Academic journal article Transactions of the American Philosophical Society

Innovation and Stagnation in Medieval Indian Astronomy

Academic journal article Transactions of the American Philosophical Society

Innovation and Stagnation in Medieval Indian Astronomy

Article excerpt

The largest pre-modern literature on astronomy still extant today - precariously preserved on hundreds of thousands of rapidly deteriorating manuscripts - is that composed in India, overwhelmingly in the Sanskrit language, in the fourteen centuries between about 400 A.D. and 1800 A.D. But while India was far ahead of Europe, the Islamic countries, and China in the quantity of its publications in this field, its record in quality as judged by modern Western standards is ambiguous. For, despite India's great contributions to the world's sciences of astronomy, the fundamental breakthroughs that led to the almost universally received modem form of astronomy occurred elsewhere.

The basic elements of Indian mathematical astronomy came from the West in several stages. The first of these was the transmission to India in about the eighth century B-C. of Mesopotamian descriptions of the motion of the Sun's rising-point along the Eastern horizon, their recognition of the usefulness of intercalation, their use of New Moon as the beginning of the month, and various elements of their star-lore. The second was the transmission in the late fifth or early fourth century B.C. of Babylonian arithmetical methods of computing the passage of time and the progress of the Sun, the Moon, and the planets; the third was the introduction of Greek adaptations of Babylonian planetary theory in the second century A.D.; and the last an influx of pre-Ptolemaic, Hellenistic astronomy in the third and fourth centuries A.D. This last transmission included geometrical models of planetary motion (eccentric deferents, epicycles, and equants), the parameters of these models, eclipse theory, and some basic mathematical tools for solving problems in plane and spherical trigonometry, though without Menelaus' theorem for dealing directly with angles on the surface of a sphere. Indeed, the Sanskrit texts are now one of our primary sources for the reconstitution of Hellenistic astronomical theory and practice. Indian astronomers made great advances in the mathematics of the Greek systems that they had adopted; for instance, already in the fifth century A.D. they had applied the Euclidean algorithm of continued fractions to the solution of indeterminate equations, a crucial step toward the development of their characteristic mode of expressing the mean motions of the planets in terms of their integer numbers of revolutions in vast periods of time - in mahâyugas of 4,320,000 years and in kalpas of 4,320,000,000 years; they had derived from the Chords of Hipparchus the Sine, Cosine, and Versine funcions that are the foundations of modem trigonometry; and they had fully exploited the possibilities of applying the rudimentary analemmas of Hellenistic astronomy to the solution of numerous problems in spherics and in time-keeping.

Their prestige, as a result of this brilliance, was so great that in the middle of the sixth century the astronomers of the Sasanian Shah of Iran, Khusrau Anüshirwän, chose to follow the Indian Zij al-Arkand in composing the Royal Astronomical Tables rather than Ptolemy's Almagest, and in 718 parts of Varáhamifura's Pañcasiddhdntika served as the basis for the Chiu-chih li that Gu-tan Hsi-ta composed at the T'ang court. And in trigonometry and analemmas the Indians were the teachers of the Arabs, and ultimately of the West. Indeed, the first work on mathematical astronomy in Arabic that we know of is an adaptation of Brahmagupta's Khandakhddyaka made in Sind in 735, while the first serious work in this field available in Western Europe was the Latin translation, made by Adelard of Bath in Spain in 1126, of al-Majriti's revision of the Arabic Zij al-Sindhind of al-Khwârizml; al-Khwarizmi's main sources were Arabic versions of a Mahdsiddhdnta based on Brahmagupta's BrähmasphulasiddhQnta As a result, for much of the medieval period many European astronomers computed the positions of the planets, predicted eclipses, and cast horoscopes with methods and tables derived from or influenced by Indian astronomy, and they regarded an Indian city, Ujjayini, as lying on the world's prime meridian. …

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