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

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∴ Mahā-Sanku = H cos z = (R × 12) / K = (3438 × 12) / 15 = 2750 - 24.
We know that Mahā-Sanku forms a latitudinal triangle
with Iṣṭa Hṛti.
So (H cos z) / (Iṣṭa Hṛti) = 12 / k ∴ Iṣṭa Hṛti = (H cos z × k) / 12
∴ Iṣṭāntyā = (Iṣṭa Hṛti × R) / (H cos δ) ie. H cos δ = (Iṣṭa. Hṛti × R) / Iṣṭāntyā
= (H cos z × k × R) / (12 × I. A.) substituting the above value of Iṣṭa
Hṛti. Here H cos z is got above and I. A. has been assu-
med above as H sin (Unnatakāla).
Note. (1) Computing
H cos δ = (12 R / 15) × (√(s² + 12²) × R) / (12 × H sin (60))
= (R² × 13) / (15 H sin 60) = (13 R × 2) / (15 × √3). Here H cos δ > R which is
invalid.
(2) This is the only place where Bhāskara gave a
numerical example with a slight flaw. In other words,
under the given circumstances the shadow must be greater
than what is given. However, the procedure indicated is
mathematically correct.
(3) It is interesting to note that the flaw was noted
by a commentator named Lakṣmīdāsa as reported by
Munīśwara in his Marīchi Bhāṣya. Munīśwara also
noted the flaw but argues away in an untenable way.
Another commentator named Gaṇeśa who was the author
of the commentary named Śiromaṇipracāśa, does not seem
to have noticed the flaw, or even if he did notice, probably
he fought shy of pronouncing that there was a flaw. In
fact a simple flaw like this in numerical examples, is not
in the least derogatory to the prestige of Bhāskara. So,
the commentators who happened to notice the flaw need
not have pointed the same.