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

310 Comm. The questions are clear the second verse illustrating the first. Verse 76. Answer of the first question. (b₁ K₂ ⁺~ b₂ K₁) / (K₂ ~ K₁) = s according as the bhujas are of the same or opposite directions. Comm. Suppose b₁ and b₂ are of the same direction so that b₁ = a₁ - s and b₂ = a₂ - s, taking the modern convention of signs. But a₁ = (K₁A) / R and a₂ = (K₂A) / R ∴ b₁ = (K₁A) / R - s and b₂ = (K₂A) / R - s ∴ (b₁ + s) / K₁ = A / R = (b₂ + s) / K₂ ∴ K₂ b₁ - K₁ b₂ = s (K₁ - K₂) ∴ s = (K₂ b₁ - K₂ b₂) / (K₁ - K₂) If, however b₁ and b₂ are of opposite directions ie. of opposite signs, writing - b₂ for b₂, we have s = (K₂ b₁ + K₁ b₂) / (K₁ - K₂) . Here we have chosen to follow the modern convention of signs; otherwise we have to con- sider four alternatives, for, bhujas of the same direction might mean both of the type OC (fig. 60) or both of the type of OB or one of the tyye OB and one of the type of OA or both of the type OA. Verses 77 and 78. Answer to the second question. Let Laghu ≡ L = ((KH sin δ) / R)² ; 12² (L - b²) ≡ Ādya ; Para = 12² b. Let Ādya and Para be divided by L ~ 12² ; call them still Ādya and Para; then √(Para² + A) ± Para = s according as b is north or south.