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

198 log tan α = log cos ω + log tan λ; Put λ₁ = 30, and λ₂ = 60 and take ω = 24°; Let the corresponding α's be α₁, α₂ log tan α₁ = log cos 24 + log tan 30° (1) log tan α₂ = log cos 24 + log tan 60° (2) log tan α₁ = 9.9607 + 9.7614 = 9.7221 ∴ α₁ = 27° - 48' log tan α₂ = 9.9607 + 10.2386 = 10.1993 ∴ α₂ = 57° - 42' At the rate of 1 asu for 1', α₁ = 1668 asus α₂ = 3462; α₂ - α₁ = 1794 and since α₃ = the right ascension of 90° Longitude = 90°, α₃ = 5400 so that α₃ - α₂ = 1938. These are given by Bhāskara as 1670, 1793, 1937, the first exceeding by 2 asus, the second and third each less by one asu and the total according with the total. The rising times of Karkaṭa etc. will be 1937, 1793, 1670, 1670, 1793, 1937, 1937, 1793, 1670 respectively. Let us then find the rising times of these Sāyana Rasis at a locality say of latitude 13°. Refer to fig. 21. Let rS represent Meṣa so that the rising times of rE is equal to that of rS. But rE = rA - AE. We have seen rA = 1670 using Bhāskara's value. Sin EA = tan 13° tan δ₁ where δ₁ is the declination of S where rS = 30°. Sin δ₁ = sin 30° sin 24°. log sin δ₁ = 9.6990 + 9.6093 = 9.3083 ∴ δ₁ = 11° - 44' ∴ log sin EA = log tan 13° + log tan 11° - 44 = 9·3634 + 9.3175 = 8.6809 ∴ EA = 2° - 45' ∴ rE = 1670 - 165 = 1505 asus. Similarly for λ = 60°, putting α₂, δ₂ in the place of α₁, δ₁ and proceeding as before rE = rA₁ - A₁E; rA₁ = 3463; sin EA₁ = tan 13° tan δ₂ sin δ₂ = sin 60° sin 24° 25