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'.