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

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

Siddhanta Shiromani Ganitadhyaya of Bhaskaracharya with Commentary

भास्कराचार्य द्वितीय द्वारा

DevanagariHindipublished573 पृष्ठ

पृष्ठ 183, कुल 573 में से

संदर्भ में पढ़ें
पृष्ठ 183

163
H̄ cos 225 = R and H sin 225 = 225 which is rather crude.
Bhāskara of course improved on this crudeness by taking
δm to be an increment in E.
In the commentary under this verse, Bhāskara,
having misinterpreted Lallācharya's phrase आशुचाप as
meaning आशुकेन्द्रचाप and not as आशुफलचाप which was
in the mind of Lallācharya, goes on recounting examples
where the wrong formula attributed to him would give
wrong results. So, we need not enter into those details.
Now we shall correlate Bhāskara's formula with its
modern counterpart. Assuming coplanar heliocentric cir-
cular orbits for planets, let us see at what points two planets
appear mutually stationary, that is, have a Zero relative
angular velocity before they appear mutually retrograde.
Let S = Sun, E = Earth, J = Jupiter, u = Earth's
linear velocity, v = Jupi-
ter's linear velocity r and
R the orbital radii of the
Earth and Jupiter respe-
ctively. Let EE' and JJ'
be perpendiculars to EJ so
that when the relative velo-
city of Jupiter with respect
to the Earth perpendicular
to EJ is Zero, Jupiter will
appear stationary as seen
from the Earth. This
Fig. 17
means that u cos θ + v cos ξ = 0 I
∴ u / v = - cos ξ / cos θ II
But from triangle ESJ,
R cos ϕ + K cos θ = r III and
r cos ϕ + K cos ξ = R IV