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empire; and to form those ancient astronomical tables mentioned abdve which have so highly excited the astonishment of the literati of Europe.

It was long supposed that the ten numerical characters of Arithmetic were the invention of the Arabians: that nation, however, only introduced them into Europe, and confess themselves obliged to the Indians for them, among whom they were immemorially used. A nation, indeed, so devoted to commerce, as the Indians, could not carry on their concerns without this aid; and, while the polished governments of Rome and Greece were awkwardly using, for the purpose of enumeration, the letters of the alphabet, this wife and ingenious people, by the invention of the figures in question, were performing, with the utmost facility, the most complex calculations. Indeed, their adroitness in this respect has often been the admiration of foreigners, as a Banyan merchant, by the operation of memory only, and without pen or paper, is said to sum up his accounts with the greatest accuracy; and even the vulgar Indian, with his fingers, drawing the symbols of arithmetic in tfae

sand, sand, will go, with ease and celerity, through the most intricate numerical details. The art of ready computation was essentially necessary where the property was so various, where the annual revenues both of the sovereign and of many individuals among his subjects were so immense, and where such accuracy was necessary with respect to the number, weight, and measure, of the commodities trafficked* in. Connected with geometry qnd arithmetic is the invention of the balance, a symbol early exalted to the zodiac by the Brahmin astronomers, and in all likelihood also the product of the genius of this commercial people. The advance of the ancient Indians in mechanic science of every kind must, for the reasons above-mentioned, have been very early and very great; and; in, fact, like the venerable fabricators of Stonehenge and Abury, they seem to have been in possession of some secrets in that science which have not been transmitted to their posterity.

The same species of injustice that would rob them of the honour of inventing the decimal scale, the Indians appear to have suffered in regard to Algebra, which,

R 4 though though long attributed to Arabian ingenuity, is the undoubted fruit of Indian ge* nius; for, various treatises on this useful science,' as well as geometry, are alluded to in Sir William Jones's Dissertation (the last which he wrote) on the Philosophy of India ;* and, being in Sanscreet, they must necessarily be of an age far anterior to that of Archimedes, the great practical geometrician of Greece. With respect to the substance of these treatises, that is stijl among the Indian desiderata; though probably this will not long be the cafe, if Mr. Davis should fortunately have health and leisure to pursue the peculiar line of study which he has chosen for his province, and by which he has already been enabled so successfully to elucidate the abstruse mathematical sciences of the Brahmins.

The great advance, also, which we shall hereafter fee the ancient Indians had made in music, a science in which sounds are expressed by lines or chords accurately divided and arranged according to geometrical rules, exhibits an additional proof of their progress in this

• Asiatic Researches, vol.iv. p. 178, London, quarto edit.

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species of necessary knowledge. But what most of all proves their attachment to this science, as well as their exalted opinion concerning it, is, that, in their mysterious and hieroglyphic theology, they were accustomed to apply the figures and characters used in it to illustrate their ideas of the sanctity and perfection of the Deity. They transferred their geometrical speculations from body to spirit; and, from measuring terrestrial objects, they attempted to define subjects immeasurable, in-> finite, eternal. They compared the Deity to a Circle, that most perfect and comprehensive of all mathematical figures, whose centre is every where but whose circumference is no where to be found; and in allusion to the ancient doctrine of a certain plurality, which it has been demonstrated in preceding pages they believed to exist in the divine nature, they d<> signated it by the expressive symbol of an equilateral Triangle. Hence the winged globes that decorate the front of all the Egyptian temples, and the triangular columns in memorial of their sacred triad, at the entrance of most of the Indian pagodas.


To a minute investigation of the peculiar virtues and qualities contained in certain plants and herbs the old Indians were naturally incited by the vast variety and beauty of those innumerable vegetable productions that cover the face of that fertile region. These in many places grow up spontaneously; ma-* ny, applied to sacred uses, the ministers of religion ieverently cherished; and many the hand of traffic diligently cultivated for expor^ tation. Her rich spices and aromatics of every kind, her costly gums, and fragrant nards, of sovereign efficacy in the healing art, exceed all calculation in number and value.

Their beauty, number, and variety, indeed, could not fail of being most attentively marked by a race, who lived almost wholly in the open air; who ranged through vast forests, barefoot, in penances and in distant pilgrimages$ or resided in delicious groves; and, if th$ scenes of the Sacontala represent them justly, who cultivated in delicious gardens the sacred


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