The Āryabhaṭīya by Āryabhaṭa

By David Reigle on June 10, 2012 at 8:47 pm

The Āryabhaṭīya was not as well known in old India as the Sūrya-siddhānta. In modern times, however, it has attracted more attention than any other Sanskrit text on astronomy. This is because, among other things, as far back as the year 499 C.E. it taught the rotation of the earth on its axis. Āryabhaṭa made no claim to have discovered this. Rather, he simply included it in a matter-of-fact manner in his brief treatise, which purports to present the system of astronomy taught by Brahmā. Despite the authority of this ancient system, other famous Indian astronomers (including Varāha-mihira and Brahmagupta) were quick to criticize Āryabhaṭa for teaching the rotation of the earth on its axis. Āryabhaṭa also gave another teaching, anomalous in Indian tradition, which he was criticized for. Rather than the standard 4:3:2:1 ratio for the lengths of the four yugas, he taught that they are of equal length. He gives the overall length of a mahā-yuga the same as everyone else does: 4,320,000 years (chapter 1, verse 3). But the four yugas that comprise it are each 1,080,000 years in length. This gives us another method of calculation to work with. It is noteworthy that equal length yugas are also found in the Buddhist Kālacakra astronomy.

The Āryabhaṭīya and the Sūrya-siddhānta agree fully on the starting point of the present kali-yuga (3102 B.C.E.), and they agree in general that the length of a kalpa or day of Brahmā is more than four billion years, while we are about two billion years into this at present. But there are some differences. The Āryabhaṭīya says in chapter 1, verse 5 (translated by Kripa Shankar Shukla, 1976): “A day of Brahmā (or a Kalpa) is equal to (a period of) 14 Manus, and (the period of one) Manu is equal to 72 yugas. Since Thursday, the beginning of the current Kalpa, 6 Manus, 27 yugas and 3 quarter yugas had elapsed before the beginning of the current Kaliyuga (lit. before Bhārata).” This means that a kalpa is 14 times 72 making 1008 yugas. Thus, unlike in the Sūrya-siddhānta where a kalpa is 1000 yugas or 4,320,000,000 years, in the Āryabhaṭīya a kalpa is 4,354,560,000 years. The period of a manu, consisting of 72 yugas (rather than 71 yugas as in the Sūrya-siddhānta), is 311,040,000 years. Up to the beginning of the present kali-yuga, we have:

6 manus (311,040,000) equals 1,866,240,000 years, plus

27 yugas (4,320,000) equals 116,640,000 years, plus

3 quarter yugas (1,080,000) equals 3,240,000 years, yields

1,986,120,000 years.

As stated in an earlier post, the Sūrya-siddhānta gives the figure 1,953,720,000 years from the beginning of the epoch (17,064,000 years after the beginning of the kalpa) to the end of the last kṛta-yuga. Up to the beginning of the present kali-yuga we would have to add to this the 1,296,000 years of the tretā-yuga and the 864,000 years of the dvāpara-yuga. This yields 1,955,880,000 years. So while the number of years that have elapsed in our world-period is in the same general range of two billion years, the specific numbers differ. The information given in this verse also tells us the number of years that have elapsed of our current or Vaivasvata manvantara up to the beginning of the present kali-yuga: 116,640,000 (27 times 4,320,000) plus 3,240,000 (3 times 1,080,000) equals 119,880,000 years. The information given in the Sūrya-siddhānta provides a little different result for this: 116,640,000 (27 times 4,320,000) plus 3,888,000 (1,728,000 + 1,296,000 + 864,000) equals 120,528,000 years. Perhaps a lost work by Āryabhaṭa, known to have once existed, would shed light on the reasons for these differences.

The Āryabhaṭīya is a brief and somewhat cryptic text, consisting of only 108 verses plus its 10 (or 13) verse summary given at the beginning. The extant Sūrya-siddhānta consists of 500 verses. As noted earlier, the old Sūrya-siddhānta (as summarized in the Pañcasiddhāntikā) was determined to have used the astronomical constants found in a lost work by Āryabhaṭa. Prabodh Chandra Sengupta showed the close agreement of the astronomical constants used in the old Sūrya-siddhānta with those given in Brahmagupta’s Khaṇḍa-khādyaka, which had been published in 1925. The source of the Khaṇḍa-khādyaka’s astronomical constants, as shown by Sengupta, is a lost work by Āryabhaṭa (“Aryabhata’s Lost Work,” Bulletin of the Calcutta Mathematical Society, vol. 22, 1930, pp. 115-120). This was confirmed by the discovery of the Mahābhāskarīya (written by an earlier Bhāskara than the author of the famous Siddhānta-śiromaṇi), announced by Bibhutibhusan Datta (“The Two Bhāskaras,” Indian Historical Quarterly, vol. 6, 1930, pp. 727-736), and first published in 1945 in the Ānandāśrama Sanskrit Series, no. 126. It gives in its chapter seven the astronomical constants of the two different systems used by Āryabhaṭa: those of the day reckoned from sunrise, used in his Āryabhaṭīya, and those of the day reckoned from midnight, used in his now lost work. Strangely, it is these latter astronomical constants that were used in the old and now lost version of the Sūrya-siddhānta.

Like with the Sūrya-siddhānta, there are at present three complete English translations of the Āryabhaṭīya. The first is “The Aryabhatiyam,” Translation by P. C. Sengupta, Journal of the Department of Letters, University of Calcutta, vol. 16, 1927, pp. 1-56, also published as a separate offprint. Much supplemental material was published in separate articles by Sengupta; e.g., “Aryabhata: The Father of Indian Epicyclic Astronomy” (op. cit., vol. 18, 1928, pp. 1-56), and “Greek and Hindu Methods in Spherical Astronomy” (op. cit., vol. 21, 1931, pp. 1-25). The second translation is The Āryabhaṭīya of Āryabhaṭa, Translated with Notes by Walter Eugene Clark, Chicago: University of Chicago Press, 1930. However, Clark’s translation had been done about five years before its publication, with his student Baidyanath Sastri, and could not utilize Sengupta’s translation (see Preface, p. xvii). Clark describes his translation made with Sastri as “a preliminary study based on inadequate material,” adding that: “Of several passages no translation has been given or only a tentative translation has been suggested” (p. vii). The third translation is Āryabhaṭīya of Āryabhaṭa, Critically edited with Introduction, English Translation, Notes, Comments and Indexes, by Kripa Shankar Shukla in collaboration with K. V. Sarma, New Delhi: Indian National Science Academy, 1976. This translation is quite the most definitive, due in no small measure to the fact that, in the interim, Bhāskara I’s three expository works on the Āryabhaṭīya became available: the Mahā-bhāskarīya, the Laghu-bhāskarīya, and Bhāskara’s direct commentary on the Āryabhaṭīya. Kripa Shankar Shukla writes in his Introduction to the Laghu-bhāskarīya (1963, p. xxiv): “In the absence of the works of Bhāskara I, many a passage in the Āryabhaṭīya of Āryabhaṭa I would have remained obscure to us.”

The Sanskrit text of the Āryabhaṭīya was first published in 1874, along with the commentary by Parameśvara (called Paramādīśvara on the title page), edited by H. Kern (Leiden: E. J. Brill). This edition was admittedly based on inadequate manuscript material (Preface, p. v: “This first edition of the Āryabhaṭīya . . . is mainly based upon two manuscripts”; p. xi: “It will be understood that with the scanty, however valuable, materials at my disposal, I could not attempt to constitute the text such as the author published it.”). Nonetheless, it made the text available. The Āryabhaṭīya was then edited by K. Sāmbaśiva Śāstrī with the commentary by Nīlakaṇṭha-somasutvan, published in the Trivandrum Sanskrit Series, no. 101, 1930, and no. 110, 1931, with the third volume edited by Śūranāḍ Kuñjan Pillai, no. 185, 1957. Then followed an edition in 1966 by S. V. Sohoni with a modern Sanskrit commentary and Hindi commentary, both by Baladeva Mishra (Patna, Bihar Research Society). A critical edition of the Sanskrit text of the Āryabhaṭīya, prepared by K. V. Sarma, accompanied the 1976 English translation by Kripa Shankar Shukla listed above. Unlike the Sūrya-siddhānta, the text of the Āryabhaṭīya seems to be well established (Introduction, p. lxxiii: “The collation of the manuscripts did not reveal many significant variations in the text.”). Two more volumes were published along with this 1976 volume, providing Sanskrit editions of important commentaries. One is the Āryabhaṭīya with the commentary of Bhāskara I and Someśvara, edited by Kripa Shankar Shukla (New Delhi: Indian National Science Academy, 1976). The other is the Āryabhaṭīya with the commentary of Sūryadeva Yajvan, edited by K. V. Sarma (New Delhi: Indian National Science Academy, 1976).

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