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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t9: The Five Modern Siddhāntas

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t9

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The Five Modern Siddhāntas

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(SŪRYA, SOMA, VASIṢṬHA, ROMAŚA AND ŚĀKALYA’S BRAHMA SIDDHĀNTAS)

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The Pañcasiddhāntikā included all the siddhāntas excepting the Somasiddhānta, and it has already been shown that these siddhāntas and those which are to be considered now, are different, and this fact will be further corroborated by the discussion which will follow. The siddhāntas whose study is going to be made now are extant present and are different from those belonging to the Pañcasiddhāntikā group; and that is why the epithet ‘modern’ has been applied to them. Although there is no definite evidence to show that there existed or still exist two Somasiddhāntas, still it is completely similar to the other four, and it is desirable to study it (i.e. Somasiddhānta) along with them. After a general discussion of the five siddhāntas, each of them will be considered separately later on.

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∗ After studying the contents of Vedāṅga Jyotiṣa and the above discussion, it will be seen that there is no sense in the suspicion expressed by Weber that Lāṭa must be the same as Lagadha.

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APAURUṢEYA *i.e.* DIVINE

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All the five siddhāntas declare themselves to be divine and they are actually so regarded. No other siddhānta is regarded as divine except these five siddhāntas, and some or all of the siddhāntas from Pañcasiddhāntikā, and Viṣṇudharmottara Brahmasiddhānta. Even if there were some other siddhāntas regarded as divine before, they are not at present available. The Vyāsasiddhānta, Garga siddhānta, Nārada siddhānta and Parāśara siddhānta are also divine; but these should better be called Saṃhitās than Siddhāntas. The author does not think that a work known after Vyāsa and others, and dealing with subjects usually found in siddhānta and in their usual order can be available at present; and if there be one, he has neither seen nor read it. The number of revolutions and other elements are quoted by European scholars from the Parāśara siddhānta; but these are given in one of the Chapter of second Āryasiddhānta as taken from Parāśarasiddhānta. The siddhānta as an independant work is not available. This point will be considered at greater length in the study of the second Āryasiddhānta. The Brahma-siddhānta by Viṣṇudharmottara (Puraṇ) will later on be discussed at greater length. The most ancient of the ‘pauruṣa’ (i.e. human) siddhāntas is the first Āryasiddhānta. Its date is Śaka 421. All the siddhāntas enumerated at the top may not necessarily be more ancient than this. It is, however, felt that at least one of them must be older than that. Because all are similar to one another, and because these are also regarded as divine, it will be proper to describe them first, just after the discussion of Pañcasiddhāntikā.

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At first the numbers of revolutions and other elements mentioned by all the five siddhāntas, which are the same in all the works, are given below :—

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The elements given by the Sūrya, Soma, Vasiṣṭha, Romaka Siddhāntas and Śakalya’s Brāhma Siddhāntas :—

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Years spent in Creation . . . . . . 17064000

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| Number | In a Mahāyuga |
| Revolutions of ‘stars’ . . . . . . 1582237828 |
| Revolutions of the Sun . . . . . . 4320000 |
| Sāvana days . . . . . . . . 1577917828 |
| Revolutions of the Moon . . . . . . 57753336 |
| “ Moon’s apogee . . . . . . . 488203 |
| “ Moon’s anomaly . . . . . . . 57265133 |
| “ Moon’s node . . . . . . . . 232238 |
| “ Mars . . . . . . . . . 2296832 |
| “ Mercury . . . . . . . . 17937060 |
| “ Jupiter . . . . . . . . 364220 |
| “ Venus . . . . . . . . . 7022376 |

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Revolutions of Saturn . . . . . . . 146568 Lunar months . . . . . . . 53433336 Lunar tithi . . . . . . . 1603000080 Solar months . . . . . . . 51840000 Intercalary months . . . . . . . 1593336 Suppressed tithis . . . . . . . 25082252

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| Planet | No. of revolutions in a Kalpa | |
| | Aphelion | Node |
| Sun | 387 | .. |
| Mars | 204 | 214 |
| Mercury | 368 | 488 |
| Jupiter | 900 | 174 |
| Venus | 535 | 903 |
| Saturn | 39 | 60 |

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These give 17064000 as the number of years elapsed after Creation, and some thing must be stated about this. Some idea about the yuga system has already been giver in the Introduction. According to Brahmagupta and his followers, the creation took place at the beginning of Brahma’s day, and at that moment, i.e. in the beginning of Kalpa, all the planets, their aphelia and nodes were conjoined together with the first point of Aries. According to Modern Sūryasiddhānta and other siddhāntas which follow it, the world was not created at the beginning of Kalpa but Brahmā required 47400 divine years that is a period equivalent to 39½ Kali yugas for creating the world. All planets, their aphelia and nodes came together when so much time elapsed after the beginning of Kalpa, and then the planets began to move. Āryabhaṭa II holds almost the same view. He, however, supposed a different number for the period elapsed in Creation, which will be mentioned later on. Similarly, the views of Āryabhaṭa I, will be given later on. We have no means to know the views of Sūrya and other Siddhāntas of the Pañcasiddhāntikā.

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According to the modern Sūryasiddhānta, all planets are supposed to come together by mean motion, in the beginning of the present Kaliyuga. Similarly, all the planets were together, at the end of the Kṛtayuga when the Sūryasiddhānta was compiled. The numbers denoting revolutions of planets in a Mahāyuga are divisible by 4. Hence, each planet makes complete revoultions in a period equivalent to 2½ (i.e. 10÷4) Kaliyugas, and therefore, all planets will come together after each such periods of 2½ Kaliyugas. A period equal to 4567 Kaliyugas passed after the beginning of Brahma’s day till the beginning of the present Kaliyuga. This number is not divisible by 2½; hence, all the planets cannot be shown to be together at the beginning of Kalpa unless it be assumed that some years must have been spent in creation. Supposing that a period equal to 39½ Kaliyugas passed in creation, the period elapsed between the setting in motion of planets to the commencement of the presen Kaliyuga comes to be (4567—39½=4527½) Kaliyugas. This number is divisible by 2½. Hence, after supposing that all planets were together in the beginning of creation, they will be found to be together in the beginning of the present Kaliyuga and at the end of Kṛtayuga before it. Similarly, starting with the assumed number of revolutions in a Kalpa, the aphelia and nodes will be seen to be together only in the beginning of creation and at no other time.

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General Description

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Of these five Siddhāntas, the Sūryasiddhānta is very famous. It has been commented upon by mary, ard it has been even printed and published. The remaining four Siddhāntas are not much known. Of them, the Vasiṣṭha siddhānta, consisting of 94 couplets ir 4 Chapters, has been published by Vindhyeśvarī Prasād Śarmā of Vārāṇasī. No other siddhānta in printed form has come to my notice. I have, with great difficulty, procured copies of all the four siddhāntas. There is a manuscript in the Deccan College collection entitled ‘Vasiṣṭhasiddhānta-Bhūgolādhyāya’ which is different only in wording from the Vasiṣṭhasiddhānta published at Vārāṇasī, (D.C. collection No. 78 of 1869-70 A.D.). It has two chapters which contain 133 verses in all. Of them, the first chapter, consisting of 121 couplets, contains a description of the Universe as ir other siddhāntas. The second chapter gives only the measures of orbital lengths. The numbers of revolutions and other elements in both the Vasiṣṭha Siddhāntas are exactly the same ; and hence it would be correct to say that there is only one Vasiṣṭha Siddhānta and not two. This point will be discussed to some extent later on.

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It has no doubt been remarked above that the numbers of revolutions and other elements are the same in all the above mentioned five siddhāntas ; but a slight departure was noticed which ought to be mentioned. A manuscript copy of the printed Vasiṣṭha Siddhānta is kept in the Deccan College collection (under No. 36—1870-71) and the following couplet is found in the first Chapter :—

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नृपेषु सप्तवह्य (*शिव?*) यमेभेषुधरोन्मिताः (१५८२२३७५१६)॥ अश्रमाः पश्चिमायां च दिशि स्युर्वै महायुगे ॥ १७ ॥

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“The number of revolutions of ‘stars’ in a westerly direction is 1582237516 in one Mahāyuga.”

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The number of sāvana days in a Mahāyuga, as deduced from the number of revolutions of ‘stars’ mentioned in this couplet, prove to be 1577917516, which gives 365ᵈ-15ʰ-31ᵐ-15ˢ-48†ᵛᵖ as the length of the year. This measure is different from that of all other Siddhāntas. But this verse is not found in the book printed in Vārāṇasī. Even the second version of Vasiṣṭha Siddhānta referred to above (Deccan College collection, No. 78 of 1869-70) does not give the number of revolutions of stars. Again, the Siddhāntas†, which have been mentioned by Kamalākara (S. 1580), the author of Siddhānta-tatvaviveka as being quite similar to Sūryasiddhānta include even this very Vasiṣṭhasiddhānta. It appears from this that the couplet given in the Deccan College copy is interpolated, and that is why the numbers of revolutions and other elements in the Vasiṣṭhasiddhānta have been mentioned as bearing a resemblance with those of other Siddhāntas.

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[^ *]: The 8th letter is missing in this copy ; there must have been some letter denoting the number 2, and hence, I have inserted ‘śvi’ as the letter. [^ †]: See Chapter on “Bhagaṇa māna” verse 65.

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THE DATE

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Let us corsider in a general way the dates of these five Siddhāntas.

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Bentley has found out a method of determining the date of compilation of a work on astronomy and from it he has fixed 1091 A.D. or Śaka 1013 as the date of the modern Sūrya Siddhānta. The method is as follows :—

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To calculate the mean positions of planets with respect to the sun from the formulae given by the siddhānta whose date is to be found, and ther after comparing them with the corresponding mean positions calculated from modern European books on astronomy, to see for what date, the planetary positions, as given by the siddhānta prove to be true in the case of each planet, and then to fix up the date of the siddhānta by adopting the average date. This method appears to be correct at first sight, and there can be no mistake if we accept Bentley's assumptions. But it is wrong to follow this method as can be seen from all considerations and the dates found out on that basis will not be reliable. The reasons are as follows :—Bentley's big mistake lies in the fact that he compared the mean places of planets calculated from the correct European tables, with those obtained from the Hindu astronomical works. But the mean planets cannot be seen in the heavens ; what is meant is that the planets will be seen to occupy those positions in the heavens which are found as true longitudes and not as mean. Whenever the Indian astronomers compiled their original works or found that the planets did not occupy places as indicated by their original works, they rectified their original works by applying suitable corrections (bījasamskāra) as applicable at their time. They must have done this with the help of observed positions, i.e. the places which they saw the planets actually occupying in the sky. The difference between the mean and the true place of a planet may be termed as ‘phalasamskāra’ (equation of centre). If the value of this ‘phalasamskāra’ and the method of applying it be the same in the European and Hindu works, there would be no harm if the method of finding the date of a work on the basis of mean place be followed ; but it is not so. The ‘phalasamskāra’ to be given to the Sun is never less than 2° 10′ according to any Indian work while that according to the European works it is about 1° 55′ at present ; and this equation is not always the same. The authors of European works have proved that this equation was 2° 10′ at 3000 B.S. (before Śaka), but is gradually decreasing. The Moon's equation according to the Hindu works is about 5°, while according to European works it sometimes comes to 8°. The equation adopted by the Hindus is very erroneous. The figures denoting equations for other planets also are somewhat different. Similarly, the methods of finding the true place from the mean place and the elements for the ‘mandocca and śīghrocca’ (aphelia) are different in the two kinds of works. Hence, it should not be taken to be a rule that even if the mean longitudes of planets, as calculated from the Hindu as well as the European works agree, that will result in the same figure for true place, and conversely, it cannot be said that a similar figure for the true place obtained from both will not necessarily give the same figures for the mean longitudes. Similarly, whatever difference be found in the two will not be found to follow the same law for all times to come. If under a particular case, similar values of mean longitudes calculated from the two, be seen to yield similar figures for the true longitudes as well, they will be found to give different value in another case. For instance, if the mean and true places of Saturn, in Leo, be found to be the same figures according to both the works, it is not certain that similar results will be obtained for the Saturn in Scorpio. Hence, the variation in values of the equation of centre and that in the methods of finding them, would be found to lead to a variation of some centuries, even when the variation in the values of equations as found from the two works be very small. For instance, the following errors were noticed in the planetary position according to the modern Sūrya Siddhānta in the years noted below and as found by Bentley :—

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| | 538 A.D. | 1091 A.D. | Correct year A.D. |
| | ° ' " | ° ' " | |
| Moon* | -0 18 30 | -0 0 11 | 1097 |
| Mars | +2 26 30 | +0 58 29 | 1458 |
| Jupiter | -1 21 47 | +0 41 14 | 906 |
| Saturn | +1 50 10 | -1 4 25 | 887 |

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This shows that the error in the place of Mars in 538 A.D. was about 2½° and in those of others less than 2°. The error in the case of the Moon was extremely small. The places of all planets can possibly be found to be the same as the true places calculated by European tables and true for some moment during some particular revolution of those times ; that is, in other words, they can prove to be most accurate ; and hence it can be said that if the places of planets given by the Sūrya Siddhānta† agreed with those calculated from European tables for some date during the decade near about 538 A.D. ; then the Sūrya Siddhānta can be said to have been compiled about the year 538 A.D.. The compilation of original works of the Hindus or the corrections applied to them must have been based on the experience of at least 25 or 30 years ; and there are no means to know which planets were observed, on what dates and how, during this period. Hence, the method of determining the date of compilation of a work according to Bentley's method is not faultless. Prof. Whitney has pointed out some of the drawbacks of Bentley's method, but has not pointed out the above very important and main drawback.

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† *It is sure that if the positions of all planets be calculated from both the works for different dates during 5, 10 or perhaps 30 years, it can be shown that the planetary places do agree for a particular date ; but the author has not done the calculation, since it involves much time and labour.*

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Bentley himself has considered the pros and cons of this method, but has not considered these objections.

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Another point is that Bentley, while comparing the places of planets, has only calculated their distances from the Sun, but has not considered the error in the Sun's place as given by the Indian works, and which has crept in because of a small error in the length of the sidereal year adopted by our works. Prof. Whitney has pointed out that the consideration of this point will show that the Sun's place given by the Sūrya Siddhānta would be for the year 250 A. D. The Indian authors could possibly have determined the corrections (Bījasamskāra)* to be applied to planets by two methods. One method of determining the correction for a planet is by observing its conjunction with stars, and the second is by observing its place by the ‘Nalikā’ instrument. The length of a year adopted by our works which is nearly equal to that of the sidereal year but actually exceeds it by about 8 palas and this (variation) leads to a gradually increasing error in the longitudes of stars. The error at present is about 4½ degrees. (The difference in the Paṭawardhan’s almanac and other nirayaṇa almanacs is due to this fact). Hence, if the corrections were determined from the conjunction of the planet with a star, it is bound to err, because the place of the star with which the planet was conjoined, was erroneous, and the date of compilation of work found on this basis must also err. The second method is that of observing a planet by the ‘nalikā’ instrument. These methods of observation necessitate the conversion of the planet’s place into a tropical (sāyaṇa) form; and although the adopted motion for the equinox is somewhat erroneous, the correction is not likely to go very wrong because the time taken by a planet or the sun to come to equinox does not differ much. Hence, because the corrections have been determined by this method, the date of compilation of a work, as found by Bentley’s method of comparison of errors in planetary places with respect to the sun, can be accepted; but the time when the sun, according to our works is found to come to the equinox, is somewhat erroneous. Because of this and also because the correction can possibly have been erroneous to the extent to which the observed results would be approximate, the date of compilation of a work can also be erroneous. The third point to consider is that, if it be supposed that Bentley’s method is correct, it will be proper to use his method, if the author of the work, whose date is to be determined, has given the positions of planets by actual observation. But it will be of no use to apply the method, if the author has incorporated in his work the planet’s places exactly as they are given in another work. If the correction given by Bhāskarācārya in his work be set aside, the elements of revolution etc. given by him are exactly the same as those given by Brahmaguptasiddhānta, and hence, the date of compilation of both these works will, by Bentley’s method, come to be the same; but the fact remains that Bhāskarācārya compiled his work, “Śiromaṇi”, 522 years after Brahmagupta’s Siddhānta. The correction given by Bhāskarācārya’s work is found even in Rāja Mṛgāṅka, a work of Śaka 964. (More discussion about this will be given later on.) Hence, the dates of Rāja Mṛgāṅka (Śaka 964), Siddhānta Śiromaṇi (Śaka 1072) or of Karaṇakutūhala (Ś. 1105) will come to be the same by Bentley’s method.

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∗ *When the planet's place is seen to be in advance of that obtained by European tables, the variation is indicated by plus (+) sign, and when it is behind, it is denoted by Minus (—). The error in the case of Mercury and Venus exceeded 3° and hence, the difference has not been shown here.*

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Bentley’s method proves useless if the dates found by it are compared with the actual dates. The author attempted to apply the method in the case of the Sūrya Siddhānta of the Pañcasiddhāntikā and the first Āryasiddhānta and these are the inferences :—

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∗ If it is found that the place of a planet as calculated from a Siddhānta does not agree with the observed place, it is decided to apply suitable correction to the motion and place of the planet as given by the work and this correction is known as ‘Bīja’.

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| | The year when the planet according to Sūryasiddhānta would be correct | The year when the planet according to first Āryasiddhānta would be true |
| | Śaka | Śaka |
| Moon . . . . . . . | 520 | 468 |
| Moon's apogee . . . . . | 482 | 482 |
| Moon's asc. node . . . . | — | 523 |
| Mars . . . . . . . | 457 | 457 |
| Mercury . . . . . . | 93 | 734 |
| Jupiter . . . . . . | 772 | 480 |
| Venus . . . . . . | 409 | 409 |
| Saturn . . . . . . | 574 | 574 |
| | 3307÷7=472 | 4127÷8=516 |

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This leads one to infer* that the Sūrya Siddhānta of Pañcasiddhāntikā was compiled in Śaka 472 and the first Ārya Siddhānta in Śaka 516. But it is beyond controversy that the first Ārya Siddhānta was compiled in Śaka 421 and it has also been shown before that the Sūrya Siddhānta of Pañcasiddhāntikā must have belonged to a period much earlier than Śaka 421. Bentley† has determined 1288 A. D. (Śaka 1210) as the date of the Ārya Siddhānta consisting of 18 chapters (i.e. the second Ārya siddhānta) and 1384 A. D. (Śaka 1306) as that of the Parāśara siddhānta; but reference to some subjects in the second Ārya Siddhānta is found in the Siddhānta Śiromaṇi. This shows that the second Ārya Siddhānta must belong to a period earlier than Śaka 1072 A. D. and references to Parāśara Siddhānta also are found in the second Ārya Siddhānta. (More discussion about this will follow later on).

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† See Bentley's work (1823 A.D.) Part II, Section III.

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This will clearly show that the dates found by Bentley are not at all reliable and that the date of the Sūrya Siddhānta (viz. Śaka 1013) determined by Bentley is not worth considering.

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Let us, therefore, independently consider the matter of dates of the five Siddhāntas.

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Brahmagupta observes,

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अयमेव कृतः सूर्येंदुपुलिशरोमकवसिष्ठवचनाद्यैः ।। ३ ।।

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अध्याय २४

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"This very Siddhānta has been compiled by Sūrya, Indu, Puliśa, Romaka, Vasiṣṭha, Yavanācārya and others".

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The Indu Siddhānta, mentioned in this, is the Soma Siddhānta itself. It shows that there existed a Soma Siddhānta before the time of Brahmagupta. No evidence is available to show that there existed some time before, a Soma Siddhānta, different from the Soma Siddhānta now available. No such Siddhānta is either available at present, or there is no evidence of its availability. Where then is the harm, if we say that, in the absence of any evidence to the contrary, the Soma Siddhānta existing in Brahmagupta's time, is the same as the modern one? It is just possible that the Soma Siddhānta in Brahmagupta's time might have been different in size and form, than the modern Soma Siddhānta; but both of them must be similar in the matter of numbers of revolutions and other elements etc.

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∗ Places of planets to be calculated from European tables have been calculated from the Keropant's Planetary Tables. If more accurate table would be followed, a variation of only 5 to 10 years may possibly occur.

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It has been shown above that there existed in the time of Brahmagupta a Romaka Siddhānta by Śrīṣeṇa and a Vasiṣṭha Siddhānta by Viṣṇucandra and different from the Romaka and Vasiṣṭha Siddhāntas of the Pañcasiddhāntikā. It has also been pointed out before that the Romaka and Vasiṣṭha of the Pañcasiddhāntikā are different from the modern Romaka and Vasiṣṭha Siddhāntas. A comparison of the numbers of revolutions and other elements etc. corroborates the same fact. One is, therefore, naturally led to the inference that the Śrīṣeṇa's Romaka and Viṣṇucandra's Vasiṣṭha, available at Brahmagupta's time, are the same as the modern Romaka and Vasiṣṭha Siddhāntas and we have reasons in support of them. One of them is that there is no evidence to show that there ever existed a third set of Romaka and Vasiṣṭha Siddhāntas other than the Romaka and Vasiṣṭha Siddhāntas of the Pañcasiddhāntikā and the modern Siddhāntas of the same names nor are they available at present. The second reason is that the three couplets of Brahmagupta, quoted before on page 7, giving the basis on which Śrīṣeṇa compiled his Romaka and Viṣṇucandra his Vasiṣṭha, show that both of them appear to be similar; that is the numbers of revolutions and other elements etc. in both must be the same. The third reason is that Brahmagupta remarks that 'Viṣṇucandra has compiled the second Vasiṣṭha siddhānta.' The following couplet* is found in that version of the modern Vasiṣṭha Siddhānta which is printed at Vārāṇasi :—

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इत्थं मांडव्य संक्षेपादुक्तं शास्त्रं मयोदितं ॥
विस्तृतिर्विष्णुचंद्राद्यैर्वियति युगेयुगे ।। ८० ।।

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"Oh Māṇḍavya! This science has thus been described by me in brief. It will be expanded by Viṣṇucandra and others, as yugas will roll by".

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This is addressed to Māṇḍavya by Vasiṣṭha and it shows that Viṣṇucandra has been associated with this. Viṣṇucandra's name has been anyhow brought in. This clearly shows that, if it is not the one actually compiled by Viṣṇucandra, it must have been written out by some one else, after borrowing Viṣṇucandra's elements. It has been mentioned in the above couplets of Brahmagupta, concerning the Romaka Siddhānta, that the Romaka has been compiled with the help of Lāṭa, Vasiṣṭha and Vijayanandi; and the modern Romaka Siddhānta contains the following lines in the beginning :—

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वसिष्ठो† रोमशमुनिः कालज्ञानाय तत्त्वतः ।। उपवासं ब्रह्मचर्यं प्रागेकं विष्णुतत्परौ ।। २ ।।
वसिष्ठसदाभिप्रायं ज्ञात्वापि मधुसूदनः ।। अर्पयामास तत्सिध्यै तावच्छास्त्रार्थपारगः ।। ३ ।।
उभाभ्यां तोषितो विष्णुर्योयं तन्मुखद्वयात् ।। उच्चारयामास . . . . . ।। ४ ।।

v2.c12.s2.t9.49

† We come across versions like Lomaśa for Romaśa, 'tadabhiprāyam' for 'sadabhiprāyam' etc. Even the name of the siddhānta is found as Romaka and Romaśa, in two ways.

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(The general sense is as follows) :

v2.c12.s2.t9.51

Once upon a time Vasiṣṭha and sage Romaka, started a penance, in celibate condition, invoking the favour of God Viṣṇu, for obtaining the knowledge of time (principles of science of astronomy). God Madhusūdana who is proficient in this science, appreciating the good motives of Vasiṣṭha and being pleased with them both, gave them away the science, as a reward for penance. He uttered the words of Science through the two mouths (Vasiṣṭha and Romaka).

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∗ This verse is found also in the copy of the copy of the Deccan College collection; but its latter half begins with "Vistṛtiśecca Candrādyaiḥ" which appears to be a mistake.

v2.c12.s2.t9.53

Even though these contain certain errors, the verses show that Romaka and Vasiṣṭha are both associated with the modern Romaka Siddhānta. The Romaka Siddhānta existing at the time of Brahmagupta had definitely a support from Vasiṣṭha (siddhānta). Hence, an inference can be drawn that Śrīṣeṇa’s Romaka and Viṣṇucandra’s Vasiṣṭha, existing in the time of Brahmagupta, are the same as the modern Romaśa and Vasiṣṭha Siddhāntas. The modern Romaśa Siddhānta does not mention Śrīṣeṇa’s name and the name of the Siddhānta has been maintained, through an imaginary sage Romaśa. It, therefore, seems probable that the modern Romaka may be different from Śrīṣeṇa’s Romaka in respect of its wording, still the revolutions and other elements must have been the same in both.

v2.c12.s2.t9.54

If it be admitted that there existed before Brahmagupta (Śaka 550) Siddhāntas which were either completely similar or similar in respect of the numbers of revolutions and other elements to the Soma, Romaśa and Vasiṣṭha etc. how can it be said that the modern Sūrya Siddhānta, which resembles these three in respect of elements and which is commanding a greater reverence and importance at present than these three could not have existed before Brahmagupta’s time? The modern Sūrya Siddhānta or the Soma, Romaka and Vasiṣṭha, have no similarity with elements with the first Ārya Siddhānta, which existed before Brahmagupta, and with any of the earlier five Siddhāntas of the Pañcasiddhāntikā. It has already been shown above that Lāṭācārya had compiled a work quite independently; and according to Brahmagupta’s remarks, the figures for the mean places* of all planets in Śrīṣeṇa’s Romaka and Viṣṇucandra’s Vasiṣṭha had been borrowed from Lāṭa’s work. It appears from this that it was only Lāṭācārya’s work which was similar to modern Soma, Vasiṣṭha and Romaka, out of those, which existed before Brahmagupta’s time. This fact, which emerges from the above considerations, when weighed together with Albiruni’s statement that Sūrya Siddhānta was compiled by Lāṭa, lead one to draw the definite conclusion that, the mean places of planets i.e. and the numbers of revolutions and other elements in the modern Sūrya Siddhānta, have been taken from Lāṭācārya’s works and Lāṭa lived before Varāhamihira (Śaka 427). Hence, it is the author’s opinion that the elements in the modern Sūrya Siddhānta belong to a period prior to Śaka 427. Even if the modern Sūrya Siddhānta is not supposed to have been compiled by Lāṭa, the modern Soma, Romaka and Vasiṣṭha Siddhāntas definitely existed before Brahmagupta’s time; and the modern Sūrya Siddhānta is much more revered and regarded as important than any of these three. This shows that the modern Sūrya Siddhānta existed before the three Siddhāntas and hence, the date of its compilation cannot be later than the 5th century of Śaka era.

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Let us now consider the five Siddhāntas separately and in greater details.

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∗ Colebrooke interprets the words as “Mars and other planets were taken from Vasiṣṭha” But considering all facts with reference to the context, I think that the lines should be interpreted in the very way in which I have rendered them.

Cites (14)