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

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Kendras on two consecutive
days whereas Madhyakendragati
^
is P₁E₂P₂. Also, we have the
equation.
Sīghra — Sphutagraha =
Sphutakendra so that Sīghra-
gati — Sphutagati = Sphuta-
kendragati. Hence Sphutagati
= Sīghragati — Sphutakendra-
Fig. 16 gati. So we have now to seek
the value of P₁Ê₂P₂. Let P₁a stand for the Sīghra-
phala of the first day which is equal to e f, f being the true
planet of the first day. E₂ d will be parallel to E₁ f because
P₁ e being parallel to E₁ E₂ and e f being equal to P₁ d, d f
11 P₁ e (parallels to E₁ E₂ cut off equal arcs on the two
circles). This may be seen also as follows. Since P₁ d is
taken to be equal to e f, e being the mean planet and f the
true on the first day e Ê₁ f = P₁ Ê₂ d. But E₁ e 11 E₂ P₁
∴ e E₁ f = E₁ P̂₁ E₂ ∴ P₁ Ê₂ d = E₁ P̂₁ E₂ and alter-
nate angles being equal E₁ P₁ 11 E₂d. P₁ a is the H sine
of P₁ d where P₂ b is the H sine P₂ d. Looking upon P₁P₂
as an increment in P₁ d i.e. looking upon the Kendragati
P₁ Ê₂ P₂ as an increment in Sīghraphala, Bhāskara uses
the method of Bhogyakhanda sphuti Karana to obtain the
Sphutakendragati. From the figure.
P₂c = P₂b — P₁a = H sin (G + δm) — H sin E
H sin E H cos δm + H cos E H sin δm
= ————————————————————————————————————— — H sin E
R