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

258 Comm. This formula is a special case of the formula A = S + B since the H sine of the meridian zenith distance is the Śaṅku-Bhuja at noon. From fig. 39 (Hṛti × bhuja of a latitudinal triangle) / (Karṇa of a latitudinal triangle) = O₁a = Dinārdha Śaṅkutala. The operation of sign has been already explained. Verse 38. An alternative method. The meridian zenith distance of the Sun can be had also by the formula (Hṛti ± Taddhṛti) B.L.T. / K.L.T. where B.L.T. and K.L.T. are the bhuja and karṇa of any latitudinal triangle. Comm. (Ref. figures 43 and 21). Let E₁ be the centre of the armillary sphere so that QE₁R is the diameter of the celestial equator which is on the median plane. Let S₁ F₁ S be the diameter of the diurnal circle of the Sun, which is also on the meridian plane so that S₁ F₁ is the Taddhṛti, S₁ S is the Hṛti and S the position of the Sun on the meridian. H sin z = SM = SF₁ sin F̂₁ = SF₁ sin ϕ = (Hṛti − Taddhṛti) × s/K where s/K can be replaced by B.L.T. / K.L.T. (s=equinoctical shadow and k the Viṣuvat-Karṇa). In the Southern sphere, H sin z = S′N = S′F₁′ sin ϕ = (S′S₂ + S₂F₁′) sin ϕ = (Hṛti + Taddhṛti) × s/k. Verse 39. Still another way of obtaining the m. z. d. (meridian-zenith-distance). R − H versin (altitude) = H sin z