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

TIME-ALTITUDE EQUATION 133 Let CC' be the line of inter- section of the diurnal circle and the 'six o'clock 'circle EPW. Let SK cut CC' in M. Then. SK = SM + MK Here SM, the 'sine' in the diurnal circle of the complement of the hour angle is given a distinct name 'Kāla'¹ and MK as explained before is known by the name Fig. 8 'Kujyā.' This 'Kāla' is constructed from the point S in the diurnal circle. Thus the triangles like SKL were not taken in their projections on the meridian plane as Braunmühl would suggest. From the triangle KSK, we get, 'Cheda' : 'Śaṅku' = R : R cos ϕ where ϕ is the latitude of the observer; 'Śaṅku' is here = R cos Z, Z being fhe Sun's zenith distance. ∴ 'cheda' = (R cos Z × R) / (R cos ϕ) Now 'Cheda' = radius of the diurnal circle + Kujyā - versed sine of the hour-angle in the diurnal circle O' B + O' V - BR, = R cos δ + (R sin δ × R sin ϕ) / (R cos ϕ) - (R vers H × R cos δ) / R As in the previous problem, Kujyā = SK = (R sin δ × R sin ϕ) / (R cos ϕ) or (R cos Z × R) / (R cos ϕ) = (R cos δ / R) { R + (R sin δ × R sin ϕ) / (R cos ϕ) × R / (R cos δ) - R vers H } The above equation simplified becomes cos Z = sinδ sin ϕ + cos δ cos ϕ cos H. In this connection we consider the altazimuth equation by the Indian method.

1. Bhāskara's Grahagaṇita, VIII, 55. O' is the middle point of CC' or it is the centre of the diurnal circle ABB'.