Varahamihira

Varahamihira , also Varaha Mihira, (6th century AD) was an Indian astronomer , mathematician and astrologer .

Life

Varahamihira was the son of Adityadasa and a brahmin of the Maga sect ( descended from the Iranian Zoroasters ). It comes from the Avanti region in the West Indies. According to one of his works, he is said to have lived in Kapitthaka, but it is not known exactly where that was. He mentions the astronomical center in Ujjain in one of his works, where Brahmagupta later also worked, but there is no explicit evidence that he worked there, but there are uncertain traditions and legends in both Hinduism and Jainism . He is said to have worked at the court of the ruler Chandragupta II Vikramaditya, but the known dates of life contradict this. The exact dates of his life are not known. Some of the astronomical dates in his major astronomical work are dated 505 AD. Since Brahmagupta also mentions him in 628, he lived in the 6th century.

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He is known for the Pancha-Siddhantika (Canon of the Five Books), a book on astronomy from around 575. There are references to older, now lost astronomical works and summarizes the contents of five treatises (Surya, Romaka, Paulisa, Vasistha, Paitamaha). Some (Romaka Siddhanta - doctrine of the Romans) reproduce the Greek epicyclic theory of the planets and the movement of the sun and moon from the 1st century AD (including Ptolemaic tablets ). Varahamihira corrects the observation values ​​according to the precession that has taken place in the meantime . The influence of ancient Western Greco-Roman and Babylonian science on his work is, however, controversial. The Paulisa Siddhanta also gives Greek knowledge, including the calculation of moon phases and eclipses. The name refers to an unknown Greek Paul. The Surya Siddhanta gives the oldest known knowledge of the Indians about astronomy and it was also known to Aryabhata I. The Vasistha Siddhanta is said to go back to the legendary sage of the same name.

The work also contains interesting information on the history of mathematics. In his canon there are many references to a place value system for numbers and he discovered some trigonometric identities:

${\displaystyle \sin ^{2}x+\cos ^{2}x=1}$

${\displaystyle \sin x=\cos \left({\frac {\pi }{2}}-x\right)}$

${\displaystyle {\frac {1-\cos 2x}{2}}=\sin ^{2}x}$

He improved the sine tables of Aryabhata I. He made discoveries about magic squares and he found a version of Pascal's triangle for calculating binomial coefficients .

He is also known as an important astrologer with several widespread (to this day popular) treatises such as the Brihat-Jataka (Great Birth or Great Horoscope, also called Horasastra - science of the hours, 400 verses in 25 chapters), Laghu-Jataka ( Little Birth, an abridged edition of the Brihat Jakata) about horoscopes (with clear influences from Greek astrology), Brihat Yogayatra (about favorable omens for campaigns and journeys, there is also an abbreviated version of this) and Brhadvivaha-patala (about the right time of the Marriage). He wrote an encyclopedia Brihatsamhita (large collection) with entries on a wide variety of topics such as astrology, meteorology, agriculture, architecture, gemstones and perfume, rituals and marriage, geography, calendar, plants, politics, economy, animals, astronomy (planetary movement, eclipses) . There are also shorter versions of this last work, his main work on natural astrology , but these are only known through quotations.

His works also have literary quality and passages from his works were therefore cited as exemplary examples by later writers.

literature

• G. Abraham Theories for the Motion of the Sun in the Pancasiddhantika , Arch. Hist. Exact Sci., Vol. 34, 1985, pp. 221-230
• KS Shukla The Panca-siddhantika of Varamihira , Part 1, Proc. Symp. Copernicus and Astronomy, New Delhi 1973, Indian J. History Sci., Volume 9, 1974, pp. 62-76, 141, Ganita, Volume 24, 1973, pp. 58-73, Part 2, Ganita, Volume 28 , 1977, pp. 99-116
• David Pingree Census of the Exact Sciences in Sanskrit , Series A, Volume 5, Philadelphia, American Philosophical Society 1970, pp. 563-595
• David Pingree History of Mathematical Astronomy in India , Dictionary of Scientific Biography
• Sudhakara Dvivedi Ganaka Tarangini or Lives of Hindu Astronomers , Benares, Jyotish Prakash Press 1933 (editor Padmakara Dvivedi)
• Ajay Mitra Shastri Varamihira and his times , Jodhpur: Kusumanjali Prakashan 1991
• Ajay Mitra Shastri India as seen in the Brhat-samhita of Varamihira , Delhi: Motilal Banarsidass 1969
• Srinivas Madabhushi, P. Srirama Murty Seismological Zones of Varamihira , Indian J. History of Science, 33, 1998, 111-117
• JF Fleet The topographical list of Brhat-samhita , Calcutta: Semushi 1973 (editor Kalyan Kumar Dasgupta)
• KV Sarma , article in Helaine Selin (editor) Encyclopedia of the History of Science, Technology and Medicine in non-western Cultures , Kluwer 1997

Fonts

Editions of his works

• Otto Neugebauer , David Pingree The Pancasiddhantika of Varamihira , part 1,2, Hist.-Filos. Skr. Danske Vid. Selskab, Volume 6, 1970, Issue 1,2, Copenhagen: Munksgaard 1970/71
• George Thibaut , Sudhakara Dvivedi (Editor): The Panchasiddhantika of Varaha Mihira , Chowkhamba Sanskrit Studies 68, Varanasi, 2nd edition 1968
• KV Sarma (editor), TS Kupanna Sastry (translator): The Pancasiddhantika of Varahamihira , Madras: PPST Foundation 1993
• David Pingree (Editor) Brhad-yatra of Varahamihira , Madras, Governmental Oriental Manuscript Library 1972
• M. Ramakrishna Bhat (editor and translator): Brhat-samhita of Varahamihira , 2 parts, Delhi, Motilal Banarsidass 1982
• V. Subrahmanya Sastri (editor and translator): Brhajjatakam of Varahamihira , 2nd edition, Bangalore: KR Krishnamurty 1971

Web links

• John J. O'Connor, Edmund F. Robertson :  Varahamihira. In: MacTutor History of Mathematics archive .
• Various editions of his works

Individual evidence

1. ↑ An outdated name for the region in which Ujjain is located
2. ↑ Kim Plofker Mathematics in India , Princeton University Press 2009, p. 326
3. ↑ DG Dhavale The Kapitthaka of Varahamihira , in Proceedings of the Symposium on Copernicus and Astronomy, New Delhi, 1973, Indian J. History Sci. 9, 1974, 77-78. KV Sarma in Selin (see literature) considers today's Kapitha in Uttar Pradesh to be probable and refers to the mention of the Chinese pilgrim Yuan-Chwang .
4. ↑ KV Sarma (in Selin, see literature) considers an activity at the court of King Maharajadhiraja Dravyavardhana in Ujjain in the middle of the 6th century to be proven.
5. ↑ Both in the Romaka, Paulisa and the Surya of his major astronomical work. The epoch dating 21 March 505 is more precise there
6. ↑ Kim Plofker, loc. cit.
7. ↑ So Al-Biruni in one of his works. Al-Biruni traveled to India in the 11th century
8. ↑ T. Hayashi, Historia Mathematica, Volume 14, 1987, pp. 159-166
9. ↑ RC Gupta, Ganita, Volume 14, 1992, pp. 45-49
10. ↑ Sarma, loc. cit.