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

274 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