QUESTIONS AND REMARKS

ON THE

ASTRONOMY OF THE HINDUS.

BY JOHN PLAYFAIR, A. M.

PROFESSOR OF MATHEMATICS, AT EDINBURGH,

WRITTEN 10th of OCTOBER, 1792.

PRESUMING on the invitation given, with so

much liberality, in the Advertisement prefixed to the second volume of the Asiatic Researches, I have ventured to submit the following queries and observations to the President and other Members of the learned Society of Bengal,

1.

Are any Books to be found among the Hindus, which treat professedly of

Geometry?

I AM led to propose this question by having observed, not only that the whole of the Indian Astronomy is a system constructed with great geometrical skill, but that the trigonometrical rules, given in the translation from the Súrya Siddhanta, with which

Mr. DAVIS

Mr. DAVIS has obliged the world, point out some very curious theorems, which must have been known to the author of that ancient book. The rule, for instance, by which the trigonometrical canon of the Hindu Astronomers is constructed, involves in it the following theorem: "If there be three arches "of a circle in arithmetical progression, the sum of "the sines of the two extreme arches is to twice the "sine of the middle arch, as the cosine of the com"mon difference of the arches to the radius of the "circle." Now this theorem, though not difficult to be demonstrated, is yet so far from obvious, that it seems not known to the Mathematicians of Europe till the beginning of the last century, when it was discovered by VIETA: it has ever since been used for the construction of trigonometrical tables, as it affords a method of calculating the sines and arches much easier than that, which depends on successive extractions of the square root. To find, that this theorem was known to the Brahmens many ages ago, is therefore extremely curious: and the more so, because there is some reason to think, that the commentator on the Siddhánta, quoted and translated by Mr. DAVIS, did not understand the principle of this rule, since the method, which he lays down, is entirely different, much less profound in theory, and much more difficult in practice. If this be true, it indicates a retrograde order in the progress of eastern science, which must have had its orgin in a very remote age,

Are

II.

Are any books of Hindu Arithmetic to be procured?

It should seem, that, if such books exist, they must contain much curious information, with many abridgements in the labour of calculating, and the like, all which may be reasonably expected from them, since an arithmetical notation, so perfect as that of India, has existed in that country much longer than in any other; but that, which most of all seems to deserve the attention of the learned, is the discovery said to be made of something like Algebra among the Hindus, such as the expression of number in general by certain symbols and the idea of negative quantities: These certainly cannot be too carefully inquired into, and will, it is hoped, be considered by the Society at Calcutta as a part of that rich mine, from which they have already extracted so many_valuable materials. The problem, mentioned by Mr. BURROW (c) proves, that the Hindus have turned their attention to certain arithmetical investigations, of which there is no trace in the writings of the Greek mathematicians.

III.

Must not a complete translation of the Surya Siddhanta be considered as the grand desideratum with respect to Indian Astronomy?

(c.) 3 Asiat. Res. 410. VOL. IV.

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SIR

SIR W. JONES gives us reason, I think, to hope, that this will be executed by Mr. DAVIS; and the specimen, which that gentleman has exhibited leaves as little reason to doubt of his abilities to translate the work accurately, as of the great value of the original: I have therefore only to express a wish, that, if there be any diagrams in the Súrya Siddhánta, they may be carefully preserved."

IV.

Would not a Catalogue Raisonne, containing an enumeration and a short account of the Sanscrit books on Indian Astronomy, be a work highly interesting and useful?

Might not an actual examination of the heavens, in company with a Hindu Astronomer, to ascertain all the stars and constellations, for which there are names in Sanscrit, prove a most valuable addition to our knowledge of Indian Astronomy? .

LET me here take the liberty of reminding the President of his promise to make such an examination; by which the mistakes concerning the Indian Zodiac, some of which he has already pointed out, may be decisively corrected.

May

VI.

May it not be of consequence to procure descriptions of the principal astronomical buildings and instruments, of which any. remains are still to be found, and which are certainly known to be of Hindu origin?

UNDER this head I would comprehend not only such works as the Observatory at Benares, which is well described by Sir ROBERT BARKER, but also such instruments as the Astrolabe, mentioned by Mr. BURROW in the appendix to the second volume of the Asiatic Researches; and engravings of such instruments will be necessary to accompany the descriptions.

THOUGH, in the preceding questions, there may be nothing, that has ecaped the attention of the Society in Bengal, yet they will, perhaps, be forgiven to one, who feels himself deeply interested in the subject, to which they relate, and who would not lose even the feeblest ray of a light, which, without the exertions of the Asiatic Society, must perish for ever.

REMARK BY THE PRESIDENT.

WE shall concur, I am persuaded, in giving our public thanks to professor PLAYFAIR for the Questions, which he has proposed, and in expressing our wish, that his example may be followed by the learned in Europe: concise answers to his queries will be given in my next annual discourse, the subject of which will comprise a general account of Indian astronomy

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