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

420 divided by the Chāyākarṇa of the Vitribha will also give the Sphuta-lambana. Comm. From Tripras'nādhikāra, we have 12 / K = (H cos Z) / R so that in the formula cited above instead of (H cos ZV) / R we are asked to use 12/K. Latter half of verse 5 and first half of verse 6. Dṛk-nati² = H cos² ZV − H cos² Z☉ = H sin² Z☉ − H sin² ZV (fig. 92) (4 Dṛk-nati) / R = Sphutalambana. Comm. We shall first prove this on modern lines. Cos Z☉ = cos ZV cos Z☉ ∴ cos² ZV − cos² Z☉ = cos² ZV (1 − cos² V☉) = cos² ZV sin² V☉ = (H cos² ZV H sin² V☉) / R⁴ Also cos² ZV − cos² Z☉ = sin² Z☉ − sin² ZV = (H cos² ZV − H cos² Z☉) / R² = (H sin² Z☉ − H sin² ZV) / R² ∴ H cos² ZV − H cos² Z☉ = H sin² Z☉ − H sin² ZV = (H cos² ZV H sin² V☉) / R⁴ ∴ Dṛk-nati defined above = √(H cos² ZV − H cos² Z☉) = √(H sin² Z☉ − H sin² ZV) = (H cos ZV H siu V☉) / R ∴ (4 Dṛk-nati) / R = (4 H cos ZV H sin V☉) / R² = Sphutalambana.