The trigonometric tables of the Brahmins

One of my favourite pastimes is to dip into Google Books and scan through books concerning India and published 250-300 years back by the British when they were slowly and steadily gaining control over the vast territory. The area was relatively new to them and they were in an exploratory mode. Their penchant for meticulously recording their observations resulted in many, many books which, thanks to Google, we can access easily now.

This is my 37th post under the label, “Britindia” and I find that, even given the general poor readership of this blog, the series has attracted the least attention. To my dismay, my wife told me yesterday that if she finds the tag “Britindia’, she gives that post a miss.

Be that as it may, I shall carry on bravely…..

In an earlier post, I had linked to a report on the mathematical discoveries of the school of Madhava and their knowledge of the infinite series. In another post, I had linked to a book published in the year 1799 that had provided proof that the Hindus were aware of the binomial theorem.

To add to above, the “Transactions of the Royal Society of Edinburgh” published in the year 1798, contains on page 83,  a chapter titled, “Observations on the trigonometric tables of the Brahmins”. The author provides evidence of the existence of well laid-down trigonometric principles in India, 2000 years before the Europeans arrived at the same conclusions.

In the second volume of the Asiatic Researches, an extract is given from the Surya Siddhanta, the ancient book which has been long, though obscurely pointed out as the source of the astronomical knowledge of the Brahmins. The Surya Siddhanta is in the Sanscrit language: It is one of the Sastras, or inspired writings of the Hindoos, and is called the Jyotifh, or Astronomical, Sastra. It professes, to be a revelation from heaven, communicated to Meya, a man of great sanctity, about four millions of years ago, toward the close of the Satya Jug, or of the Golden Age of the Indian mythologists ; a period at which man is said to have been incomparably better than he is at present ; when his stature exceeded twenty-one cubits, and his life extended to ten thousand years.

Interwoven, however, with all these extravagant fictions, this singular book contains a very sober and rational system of astronomical calculation ; and even the principles and rules of trigonometry, a science of all others the most remote from fable, and the least susceptible of poetical decoration.

It is not a little singular, that we should find a table of versed sines in the Surya Siddhanta; for neither the Greek nor the Arabian mathematicians, had any such, nor had we, in modern Europe, till after the time of Petiscus, who wrote about the end of the century just mentioned. I think it might fairly be concluded, even if we had had no knowledge of the antiquity of the Surya Siddhanta, that the trigonometry contained in it is not borrowed from Greece or Arabia, as its fundamental rule was unknown to the geometers of both those countries, and is greatly preferable to that which they employed.

If we were not already acquainted with the high antiquity of the astronomy of Indostan, nothing could appear more singular, than to find a system of trigonometry, so perfect in its principles, in a book so ancient as the Surya Siddhanta. The antiquity of that book, the oldest of the Sastras, can scarce be accounted less than 2000 years before our era, even if we follow the very moderate system of Indian chronology laid down by Sir William Jones. It is remarkable that the Hindoos should have been thus led, at so early a period, to put in practice a method which has been but lately suggested in Europe as an important improvement in trigonometrical calculation.

If these are claims made by Indians, I would discount them immediately, prone as we are to making exaggerated assertions on our glorious past. But, these conclusions were arrived at by British scholars after a fairly rigourous and impartial analysis, and so carries more credibility.