The Recovery of Early Greek Astronomy from India

Abstract

(ProQuest: ... denotes formulae omitted.)(ProQuest: ... denotes non-USASCII text omitted.)The recent publication by O. Neugebauer of his monumental A history of ancient mathematical astronomy1 provides us with penetrating analyses of remnants of Greek astronomy. Those remains are dominated by the Greatest, Ptolemy's ZiivTaCic fiadruiariK-f),2 which appears to have been so enormously successful that his principal successors-Pappus,3 Theon,4 and Stephanus6- limited their activities to writing of commentaries on it and on Handy tables8 that are largely based on it. And of his predecessors' works virtually all that survive intact are elementary treatises on spherics by Euclid, Autolycus, and Theodosius,7 that were incorporated in early Byzantine period into a collection used for instruction in schools. To supplement Ptolemy's accounts of work of Apollonius,8 Hipparchus,9 and other early Greek astronomers, historians have had to rely on disparate and often desperate sources: on handbooks written by Geminus10 in about 50 ad and by Cleomedes11 in about 370 ad; on encyclopedias of Pliny1* and of Martianus Capella;13 on philosophical treatise of Adrastus pillaged by Theon of Smyrna and Chalcidius; on summaries and commentaries of Proclus and of Simplicius; on astrological compendia of Vettius Valens, pseudoRhetorius, and pseudo-Heliodorus; and on fragmentary inscriptions and papyri.However, one of those civilizations that were profoundly influenced by Greek culture has preserved a number of texts (composed in second through seventh centuries ad) that represent non-Ptolemaic Greek astronomy. This civilization is that of India, and texts are in Sanskrit.14 It is certain that Greek astronomical texts were translated into Syriac and into Pahlavi, as well as into Sanskrit, but of former we still have but little, and of latter almost nothing; and in both cases we must rely for much of our knowledge on late accounts in Arabic.16 The Sanskrit texts, however, though often either incorrectly or not at all understood by those who have transmitted them to us, formed basis of a scientific tradition that only in this century has been destroyed under impact of Western astronomy. The object of this paper is to characterize Greek astronomy transmitted to India and to determine times and places in which this transmission was effected, in so far as that is possible.The transmission was certainly very complex. It involved many levels and periods of Greek astronomy: adaptations of Babylonian lunar and planetary theories; year-length of Hipparchus, an adaptation of his coordinate-system for fixed stars, and his theories of precession and trepidation; tables of chords transformed into tables of sines; Peripatetic planetary models employing double epicycles and concentres with equants; non-Ptolemaic planetary models combining an eccentre with an epicycle; solution of problems in spherical astronomy by means of gnomons and analemmata; computation and, probably, projection of eclipses; essential data for computing planetary parameters; models for determining planetary latitudes; and basic theory used in determining planetary distances. And this transmission extended over several centuries; it apparently began in second century of our era, and continued till late fourth or early fifth century. The locations of recipient Indians indicate Western India as point of entry of these various Greek theories; there exists literary, epigraphic, archaeological, and numismatic evidence for a massive Greek influence on this area in precisely period of this transmission.16Since none of original translations of Greek texts into Sanskrit survives, we must try to disentangle transmitted material from adaptations of later authors. Often we have not sufficient evidence to be very confident about particular details in historical process that led to creation of astronomy of siddhântas, though general trend of events is now quite clear. …