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Varahamihira is considered one of the Navaratna's in King Vikramaditya's court. I would like to know if anybody has authentic ancient reference to when he or King Vikramaditya lived and which year was Brihat Samhita written?

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Varahamihira himself gives a hint of the current date in verse 3.2 of his book, the “Brihat-samhita”:

(2) “Whereas at present the one course of the sun commences at the beginning of Cancer, and the other at the beginning of Capricornus. That it is so, and different from what it was at one time can easily be ascertained from actual observation as follows:” (source)

N. Chidambaram Iyer, in the introduction of his translation of said work, interprets the verse as follows:

In verse 2 of Chapter III of his Brahat Samhita Varaha Mihira says:—

“At present the Solsticial points coincide with the beginning of Karkataka (Sign Cancer) and with the beginning of Makara (Sign Capricornus).”

This amounts to saying that the Vernal equinox, which is midway between the Solstices (90° from each), was at the commencement of Mesha (Sign Aries) i.e. coincided with the Star Revati where the fixed Hindu Zodiac commences. The precession of the equinoxes was known to the Hindus long before it was known to the Europeans, although Hindu astronomers are not agreed as to the nature of its course—some asserting that it oscillates on both sides of the star Revati while others that it makes a complete revolution round the heavens, a point about which even European astronomers have not arrived at any conclusion.

What follows is a calculation on the basis of the above verse deriving to the date of either 416 A.D. or 572 A.D., according to two different methods, explained in the article:

Substituting these values, we get n= 14,66 and 4,17,368 years, or = 1310 and 4,17,523 years, before first January 1883 where the bigger figures may be rejected as they refer to the position of the vernal Equinox in its second revolution. So that Varaha Mihira’s time is found to be either 1882-1466= 416 A.D. or 1882-1310=572 A.D., according to me or Mr. K. L. Chatrai respectively. Now it is true that 572 A.D. is in support of the supposed dates, above given, of Varaha Mihira’s birth and death. But I cannot bring myself to believe that Zeeta piscium was the Revati of the Hindus, for this simple reason that it is not on the ecliptic.

As a sidenote, the translator also provides the following information:

Varaha Mihira was a native of Avanti and the son of Adityadasa who was an astronomer and from whom he received his education as he himself tells us in his Brihat Jataka (Chap. XXVI Verse 5). The date of his birth is involved in obscurity. It is the practice of all the Hindu astronomers to give this information in their works on astronomy; but unfortunately Varaha Mihira’s work on astronomy, known as the Panchasidhantika, is now lost beyond all hope of recovery. The popular notion is that he was one of the 12 gems of the Court of Vikramarka. Now Vikrama Era, as we find from the Hindu calendar, dates from 56 B. C. whereas Varaha Mihira is considered to have flourished in the sixth century after Christ. So the Vikramarka of the first century before Christ must be different from the Vikramarka of the 6th century after Christ, unless we go to the length of believing that Vikramarka reigned, according to the Hindu legend, for a thousand years

Which means that, according to legend, Vihara Mihira might have lived in the first century B.C.

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