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

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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 =