John Playfair

"“Aldebaran was therefore 40’ before the point of the vernal equinox, according to the Indian astronomy, in the year 3102 before Christ. (…) [Modern astronomy] gives the longitude of that star 13’ from the vernal equinox, at the time of the Calyougham, agreeing, within 53’, with the determination of the Indian astronomy. This agreement is the more remarkable, that the Brahmins, by their own rules for computing the motion of the fixed stars, could not have assigned this place to Aldebaran for the beginning of Calyougham, had they calculated it from a modern observation. For as they make the motion of the fixed stars too great by more than 3” annually, if they had calculated backward from 1491, they would have placed the fixed stars less advanced by 40 or 50, at their ancient epoch, than they have actually done.”"

"The observations on which the astronomy of India is founded, were made more than three thousand years before the Christian era. (…) Two other elements of this astronomy, the equation of the sun’s centre and the obliquity of the ecliptic (…) seem to point to a period still more remote, and to fix the origin of this astronomy 1000 or 1200 years earlier, that is, 4300 years before the Christian era."

"That observations made in India, when all Europe was barbarous or uninhabited, and investigations into the most subtle effects of gravitation made in Europe, near five thousand years afterwards, should thus come in mutual support of one another, is perhaps the most striking example of the progress and vicissitudes of science, which the history of mankind has yet exhibited. (179 0:160)"

"‘These operations are all founded on a very distinct conception of what happens in the case of an eclipse, and on the knowledge of this theorem, that, in a right-angled triangle, the square on the hypotenuse is equal to the squares of the other two sides. It is curious to find the theorem of PYTHAGORAS in India, where, for aught we know, it may have been discovered, and from whence that philosopher may have derived some of the solid, as well as the visionary speculations, with which he delighted to instruct or amuse his disciples.’"

"Now, it is worth remarking, that this property of the table of sines, which has been so long known in the East, was not observed by the mathematicians of Europe till about two hundred years ago […] If we were not already acquainted withthe high antiquity of the astronomy of Hindostan, 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 […]’ ‘In the progress of science […] the invention of trigonometry is to be considered as a step of great importance, and of considerable difficulty. It is an application of arithmetic to geometry […] (and) a little reflection will convince us, that he, who first formed the idea of exhibiting, in arithmetical tables, the ratios of the sides and angles of all possible triangles, and contrived the means of constructing such tables, must have been a man of profound thought, and of extensive knowledge. However, ancient, therefore, any book may be, in which we meet with a system of trigonometry, we may be assured, that it was not written in the infancy of science.’ ‘As we cannot, therefore, suppose the art of trigonometrical calculation to have been introduced till after a long preparation of other acquisitions, both geometrical and astronomical, we must reckon far back from the date of the Surya Siddhanta, before we come to the origin of the mathematical sciences in India […] Even among the Greeks […] an interval, of at least 1000 years, elapsed from the first observations in astronomy, to the invention of trigonometry; and we have surely no reason to suppose, that the progress of knowledge has been more rapid in other countries.’ ‘A thousand years therefore must be added to the age of the Surya Siddhanta, which we suppose here to be 2000 before Christ, in order that we may reach the origin of the sciences in Hindostan, and this brings us very nearly to the celebrated era of the Calyougham […]’"

"‘We must, therefore, enquire, whether this epoch is real or fictitious, that is, whether it has been determined by actual observation, or has been calculated from the modern epochs of the other tables. For it may naturally be supposed, that the Brahmins, having made observations in later times, or having borrowed from the astronomical knowledge of other nations […] have only calculated what they pretend that their ancestors observed. [...] In doing this, however, the Brahmins must have furnished us with means, almost infallible, of detecting their imposture. It is only for astronomy, in its most perfect state, to go back to the distance of forty-six centuries, and to ascertain the situation of the heavenly bodies at so remote a period. The modern astronomy of Europe […] could not venture on so difficult a task, were it not assisted by the theory of gravitation, and had not the integral calculus […] been able, at last, to determine the disturbances in our system, which arise from the action of the planets on one another. [...] Unless the corrections for these disturbances be taken into account, any system of astronomical tables, however accurate at the time of its formation, and however diligently copied from the heavens, will be found less exact for every instant, either before or after that time, and will continually diverge more and more from the truth, both for future and past ages. [...] It may (therefore) be established as a maxim, that, if there be given a system of astronomical tables, founded on observations of an unknown date (epoch), that date may be found, by taking the time when the tables represent the celestial motions most exactly. Here, therefore, we have a criterion, by which we are to judge of the pretensions of the Indian astronomy to so great antiquity.’ ‘...observations made in India, when all Europe was barbarous or uninhabited, and investigations into the most subtle effects of gravitation made in Europe, near five thousand years afterwards […] thus come in mutual support of one another.’"

"It was well observed by Playfair, some 90 years ago, that "a theory that explains everything explains nothing.""

"Playfair's judicious use of astronomy was countered by John Bentley with a scriptural argument which will not convince many people today. In 1825, Bentley objected: “By his [= Playfair’s] attempt to uphold the antiquity of Hindu books against absolute facts, he thereby supports all those horrid abuses and impositions found in them, under the pretended sanction of antiquity. Nay, his aim goes still deeper, for by the same means he endeavours to overturn the Mosaic account, and sap the very foundation of our religion: for if we are to believe in the antiquity of Hindu books, as he would wish us, then the Mosaic account is all a fable, or a fiction.”"

"One of the earliest estimates of the date of the Vedas was at once among the most scientific. In 1790, the Scottish mathematician John Playfair demonstrated that the starting-date of the astronomical observations recorded in the ephemeris tables still in use among Hindu astrologers (of which three copies had reached Europe between 1687 and 1787) had to be 4300 BC. His proposal was dismissed as absurd or as blasphemous by some, but it has so far not been refuted by any scientist... So, it turns out that the data given by the Brahmins corresponded not with the results deduced from their formulae, but with the actual positions, and this, according to Playfair, for nine different astronomical parameters. This is a bit much to explain away as coincidence or sheer luck."