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Art. XV.—On some Fragments of Áryabhaṭṭa
Published online by Cambridge University Press: 14 March 2011
Extract
There are few names in the history of Indian science which have acquired a celebrity equalling that of Áryabhaṭṭa. He is—to use the words of Colebrooke—“the earliest author known to have treated of Algebra among the Hindus, and likely to be, if not the inventor, the improver, of that analysis; by whom, too, it was pushed nearly to the whole degree of excellence which it is found to have attained among them.” But, notwithstanding the renown of the Indian algebraist and astronomer, not only among his countrymen, but also among the Arabian scholars, his works seemed to be lost. Neither was Colebrooke successful, nor was Davis more so, in their endeavours to find any work of his. What was known about his doctrine, which in many points deviated from the prevailing opinions among Indian astronomers, was derived from quotations occurring in various mathematical and astronomical writings. Now, it is deserving of notice, that in Southern India there are copies extant of works that most unequivocally lay claim to being the genuine productions of Áryabhaṭṭa. The late Mr. Whish knew an Áryabhaṭṭíyam, a treatise on arithmetic and mathematics, to which I shall have to revert in the course of this paper. Prof. Lassen says, in his Indische Alterthumskunde, that he has received from Southern India copies of two works ascribed to Áryabhaṭṭa, viz., of the above-mentioned Áryabhaṭṭíyam and of the Daṣagítakasútra. In an article on the Ārya-siddhánta in the 6th volume of the Journal of the American Oriental Society, Dr. Fitz-Edward Hall has verified an Ārya-siddhánta, of which he possessed two imperfect copies, by extracts occurring in the writings of various commentators.
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References
page 321 note 1 Ind. Alterth., 2nd vol., p. 1136. Prof. Lassen concludes, from the somewhat equivocal words of Reinaud, , Mémoire sur l'Inde, pp. 321 and 322Google Scholar, that the Áryabhaṭṭíyam is spoken of by Albirúiní. So far as I can see, Albirúní intimates only that the Indian astronomical systems (méthodes) could be reduced to three, the Sindhind, the Áryabhaṭṭa, and the Arkand. It is an inference of Reinaud that the system called Áryabhaṭṭa is identical with the Áryabhaṭṭíyam, which, according to Whish, is not a treatise on astronomy, but on arithmetic and mathematics.
page 372 note 1 The date in full is given in Utpala's own words:
“On the second lunar day of the dark half of the month Phálguna, on a Thursday, in the Sáka-year 888, I finished this commentary.”
page 372 note 2 One of the MSS. belonged formerly to Colebrooke: for convenience sake, I shall call it B, and the other A. The fragment is introduced, in B, by the words 
in A by 
The various readings, mere blunders being omitted, are: B 
for 
—B 
—A 
B 
.—A 
for 
.
page 373 note 1 The word Nandanavana, rendered here by Paradise, is the well-known garden of India. It is also called Nandanadyána in the Kathá-sarit-ságara, taranga 28, vs. 52 (edition of Brockhaus, in the Abhandlungen für die Kunde des Morgeniandes, 1862)Google Scholar.
page 374 note 1 See Colebrooke, , On the sect of the Jainas, and As. Beg., xii, p. 228Google Scholar.
page 374 note 2 They are to be found in Cod. A, fol. 29, in B, fol. 33. The latter MS. has 
.
page 374 note 3 Here both copies concur in reading 
intending, very likely, 
—A 
, B 
.
page 375 note 1 The word mzshíbhútá is omitted in the translation, since it is devoid of meaning in this connexion. I surmise that we ought to read medhíbhútá, medhí being “a post fixed in the centre of a threshing-floor or barn, to which the cattle are attached, as they turn round it to tread out the corn.”—Wilton.
page 375 note 2 A has 
B 
page 376 note 1 The reading is conjectural, A exhibiting 
B 
. As to the general meaning there can be no doubt.
page 377 note 1 For the sense of the terms savyaga and apasavyaga, see Súrya-siddhánta, ch. 12, vs. 55, and the valuable translation of it by the Rev. Mr. Burgess and Prof. Whitney.
page 378 note 1 Both MSS. have 
which here is devoid of sense, and moreover disturbs the metre. Further, A has 
B 
—B 
A 
page 378 note 2 B has 
for 
and 
. The latter is unobjectionable, provided it be taken for two words, not for a compound.—A 
. Both have 
:, and have added, in numerals, 
.
page 379 note 1 Var. Sanh., ch. 8, TB. 1.
page 380 note 1 Transactions of the Lit. Soc. of Madras, 1827.
page 380 note 2 Zeitschrift für die Kunde des Morgenlandes, vol. iv, p. 81.
page 380 note 3 Mémoire sur l'Inde, p. 299.
page 382 note 1 B, the MS. formerly in the possession of Colebrooke, omits 
which may account for his knowing only three schools, instead of four. See Algebra, Dissert., p. viii. Cf., however, Davis, As. Ees., ii, p. 261.
page 383 note 1 A has of 
—B 
page 383 note 2 B omits 
—A 
.
page 383 note 3 A 
which is wholly out of the question. The reading of B, 
however, is also against the metre; and therefore I venture to read 
a form not infrequent in MSS., and in favonr of which might be urged the fact that the Arabian transcription sounds Arjabhar. A has 
page 383 note 4 A 
, B 
page 384 note 1 A 
page 384 note 2 The meaning of this obscure stanza seems to be, that there is no general rule for determining the commencement of the days of the week, this depending not only upon longitude, but also on the particular custom of a country. What, nevertheless, can be brought under scientific rules, is the correspondence of time. In other words, the rules are only theoretic, yalháṣástram.
page 384 note 3 U'narátraand its synonym Kinarátra are wanting in the dictionaries. With the aid of etymology, we can make out that they mean the night, or nearly so, by which the synodical lunar month of thirty tithis is less than thirty solar days. The number of tithis continually gaining upon that of the solar days, the difference will amount, in a little more than two months, to a whole tithi, which must be expunged. Therefore, únarátrais rendered by tithinaya; it properly being the cause of the latter becoming necessary.—The days of the planets mean here, I think, the days of the week.
page 385 note 1 Mém. tur l'Inde, p. 341.
page 385 note 2 This word is certainly wrong. For j one may read j, and pronounce nilahha, closely approaching the Sanskrit nirakshu.
page 387 note 1 As a date requires precision, I should surmise that adhiká is a misread tryadhiká; the characters 
and 
being liable to be confounded. The rendering, in this case, would be, “twenty-three years,” and the date, A.D. 475.