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

287 Comm. We computed Dinārdha Śaṅku by the formula. D.S. = (Antyā × U.S.) / Charajyā = (Hṛti × Koṭi of a L.T.) / (Karṇa of L.T.) under verse 36 ; similarly Iṣṭa Śaṅku (I.S.) will be given by Iṣṭa Śaṅku = (Iṣṭāntya × U.S.) / Charajyā = (Iṣṭa Hṛti × Koṭi of a L.T.) / (Karṇa of the L.T.) But Iṣṭāntyā = [R (sin φ sin δ + cos φ cos δ cos h)] / [cos φ cos δ] (as under verse 56) ∴ Iṣṭa Śaṅku = [R (sin φ sin δ + cos φ cos δ cos h)] / [cos φ cos δ] × (R sin δ sin φ) / (R tan φ tan δ) from formulae (13) and (19) = R (sin φ sin δ + cos φ cos δ cos h) = R cos z = H cos z Or again Iṣṭa Hṛti = (R cos z) / (cos φ) from formula (11) ∴ Iṣṭa Śaṅku = (R cos z / cos φ) × (H cos φ / R) = R cos z = H cos z Having got H cos z, using the formula H sin² z = R² — H cos² z, H sin z ie. Dṛk-jyā can be computed. Also K = 12R / (H cos z) and S = (KH sin z) / R give the Chāyā Karṇa and Chāyā. Bhāskara cautions us that H sin z cannot be computed from Hṛti as mentioned in verse 37. because there in that verse, the H sin z computed is that at noon alone. Verse 62. Alternate method of obtaining K. The Chāyākarṇa when the Sun is on the unmaṇḍala multiplied by Kujyā or that when the Sun on the prime- vertical multiplied by Taddhṛti, or again that when the Sun is on the meridian multiplied by Hṛti, divided by Iṣṭa Hṛti, will be equal to the Iṣṭa-Karṇa K.