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

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= (R+r-g)²-β² / (m₁-s₁)² so that δt = -βδβ / (t (m₁-s₁)²)
and T² = (R+r)²-β² / (m₁-s₁)² so that δT = -βδβ / (T (m₁-s₁)²)
Thus we see that as β increases both t and T decrease
on account of the minus signs in δt and δT. Also if I
were to increase, βδβ / (t (m₁-s₁)²) should be greater than
βδβ / (T (m₁-s₁)²) ie. 1/t must be greater than 1/T ie.
T should be greater than t and this is so. Hence as
β increases t and T decrease but T-t increases ie. as T
decreases T-t increases ie. I increases. So, roughly I is
taken to be inversely proportional to T so that I' = (I × T) / T'
If strict inverse proportionality is there, since,
t + δt = t' = t - βδβ / (t (m₁-s₁)²)
and T + δT = T' = T - βδβ / (T (m₁-s₁)²) and therefore
t'/T' = (t/T) · { 1 - βδβ / (t² (m₁ - s₁)²) } / { 1 - βδβ / (T² (m₁ - s₁)²) } = (t/T) · { t² - βδβ / (m₁ - s₁)² } / { T² - βδβ / (m₁ - s₁)² }
t² must be roughly equal to T² which means T - t = I
must be small. In other words the formula of the verse
holds good only for small I's or Iṣṭakālas.
In fact this process of rectification of the Bhuja was
first given by Brahmagupta in verses 18 and 19 of Sūrya-
grahaṇādhikāra and accepted by Śrīpati in verse 14.
The verse 19 under Lunar eclipses in the Sūrya-
siddhānta also seems to indicate this process but uses the
words Madhya-Sthiti-khaṇḍa and Spaṣṭa-Sthiti-khaṇḍa in