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

327 the various magnitudes are H sin δ, (H sin δ × 13) / 5 , (H sin δ × 13²) / 60 , (H sin δ × 5) / 12 and (H sin δ × 13) / 12 The sum of these is H sin δ (1 + 13/5 + 169/60 + 5/12 + 13/12) = H sin δ ((60 + 156 + 169 + 25 + 65) / 60) = 475/60 H sin δ = 95/12 H sin δ = 9500 ∴ H sin δ = 1200 from which by substi- tution the remaining magnitudes could be obtained. Verse 104. If the sum of Agrā, H sin δ and Kujyā be 2000 find them individually, oh ! mathematician if thou be an adept in the geometry of the sphere and compu- tation. Comm. Here the quantities are respectively (R H sin δ) / (H cos φ), H sin δ and (H sin δ H sin φ) / (H cos φ) so that their sum is H sin δ (1 + R / (H cos φ) + (H sin φ) / (H cos φ)) = (H sin δ (H sin φ + H cos φ + R)) / (H cos φ) Here also we are to presume s = 5 so that the above sum is (H sin δ (s + 12 + k)) / 12 (by proportion of the first and second latitudinal triangles) = (H sin δ (5 + 12 + 13)) / 12 = 5/2 H sin δ = 2000 ∴ H sin δ = 800. Substituting this value in the above formula, Agrā = (RH sin δ) / (H cos φ) = (3438 × 800 × 13) / (3438 × 12) = 10400 / 12 = 866-40 ; Kujyā = (H sin δ H sin φ) / (H cos φ) = (800 × 5) / 12 = 4000 / 12 = 333-20