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

492
is the moment of conjunction. When the Sun has moved
from the point S₁ to S₃, S₁ Ê S₃ being 90°, there is a
deficiency of magnitude S₁ E S₂. In other words, when
S₂ N has assumed the position S₃ E there is a deficiency
of 4°-15′ ie. for an increase of 90° of elongation, there
is a deficiency of 4°-15′ in the longitude of the Moon.
Hence, for the Hsine to become the radius, there corres-
ponds a portion E M₂ or S₂ N, which is the Hsine of 4°-15′,
so that the following rule of three is adopted. 'If the
Sun's distance E S₃ corresponds to the radius, what does
E M₂ the distance of the Moon correspond to ?' The
result is (m / s) × R, m and s being the respective distances.
Then the following proportion is used "If by H sin ξ
equal to R, ξ being the Moon's elongation, we have mR/s,
what shall we have for an arbitrary H sin ξ ?" Thus the
answer is
(H sin ξ × mRs) / R = H sin ξ · (m / s) . H sin⁻¹ ((m / s) × H sin ξ)
where m and s are the distances of the Moon and the Sun,
is to be added to the longitude of the Moon or to be
subtracted as the case may be, to have the rectified
longitude of ths Moon from which the phase is to be
calculated according to Bhāskara.
Here we are to offer the following remarks. No doubt,
Bhāskara was correct in estimating the moment of
dichotomy to be that when ξ the Moon's elongation is not
90° but 85°-45. But the amended formula is not the
correct mathematical form. The modern formula to find
the phase is (1+ cos EMS) / 2 aud since from fig. 116, SM is
nearly equal to SE, so EMS is very nearly equal to