ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

ĀRYABHAṬA & BRAHMAGUPTA CONTROVERSY 93 already been said that perhaps to meet the popular demand, Brahmagupta in this treatise took upon himself the task of sim- plifying Āryabhaṭa's ardharātrika system or the system of midnight day reckoning. Alberuni, the author of the Indika has made several references or quotations from the Khaṇḍakhādyaka proper and also its supplement, known as Uttara-Khaṇḍa- khādyaka. (a) There is a reference to the accepted circumference of the Earth, as given in the Khaṇḍakhādyaka (Sachau's Alberuni, Vol. I, p. 312) Multiply the difference in longitude (from Ujjayinī) 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- yinī and positively in places lying west.¹ (b) The rules for finding the ahargaṇa as given in the Khaṇḍakhādyaka in I. 3-5 (Sachau's Alberuni, Vol. II, 46-47), to which Dr. Schram adds a valuable anno- tation, the constants being taken from the later Pauliśa Tantra as known to Bhaṭṭotpala. This Pauliśa astronomy is derived from Āryabhaṭa I's ardharātrika system.² (c) A quotation from the Uttara Khaṇḍakhādyaka (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 Khaṇḍakhā- dyaka (Sachau's Alberuni, Vol. II, p. 87). These stanzas are found in the Brāhmasphuṭasiddhānta, XIV, 47-52, also quoted by Bhaṭṭotpala as occurring in the Brahma Siddhānta in his commentary on the Bṛhat-Saṁhitā, IV, 7. The manuscripts which Sengupta used did not show them as occurring in the Uttara Khaṇḍakhādyaka. These relate to the dimensions of the nakṣatras as seen, as distinguished from the same as calculated.

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1. उज्जयिनी-याम्योत्तर-रेखायाः प्रागृणं धनं पश्चात् । देशान्तर भुक्तिवधात् ख खाष्टवेदैः कलाद्याप्तम् ॥

• KK. I, 15.

2. • KK, Pt. B. Misra's edition, p. 145.