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

440 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)