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Elements of table texts

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Sanskrit Astronomical Tables

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Abstract

The canonical structure and sequence of astronomical topics as represented in most major siddhānta and karaṇa works (see Section 1.4) are modified in the table-text genre in a number of different ways.

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Notes

  1. 1.

    Such combinations of mean longitudinal increments for multiples of different periods had been employed in Greek and Islamic astronomical tables at least since the Almagest of Ptolemy, in which the increments are tabulated for 1–24 hours, 1–30 days, 1–12 30-day “months,” 1–18 years, and 1–45 18-year periods. As the following examples show, Indian mean longitude tables employ very diverse combinations of time-units, usually in decimal multiples.

  2. 2.

    See, for example, the multi-billion-year framework described in Table 4.1 in Section 4.1.

  3. 3.

    See Table 5.11 for a summary of the varying systems of tabulating mean longitude increments in different recensions of the Grahalāghavasāriṇı̄. These recensions illustrate how variously table compilers might approach the task of recasting the same karaṇa in table-text form.

  4. 4.

    Although this appears to read 2 14 45, an overwritten correction by the scribe suggests it should be read as 2 10 45.

  5. 5.

    Using the standard Indian rule of one arcminute of precession per year, 21∘ corresponds to an interval of 1260 years since the canonical precession zero-point of 523 CE. See Pingree (1972) and compare the tables described in Pingree (1968, pp. 31–32).

  6. 6.

    The structure and labelling of these tables are evidently strongly influenced by the corresponding tables in the work that served as the model for the Siddhāntasindhu, the Zı̄j-i Shāh Jahānı̄. Similarities between manuscripts of the two works that we have consulted (MSS British Library OR 372 and Jaipur Khasmohor 4962) include the use of time-degrees rather than ghaṭı̄s, the use of black ink for tabulated ascension values and red ink for their differences, and the ordering of pairs of zodiacal signs sharing the same table arguments.

  7. 7.

    For instance, verses containing values of ecliptic declination appear in the Khaṇḍakhādyaka (Misra 1925, p. 103, verse 3.11) and in the Karaṇakutūhala (Mishra 1991, p. 43, verses 3.13–14).

  8. 8.

    The former category includes table texts such as the Gaṇitarāja of Kevalarāma Pañcānana, the Grahasāraṇı̄ (also known as the Khecaraśı̄ghrasiddhi) of Gaṅgādhara, and the Makaranda of Makaranda. The latter category contains, e.g., the Karaṇakesarı̄ of Bhāskara (fl. 1681) (Montelle and Plofker 2013) and the Parvadvayasādhana of Mallāri (Pingree 1981, pp. 46, 55). See the summaries of these works in Appendix A.

  9. 9.

    These verses have been critically edited, translated, and analyzed in Dhammaloka et al. (2016) and Montelle and Ramasubramanian (2018).

  10. 10.

    See Van Brummelen (2009, pp. 147–149), Rosenfeld and Hogendijk (2003), and Aaboe (1954). The value employed for the R sin of one degree is 1;2,49,43,15.

  11. 11.

    For further information about these tables see van Dalen (2002a) and their transmission.

  12. 12.

    The horoscope is cast for Saṃvat 1903/Śaka 1768, Winter, Kārttika-māsa, kṛṣṇapakṣa, 12th tithi, 48th ghaṭı̄, 49th pala, Sunday (15th November 1846).

  13. 13.

    Note that this table illustrates the astrological convention of unequal house division: In quadrants 1 and 3, i.e., houses 1–3 and 7–9, the total length of each house is 2 × 12∘;54, 20 or one-third of the ecliptic arc between the ascendant and the meridian. The length of each of the remaining houses in the other two quadrants is 2 × 17∘;5;40.

  14. 14.

    These table entries reflect the traditional associations attested in the Bṛhajjātaka (2.15–17) except for the inclusion of Rāhu as the enemy of sun and moon (Jhā 1934, pp. 33–37; Aiyar 1905, pp. 20–21).

  15. 15.

    These assignments appear to be based on those given in Varāhamihira’s Bṛhajjātaka (Jhā 1934, pp. 135–145; Aiyar 1905, pp. 97–99).

  16. 16.

    The scheme is similar to that given in Varāhamihira’s Bṛhatsaṃhitā (5.19) (Subrahmanya Sastri and Bhat 1946, p. 50; Kern 1865, p. 26).

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of Canterbury, Christchurch, Canterbury, New Zealand

    Clemency Montelle

  2. Department of Mathematics, Union College, Schenectady, NY, USA

    Kim Plofker

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  1. Clemency Montelle
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  2. Kim Plofker
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Montelle, C., Plofker, K. (2018). Elements of table texts. In: Sanskrit Astronomical Tables. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-97037-0_4

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