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

281 First half of verse 56. The Unmandala S'anku multiplied by the Sūtra and divided by Charajyā is also Iṣṭayaṣṭi. Comm. The Unmandala S'anku and Iṣṭayaṣṭi are the lines in vertical planes corresponding to Charajyā and Sūtra in the Equatorial plane. Hence the proportion. It will be noted that the Unmandala S'anku and Iṣṭayaṣṭi are not in the same vertical plane but parallel vertical planes. None the less the proportionality holds good. Latter half of verse 56 and first half of verse 57. The Sūtra increased or decreased by the Charajyā according as the Sun is in the northern or southern hemi- sphere is what is known as Iṣṭāntyā ; similarly the Kalā increased or decreased by Kujyā is what is known as Iṣṭa- Hṛti. Comm. In fig. 52, Iṣṭāntyā = AN = AB + BN = ME + BN = Charajyā + Sūtra. Similarly in fig. 53, Iṣṭa Hṛti = an = ab + bn = sg + bn = Kujyā + Kalā. ∴ Iṣṭāntyā = H cos h + R tan δ tan φ = R (sin φ sin δ + cos φ cos δ cos h) / (cos φ cos δ) in modern terms (28) Latter half of verse 57. Similarly Iṣṭayaṣṭi increased or decreased by the Unmandala S'anku is Iṣṭa S'anku or H cos z. Comm. Let in fig. 54 which represents the plane of the prime-vertical AA', EW, BB', FF', qq' represent the lines of intersection of this plane with planes parallel to the horizon and passing through A, B, F, q of fig. 21. Then Oa = Unmanda-S'anku, Oβ = Sama S'anku, Or = Dinārdha S'anku. If xx' be the line of intersection of this plane of the prime-vertical with a plane passing through an arbitrary position of the Sun in the diurnal circle and 36