II.-MATHEMATICS. In Mathematics he was greater -BUTLER: Hudibras. IN mental abstraction and concentration of thought the Hindus are proverbially happy. Apart from direct testimony on the point, the literature of the Hindus. furnishes unmistakable evidence to prove that the ancient Hindus possessed astonishing powers of memory and concentration of thought. Hence all such sciences and branches of study as demand concentration of thought and a highly-developed power of abstraction of the mind were highly cultivated by the Hindus. The science of mathematics, the most abstract of all sciences, must have had an irresistible fascination for the minds of the Hindus. Nor are there proofs wanting to support this statement. The most extensive cultivation which astronomy received at the hands of the Hindus is in itself a proof of their high proficiency in mathematics. The high antiquity of Hindu astronomy is an argument in support of a still greater antiquity of their mathematics. That the Hindus were selected by nature to excel all other nations in mathematics, is proved by her revealing to them the foundation of all mathematics. It has been admitted by all competent authorities that the Hindus were the inventors of the numerals. The great German critic, Schlegel, says that the Hindus invented "the decimal cyphers, the honour of which, next to letters the most important of human discoveries, has, with the com mon consent of historical authorities, been ascribed to the Hindus."1 Prof. Macdonell says: "In science, too, the debt of Europe to India has been considerable. There is, in the first place, the great fact that the Indians invented the numerical figures used all over the world. The influence which the decimal system of reckoning dependent on those figures has had not only on mathematics but on the progress of civilization in general, can hardly be over-estimated. During the eighth and ninth centuries the Indians became the teachers in arithmetic and algebra of the Arabs, and through them of the nations of the West. Thus, though we call the latter science by an Arabic name, it is a gift we owe to India."* Sir M. Monier Williams says: "From them (Hindus) the Arabs received not only their first conceptions of algebraic analysis, but also those numerical symbols and decimal notations now current every where in Europe, and which have rendered untold service to the progress of arithmetical science."3 Says Manning: "To whatever cyclopædia, journal or essay we refer, we uniformly find our numerals traced to India and the Arabs recognised as the medium through which they were introduced into Europe."4 Sir W. W. Hunter also says: "To them (the Hindus) we owe the invention of the numerical symbols on the decimal scale, The Indian figures 1 to 9 being abbreviated forms of initial letters of he numerals themselves, and the zero, or 0, 1 Schlegel's History of Literature, p. 123, 4 Ancient and Meliæval India, Vol. I, p. 376. representing the first letter of the Sanskrit word for empty (súnya). The Arabs borrowed them from the Hindus, and transmitted them to Europe." Professor Weber says: "It is to them (the Hindus) also that we owe the ingenious invention of the numerical symbols, which in like manner passed from them to the Arabs, and from these again to European scholars. By these latter, who were the disciples of the Arabs, frequent allusion is made to the Indians and uniformly in terms of high esteem; and one Sanskrit word even (uchcha) has passed into the Latin translations of Arabian astronomers."2 Professor Wilson says: "Even Delambre concedes their claim to the invention of numerical cyphers." ARITHMETIC. Mrs. Manning says: "Compared with other ancient nations, the Hindus were peculiarly strong in all the branches of arithmetic."3 Professor Weber, after declaring that the Arabs were disciples of the Hindus, says: "The same thing (i.e.. the Arabs borrowed from the Hindus) took place also in regard to algebra and arithmetic in particular, in both of which it appears the Hindus attained, quite independently, to a high degree of proficiency." Sir W. W. Hunter also says that the Hindus attained a very high proficiency in arithmetic and algebra independently of any foreign influence.”4 1 Imperial Gazetteer, p. 219. "India." 2 Weber's Indian Literature, p. 256. The English mathematician, Prof. Wallace, says: "The Lilavati treats of arithmetic, and contains not only the common rules of that science, but the application of these to various questions of interest, barter, mixtures, combinations, permutations, sums of progression, indeterminate problems, and mensuration of surfaces and solids. The rules are found to be exact and nearly as simple as in the present state of analytical investigation. The numerical results are readily deduced, and if they be compared with the earliest specimens of Greek calculation, the advantages of the decimal notation are placed in a striking light."1 It may, however, be mentioned that Lilavati, of which Professor Wallace speaks, is a comparatively modern manual of arithmetic ; and to judge of the merits of Hindu arithmetic from this book is to judge of the merits of English arithmetic from Chambers' manual of arithmetic. It may be added that the enormous extent to which numerical calculation goes in India, and the possession by the Hindus of by far the largest table of calculation, are in themselves proofs of the superior cultivation of the science of arithmetic by the Hindus. GEOMETRY. The ancient Hindus have always been celebrated for the remarkable progress they made in geometry. Professor Wallace says: 66 However ancient a book may 1Edinburgh Review, Vol. 29, p. 147. be in which a system of trigonometry occurs, we may be assured it was not written in the infancy of the science. Geometry must have been known in India long before the writing of the Surya Siddhanta," which is supposed by the Europeans to have been written before 2,000 B.C.2 Profesor Wallace says: "Surya Siddhanta contains a rational system of trigonometry, which differs entirely from that first known in Greece or Arabia. In fact it is founded on a geometrical theorem, which was not known to the geometricians of Europe before the time of Vieta, about two hundred years ago. And it employs the sines of arcs, a thing unknown to the Greeks, who used the chords of double arcs. The invention of sines has been attributed to the Arabs, but it is possible that they may have received this improvement in trigonometry as well as the numerical characters from India.”3 Mr. Elphinstone says: "In the Surya Siddhanta is contained a system of trigonometry which not only goes far beyond anything known to the Greeks, but involves theorems which were not discovered in Europe till two centuries ago. 194 Professor Wallace says: "In expressing the radius of a circle in parts of the circumference, the Hindus are quite singular. Ptolemy and the Greek mathematicians in their division of the radius preserved no reference to the circumference. The use of sines, as it was unknown to the Greeks, forms a difference between theirs and the Indian trigonometry. Their rule for the computation 1 Mill's India, Vol. II, P. 150. 2See Mill's India, Vol. II, p. 3, footnote. "Edinburgh Encyclopædia, "Geometry," p. 191, |