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

160
The answer is (H sin m × 2°-10'-31") / 120 = (2 21/120°) / 120 × H sin m
very approximately = 261 / 14400 H sin m = 20 / 1103 H sin m
Similarly in the case of the Moon, the maximum equation
of centre is 5°-2'-8". By the same argument as above we
have (H sin m × 1133) / (225 × 120) = (H sin m × 20) / (54000 / 1133) = (H sin m × 20) / 477
Verse 31. Rectification of the mean daily motion of
the Sun and the Moon.
The H cosine of the mean anomaly divided by 54 in
the case of the Sun and in the case of the Moon multiplied
by 4 and divided by 7 gives the increment or decrement in
the respective mean motions according as 90 < m < 270 or
270 < m < 360 + 90.
Comm. We have Equation of centre = r / R H sin m =
E (say) so that differentiating δE = r / R H cosm δm / R . But
r / R H cosm is called kotiphala and δm is called Kendra
gati so that δE = Kotiphala × Kendragati / R . Since Koti-
phala is negative when 90 < m < 270 δE is negative but in
Hindu Astronomy we measure the Kendra not from perigee
as in modern astronomy but from aphelion so that the equ-
ation of centre is strictly - r / R H sin m if sign is also
taken into consideration. Hence δE must be + ve. Since
M + E = S where M is the mean planet, E the equation of
centre and S the true planet δS=δm+δE so that the true
motion is equal to the mean motion plus δE. As δE is +ve
when 90 < m < 270 as mentioned above we have to add
this to the mean motion to get the true motion. This δE