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

328 BRAHMAGUPTA A GREAT CRITIC (viii) Moon’s true latitude = Moon’s latitude × nati. The present Sūryasiddhānta and Brahmagupta both utilise the following expressions for lambana and nati which give more accurate values : lambana = [Rsin (M - ☉) × dṛggatijyā] / {Rsin (30°)}² ghaṭis where M and ☉ denote the longitudes of the meridian ecliptic and the Sun respectively. nati = (dṛkkṣepajyā × d) / (15 × R) where R is the radius of the celestial sphere and d denotes the difference between the daily motions of the Sun and the Moon¹. Brahmagupta has raised objections to the Āryabhaṭa system regarding lambana (XI. 26-28), dṛkkṣepa (XI. 30-31) ayanadṛk- karma (XI. 35), elevation of Moon’s horns (śṛṅgonnati) (XI. 39) and similar several other points. He is so vehemently opposed to Āryabhaṭa that finally he declares : “It is beyond my capacity to enumerate all the defects of Āryabhaṭa. Only a few have been given here as illustration. Intelligent people can easily find out others².” He also says : Āryabhaṭa is neither conversant with the Gaṇita (mathematics), nor Kāla (time calculations) nor Gola (celestial or spherical calculations). It is difficult to enumerate separately the fallacies committed by him in the respective chapters of the Gaṇitapāda, Kālakri- yapāda and Golapāda³.

1. loc. cit. BrSpSi. XI. 23.
2. आर्यभटदूषणानां संख्या वक्तुं न शक्यते यस्मात् । तस्मादयमुद्देशो बुद्धिमताऽन्यानि योज्यानि ॥ —BrSpSi. XI. 44
3. जानात्येकमपि यतो नार्यभटो गणितकालगोलानाम् । न मया प्रोक्तानि ततः पृथक् पृथग् दूषणान्येषाम् ॥ —BrSpSi. XI. 43.