सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

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QST at the locality S is a small circle whose circumference
is smaller than that of ABC. The problem is now to find
the length of this circle QST. Evidently QST / ABC = 2 π r / 2 π R
= r / R where r and R are respectively the radii of the two
circles. But r / R = Cos ϕ from the triangle OSO', where
Ô'₁SO = ŜOA = latitude of the place S. ∴ QST =
ABC × Cos ϕ = (ABC × H Cos ϕ) / R I where H Cos ϕ is
the Hindu cosine of ϕ known as lambajyā and stands for
OS₁ = O'₁S = r. This lambajyā is also called Dyujya if
the small circle is the diurnal circle of a Star. The diurnal
circle of a Star is called Dyujya-Vritta and its radius is
called Dyujyā-Equation I proves the first statement of the
Fig. 5
verse. In fig. 5 Gn N is called the fundamental gnomonic
triangle where Gn is the vertical gnomon pointing to the
Zenith Z of the celestial sphere and is considered to be of
12 units (Angulas as they are called), GN the midday-
shadow of the gnomon cast on an equinoctial day when the