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

BRAHMAGUPTA A GREAT CRITIC 325 Usually by agra, we mean the arc of the celestial horizon lying between the east point and the point where a heavenly body rises ; or between the west point and the point where a heavenly body sets. Declination is krānti. 16. Brahmagupta has criticised Āryabhaṭa and his group for their expressions for determining lambana (i. e. the difference of the parallaxes, in longitude, of the Sun and the Moon), and the rule for determining the avanati or nati (i.e. the difference in parallaxes, in latitude of the Sun and Moon).¹ Lambana is obtained with the help of the five Rsines : (i) madhya-jyā, (ii) udaya-jyā, (iii) dṛk-kṣepa-jyā, (iv) dṛg-jyā, and (v) dṛg-gati-jyā. (i) The madhyajyā is the Rsine of the zenith distance of meridian ecliptic point : madhyajyā=Rsin (ϕ± declination of the meridian ecliptic point).² In this expression ϕ is the latitude of the place, and by R sin is meant R × sine, R being the radius of the celestial sphere. (ii) The udayajyā is the Rsine of the arc of the horizon intervening between the equator and the ecliptic, and is given by : udayajyā = (R sin L × R sin ε) / (R cos ϕ) where L is the longitude of the horizon ecliptic point in the east. and ε the obliquity of the ecliptic. (iii) The dṛkksepajyā is the R sine of the zenith distance of the central ecliptic point³, and is given by :

1. व्यासार्धेन विभक्ता दृग्गति जीवा चतुर्गुणा लब्धम् । लम्बननाड्यः पञ्चदशगुणिताया त्रिज्यया भक्ता ॥ दृक्क्षेपज्या भुक्त्यन्तराहता लब्धमवनतिर्भवति । स्फुटयोजनकर्णाभ्यां भूव्यासेन च विना स्पष्टे ॥ आर्यभटेनास्मिन् सति लघुनि किमर्थं महत् कृतं कर्म । गणित ज्ञानाज्जाड्यं विजानता यदि ततः सुतराम् ॥ —BrSpSi. XI. 23-25
2. The meridian ecliptic point is the point of the ecliptic on the meridian.
3. The central ecliptic point is the central point of the portion of the eclip- tic lying above the horizon.