Pancha-Siddhantika

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Pancha-Siddhantika, Les Cinq Canons astronomiques, de l'astronome et astronome hindou Varahamihira.

Les cinq canons sont : , , , et

  • Surya Siddhanta,
  • Romaka Siddhanta,
  • Paulisa Siddhanta,
  • Vasishtha Siddhanta,
  • Paitamaha Siddhantas.

Surya Siddhanta

Surya Siddhanta is a treatise of Indian astronomy.

Later Indian mathematicians and astronomers such as Aryabhata and Varahamihira made references to this text.

Varahamihira in his Panchasiddhantika contrasts it with four other treatises, besides the Paitamaha Siddhantas (which is more similar to the "classical" Vedanga Jyotisha), the Paulisha and Romaka Siddhantas (directly based on Hellenistic astronomy) and the Vasishta Siddhanta.

The work referred to by the title Surya Siddhanta has been repeatedly recast. There may have been an early work under that title dating back to the Buddhist Age of India (3rd century BC). The work as preserved and edited by Burgess (1858) dates to the Middle Ages. Utpala, a 10th century commentator of Varahamihira, quotes six shlokas of the Surya Siddhanta of his day, not one of which is to be found in the text now known as the Surya Siddhanta. The present Surya Siddhanta may nevertheless be considered a direct descendant of the text available to Varahamihira.[1] This article discusses the text as edited by Burgess. For what evidence we have of the Gupta period text, see Pancha-Siddhantika.

It has rules laid down to determine the true motions of the luminaries, which conform to their actual positions in the sky. It gives the locations of several stars other than the lunar nakshatras and treats the calculation of solar eclipses.

The table of contents in this text are:

  1. The Motions of the Planets
  2. The Places of the Planets
  3. Direction, Place and Time
  4. The Moon and Eclipses
  5. The Sun and Eclipses
  6. The Projection of Eclipses
  7. Planetary Conjunctions
  8. Of the Stars
  9. Risings and Settings
 10. The Moon's Risings and Settings
 11. Certain Malignant Aspects of the Sun and Moon
 12. Cosmogony, Geography, and Dimensions of the Creation
 13. The Gnomon
 14. The Movement of the Heavens and Human Activity

Methods for accurately calculating the shadow cast by a gnomon are discussed in both Chapters 3 and 13.

The astronomical time cycles contained in the text were remarkably accurate at the time. The Hindu Time Cycles , copied from an earlier work, are described in verses 11–23 of Chapter 1:

   11. That which begins with respirations (prana) is called real.... Six respirations make a vinadi, sixty of these a nadi;
   12. And sixty nadis make a sidereal day and night. Of thirty of these sidereal days is composed a month; a civil (savana) month consists of as many sunrises;
   13. A lunar month, of as many lunar days (tithi); a solar (saura) month is determined by the entrance of the sun into a sign of the zodiac; twelve months make a year. This is called a day of the gods.
   14. The day and night of the gods and of the demons are mutually opposed to one another. Six times sixty of them are a year of the gods, and likewise of the demons.
   15. Twelve thousand of these divine years are denominated a caturyuga; of ten thousand times four hundred and thirty-two solar years
   16. Is composed that caturyuga, with its dawn and twilight. The difference of the krtayuga and the other yugas, as measured by the difference in the number of the feet of Virtue in each, is as follows:
   17. The tenth part of a caturyuga, multiplied successively by four, three, two, and one, gives the length of the krta and the other yugas: the sixth part of each belongs to its dawn and twilight.
   18. One and seventy caturyugas make a manu; at its end is a twilight which has the number of years of a krtayuga, and which is a deluge.
   19. In a kalpa are reckoned fourteen manus with their respective twilights; at the commencement of the kalpa is a fifteenth dawn, having the length of a krtayuga.
   20. The kalpa, thus composed of a thousand caturyugas, and which brings about the destruction of all that exists, is a day of Brahma; his night is of the same length.
   21. His extreme age is a hundred, according to this valuation of a day and a night. The half of his life is past; of the remainder, this is the first kalpa.
   22. And of this kalpa, six manus are past, with their respective twilights; and of the Manu son of Vivasvant, twenty-seven caturyugas are past;
   23. Of the present, the twenty-eighth, caturyuga, this krtayuga is past....

When computed, this astronomical time cycle would give the following results:

   * The average length of the tropical year as 365.2421756 days, which is only 1.4 seconds shorter than the modern value of 365.2421904 days (J2000). This estimate remained the most accurate approximation for the length of the tropical year anywhere in the world for at least another six centuries, until Muslim mathematician Omar Khayyam gave a better approximation, though it still remains more accurate than the value given by the modern Gregorian calendar currently in use around the world, which gives the average length of the year as 365.2425 days.
   * The average length of the sidereal year, the actual length of the Earth's revolution around the Sun, as 365.2563627 days, which is virtually the same as the modern value of 365.25636305 days (J2000). This remained the most accurate estimate for the length of the sidereal year anywhere in the world for over a thousand years.

The actual astronomical value stated for the sidereal year however, is not as accurate. The length of the sidereal year is stated to be 365.258756 days, which is longer than the modern value by 3 minutes 27 seconds. This is due to the text using a different method for actual astronomical computation, rather than the Hindu cosmological time cycles copied from an earlier text, probably because the author didn't understand how to compute the complex time cycles. The author instead employed a mean motion for the Sun and a constant of precession inferior to that used in the Hindu cosmological time cycles.


Romaka Siddhanta

The Romaka Siddhanta (literally "Doctrine of the Romans") is an Indian astronomical treatise, based on the works of the ancient Romans.[1] "Siddhanta" literally means "Doctrine" or "Tradition".

It follows the Yavanajataka ("Saying of the Greek") as an example of the transmission of Western astronomical knowledge (especially the Alexandrian school) to India during the first centuries of our era.

The Romaka Siddhanta was particularly influential on the work of the Indian astronomer Varahamihira. It is the only one of all Indian astronomical works which is based on the tropical system. It was considered as one of "The Five Astronomical Canons" in Indian in the 5th century.


Paulisa Siddhanta

The Paulisa Siddhanta (literally, "Doctrine of Paul") is an Indian astronomical treatise, based on the works of the Western scholar Paul of Alexandria (c. 378 CE).[1] "Siddhanta" literally means "Doctrine" or "Tradition".

It follows the Yavanajataka ("Saying of the Greek") as an example of the transmission of Western astronomical knowledge (especially the Alexandrian school) to India during the first centuries of our era.

The Paulisa Siddhanta was particularly influential on the work of the Indian astronomer Varahamihira. It was considered as one of "The Five Astronomical Canons" in India in the 5th century.


Vasishtha Siddhanta

Vasishtha Siddhanta is one of the earliest astronomical systems in use in India, which is summarized in Varahamihira's Pancha-Siddhantika (6th century). It is attributed to sage Vasishtha and claims a date of composition of 1,299,101 BCE.[1] The original text probably dated to the 4th century, but it has been lost and our knowledge of it is restricted to Varahamira's account. Alberuni ascribes the work to Vishnuchandra.

Paitamaha Siddhantas

Paitamaha Siddhanta is one of the earliest astronomical systems in use in India, which is summarized in Varahamihira's Pancha-Siddhantika. It is the precursor to Aryabhata's astronomy, for it is so acknowledged by Aryabhata at the end of his Aryabhatiya.