The Mesopotamian Origin of Early Indian Mathematical Astronomy

This relationship I originally proposed in Isis, liv (1963), 231–3.

Both recensions along with Somākara's commentary were first edited by Weber A. , Über den Vedakalender, namens Jyotisham (Berlin, 1862) (the text of one recension had been published at Bombay in 1833); the text of the Yajur-recension along with the non-Yajur verses of the Rk-recension were reprinted by Thibaut G. , “Contributions to the Explanation of the Jyotisha-Vedánga”, Journal of the Asiatic Society of Bengal, xlvi (1877), 411–37, esp. 413–6; the Rk-recension was reprinted by Modaka J. B. of Thana in 1885; one recension was included in Vedasya sadaṅga (Bombay, 1892); both recensions were edited and commented on by Bārhaspatya (Lāla Chotelāl) in the Hindustan review for 1907 (reprinted Allahabad, 1960) and again, with Somākara's bhāsya, by Dvivedin S. (Benares, 1908). The most recent attempt at an edition and at an understanding of both texts is by Shamasastry R. (Mysore, 1936). The more recent efforts by Kulkarni B. R. , The Lagna System of the Vedanga Jyotisha (Dhulia, 1943); by Prasad G. , “The Astronomy of the Vedāṅga Jyotisa”, Journal of the Ganganath Jha Research Institute, iv (1946–47), 239–48; and by Chakravarty A. K. , “The Working Principle of the Vedāṅga Jyotisa Calendar”, Indian studies past and present, x (1968–69), 31–42, as well as the older work by Tilak B. G. , Vedic chronology and Vedanga Jyotisha (Poona, 1925), do not advance our understanding of this text.

I have used the recent edition with translation and commentary by Kangle R. P. (3 vols, Bombay, 1960–65).

Trautmann T. R. , Kautilya and the Artha⋅āstra (Leiden, 1971), 176–84.

I have used the edition by Mukhopadhyaya S. (Santiniketan, 1954); this is reprinted in Vaidya's P. L. edition of the Divyāvadāna, Buddhist Sanskrit texts, xx (Darbhanga, 1959), 314–425.

Zürcher E. , The Buddhist conquest of China (2 vols, Leiden, 1959), i, 32–4.

Zürcher , op. cit., i, 47–51.

Ibid., 65–71.

Edited, translated, and commented on by Neugebauer O. and Pingree D. (2 vols, Copenhagen, 1970–71).

Edition, translation, and commentary by Pingree D. to appear in the Harvard oriental series; the reference is to 79,3.

These works have been printed several times by the Jainas in India; I have used the edition of the first two by Kohl J. F. (Stuttgart, 1937). See also Thibaut G. F. , “On the Sūryaprajñapti”, Journal of the Asiatic Society of Bengal, xlix (1880), 107–27 and 181–206.

Sūriyapannatti, I, 3, and XX, 59.

On the various Gargas see Pingree D. , Census of the exact sciences in Sanskrit, Series A, ii (Philadelphia, 1971), 115b–126a.

For the Paitāmahasiddhānta, see Pingree D. , “The Paitāmahasiddhānta of the Visnudharmottarapurāna”, Brahmavidyā, xxxi-xxxii (1967–68), 472–510. Compare Garga as cited by Somākara on Yajur-recension 11 and Paitāmahasiddhānta, III, 1; cf. Yavanajātaka, 79, 6.

Pp. 57–8.

II, 20, 35.

Yavanajātaka, 79, 27; this could be interpreted as either an out-flowing or an in-flowing clock.

Pañcasiddhāntikā, 14, 31–2.

See Neugebauer O. , “The Water Clock in Babylonian Astronomy”, Isis, xxxvii (1947), 37–43.

See, e.g., van der Waerden B. L. , “The Earliest Astronomical Computations”, Journal of Near Eastern studies, x (1951), 20–34.

II, 20, 37–8.

II, 20, 61–64.

Pp. 53 and 100–8.

79, 26 and 31.

Pañcasiddhāntikā, 2, 8.

II, 20, 39–42.

Pañcasiddhāntikā, 2, 9–10.

Weidner E. F. , “Ein babylonisches Kompendium der Himmelskunde”, American journal of Semitic languages and literatures, xl (1924), 186–208, esp. 198.

Pp. 54–5.

Translated by West E. W. , Sacred books of the East, v (Oxford, 1880), 397–400.

Pp. 100–3.

MacDonell A. A. and Keith A. B. , Vedic index (2 vols, London, 1912), ii, 412; for a fifth-century reference to the five-year cycle see Paitāmahasiddhānta, IV, 4.

II, 20, 65–6.

Pp. 103–4.

Pañcasiddhāntikā, 12, 1.

III, 32.

Daśagītikā, 1.

Yavanajātaka, 79, 8.

Published by Neugebauer O. and Sachs A. , “Some Atypical Astronomical Cuneiform Texts. I”, Journal of cuneiform studies, xxi (1967), 183–218, esp. 183–90; for the use of tithis in this text see 189–90.

So, for instance, argues Taqizadeh S. H. , Old Iranian calendars (London, 1938), on not entirely convincing evidence.

Sachs A. J. , Late Babylonian astronomical and related texts (Providence, 1955), p. xxxi. A crude relation.

months ≈ 18 solar rotations + 10;30° is found in a “saros”-text of the early fifth century b.c.; see Aaboe A. and Sachs A. , “Two Lunar Texts of the Achaemenid Period from Babylon”, Centaurus, xiv (1969), 1–22, esp. 18. In a later “saros”-tablet there occurs a column X which registers the difference between a year and 12 months; see Aaboe A. , Some lunar auxiliary tables and related texts from the Late Babylonian Period (Copenhagen, 1968), 28–30.

De die natali 18,5; Diels H. and Kranz W. , Die Fragmente der Vorsokratiker, I⁷ (Berlin, 1954), 42.

van der Waerden B. L. , Die Anfänge der Astronomie (Groningen [ND]), 112.

See Parker R. A. and Dubberstein W. H. , Babylonian chronology (Providence, 1956), 6.

Parker R. A. , The calendars of Ancient Egypt (Chicago, 1950).

On the difficulties involved in accepting the precision of the statements in the Jyotisavedāṅga required for their use as chronological indicators see Whitney W. D. , “On the Jyotisha Observation of the Place of the Colures, and the Date derivable from it”, Journal of the Royal Asiatic Society, n.s, i (1865), 316–31; cf. also Pingree D. , “Precession and Trepidation in Indian Astronomy before a.d. 1200”, Journal for the history of astronomy, iii (1972), 27–35.

Most of the literary evidence is discussed in Chattopadhyaya S. , The Achaemenids in India (Calcutta, 1950); cf. also Jairazbhoy R. A. , Foreign influence in Ancient India (London, 1963), 38–47. For the archaeological evidence see Wheeler R. E. M. , “Iran and India in Pre-Islamic Times”, Ancient India, iv (1948), 85–103, esp. 92 sqq.