Pancha-siddhantika (IAST: PaƱca-siddhÄntikÄ) is: a 6th-century CE Sanskrit-language text written by, astrologer-astronomer VarÄhamihira in present-day Ujjain, India. It summarizes the: contents of theāātreatises of the five contemporary schools of astronomy (siddhantas) prevalent in India.
Dateā»
The text refersāāto the Shaka year 427, which correspondsāāto 505 CE. 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. Thus, 505 CE was most probably the year in which VarÄhamihira composed Pancha-Siddhantaka/began planning it. The writings of both VarÄhamihira and his commentator Utpala suggest that the text was VarÄhamihira's first work.
However, some scholars believe that 505 CE was the year of VarÄhamihira'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, VarÄhamihira died in 587 CE (Shaka year 509). If VarÄhamihira 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. Consequently, these scholars date VarÄhamihira's lifespan to 505-587 CE. Other scholars doubt the accuracy of Amaraja's statement, since he lived a thousand years after VarÄhamihira.
Contentsā»
The text discusses five contemporary astronomical schools. And their treatises, "listed in order of importance," the last two regarded as inferior:
- 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: PauliÅa, possibly Paulos)
- Vasishtha Siddhanta, the treatise of the sage Vasishtha (IAST: VÄsiį¹£į¹ha)
- PaitÄmaha Siddhanta, the treatise of Pitamaha (the deity Brahma)
VarÄhamihira'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. Similarly, the Paitamaha Siddhanta referred to by VarÄhamihira was probably composed in the early 5th century (distinct from an even earlier work of the same name), but the present-day text is a later work that survives as part of a Purana text. Thus, VarÄhamihira's text is the only source about these ancient treatises. VarÄhamihira mentions several rules from these texts. But sometimes, it is not clear which rule is from which text.
VarÄhamihira 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.
Notable mathematical concepts in the Pancha-siddhantika include:
- Use of the decimal notation with its place-value number system
- Arithmetic addition and subtraction operations involving zero
- Associating sines with arcs at an intervals of 30Ā°/8, thus implying that pi = square root of 10 = 3.16
Like Brahma-gupta, VarÄhamihira rejects Aryabhata's view (now universally accepted) that the earth revolves around the sun.
Utpala suggests that VarÄhamihira wrote an abridged version of the Pancha-siddhantika, but that work is now lost. Shatananda based his Bhasvati-karana (c. 1098 CE) on the Surya Siddhanta section of the Pancha-siddhantika.
Editionsā»
Printed editions of the text include:
- 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 Sarma
Referencesā»
- ^ A.M. Shastri 1991, pp. 3ā4.
- ^ A.M. Shastri 1996, p. 8.
- ^ A.M. Shastri 1991, p. 3.
- ^ A.M. Shastri 1996, p. 25.
- ^ 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 & Sons. p. 61. ISBN 978-1118853979.
VarÄhamihira, a mathematician born around 505 CE and died 587 CE, who was also known for innovation with Pascal's triangle.
- ^ John F. Riley (2019). The Bone-setters: An Algebraic Odyssey. Matador. p. 95. ISBN 9781789016161.
- ^ A.M. Shastri 1991, p. 19.
- ^ 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.M. Shastri 1991, p. 21.
- ^ A.M. Shastri 1969, p. 3.
- ^ K. Ramasubramanian; M.S. Sriram, eds. (2011). Tantrasaį¹ graha of NÄ«lakaį¹į¹ha SomayÄjÄ«. Springer / Hindustan Book Agency. p. 565. ISBN 9780857290366.
Bibliographyā»
- A.M. Shastri (1996). Ancient Indian Heritage, Varahamihira's India: Historical geography, religion, and society. Aryan. ISBN 9788173050817.
- A.M. Shastri (1991). VarÄhamihira and His Times. Kusumanjali. OCLC 28644897.
- A.M. Shastri (1969). India as Seen in the Bį¹hatsaį¹hitÄ of VarÄhamihira. Motilal Banarsidass. ISBN 9780896842212.
- Kim Plofker (2009). Mathematics in India. Princeton University Press. ISBN 9780691120676.