Pramāṇa · Search · About · API

Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t20: Lalla (About Śaka 560)

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t20

Language
English

Lalla (About Śaka 560)

v2.c12.s2.t20.1

Works

v2.c12.s2.t20.2

A work, ‘dhīvṛddhidatantra’, on planetary calculation stands to his credit. Sudhākara Dvivedī, procured it, and got it printed in Vārānasī, in 1886 A.D. He has written a Muhūrtawork, named ‘Ratnakośa’.

v2.c12.s2.t20.3

Date

v2.c12.s2.t20.4

Lalla has not mentioned his date or place of his residence. In the chapter on mean places, in Dhīvṛddhidatantra, he remarks,

v2.c12.s2.t20.5

विज्ञाय शास्त्रमलमार्थभटप्रणीतं । तंत्राणि यद्यपि कृतानि तदीयशिष्यैः ॥ कर्मक्रमो न खलु सम्यगुदीरितस्तैः । कर्म ब्रवीम्यहमतः क्रमशस्तु सूक्तं ॥ २ ॥ "Although his disciples, after completely studying the scientific works by Aryabhata, have compiled the 'tantra' works, they have not described the methods of calculation in proper manner. Hence I am properly describing in brief the methods."

v2.c12.s2.t20.6

He has mentioned, in the Uttaradhikara, corrections to be applied to planets obtained from the Aryasiddhanta. They are :-

v2.c12.s2.t20.7

बाके नखाब्धि ४२० रहिते शशिनोक्षदस्त्रं २५ स्तनुगतः कृतशिवं ११४ स्तसः षडर्कः ॥ ६ ॥ शैलाब्धिभिः ४७ सुरगुरोर्गजिते सितोच्चात् शोध्यं त्रिपंचकु १४३ हतेभ्यशराशि २५० भक्ते ॥ १ ॥

v2.c12.s2.t20.8

स्तबरेमांबुधि ४८ हते क्षितिनंदनस्य सूर्यात्मजस्य गुणितबेरलोचनै २० इच ॥ व्योमाशिवेद ४२० निहते विवधीत लब्धं शोंनाशुसूनुचलतुंगकलासुबुद्धिं ॥ १६ ॥ इति...महकर्म दृकप्रभावत् ॥ २० ॥ आसीदशेषबुधर्वदितपादपद्मः...... ॥ शाम्बततोजनि जनेक्षणकर्वेंद्रभट्टसिविक्रम इति प्रथतः पृथिव्यां ॥ २१ ॥ लल्लेन तस्य तनयेन शशांकमौलेः शैलाधिराजतनयादयितस्य शंभोः ॥ संपूज्य पादयुगमार्यभटाभिधानसिद्धांततुल्यफलमेतदकारि तंत्रं ॥ २२ ॥

v2.c12.s2.t20.9

"(18 & 19) Subtract 420 from the Saka year. The corrections for the planets are as follows :- Moon, -25'; Moon's apogee, -114'; Moon's node, -96'; Jupiter, -47'; Venus, -153'; Mars, +48'; Saturn, +20' and Mercury, +420' (20) This, the calculation of planets...as supported by observation. (21) There lived one,...Samba by name, who was revered by all learned men, and from him was born one, known as Trivikrama Bhatta in the world and who was the "moon for lilies in the eyes of the people". (22) His son Lalla who worshipped the feet of Siva, the moon-crested Lord and the beloved of Parvati complied a 'tantra' equal in merit to the Aryabhata-Siddhanta."

v2.c12.s2.t20.10

The numbers of revolutions and other elements given in Lalla's works all agree with those of Aryabhata I; and Lalla has given only the corrections mentioned in the above verses, 18 and 19. From this it is clear that he lived after Aryabhata I. Some evidence is available to determine his date.

v2.c12.s2.t20.11

The above verse, relating to corrections, has been given in his commentary by Paramadisvara, the commentator of Aryabhata. There he describes him in the words "tacchisyo Lallacaryah", calling Lalla as Aryabhata's disciple. From this and mainly from the method of applying corrections in which 420 has been asked to be subtracted from Saka, Dr. Kern thinks that the date of Lalla may be Saka 420 itself. Even the late Janardana Balaji Modaka expreses the same view (See Srstijnana monthly, August, 1885, p. 120). There may be many others holding the same view, but they are incorrect. The first reason is that if Lalla had been Aryabhata's disciple and his contemporary, he would not have committed errors in trifling matters which have been pointed out by Bhaskaracarya about Lalla. These errors do not exist in the works of Aryabhata I. The second reason is that if the date of Lalla had been Saka 420, Brahmagupta would have played seriously in condemning Lalla's works which contain many faults, inasmuch as he (Brahmagupta) has fired volleys of criticism against the works of Aryabhata I even when they do not contain many faults. But the Brahma Siddhanta contains neither Lalla's name nor any of his view. The third reason is that an occasion for applying a correction to a siddhanta does not arise at the very time of its compilation. Some one suggests a correction to a work only when a perceptible difference in the planets' places, as obtained from the work, comes to notice. Āryabhaṭa compiled his work in Śaka 423, and it is quite impossible that his disciple began to make changes in it from that very date. Had it been the case, Āryabhaṭa himself would have given revolutions (of planets) after taking into consideration this correction. The method of finding Lalla's corrections requires one only to subtract 420 from the Śaka year; but it does not mean from this that the corrections were made in that year. The corrections suggested to the Brahma Siddhānta have to be applied from the beginning of Kaliyuga. Similarly, corrections to modern Sūrya Siddhānta are to be applied from the beginning of Kaliyuga. It will, therefore, be ridiculous to say, that becuase of this fact, the corrections came into existence in the beginning of Kaliyuga. The statement that Lalla's corrections were suggested in Śaka 420, is equally ridiculous. One more evidence may be added to this. It is as follows :—

v2.c12.s2.t20.12

Lalla observes, in the Chapter on "misconceptions"

v2.c12.s2.t20.13

यदि च भ्रमति क्षमा तदा स्वकुलायं कथमाप्नुयुः खगाः ॥ ४२ ॥

v2.c12.s2.t20.14

"If it be accepted that the earth rotates, then how can the birds flying in the sky, find their own nests ?"

v2.c12.s2.t20.15

In this, Lalla has criticised those who maintain that the earth rotates. But it is only Āryabhaṭa I who states that the earth rotates. It is, therefore, not probable that his own disciple would hold the opposite view or at any rate criticise him. On the whole, Lalla cannot be the disciple of Āryabhaṭa. Bhāskarācārya's works mention Lalla's name at several places; but nowhere has he mentioned him as Āryabhaṭa's disciple or even merely as a disciple. Raṅganātha, the commentator of Sūrya Siddhānta, has at one place mentioned "śiṣyādhivṛddhi-datantra" which simply means' a 'tantra' work which increases the intellectual power of disciples". It is not understood on what basis Parameśvara has called Lalla as Āryabhaṭa's disciple. The above verses compiled by Lalla himself show that he has nowhere called himself as Āryabhaṭa's disciple. On the contrary from the words in those verses it appears that he was not Āryabhaṭa's disciple.

v2.c12.s2.t20.16

From this, Śaka 420 does not seem to be his date. He must have lived many years after Āryabhaṭa.

v2.c12.s2.t20.17

Lalla has given 359° as the longitude of the junction-star of Revatī. The time for the junction-star of Revatī to cover one degree to the West of the initial point, according to Lalla tantra (that is, from the point occupied by the sun at the moment of the actual Aries Ingress) comes to about Śaka 600. But it has been shown above that Brahmagupta knew nothing about Lalla's work; Lalla's works describe all instruments except the 'turiya' (quadrant) instrument described by Brahmagupta. It shows that Brahmagupta's work was not known to Lalla. This leads one to surmise that both were contemporaries, but residing at distant places.

v2.c12.s2.t20.18

Śrīpati has compiled his work 'Ratnamālā' with the help of Lalla's, 'Ratnakośa'. Śrīpati's date is Śaka 961. Lalla must have lived long before this date.

v2.c12.s2.t20.19

His work does not discuss the question of the precession of equinoxes. This shows that he must have lived about the time of Brahmagupta.

v2.c12.s2.t20.20

From all these considerations, the author thinks that Lalla's date might be a time near about Śaka 560.

v2.c12.s2.t20.21

His Ability

v2.c12.s2.t20.22

It is true that Bhāskarācārya has criticised Lalla, the author of "Dhīvṛddhida", but he states in the 20th verse above, that he has determined these corrections already mentioned, after ensuring agreement with the observed positions himself. This shows that he used to take observations himself and was a researcher; and this fact was very creditable to him. The corrections given to Mercury and other planets show that the need to find them out must have arisen after a period of time had elapsed after Āryabhaṭa. It has already been mentioned that the Karaṇa works ‘Karaṇaprakāśa’ (Śaka 1014) and ‘Bhaṭatulya’ (Śaka 1339) were compiled after applying Lalla's corrections to the planets calculated according to the Siddhānta of Āryabhaṭa I.

Cites (6)