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

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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>