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

312 So the equation reduces to s² (12² - L) + 2. Para. s = Ādya ; Divide throughout by 12² - L and put again Para / (12² - L) as Para and Ādya / (12² - L) = Ādya Then the equation reduces to s² + 2 Para s = Ādya ; completing the square (s + Para)² = Para² + Ādya ∵ s + Para = √(Para² + Ādya) ∴ s = √(Para² + Ādya) - Para as one solution. We have taken to start with a = b + s which holds good according to the Hindu convention when b is south ; if, however b is north a = b ~ s so that (b ~ s)² = s² + b² - 2bs. So in the equation we have to write -s for s, so that we have now s² - 2 Para s = Ādya ie. (s - Para)² = Para² + Ādya ∵ s = √(Para² + Ādya) + Para as the second solution. Verse 79. When the Sun's longitude is 135°, the shadow of the gnomon is 12 units and west. What is the latitude? Comm. Here is a method of obtaining the latitude of the place by observing the gnomon's shadow when the Sun is on the prime-vertical. Verse 80. Answer to the question above. (12 R) / K = H cos z ; s = (12 H sin δ) / √(Sama-Sanku² - H sin² δ) Comm. Solution in modern terms. S = 12 ∴ tan z = 1 ∴ z = 45; but when the Sun is on the prime-vertical, we have by Napier's rule Sin δ = sin ϕ cos z = sin ϕ √2. But since λ = 135°