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

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Again the following relation holds good between T
and l, l² = (p+r)² – β² II and
l / (m₁–s₁) = T with the nomenclature already employed which
means T = √(p+r)²–β² / (m₁–s₁) III
In the above working, the fundamental elements are
p, r, β, m₁ and s₁ with which the other elements could be
worked out. Replacing the other elements from equation
I, we have
{(p+r)²–β²} { √(p+r)²–β² / (m₁–s₁) – t }² +
β² (p+r²–β²) / (m₁–s₁)² = (p+r)²–β² / (m₁–s₁)² (p+r–g)²
ie. {(p+r)²–β²} [√(p+r)²–β² – t (m₁–s₁)]² +
β² (p+r²–β²) = (p+r²–β²) (p+r–g)²
ie. {√p+r²–β² – t (m₁–s₁)}² + β² = (p+r–g)² IV
Putting t=0 in this equation, we have
(p+r)² = (p+r–g)² ie. g=0 which means at the moment
of first contact, the grāsa is zero. Again putting
t = T ie. t = √(p+r)²–β² / (m₁–s₁) ie. t (m₁ – s₁) = √p+r²–β²
we have
β² = p+r–g² ie. g = p+r–β which gives the grāha
at the middle of the eclipse which was defined as the
Sthagita. In equation IV which we may take as a funda-
mental equation, the two unknowns are t and g one of
which being given the other could be got.
Verse 36. The colour of the eclipse.
When less than half the disc of the Moon is eclipsed,
the colour will be what is called Dhumra ie. of the colour