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

428 the zenith-distance pertaining to the observer and not the geocentric zenith-distance, which are respectively called prṣṭhīya and garbhīya natāṁsas. Also the parallax is the angle between the geocentric direction of the Moon and that of the observer. (Vide fig. 91 where parallax = E M̂ A). In deriving this parallax, we are using the apparent zenith-distance of the Moon and not the geocentric zenith- distance of the Moon. In fig. 92 the position of ⊙ corres- ponds to the geocentric position, whereas D corresponds to the position of the observer on the surface of the Earth. So, as we use the apparent zenith-distance as argument to obtain parallax along the vertical, so we have to use, VD as the argument to derive the parallax in longitude and not V ⊙. So, the method of suceessive approximations is called for as ⊙ D is first computed from the argument V ⊙ and VD is to be made the argument thereafter. This means that V ⊙ may be construed as Madhyakēndra and VD as Sphuṭakēndra. Now applying this idea to fig. 95, V₂ E₂ ⊙ may be construed as Sphuṭakēndra whereas V₂ E₁ ⊙ may be construed as Madhyakēndra. From the similarity of the triangles ⊙ NM, and E₂ LM, ⊙N / LM = ⊙M / E₂M ∴ ⊙N = (⊙M / E₂M) × LM = (Para / K) × ⊙K = (Para / K) × H sin K Ê₂ ⊙ where E₂M is termed the Karṇa and K Ê₂ ⊙, the Sphuta- kēndra is made the argument. Thus parallax in longitude which was originally formulated as (Para × H sin (⊙ - v)) / R (in which case, the method of successive approximation was called for), is now formulated as (Para / K) × H sin (KE₂ ⊙)