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

427
Para. This formula by its similarity with the formula
pertaining to the eccentric theory led Bhāskara to use the
method of eccentric circles to obtain the parallax. It is
indeed ingenious on his part to have conceived the appli-
cability of that method.
Further it is rather curious that 4 nādīs of the
maximum parallax should correspond to 24°. This also
led Bhāskara to conceive similarity between the formulae
H sin δ = (H sin λ × H sin 24°) / R (the formula used to
obtain the declination δ given the longitude λ of a point
of the Ecliptic) and the formula (H cos ZV × H sin 24) / R
= Para. So from an arbitrary H sin λ equal to Vitribha-
Sanku, Para is derivable as H sin δ. In other words Para
is called Vitribha-S'anku-Rūpa-Krānti-Vṛttiya-Bhujajyā-
Janita-Krāntijyā.
Now the doubt arises, namely that when the formula
longitudinal parallax = (Para × H sin (☉ — v)) / R resembles
the formula a/R H sin m which pertains to the Equation of
centre, why does Bhāskara suggest that the parallax is
derivable without the application of the method of succes-
sive approximations, by appealing to the method S'īghra-
phala. The doubt is here two fold (1) where is the
necessity for the method of successive approximation to
obtain the parallax, though it be called for, to obtain the
moment of conjunction ? (2) why does Bhāskara appeal
to S'īghrakarma and not Mandaphala, when the formula
suggests the latter, by the presence of R and there is no
K at all ?
The answer is as follows. In the first place, even in
the modern formula for parallax namely a/d sin z, Z is