Gleanings from Dharampal (2000)
by D.P. Agrawal

It is heartening to learn that Dharampal's collected works (the set costs less than $30) have been republished by Other India Publishers.  Quoting the British authorities themselves, he shows that Indian science was far too developed in comparison to that of the West. Below are a few examples of Indian astronomy and mathematics (Chapters refer to the book reference given below).

But before that, let us briefly describe the monumental contribution of Dharampal. Dharampal realized that if one wanted to have knowledge in any detail of society and life of India prior to British dominance, the obvious thing to do was to carefully peruse British-generated archives.  Notwithstanding his small income, he became a regular visitor to the India Office and the British Museum.  Photocopying required money and often, old manuscripts could not be photocopied.  So, he copied them in long hand, page after page, millions of words, day after day.  Thereafter, he would have the copied notes typed.  He thus retrieved and accumulated thousands of pages of information from the archival record.  When he returned to India, his most prized possessions were these notes which filled several large trunks and suitcases.  This picture that emerged from the total archival record was nothing short of stunning.  Contrary to what millions were taught in school textbooks, his notes indicated the existence of a functioning society, extremely competent in the arts and science of its day.  Its interactive grasp over its immediate natural environment was undisputed.  He showed that until approximately 1750, India and China were producing about 73% of the world’s total industrial production. And even until 1830 what both of these economies produced still amounted to 60% of the world’s industrial production.  As he recorded all this, Dharampal also saw how it was being undermined and how the British in fact went about pulverizing the Indian economy and society (Alvares 2000).

Regarding the astronomical knowledge, Dharampal says,

Even when the antiquity of Indian astronomy was being conceded, it was difficult to admit the eighteen-century Indian astronomers had any real competence.

The general incommunicativeness of eighteen-century Indian scholars in various fields had two probable roots:

1.      The usual secretiveness of such persons and

2.      The very sophistication and complexities of the theories, which was viewed as not having been understood by most Europeans

The paper (Chapter IV) by Colonel T. D. Pearse, sent to him by the Royal Society in London, and surviving in their archives, refers to the Indian knowledge of the four satellites of Jupiter and the seven satellites of Saturn.  Pearse further felt that the Indians must have possessed some kind of telescopic instruments to have acquired such detailed knowledge.  The author of Pearse's memories, while including a slightly modified version of this place in the memoirs, states:

We cannot pass this interesting communication without offering some reflection upon the subjects it embraces.  The circumstances of the four girls dancing the figure of Jupiter, as they ought to be according to the Brahmin's statement to Colonel Pearse, is a strong argument in favor of the superior knowledge of the heavenly bodies which the ancient Arabians and Hindus possessed.  The four dancing girls evidently represent the four satellites of Jupiter.  These circumjovial satellites (as they are styled by modern astronomers from the quirk of their motions in their orbits) were not known in Europe before the year 1609, and the third and fourth only are visible, and this but rarely and in the clearest atmosphere to the naked eye.  But it is truly interesting and curious that the figure of Saturn should be represented with seven arms.  At the time Colonel Pearse wrote his letter to the Royal Society, the sixth satellite of Saturn had not been discovered: it was first discovered by Herschel on the 28 August 1789; and the seventh satellite, which the seventh arm of the figure, without dispute, must be intended to represent, was not discovered by Hershel until he had completed his grand telescope of 40 feet focal length, when it was first observed by him on the 17 September 1789.  All the satellites of the Saturn are so small, and the planet is so remote from the earth, that the best telescopes are necessary for observing them.  May not the seventh arm having hold of the ring denote a circumstance connected with the orbits of these planets, which is that the planes of their orbits so nearly in accord with that of the ring, that the difference is not perceptible?  Undoubtedly, the ancient astronomers must have possessed the best instruments; probably differing from modern ones, but fully as powerful.

The writer further added: 'We are not aware that the Royal Society in any of its printed papers have noticed Colonel Pearse's communication, but our imagination, warmly interested as it has been in all that relates to the subject of the present memoir, has pictured the probability that Colonel Pearse's paper may have met the eye of Hershel, and may have been an additional spur to the indefatigable and wonderful labors of that great man.'

Reuben Burrow's unpublished paper (Chapter III) was addressed to the British Governor General Warren Hastings soon after Burrow came to India to take up his new job in Calcutta.  It is highly speculative and in a way, more in line with the contemporary intellectual tradition of the European enlightenment of the eighteenth century.  Though in itself it does not provide much factual data, and perhaps comes to even several erroneous conclusions as we would see them today, its very speculativeness seems to have provided inspiration and stimulus to a number of subsequent enquires about Indian sciences and mathematics.  The article 'A Proof that the Hindus had the Binomial Theorem' by Burrow himself, and the later dissertation by H. T. Colebrooke on 'Hindu Algebra' (given as introduction to his translation of 'Algebra with Arithmetic and Mensuration' of Brahmagupta and Bhascara) decidedly follow such speculativeness.  Acknowledging Burrow's contribution, particularly in bringing Indian algebra to the attention of Europeans, the article on 'Algebra' in the Encyclopaedia Britannica (8th edition) stated:

We are indebted, we believe, to Mr. Reuben Burrow for some of the earliest notices which reached Europe on this very curious subject. His eagerness to illustrate the history of the mathematical sciences led him to collect oriental manuscripts, some of which in the Persian language, with partial translations, were bequeathed to his friend Mr. Dalby of the Royal Military College, who communicated them to those interested in the subject, about the year 1800.

The article (Chapter V) on 'the Binomial Theorem' was published in 1790 in Calcutta. Until then, and in British reference like the Encyclopaedia Britannica well into the twentieth century, the discovery of this theorem has been credited to Newton.  Some 30 years later, Burrow's article was followed by another one, entitled 'Essay on the Binomial Theorem; as known to the Arabs.’  This later article was a sequel to the first by R. Burrow, and it concluded: 'It plainly appears, that whatever may have been the case in Europe, yet long before the time of Briggs the Arabians were acquainted with' the Binomial Theorem (Briggs was teaching around 1600, about a century before Newton).

This later author quoted Dr Hutton concerning the origin of the Binomial Theorem in Europe.  The following, from the longer extract of Hutton's account, is worth quoting:

Lucas De Burgo extracted the cube root by the same coefficients, about the year 1470. Briggs was the first who taught the rule for generating the coefficients of the terms, successively one from another, of any powers of a binomial, independent of those of any other power… This theorem then being thus plainly taught by Briggs about the year as Dr Wallis was, could be ignorant of it… and fully ascribe the invention to Newton… But I do not wonder that Briggs remark was unknown to Newton, who owed almost everything to genius and deep mediation, but very little to reading: and I have no doubt that he made the discovery himself, without any light from Briggs.

H. T. Colebroke's dissertation on 'Hindu Algebra,’ resulting from all the preceding investigations by men like R. Burrow, F. Wilford, S. Davis, Edward Strachey, and John Taylor, and from his own considerable knowledge, is a learned survey and comparison of the developments in Europe and India.  But the comparison that Indian Algebra may have had an independent development proves difficult for him to digest.  Reversing the speculations of Burrow, he comes to the conclusion that the 'Algebra of the Greeks,’ imperfect though he admits it to be, 'was made known to the Hindus by their Grecian instructors in improved astronomy.'  But wishing to be gracious and charitable, he infers that 'by the ingenuity of the Hindu scholars, the hint was rendered fruitful and the algebraic method was soon ripened from that slender beginning to the advanced state of a well arranged science.'

Sources:

Alvares, Claude. 2000. Preface. Indian Science and Technology in the Eighteenth Century. Goa: Other India Press. Pp i-xv.

Dharampal. 2000. Indian Science and Technology in the Eighteenth Century. Goa: Other India Press. Pp. 1-36.