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

256 Hence H cos z (at Noon) = Natajyā = (H cos φ H cos δ ± H sin φ H sin δ) / R or in modern symbolism cos (φ ∓ δ) already derived under (20). We shall now show how the formulation is done by the simple rule of three (Ref. fig. 39). If a parallel through o₄d is drawn to cut Aa at a₁, then Aa₁ is called the Yaṣṭi, which is vertical. The triangles Aoa₁ and Do₄d are similar so that Aa₁ / Ao = Dd / Do₄ ∴ Aa₁ = (DD × Ao) / Do₄ . But Ao / Do₄ = R / Charajyā for, all the lines of the diurnal circle and the equator stand in the ratio (H cos δ) / R = Ao / R = Do₄ / Charajyā = Kujyā / Charajyā ∴ Ao / Do₄ = R / Charajyā ∴ Aa₁ = (Unmandala Śaṅku × R) / Charajyā = Yaṣṭi as formulated. Now Dinardha Śaṅku = Aa = Aa₁ + a₁ a = Aa₁ + Dd = Yaṣṭi + Unmandala Śaṅku. It is evident from fig. 21 why in the northern sphere the sum is to be taken whereas in the southern, the difference is to be taken. Latter half of verse 34. Definition of Hṛti and Antyā. The sum or difference of Dyujyā and Kujya will be similarly Hṛti, whereas the sum or difference of Charajyā and radius will be Antyā. Comm. We defined formerly Hṛti and Antyā under our commentary on the latitudinal triangles. From fig. 39 Hṛti = o₁A = o₁o + oA = o₄D + oA = Kujya + H cos δ (Dyujyā) (22).