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

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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°