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