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

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In modern terms, the rising times of Rasis could be
found by solving the spherical triangle γEA (fig. 28) using
the Inner side inner angle formula namely .
[Fig. 28]
Fig. 28
cos 𝑥 ✕ cos 𝜔 = sin 𝑥 cot 𝜆 + sin 𝜔 tan 𝜙 I
sin 𝑥 cot 𝜆 − cos 𝑥 cos 𝜔 = − sin 𝜔 tan 𝜙
putting sin 𝑥 = t, this reduces to
t cot 𝜆 − √(1 − t²) cos 𝜔 = − sin 𝜔 tan 𝜙
or (t cot 𝜆 + sin 𝜔 tan 𝜙)² = (1 − t²) cos² 𝜔
∴ t² (cos² 𝜔 + cot² 𝜆) + 2t ✕ sin 𝜔 tan 𝜙 cot 𝜆 −
cos² 𝜔 = 0
∴ t =
−sin 𝜔 tan 𝜙 cos 𝜆 ± √[sin² 𝜔 tan² 𝜙 cot² 𝜆 + cos² 𝜔 (cos² 𝜔 + cos² 𝜆)]
──────────────────────────────────────────────────────────────────────────
cos² 𝜔 + cot² 𝜆
Putting successively 𝜆 = 30°, 60°...360° and ignoring
the negative sign of the radical we have the sines of rising
times of arcs of the ecliptic of 30°, 60° etc. Subtracting
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