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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t87: The Puliśa Siddhānta

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t87

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The Puliśa Siddhānta

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Beruni had this Siddhānta with him together with a commentary on it. He was translating it into Arabic. He has given the number of revolutions of planets and those sāvana days in a Mahāyuga, etc., as mentioned by Puliśa, and they agree entirely with those cited by Utpala as belonging to Puliśa Siddhānta. These numbers have been mentioned before (page 18). They do not contain the numbers of the revolutions of Rāhu and moon's apogee which have been given by Beruni as 488219 and 232226 respectively. The longitude of the sun's apogee has been stated to be 80°. Beruni states that the Puliśa siddhānta describes the yuga system according to the Smṛtis, but it gives 1008 as the number of Mahāyugas in a Kalpa and 14 Manus consisting of 72 Mahāyugas each. The ‘twilights’ (Sandhyās) and ‘semi-twilights’ (Sandhyāṁśas)

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dhyānśas) are, of course, absent, and the Yuga is supposed to begin at midnight. He says “I think that Puliśa siddhānta is the name given after Paulis, the Greek resident of the city of Saintra, and that Saintra is the same as Alexandriā.” But he also observes that the Greeks had no yuga system among them. It clearly shows that Utpala’s Puliśa siddhānta was widely used at the time of Beruṇī.

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ĀRYABHAṬA I* :—Beruṇī cites the numbers of revolutions of planets given in Abu-al-Ḥāsān’s work and most of these tally with the numbers given by Āryabhaṭa I ; and those that do not differ probably through the errors of copying. Beruṇī had with him some part of the work Āryabhaṭīya and its Arabic translation. This translation must have been made during the reign of Caliph Manṣur.

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VARĀHA MIHIRA :—Beruṇī has given Śaka 427 as his date. Beruṇī had translated his works Bṛhatsaṃhitā and Laghujātaka into Arabic. The commentary on the Bṛhajjātaka by Balabhadra has been referred to by Beruṇī. Sudhākara writes that Varāha’s works Yoga Yatra’ and Vivāhapaṭal are available at Vārānasī. According to Utpala, there was a work entitled “Samāsa Saṃhitā” by Varāha. It may have been an abridged version of Bṛhatsaṃhitā.

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BRAHMAGUPTA :—On the basis of Beruṇī’s works, Prof. Sachau observes, “Brahmagupta occupies an important place in the history of oriental culture. Brahmagupta taught astronomy to the Arabs before they came to know of Ptolemy’s works, since, references to the works ‘Sindhind’ and ‘Al-Arkand’ frequently occur in Arabic literature ; these are the translations of Brahmagupta’s works, Brahma Siddhānta and Khaṇḍakhādya”. The translations may have been made during the reign of Caliph. Mansur, and it appears from this, that Brahmagupta’s works had a wide spread influence in the Sind Province. Beruṇī has repeatedly referred to Balabhadra’s commentary on Khaṇḍakhādya. Beruṇī had translated Brahma Siddhānta and Khaṇḍakhādya into Arabic. He observes that the Arabic translations made before his timè were not correct. These translations have not been available so far. Beruṇī had lived mainly in Sind for a good many years. His remarks, at several places, show that Brahmagupta’s works had a great influence in that province in those times.

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LALLA:—The author of the Gaṇaka Taraṅgiṇī also gives Śaka 421 as his date. But it has aready been proved (page 94) that it is wrong. Bhāskarācārya has, in the Golādhyāya, quoted Lalla’s verse on the calculation of the area of the surface of a sphere and refuted the method suggested in it. This shows that Lalla may have written a work on arithmetic. Sudhākara says that he may have a work to his credit even on algebra. Berunī's works contain something or other by way of description of famous astronomers who tlived before Śaka 950; but they do not mention Lalla's name even once. It shows that at least till Śaka 950, Lalla's works were not well known in Sind, Punjab, Kashmir, even the major part of Northern India. From this and from the fact that the first Ārya Siddhānta, as modified by the application of Lalla's corrections, was in use in the Deccan, he appears to have been a resident of the Deccan.

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∗ (Beruṇī has referred to the Āryabhaṭa of Kusumpūr and to another Āryabhaṭa who lived earlier. The author could not obtain the work of the older one, but Beruṇī remarks that the Āryabhaṭa of Kusumpūr was his follower. Both of them have been referred to by Beruṇī at 30 places. After reading all those passages, it is found that the description completely applies to the first of the two Āryabhatas formerly described (page 51 and 95) The number of revolutions of planets and such other matters referred to by Beruṇī as to differentiate one from the other very clearly, do not apply to the second Āryabhaṭa, and he was not the follower of the first. From this it follows that the two Āryabhatas referred to by Beruṇī are in fact, one and the same person. Even Prof. Sachau, did not note this fact pointed out here. The second Āryabhaṭa who figures in the auhors account, may have lived before Beruṇī, and although it is evident that his work was not seen by Beruṇī, it appears that he laboured under a misunderstanding due to hearsay reports about the existence of two Āryabhata. This leads to the inference that Āryabhaṭa II, may have lived only a century or a half before Śaka 950, and confirms the author’s former estimate of his date.

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ŚRĪDHARA :—His work on arithmetic, known as “Triśatikā” *consisting of 300 couplets, is in the Government Library, Vārāṇasī and it has been remarked in the very beginning of the work :

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नत्वा शिवं स्वविरचितपाटया गणितस्य सारमुद्धत्य । लोकव्यवहाराय प्रवक्ष्यति श्रीधराचार्यः ॥

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“Śrīdharācārya, after saluting God Śiva, compiles for the benefit of the public, this work which contains the gist of his (earlier) work on ‘Pāṭīgaṇita’.

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This means that Śrīdharācārya must have compiled a second work on Arithmetic which was larger than the Triśatikā. The Triśatikā used many unusual terms like stambhoddeśa for iṣṭakarma (unitary method), pratyutpanna** for guṇākār (multiplication) etc. which are different from those used in Līlāvatī. It includes chapters on both arithmetic and mensuration. There is a work named Nyāyakandalī on logic, and its author's name also is Śrīdhara. The work was written in Śaka 913. Authors of works other than astronomical do not generally mention their dates. It appears from this, says Sudhākara, that the author of Triśatikā and Nyāyakandalī is the same one person. Baldeva was the name of the author of Nyāyakandalī and his mother, Abvokā. The village of Bhūrisṛṣṭi in the territory of Dakṣiṇarāḍhā was his place of residence.

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Bhaṭṭa Śrīdhara compiled the work Nyāyakandalī on the request of Pāṇḍudās. This account, however, is not given in the Triśatikā; and the date of Śrīdhara, the author of Pāṭīgaṇita, as established from the date of Mahāvīra above (page 95) is more reliable than that inferred simply on the basis of the similarity of names. Mahāvīra has quoted Śrīdhara as follows :—

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ऋण धनर्वोवर्गं । मूले स्वर्णं तयोः क्रमात् ॥

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It is true that as the line is in ‘anuṣṭup’ metre it could not have occurred in Triśati which is compiled in Ārya metre; still it may have been borrowed from Śrīdhara's larger work on Pāṭīgaṇita or from his algebra. The Aufrecht Catalogue mentions “Triśatigaṇitasāra” as a work by Śrīdhara. It appears from this that Śrīdhara's work Gaṇitasāra, procured by Colebrooke and the Triśati mentioned by Sudhākara are one and the same work. There is another work, Jātakapaddhati attributed to Śrīdhara which may have been compiled by Śrīdhara, the author of the Pāṭīgaṇita.

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∗ This has been stated chiefly on the basis of the Gaṇaka Taraṅgiṇī.

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∗∗ The term pratyutpanna is found in Brahmagupta's works.

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BṚHANMĀNASA KARAṆA:—According to Beruṇī, the auhor of this work is Manu, and the work has a commentary by Utpala and it was reproduced in an abridged form under the name of Laghumānasa by Muñjāl. As the Laghumānasa belongs to Śaka 854, Bṛhanmānasa may have been compiled about Śaka 800.

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BALABHADRA:—Beruṇī has given several quotations from his works or his commentaries. According to Beruṇī, he had compiled works on each of the sections “Gaṇita, Saṃhitā and Jātaka”, and had written commentaries on the Khaṇḍa Khādya and the Bṛhajjātaka. The work on “gaṇita” has been called a ‘tantra’ by Beruṇī, which indicates that it advocated the calculation of ahargaṇa from the commencement of Yuga. The quotations given by Beruṇī show that there was also a commentary by Balabhadra on Brahmagupta’s Siddhānta. Beruṇī has given quotations from the commentary on the “yoga-śāstra’ of Patanjali, and Prof. Sachau infers that the passages were written by Balabhadra as is indicated by the context; and as the major part of the passages is devoted to questions of astronomy, the inference seems to be correct. Balabhadra’s works mentioned the latitudes of Kanauj and Sthāneśwar, which indicates that he may have been a resident of that area. His date appears to be about Śaka 800.

Cites (15)