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

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Fig. 33 Fig. 34
cos (90 — δ) = cos ϕ cos (90 — A) ie. sin δ / cos ϕ = sin A or
in the Hindu form H sin A = R (sin δ / cos ϕ) = Agrajyā (5).
This Agrajyā is in a circle of radius R, and if it be re-
duced to a circle whose radius is K, is will be (K / R) × (R sin δ / cos ϕ)
= (K sin δ / cos ϕ) which is called Karṇāgrā. Hence we have
Karṇāgrā = s + b which we shall write as a = b + s (6).
This is an important formula which is going to be
formulated later in verses 72, 73. In the above formula,
s being constant, by differentiating δa = δb which means
that the variation in the bhuja is on account of the
variation in the Karṇāgrā. If in Fig. 35, Cω', CE″ be
morning and evening shadows when they are equal as per
the verse under comment, Mω' = b the morning bhuja,
NE″ = b', the evening bhuja dE' is the variation in the
bhuja ie. b — b' = δb which is formulated and equal to
δa. But δa = δ(K sin δ / cos ϕ) = K δ (sin δ) / cos ϕ, ϕ being con-
stant and K also being constant because the shadow
S is constant and K = √(S² + 12²) = constant on both
the occasions. ∴ δb = δK = (K / cos ϕ) (sin δ₁ — sin δ₂)
as stated by Bhāskara.