ARYABHAȚA & BRAHMAGUPTA CONTROVERSY already been said that perhaps to meet the popular demand. Brahmagupta in this treatise took upon himself the task of sim- plifying Aryabhata's ardharatrika system or the system of midnight day reckoning. Alberuni, the author of the Indika has made several references or quotations from the Khandakhadyaka proper and also its supplement, known as Uttara-Khanda- khadyaka. (a) There is a reference to the accepted circumference of the Earth, as given in the Khandakhadyaka (Sachau's Alberuni. Vol. I,p. 312) 93 Multiply the difference in longitude (from Ujjayini) by the (mean) daily motion of a planet (in minutes) and divide by 4,800; apply the quotient taken as minutes negatively in places east of the meridian line of Ujja- yini and positively in places lying west.¹ (b) The rules for finding the ahargana as given in the Khandakhadyaka in I. 3-5 (Sachau's Alberuni, Vol II. 46-47), to which Dr. Schrain adds a valuable anno- tation, the constants being taken from the later Paulisa Tantra as known to Bhattotpala. This Paulisa astronomy is derived from Aryabhata I's ardharatrika system.* (c) A quotation from the Uttara Khandakhadyaka (Sachau's Alberuni. Vol. II, pp. 84-86) which Sengupta has given in his translation. Chapter X. pp. 148-152. (d) A quotation also probably from the Uttara Khandakha- dyaka (Sachau's Alberuni, Vol. II. p. 87). These stanzas are found in the Brahmasphutasiddhanta, XIV, 47-52, also quoted by Bhattotpala as occurring in the Brahma Siddhanta in his commentary on the Brhat-Samhita, IV, 7. The manuscripts which Sengupta used did not show them as occurring in the Uttara Khandakhadyaka. These relate to the dimensions of the nakṣatras as seen. as distinguished from the same as calculated. 1. उज्जयिनी - याम्योत्तर रेखायाः प्रागृणं धनं पश्चात् । देशान्तर भुक्तिवधात् ख खाटवेदैः कलायाप्तम् ॥ 2- KK, Pt. B. Misra's edition, p. 145. - KK. I. 15.
