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

486

are the straight lines joining the rising and setting points of the celestial body. As such, these Udayāstasutras are all parallel to the East-west line. In fig. 114, in the horizontal plane containing the points A's, B's and C's in the respective cases, according to the Hindu convention, we talk of Agrā and Bhuja as being Uttara Agrā, Dakṣiṇāgrā, Uttara Bhuja and Dakṣiṇa Bhuja. Śaṅkutalam is always taken to be south except in the fifth case shown in figs. 113 and 114 when the altitude happens to be below the horizon. In this case the Śaṅkutala is spoken as north. Thus the general formula A=S+B assumes the following various forms, in the respective cases. (1) Uttarāgrā—Dakṣiṇa Śaṅkutala = Uttara Bhuja. This corresponds to A, B, C of fig. 114 where AC, is Uttarāgrā, BA, Dakshina Śaṅkutala and BC, Uttara Bhuja. (2) In the case of A₃ B₃ C₃, Śaṅkutala—Agrā = Dakṣiṇa Bhuja since B₃ A₃—C₃ A₃=B₃ C₃. This occurs after the Sun's diurnal path has crossed the prime-vertical and the Sun has a position on the south of the prime- vertical, having a northern declination. In the case of A₄ B₄ C₄, B₄ C₄ = B₄ A₄ + A₄ C₄ ie. Dakṣiṇa Bhuja = Dakṣiṇa Śaṅkutala + Dakṣiṇāgrā. In the fifth case when the Sun's altitude is below the horizon, B₅ C₅ = B₅ A₅ + C₅ A₅ ie. Uttara Bhuja = Uttara Śaṅkutala + Uttarāgrā. In the sixth case when the Sun has a southern declination and an altitude below the horizon, B₆ C₆ = A₆ C₆ + A₆ B₆ ie. Dakṣiṇa Bhuja = Dakṣiṇāgrā minus Uttara Śaṅkutala. In the case of A₂ B₂ C₂, Uttarāgrā =