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

often handles vertical fractions in plain text either as: [L..] triangle (H sin δ) / x = s / 12 where x is the Koṭi OR line-by-line exact layout. Wait! Let's examine how the lines flow: If we look at: triangle H sin δ / x = s / 12 where x is the Koṭi Let's check the rest of the page: - ∴ s = (12 H sin δ) / x. But we are given that the Sama- - Śaṅku ie. - H cos z = R cos z = R / √2 because z = 45° when the - shadow equals the length of the gnomon. - and H sin δ = (H sin λ H sin ω) / R = (H sin 135 H sin ω) / R - = (H sin 45 H sin ω) / R = R/√2 × (H sin ω) / R = (H sin ω) / √2 - ∴ x = √(Sama-Śaṅku² - H sin² δ) = √( R²/2 - (H sin² ω)/2 ) - `= (H cos ω) / √2 ∴ s = (12 H sin δ × √2) / (H cos