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

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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).