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Paitamaha Siddhanta

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Title: Paitamaha Siddhanta  
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Subject: Sanskrit literature, Varāhamihira, Indian mathematics, Surya Siddhanta
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Paitamaha Siddhanta

Born 505 CE
Died 587 CE
Occupation astronomer, mathematician, and astrologer
Nationality Indian
Ethnicity Indian
Period Gupta era
Subjects Astronomy, Astrology, Mathematics
Notable work(s) Pancha-Siddhāntikā, Brihat-Samhita, Brihat Jataka

Varāhamihira Yashodharman Vikramaditya of Malwa.


He was the first one to mention in his work Pañcasiddhāntikā that the ayanamsa, or the shifting of the equinox, is 50.32 seconds.


Varahamihir's main work is the book Pañcasiddhāntikā (or Pancha-Siddhantika, "[Treatise] on the Five [Astronomical] Canons) dated ca. 575 CE gives us information about older Indian texts which are now lost. The work is a treatise on mathematical astronomy and it summarises five earlier astronomical treatises, namely the Surya Siddhanta, Romaka Siddhanta, Paulisa Siddhanta, Vasishtha Siddhanta and Paitamaha Siddhantas. It is a compendium of Vedanga Jyotisha as well as Hellenistic astronomy (including Greek, Egyptian and Roman elements).[2] He was the first one to mention in his work Pancha Siddhantika that the ayanamsa, or the shifting of the equinox is 50.32 seconds.

The 11th century Iranian scholar Alberuni also described the details of "The Five Astronomical Canons":

"They [the Indians] have 5 Siddhāntas:
  • Sūrya-Siddhānta, ie. the Siddhānta of the Sun, composed by Lāṭadeva,
  • Vasishtha-siddhānta, so called from one of the stars of the Great Bear, composed by Vishnucandra,
  • Pulisa-siddhānta, so called from Paulisa, the Greek, from the city of Saintra, which is supposed to be Alexandria, composed by Pulisa.
  • Romaka-siddhānta, so called from the Rūm, ie. the subjects of the Roman Empire, composed by Śrīsheṇa.


Another important contribution of Varahamihira is the encyclopedic Brihat-Samhita. It covers wide ranging subjects of human interest, including astrology, planetary movements, eclipses, rainfall, clouds, architecture, growth of crops, manufacture of perfume, matrimony, domestic relations, gems, pearls, and rituals. The volume expounds on gemstone evaluation criterion found in the Garuda Purana, and elaborates on the sacred Nine Pearls from the same text. It contains 106 chapters and is known as the "great compilation".

On Astrology

He was also an astrologer. He wrote on all the three main branches of Jyotisha astrology:

  • Brihat Jataka - is considered as one the five main treatises on Hindu astrology on horoscopy.
  • Laghu Jataka - also known as 'Swalpa Jataka'
  • Samasa Samhita - also known as 'Lagu Samhita' or 'Swalpa Samhita'
  • Brihat Yogayatra - also known as 'Mahayatra' or 'Yakshaswamedhiya yatra'
  • Yoga Yatra - also known as 'Swalpa yatra'
  • Tikkani Yatra
  • Brihat Vivaha Patal
  • Lagu Vivaha Patal - also known as 'Swalpa Vivaha Patal'
  • Lagna Varahi
  • Kutuhala Manjari
  • Daivajna Vallabha (apocryphal)

His son Prithuyasas also contributed in the Hindu astrology; his book Hora Sara is a famous book on horoscopy. Khana (also named Lilavati elsewhere) the medieval Bengali poetess astrologer is believed to be the daughter-in-law of Varahamihir.

Western influences

The Romaka Siddhanta ("Doctrine of the Romans") and the Paulisa Siddhanta ("Doctrine of Paul") were two works of Western origin which influenced Varahamihir's thought, though this view is controversial as there is much evidence to suggest that it was actually Vedic thought indigenous to India which first influenced Western astrologers and subsequently came back to India reformulated.

A comment in the Brihat-Samhita by Varahamihir says: "The Greeks, though foreign, must be honored since they have shown tremendous interest in our science....." ("mleccha hi yavanah tesu samyak shastram kdamsthitam/ rsivat te 'p i pujyante kim punar daivavid dvijah" (Brihat-Samhita 2.15)).



Varahamihira's mathematical work included the discovery of the trigonometric formulas

\sin^2 x + \cos^2 x = 1 \;\!
\sin x = \cos\left(\frac{\pi} {2} - x \right)
\frac {1 - \cos 2x}{2} = \sin^2x

Varahamihira improved the accuracy of the sine tables of Aryabhata I.


He defined the algebraic properties of zero as well as of negative numbers.[3]


He was among the first mathematicians to discover a version of what is now known as the Pascal's triangle. He used it to calculate the binomial coefficients.[4][5][6]


Among Varahamihira's contribution to physics is his statement that reflection is caused by the back-scattering of particles and refraction (the change of direction of a light ray as it moves from one medium into another) by the ability of the particles to penetrate inner spaces of the material, much like fluids that move through porous objects.[7]

1. ^ "the Pañca-siddhāntikā ("Five Treatises"), a compendium of Greek, Egyptian, Roman and Indian astronomy. Varāhamihir's knowledge of Western astronomy was thorough. In 5 sections, his monumental work progresses through native Indian astronomy and culminates in 2 treatises on Western astronomy, showing calculations based on Greek and Alexandrian reckoning and even giving complete Ptolemaic mathematical charts and tables. Encyclopædia Britannica (2007) s.v.Varahamihira ^

2. E. C. Sachau, Alberuni's India (1910), vol. I, p. 153

See also

  • Hora Sara


External links

  • .
  • Pancasiddhantika, Brihat Jataka, Brihat Samhita and Hora Shastra Various editions in English and Sanskrit. (PDF)
  • The Brihat Jataka (1905) Pdf edition internet archive

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