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

ANGLE BETWEEN ECLIPTIC AND HORIZON 139 (3) Determination of the culminating point of the ecliptic from the hour-angle of the Sun. (4) Finding the declination of the culminating point of the ecliptic. Having obtained the above elements, his rule can be follow- ed thus : In this Fig. 11 NZH is the meridian, HMEAN the horizon, CN'A the ecliptic. If N' be the nonagesimal or the highest point of the ecliptic, the altitude of N' is the inclination of the ecliptic to the horizon. Let ZN'M be the vertical through N', meeting the horizon at M. When the time is given, the longitudes of A and C can be found out, from which CZ the zenith distance of C and EA the amplitude of the orient ecliptic point can be determined. Fig. 11 Here HM=EA. According to Āryabhaṭa, R sin CN' = (R sin CZ × R sin HM) / R and R sin ZN' = √((R sin CZ)² - (R sin CN')²) This is only an approximate rule. As expressed here, R sin ZN' = (R sin CZ × R cos HM) / R approximately. = (¹R sin CZ × R cos HM × R) / (R × R cos CN') accurately. = (R sin CZ × R cos HM) / (R cos CN') . (B) The method of Brahmagupta² : Brahmagupta would also first determine the orient ecliptic

1. This correction was perhaps first noticed by Raṅganātha (1603 A. D.) in his commentary in the Sūryasiddhānta.
2. BrSpSi. V 3.