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

275 Taking this to be the equinoctial shadow H sin L = Rs / √(12² + s²) = R itself (Dealing this way with Kha-hara Rās'is is prohibited in modern mathematics but Bhāskara adds at the end of the commentary that dealing with them cautiously does not effect computations which is of course true, for when the equinoctial shadow is infinity φ = 90° so that H sin φ = R as got). Hence L = 90° and 180° - 90° = 90° = L'. Then H sin D = (R × 780) / (1322 - 18) = same as Sama-S'anku obtained in I = H cos z so that D = 90 - z. Now from the equation z + δ = φ, z = φ - δ = L' - D = 90° - (90 - z) where z is the zenith-distance when the Sun is on the prime-vertical. ∴ The zenith-distance is again the same z. In other words, the second zenith-distance is also that when the Sun is on the prime-vertical. Bhāskara has given this example just to obtain the second shadow as well and he has chosen the event of the Sun being on the prime- vertical to show that the procedure indicated by him may be verified to hold good. Verses 49, 50. Alternate method to find the shadow. Let R² s² + H sin² a × 12² = prathama where s = equinoctial shadow and a the Hindu azimuth. Let Anya = RsA where A is the Agrā. Divide the prathama and Anya by (H sin² a - A²) and still call them prathama and Anya. Then K = √(Adya + Anya²) ± Anya where K is the Chayā- Karṇa. Comm. Let K be the required Chayā-Karṇa. Then Karnāgrā = KA / R = s + b where b is the bhuja.