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

142
the mean anomaly is m the periphery is given to be
14° — (20' H sin m) / R. The corresponding radius will there-
fore be r — (20' / 2π) · (H sin m / R) = r — λ H sin m (say) where r =
14° / 2π. [λ = 20' / 2πR] (Ref. fig. 10) Let E be the earth's centre, A the posi-
tion of the apogee EE₁ = the radius of the epicycle meas-
ured along EA, B any arbitrary position of the mean planet
and b the position of the planet in the epicycle. Here the
radius Bb is not equal to the max. radius equal to EE₁ i.e.
r but equal to r — λ H sin m. Take E₁ as the origin and
E₁A as the y-axis and a perpendicular to E₁A through E₁
namely E₁x as the positive direction of the X-axis. If the
mean anomaly BEA be m, then the coordinates of the true
planet are given by x = BL = H sin m (1), y = E₁L +
Bb = EL — EE₁ + r — λ H sin m = H cos m — r + (r —
λ H sin m = H cos m — λx.
∴ y + λx = H cos m (2) Squaring and adding (1)
and (2) x² + (y + λx)² = H sin²m + H cos²m = R²
∴ x² (1 + λ²) + 2λxy + y² = R² which is an ellipse
with centre E₁
Verses 23, 24, 25. The peripheries of Śīghra epicycles.
The peripheries of the epicycles of the star-planets Mars,
Mercury, Jupiter, Venus and Saturn are respectively
243°-40', 132°, 68°, 258° and 40°. The H sine of the Manda
mean anomaly of Venus being multiplied by 2 and divided
by 343, and the result being subtracted from the periphery
gives the rectified Manda periphery. The H sine of its
Śīghra mean anomaly being multiplied by 5 and divided
by R, and the result being added to the Śīghra periphery
gives the rectified periphery. The smaller of the H sine or
H cosine of the Śīghra anomaly of Mars being multiplied
by 6⅔ and divided by H sin 45° and the result in degrees
being subtracted from or added to as the case may be,