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

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shadow in the given direction. Bhāskara gives an example
where he gets two shadows on a day taking the moments
when the Sun is on the prime-vertical. In fact having
this case of the East-West shadows alone, he conceived
that two shadows could be had in a given direction under
particular conditions.
He chooses a place of s = 5″ ie. a place of latitude
22° – 37′ (Bhāskara often gives this latitude which night
indicate that he was probably residing in that latitude
which passes through approximately Itarsi). He takes a
day when the Sun’s declination is given by H sin δ = 780
ie. δ = 13° – 7′. Then the Sama-Śanku is given by
R sin δ
───────── (comparing the second and the fifth latitudinal
sin φ
triangles
Sama-Śanku Krantijyā H sin δ
──────────── = ─────────── = ─────────
R H sin φ H sin φ
RH sin δ R sin δ
∴ Sama-Śanku = ────────── = ─────────)
H sin φ sin φ
3438 × 780
= ────────── = 2028 approximately. I
1322 – 18
R sin δ
Also Agrā = ───────── = 845.
cos φ
Knowing the Sama-Śanku, the East-West shadow may
be taken to be determined. Now Bhāskara proceeds to show
that at the time of having the second shadow also, in the
same East-West direction, the Śanku will be the same
Sama-Śanku itself. For this, proceeding according to the
Rs
method indicated in the verse, “Taking ─────── to be the
H sin a
equinoctial shadow etc.” we have
Rs 3438 × 5
─────── = ──────────── = what is called Kha-hara Rāsi.
H sin a 0