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

389
Comm. Bhāskara terms SL as the Dorjyāntara ' or
the variation in H sin λ, which he knows to (H cos λ Δλ) / R.
[Fig. 85: Triangle L'LM] [Fig. 86: Triangle SMO, Hypotenuse = R, SM = H Cos δ, MO = H Sin δ]
Fig. 85 Fig. 86
But proceeding from first principles, as he always does,
he asks us to consider the Bhogyakhanda at λ namely B.
If this be for an interval of 225', what will be it be for ‘b’?
The result is (b × B) / 225 . Then to rectify B, the proportion
used is as used above. Bhāskara says many a time that
the variation in Hsine is proportional to Hcosine. This
concept he might have derived by looking at the Hsine
table of 90 Hsines. Hence the argument advanced by him
to rectify B is ‘If for Hcosine equal to R (at zero-value
of the argument) the initial Bhogyakhanda is 225, what
will it be for an arbitary H cos λ? The result is
(H cos λ) / R × 225. Substituting this for B in the above, we
have (b H cos λ) / 225 × 225 = (b H cos λ) / R . This expression we
perceive as no other than (H cos λ Δλ) / R as equal to Δ (H sin λ),
for b is to be taken as Δλ. This (H cos λ × b) / R is called by
Bhāskara as Dorjyāntara meaning thereby Δ (H sin λ).