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

201 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 26