A History of Sanskrit Literature c35.s2: 2. The Period of the Siddhāntas

A History of Sanskrit Literature c35.s2

Language: English

2. The Period of the Siddhāntas

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Varāhamihira, who is asserted to have died in A. D. 587, and who wrote perhaps *c.* 550, has preserved in his *Pañcasiddhāntikā*² information of the contents of five Siddhāntas of an earlier date. Of these the *Paitāmaha* belonged to the pre-scientific period, but the other four in various degrees showed a new spirit, which it is impossible not to ascribe to Greek influence, which displayed itself also indelibly in the case of astrology. It is significant in the extreme that two of these Siddhāntas bear non-Indian names, the *Romaka*, which must be connected with Rome, and the *Pauliça*, which reminds us of the name of Paulus Alexandrinus, of whom, however, we have preserved only an astrological treatise. The *Sūrya Siddhānta*, in the form in which we have it, asserts that it was revealed by Sūrya to Asura Maya in Romaka, which is significant. The *Romaka* adopts not the Indian Yuga system, but one of its own, namely the Metonic period of nineteen years multiplied by 150 which gives the smallest Yuga exactly divisible into integral numbers of lunar months and civil days. Further, it makes calculations for the meridian¹ of Yavanapura, city of the Greeks; and the *Pauliça*, which does not adopt a constant Yuga, but operates with specially constructed short periods of time, gives the difference in longitude between Yavanapura and Ujjain. The *Romaka* again alone of Indian works operates with the tropical revolutions of the sun and moon, while the *Sūrya Siddhānta* and probably even the *Pauliça* deal with sidereal revolutions. The *Sūrya*, it seems, shows us the process of adaptation of the new science to Indian ideas in its most pronounced state; thus it accepts the Kalpa system, while, on the other hand, it is more precise in doctrine than its rivals; it alone gives a general rule for the equation of the centre, and its full treatment of eclipses contrasts with the meagre rules of the *Romaka* and the rough formulae of the *Pauliça*. The mention of Romaka, of course, need not be interpreted as an allusion to Rome; it is due to the fame of the Roman Empire when the knowledge which came probably from Alexandria came to be associated with the name of the great metropolis.

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² Ed. G. Thibaut and Sudhākara Dvivedī, Benares, 1889. See also M. P. Kharegat JBRAS. xix. 109 ff.; V. B. Ketkar, POCP. 1919, ii. 457 f., who argues that the *Sūrya Siddhānta*'s fixation of the initial point of the ecliptic points to *c.* A. D. 290; cf. Bhandarkar, *Early History of India*, p. 69.

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¹ No doubt Alexandria. Kern, *Bṛhatsaṁhitā*, p. 54.

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The evidences of Greek derivation in the Siddhāntas, and still more plainly in later works, may be summed up as follows.² The division of the ecliptic into the Nakṣatras yields to that into the signs of the zodiac, with names borrowed from the Greek; the motions of the planets, hitherto neglected, come to be explained by the doctrine of epicycles; the notion of parallax and methods of calculating it were introduced; new methods of calculating eclipses appear; the heliacal rising and setting of heavenly bodies was studied, especially with astrological reference; correct measurements of day and night were achieved; the length of the year was revised; and the names of the planetary week-days were introduced. We find already in the *Pauliça*—perhaps also in the other Siddhāntas—an important contribution to Indian trigonometry, in the shape of a table of sines, which seems clearly to have been borrowed from Ptolemy's table of chords, the device being adopted of dividing the radius not into sixty parts with Ptolemy but into 120 parts, thus enabling the value given for the chords to be taken over bodily for the sines of half the angles. It is only in Āryabhaṭa that we find the radius as 3438' with the necessary change of sine values.

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² Kaye, *Hindu Astronomy*, pp. 39 ff.

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The exact mode and date of the introduction of these Greek elements has been disputed, and Whitney¹ suggested that it fell in a period before the *Syntaxis* of Ptolemy, a view supported by the constant difference in detail as in the figures of the epicycles of the planets. The question is rendered specially obscure by the fact that we do not know how Greek astronomy progressed between Hipparchos and Ptolemy. It is true that Hipparchos already settled the theory of the sun and the moon and had discovered the mean periods of the revolutions of the planets, and it is conceivable that the *Romaka Siddhānta* may have contented itself with treating of sun and moon only, in accordance with the necessities of the calendar and the practice of the earlier Indian period. But Ptolemy claims to have been the first to take into account the anomalies in planetary motions dependent on the distance of the planet from the sun and its distance from the apsis. The *Vāsiṣṭha* and *Pauliça Siddhāntas* seem to have taken some note of planetary anomalies, though exactly what is uncertain. But apart from the similarity as regards sine values noted above, which is strongly in favour of use of Ptolemy's results, the position may best be explained on the basis of Thibaut's suggestion as to the means by which Ptolemy's views reached India. It is indeed incredible that Indian astronomers should have deviated so largely and needlessly from his work, if they had real knowledge of it. But they probably learned their views from books of a very inferior type, the sort of manual used by astrologers and calendar makers, works which troubled not at all about the basis of their *résumés*, but simply gave results convenient for practical purposes. The Indian Siddhāntas, then, of the *Sūrya* type would represent not a mere borrowing nor an adaptation, but a combination and development on independent lines of elements borrowed in the shape of practical rules and vague hints of theory from mere manuals. The date of the borrowing cannot be determined with certainty. If, as is probable, the year 505 marks the date of Lāṭa, who commented on the *Romaka Siddhānta*, it is natural to place that text about A. D. 400 at latest, and, if we place the period of reception somewhere in the time between A. D. 300–500, we reach a plausible result, though not one admitting of strict proof. This accords with the period when the Gupta Empire was showing many signs of contact with the Roman Empire in other spheres of activity, and the Sassanian dynasty's rule may have promoted intercourse. But the old *Sūrya Siddhānta* shows us a specifically Indian reaction; it accepts where it thinks fit the new matter, but it fits it in as far as may be with the old; it revels in the theory of Kalpas, restores the pre-eminence of mount Meru at the north pole, finds room for the Nakṣatras, and so forth.

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¹ JAOS. vi. 470 ff. Cf. Thibaut, *Pañchasiddhântikâ*, pp. li ff.; *Astronomie*, pp. 47 ff.

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None of the Siddhāntas which Varāhamihira had before him has come down to us in its original form. We know that Bhaṭṭotpala had before him a *Pauliça* so changed as to render the retention of the same name anomalous. The *Paitāmaha Siddhānta* of Varāhamihira differed little from the pre-scientific period; it commenced, however, a Yuga in the third year of the Çaka epoch, which may give its date. It differed from the *Brahma Siddhānta* forming part of the *Viṣṇudharmottara Purāṇa* on which Brahmagupta's *Sphuṭa Brāhmasiddhānta* is on one view based, and from the *Brahma Siddhānta* or *Çākalya Siddhānta*,¹ all of which present the orthodox modern doctrines. The *Romaka Siddhānta* was perhaps touched up by Lāṭa *c.* A. D. 505, and certainly later was revised drastically in the modern sense by Çrīṣeṇa, who wrote after Lāṭa and before Brahmagupta. The *Vāsiṣṭha Siddhānta* appears before Brahmagupta's time to have been revised by Vijayanandin and then by Viṣṇucandra, but the *Laghu Vāsiṣṭha Siddhānta*¹ which we have is clearly not connected with the original or the revision, and the *Vṛddha Vāsiṣṭha Siddhānta*,² which exists in manuscripts, seems equally far removed. The *Sūrya Siddhānta*³ which we have in fourteen chapters of Çlokas, is clearly in many respects modernized from the original; possibly Lāṭa had a hand in this, as Albērūnī ascribes the work to him, and he commented on the *Romaka* and *Pauliça* texts.

Linked texts (7)

Viṣṇudharmottarapurāṇa — Sanskrit
Sūryasiddhānta — Maya, Sanskrit
Paitāmahasiddhānta (lost early version) — Sanskrit
Vāsiṣṭhasiddhānta — Sanskrit
Pauliśasiddhānta — Sanskrit
Romakasiddhānta — Sanskrit
Pañcasiddhāntikā — Varāhamihira, Sanskrit