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

82 BRAHMASPHUṬA SIDDHĀNTA & KHAṆḌAKHĀDYAKA sphuṭasiddhānta, Brahmagupta thus speaks of the two works of Āryabhaṭa: As in both the works the number of the Sun's revolutions is spoken of as 432,000 years, their planetary cycle is clear, i. e., of 4,320,000 years. Why then is there difference of 300 civil days in the same cycle of the two books ?¹ Again, he says : In 14,400 years elapsed of the Mahāyuga, there is produced a difference of one day in the audayika and ardharāt- rika systems.² Varāhamihira in the Pañcasiddhāntikā writes - Āryabhaṭa maintains that the beginning of the day is to be reckoned from midnight at Laṅkā; and the same teacher again says that the day begins from sunrise at Laṅkā. ³ Thus from the writings of Brahmagupta and Varāhamihira, it is clear that Āryabhaṭa I was the author of both the audayika and ardharātrika systems of astronomy. In Varāhamihira's verse the phrase sa eva (स एव), meaning "he undoubtedly" is of special significance. It removes the least doubt as to Ārya- bhaṭa's authorship of both these systems. The audayika and ardharātrika astronomical constants are respectively to be found from the Āryabhaṭīya and may be deduced from the Khaṇḍa- khādyaka as well. The following is the comparative view of the constants of Varāhamihira and of the present day Sūrya- siddhānta. TABLE I Planetary revolutions in a mahāyuga of 4,320,000 years, according to various authorities.

1. युगरविभगणाः रव्यूधृति यत् प्रोक्तं तत् तयोर्यु गं स्पष्टम् । त्रिशती रव्युदयानां तदन्तरं हेतुना केन ॥ —BrSpSi XI. 5
2. अधिकैः शतैश्चतुर्भिर्वर्ष सहस्रैश्चतुर्दशभिरेकः । युगायातैर्दिनवारान्तर मौदयिकार्ध रात्रिकयोः ॥ —BrSpSi XI. 13
3. लङ्कार्द्धरात्रसमये दिनप्रवृत्तिं जगाद चार्य्यभटः । भूयः स एव सूर्योदयात् प्रभृत्याह लङ्कायाम् ॥ —PSi. XV. 20