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

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Then the next argument is 'If for H sin λ equal to R we
have the declination equal to H sin ω, what shall we have
for the above Dorjyāntara. The result is
(H sin ω / R) × (H cos λ × b / R). Since this is in modern terms
sin ω cos λ × b and b = Δλ, we perceive that this expres-
sion is Δ (H sin δ) where δ stands for LM of fig. 84, ie.
the difference of the declinations of the points S and L of
the disc of fig. 84. The next argument advanced by
Bhāskara, namely that on account of declination, the disc
is slanted and LM gets thereby enlarged into L'M of
fig. 84 and adduces proportionality from fig. 86. But this
argument seems to be faulty. In fact, the magnitude of
LM is got for the diurnal circle of radius H cos δ. To
get its value for radius R, the result would be
[(H sin ω H cos λ × b) / R²] × [R / (H cos δ)] = (b. H sin ω H cos λ) / (R. H cos δ) .
Then the argument is 'If in the disc of radius b, we have
Δδ equal to the above what will it be for radius R? The
result would be (H sin ω H cos λ) / (H cos δ) .
Note. Our argument is based on the idea that lines
of the small circle namely the diurnal circle get enlarged
for a circle of radius R in the porportion R: H cos δ.
Bhāskara's concept of enlargement on account of slanting
does not seem to be plausible because, on account of decli-
nation, the disc may occupy an overhead position when
the Equator is itself inclined. Thus slanting does not
arise out of declination.
The question might be asked as to how Bhāskara got
the right answer by such an argument. He got the answer
up his sleeves through the other methods he gave and he
adduced this argument to get at that answer.