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

315 ∴ (Taddhṛti × 12 s) / k² = sin δ. Thus assuming H sine of the given Unnatakāla to be Taddhṛti and multiplying it. by 12 s and dividing by k² we have the value of H sin δ. But this is approximate because the given Unnatakāla is not exactly Taddhṛti but only an approximate value. From this H sin δ, compute H cos δ, Charajyā, Kujyā and through the process indicated in verse 54 namely “Subtract the Characāpa from the Unnatakāla. The H sine of the result is called Sūtra. Multiply the Sūtra by H cos δ and divide by R; then we have Kalā. Add Kujyā to Kalā; we get Iṣṭa-Hṛti”, we obtain a more correct value of Taddhṛti. Then here we may cut short the process as follows namely ‘ If by the assumed Taddhṛti we had the previous H sin δ, what shall we have for this more approximate Taddhṛti ’? The result will be a more approximate value of H sin δ. Again form the Taddhṛti with this H sin δ and so repeating the process till we have a stationary value, we have the correct value of H sin δ. Note. This is a beautiful example of the method of successive approximations which is a modern technique but which was so much in vogue and favourite with the Hindu astronomers. (It will be noted how to cut short the method). Verses 84, 85. Answer to the second question. Obtain 12² R²/(R² − H sin² h) s² + 1 and divide R² by this and take the square root which gives H sin δ. Then (R × H sin δ) / (H sin ω) gives H sin λ whose Cāpa gives the longitude of the Sun. Comm. The H sine of the given Natakāla is H sin h and R² − H sin² h = H cos² h. Let H sin δ be x, which is required to be found. Then R² − x² = H cos² δ; H cos h = Sūtra and