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

320 BRAHMAGUPTA A GREAT CRITIC backing to the west) in one day. It is sufficient to postulate the existence of only one Sun, one Moon and twenty-seven nakṣatras to explain the astronomical phenomena.¹ 3. Brahmagupta differs from Āryabhaṭa I in the length of the four yugas. Ārvabhaṭa regards all the four yugas of equal lengths, i. e. 1,080,000 years; the caturyuga being of 4,320,000 years. Brahmagupta regards Kaliyuga to be of 432,000 years, Dvāpara to be twice of it, Tretā to be thrice of it and Kṛtayuga of four times of the length of the Kaliyuga. Both have the caturyuga of the same length.² 4. Āryabhaṭa was not clear with respect to the number of civil days (sāvana dina) in a yuga; in one of his treatises he gives this number to be 1,577,917,800 and in the other 1,577,917, 500 with a difference of 300 days. though in both the treatises, Ārya- bhaṭa I regards the number of solar years to be 4,320,000 in a Caturyuga or Mahāyuga. Why is this difference ? asks Brahmagupta.³ 5. Āryabhaṭa regards mandocca (the apogee) and pāta (the ascending node of the orbit on the ecliptic) as constant or stationary; then how could he propound a sphuṭa-yuga or the concept of true yuga with the concurrence of year, month and day on the Caitra Śukla Pratipadā (the first day of bright half of the month Caitra) at the same time as indicated by Āryabhaṭa in his Laghvāryabhaṭīya Tantra.⁴ Āryabhaṭa was not clear in respect to the variance in the pāta. In the Āryāṣṭa-śata (in the Aryabhaṭīya which has 108 Āryā verses), Aryabhaṭa states that the pāta of all the planets

1. भानिचतुष्पञ्चाशद्द्वा द्वावकैर्द्वौ जिनोक्तं यत् । ध्रुवमत्स्यस्यावर्त्तो भवति यतोऽन्हा ततस्तदसत् ॥ BrSpSi. XI. 3
2. आर्यभटोयुगपादांस्त्रीन् यातानाह कलियुगादौ यत् । तस्यकृतान्त्यस्मात् स्वयुगान्तौ न तत् तस्मात् ॥ —BrSpSi. XI. 4
3. युगरविभगणाः स्युर्धृति यत्प्रोक्तं तत् तयोर्युगं स्पष्टम् । त्रिशती स्युदयानां तदन्तरं हेतुना केन ॥ —BrSpSi. XI. 5
4. कुजवर्षादीन् वदतांचैत्रसितादेः समं प्रवृत्तान् यत् । उदसत् यतः स्फुटयुगं तत् स्थैर्यान्मन्दपातानाम् ॥ —BrSpSi. XI. 6