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

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wake of β being effected by parallax in longitude. The
formula for Bhuja is √(R+r -g² — β²) / (m₁ — s₁) wherein all quantities
except β may be taken to be constant. Suppose β effected
by parallax be comes β'. If β' > β, Bhuja will decrease ;
also the Sthiti-khanda whose formula is √(R+r)² — β² / (m₁ — s₁)
decreases if β' > β. Hence if T' be the new value of T
the Sthiti-khanda, T' < T. In other words when β' > β,
B' < B and T' < T. Also if β' < β, both B' and T' will
be greater than B and T respectively. Hence as a rough
measure B and T are taken to vary together positively or
negatively and as such proportionally. Though both
increase or both decrease together, strictly speaking the
concept of proportionality is there ; but roughly speaking
they are taken to vary proportionally which means
B' = (B × T') / T . The fact that proportionality is not there
could be seen in two ways. B = (T — I) (m₁ — s₁) (1) with
usual notation so that taking B and T to vary on account
of the variation in β, δB = δT (m₁ — s₁), I not varying so
that B + δB = B' = (T + δT) (m₁ — s₁) — I (m₁ — s₁) =
T' (m₁ — s₁) — I (m₁ — s₁) = (T' — I) (m₁ — s₁) (2).
Dividing (1) by (2) B/B' = (T — I) / (T' — I) which will be
approximately equal to T/T' provided I is very small
compared with T. Assuming so, B/B, could be taken to
be equal to T/T', which means B' = (B × T') / T as mentioned
in the verse. Or again, considering the formulae for B
and T and differentiating them with respect to β and
getting B' and T', we shall have the following working.
B² = ((R+r—g)² — β²) / (m₁ — s₁) so that 2 BδB = (-2 βδβ) / (m₁ — s₁)