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

178 In the triangle E₁ S₁ B₁, E₁ S₁ is called Agrajyā, S₁ B₁ Kujyā, and E₁ B₁ Krāntijyā. Of the sides of ESB. ES and EB are arcs of great circles whereas SB is the arc of a small circle. In the projected triangle E₁ S₁ B₁, E₁ S₁ will be equal to the perpendicular from S on Eω, which will be H sin (ES) and is called Agrajyā ; E₁ B₁ will be equal to the perpendicular from B on Eω which will be H sin BE and as such called Krāntijyā. But S₁ B₁ which is equal to the perpendicular from S₁ on BB' the diameter of the diurnal circle is the H sine of SB in the diurnal circle and is called Kujyā. It will be noted that the per- pendiculars from S on Eω, and BB' and the perpendicular from B on Eω do not form a triangle by themselves but by the theorem of three perpendiculars, if SL be the perpendicular from S on the plane of the unmandala ie. the great circle EBP, and if LM be perpendicular from L on Eω, SM will be perpendicular on Eω. Here the perpendicular SL will be the Kujyā, and SM the Agrajyā, whereas LM is not actually the H sine of BE but is equal and parallel to it. Similarly take the spherical triangle SAE. This is a regular spherical triangle because the three sides are arcs of great circles. Napier's rules can be applied to this triangle and we have the formula sin SA = sin SE sin SÊA or in Hindu form H sin SA = (H sin SE × H sin Ê) / R or RH sin δ = Agrajya × H cos ϕ ie. Agrajyā = (RH sin δ) / (H cos ϕ) II Again sin EA = tan SA × tan Ê where H sin EA is called Charajyā and tan E = cot ϕ so that Charajyā = tan δ tan ϕ in modern form, and the Hindu form is <u>R tan δ tan ϕ</u>