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

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have seen above that the first term is no other than the
Mean Sun ignoring the integral number.
Verses 10, 11. Proof of other methods of computing
planetary position. Even as the sums or differences of
two or more of the numbers of Adhimāsas, Kshayāhas,
lunations etc give the number of sidereal revolutions of the
planets the sums or differences of two or more of the posi-
tions of the imaginary planets which go by the names
Adhimāsa-graha, Kshayāhagraha etc computed out of the
numbers of those Adhimāsas Kshayāhas etc. give the
respective planetary positions.
Comm. This interesting concept is based upon the
following principle. Suppose P to be the number of side-
real revolutions of a planet; then (A × P) / M gives the planetary
position, where A is the Ahargaṇa, and M the number of
mean solar days in a Kalpa. Now suppose P = x ± y ± z
where x, y, z are the numbers of Adhimāsās etc in a Kalpa,
then
(A × P) / M = (A × x) / M ± (A × y) / M ± (A × z) / M •
The terms on the right-hand-side may be construed to
be the Adhimāsa-graha etc, which are the positions of
imaginary planets and their sums or differences give there-
fore the position of the planet, as could be seen from the
above equation. Thus for example, we have the equation
P₁ — 13P₂ = a where P₁ is the number of the sidereal
revolutions of the Moon and P₂ the number of the sidereal
revolutions of the Sun, a stands for the Adhimāsas because
Chāndramāsas — Sauramāsas = Adhimāsas; but Chāndra-
māsas = P₁ — P₂ and Sauramāsas = 12 P₂ so that
P₁ — P₂ — 12P₂ = a ie P₁ — 13P₂ = a. From this equation
P₁ = a + 13P₂ ∴ (A × P₁) / M = (a × A) / M + (13P₂ × A) / M •