithmetic addition and subtraction operations involving zero[7]
  • Associating sines with arcs at an intervals of 30°/8, thus implying that pi = square root of 10 = 3.16[9]

Like Brahma-gupta, Varāhamihira rejects Aryabhata's view (now universally accepted) that the earth revolves around the sun.[13]

Utpala suggests that Varāhamihira wrote an abridged version of the Pancha-siddhantika, but that work is now lost.[8] Shatananda based his Bhasvati-karana (c. 1098 CE) on the Surya Siddhanta section of the Pancha-siddhantika.[14]

Editions edit

Printed editions of the text include:[15]

References edit

  1. ^ A.M. Shastri 1991, pp. 3–4.
  2. ^ A.M. Shastri 1996, p. 8.
  3. ^ A.M. Shastri 1991, p. 3.
  4. ^ A.M. Shastri 1996, p. 25.
  5. ^ a b A.M. Shastri 1991, p. 4.
  6. ^ Evans, Brian (24 February 2014). The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Context. John Wiley & Sons. p. 61. ISBN 978-1118853979. Varāhamihira, a mathematician born around 505 CE and died 587 CE, who was also known for innovation with Pascal's triangle.
  7. ^ a b c d John F. Riley (2019). The Bone-setters: An Algebraic Odyssey. Matador. p. 95. ISBN 9781789016161.
  8. ^ a b A.M. Shastri 1991, p. 19.
  9. ^ a b c Kim Plofker 2009, p. 50.
  10. ^ Otto Neugebauer (1969). The Exact Sciences in Antiquity. Dover. p. 174. ISBN 9780486223322.
  11. ^ Kim Plofker 2009, p. 117.
  12. ^ Kim Plofker 2009, p. 67.
  13. ^ a b c A.M. Shastri 1991, p. 21.
  14. ^ A.M. Shastri 1969, p. 3.
  15. ^ K. Ramasubramanian; M.S. Sriram, eds. (2011). Tantrasaṅgraha of Nīlakaṇṭha Somayājī. Springer / Hindustan Book Agency. p. 565. ISBN 9780857290366.

Bibliography edit

January 01, 1970
pancha, siddhantika, iast, pañca, siddhāntikā, century, sanskrit, language, text, written, astrologer, astronomer, varāhamihira, present, ujjain, india, summarizes, contents, treatises, five, contemporary, schools, astronomy, siddhantas, prevalent, india, cont. Pancha siddhantika IAST Panca siddhantika is a 6th century CE Sanskrit language text written by astrologer astronomer Varahamihira in present day Ujjain India It summarizes the contents of the treatises of the five contemporary schools of astronomy siddhantas prevalent in India Contents 1 Date 2 Contents 3 Editions 4 References 4 1 BibliographyDate editThe text refers to the Shaka year 427 which corresponds to 505 CE 1 Indian writers on astrology and astronomy generally chose an epoch year close to the date of composition of their texts in order to facilitate correct astronomical calculations 2 Thus 505 CE was most probably the year in which Varahamihira composed Pancha Siddhantaka or began planning it 3 The writings of both Varahamihira and his commentator Utpala suggest that the text was Varahamihira s first work 4 However some scholars believe that 505 CE was the year of Varahamihira s birth or of another important event in his life This is because according to Amaraja the author of a commentary on Brahmagupta s Khanda khadyaka Varahamihira died in 587 CE Shaka year 509 If Varahamihira 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 5 Consequently these scholars date Varahamihira s lifespan to 505 587 CE 6 Other scholars doubt the accuracy of Amaraja s statement since he lived a thousand years after Varahamihira 5 Contents editThe text discusses five contemporary astronomical schools and their treatises listed in order of importance the last two regarded as inferior 7 8 9 Surya Siddhanta or Saura Siddhanta the treatise of the Sun Romaka Siddhanta the treatise of Romans or westerners Paulisa Siddhanta the treatise of Pulisha IAST Paulisa possibly Paulos Vasishtha Siddhanta the treatise of the sage Vasishtha IAST Vasiṣṭha Paitamaha Siddhanta the treatise of Pitamaha the deity Brahma Varahamihira 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 10 Similarly the Paitamaha Siddhanta referred to by Varahamihira was probably composed in the early 5th century distinct from an even earlier work of the same name 11 but the present day text is a later work that survives as part of a Purana text 12 Thus Varahamihira s text is the only source about these ancient treatises 13 Varahamihira mentions several rules from these texts but sometimes it is not clear which rule is from which text 9 Varahamihira refers to his Pancha siddhantika as Karana a concise exposition of astronomy but the text covers a wider range of topics that appear in the texts belonging to the karana genre 13 Notable mathematical concepts in the Pancha siddhantika include 7 Use of the decimal notation with its place value number system 7 Arithmetic addition and subtraction operations involving zero 7 Associating sines with arcs at an intervals of 30 8 thus implying that pi square root of 10 3 16 9 Like Brahma gupta Varahamihira rejects Aryabhata s view now universally accepted that the earth revolves around the sun 13 Utpala suggests that Varahamihira wrote an abridged version of the Pancha siddhantika but that work is now lost 8 Shatananda based his Bhasvati karana c 1098 CE on the Surya Siddhanta section of the Pancha siddhantika 14 Editions editPrinted editions of the text include 15 1889 Varanasi Edited by George Thibaut and Sudhakara Dvivedi with a Sanskrit commentary by Dvivedi 1970 English translation by Otto E Neugebauer and David Pingree 1993 Chennai Edited and translated by T S Kuppanna Sastry and K Venkateswara SarmaReferences edit A M Shastri 1991 pp 3 4 A M Shastri 1996 p 8 A M Shastri 1991 p 3 A M Shastri 1996 p 25 a b A M Shastri 1991 p 4 Evans Brian 24 February 2014 The Development of Mathematics Throughout the Centuries A Brief History in a Cultural Context John Wiley amp Sons p 61 ISBN 978 1118853979 Varahamihira a mathematician born around 505 CE and died 587 CE who was also known for innovation with Pascal s triangle a b c d John F Riley 2019 The Bone setters An Algebraic Odyssey Matador p 95 ISBN 9781789016161 a b A M Shastri 1991 p 19 a b c Kim Plofker 2009 p 50 Otto Neugebauer 1969 The Exact Sciences in Antiquity Dover p 174 ISBN 9780486223322 Kim Plofker 2009 p 117 Kim Plofker 2009 p 67 a b c A M Shastri 1991 p 21 A M Shastri 1969 p 3 K Ramasubramanian M S Sriram eds 2011 Tantrasaṅgraha of Nilakaṇṭha Somayaji Springer Hindustan Book Agency p 565 ISBN 9780857290366 Bibliography edit A M Shastri 1996 Ancient Indian Heritage Varahamihira s India Historical geography religion and society Aryan ISBN 9788173050817 A M Shastri 1991 Varahamihira and His Times Kusumanjali OCLC 28644897 A M Shastri 1969 India as Seen in the Bṛhatsaṁhita of Varahamihira Motilal Banarsidass ISBN 9780896842212 Kim Plofker 2009 Mathematics in India Princeton University Press ISBN 9780691120676 Retrieved from https en wikipedia org w index php title Pancha siddhantika amp oldid 1217036736, wikipedia, wiki, book, books, library,

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