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

142 GREEK AND INDIAN METHODS tracted from, or added to, γK the celestial longitude, gives γM the polar longitude. According to Āryabhaṭa¹, MK = (σK × R vers γK × R sin ω) / R² . Brahmagupta² makes a dis- tinct improvement on Āryabhaṭa and gives his rule for finding the projection MK on the celestial equator. If P be the celestial pole, PKH the secondary to the equator, Brahmagupta says that, Fig- 13 NH = (σK × R sin (γK+90°) × R sin ω) / R If from σ, σR is drawn perpendicular to PKH, it is evident that, R sin σ R = (R sin σ K × R sin σ KR) / R According to Āryabhaṭa and Brahmagupta, as explained before, R sin σKR = (R sin (γK+90°) × R sin ω) / R Hence Brahmagupta intends that, NH = σR = (σK × R sin σKR) / R which is rather a big assumption. He then directs the finding of the part of the ecliptic of which σR or NH is the projection on the equator thus approximately to MK. Āryabhaṭa, Brahmagupta³ and the modern Sūryasiddhānta take the declination σN = σK + KH where σK is small. They do not consider the case where σK is large. Bhāskara alone gives us fairly correct rules for this trans- formation of co-ordinates.

1. Āryabhaṭa, Gola, 36.
2. BrSpSi X, 17.
3. BrSpSi, X, 15, Sūryasiddhānta, II, 58.