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

455
Comm. Let rM (fig. 107) be the ecliptic and rN the
celestial equator whose poles are K and P respectively.
Let R be a celestial body whose latitude is β and whose
modern declination is RL. Let M be the foot of the
latitude circle and let δ be the declination of M. The
word Krānti in Hindu astronomy is applied to connote
the declination of a point on the ecliptic alone and not of
any other point like R. RL is called Sphuta Kranti which
is equal to R'N = R'M + MN. RM is called Vikṣepa and
R'M Sphuta Vikṣēpa. K̂MP is called the Āyanavalana at
the point M of the ecliptic. Produce MP to P' where
PP' = δ so that MK = MP = 90°. Hence P̂' is a right angle
and KP' = K̂MP' = v̂ = Āyanavalana. From the spherical
triangle KPP', cos ω = cos v cos δ. Draw perpendicular
RR' on MP so that MR' = β' = Sphuta Vikṣēpa = β cos v
= (β H cos v) / R. But H cos v = √(R² - H sin² v) = Yaṣti
∴ β' = (Yaṣti × β) / R which is to be added to δ to obtain
the Sphutakrānti R'N or RL, the modern declination.
Note (1) One Mukhopādhyāya, in his thesis ‘The
Hindu nakṣatras’ submitted to the Calcutta University,
mistook RM' to be the Sphutavikṣēpa instead of R'M and
hastily remarked that Bhāskara was wrong in making RM'
less than RM.
Note (2) v̂ shown in the fig. 107, is called Sthanīya-
valana or valana at the point M which is considered to be
place of the planet ‘Sthāna’ on the ecliptic. K̂RA, on
the other hand is called Bimbīya-valana or valana at the
bimba or disc of the planet.
Note (3) v̂ could be obtained from the spherical
triangle KMP where KM = 90°, PM = 90-δ, using the