सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)
Siddhanta Shiromani Ganitadhyaya of Bhaskaracharya with Commentary
भास्कराचार्य द्वितीय द्वारा
पृष्ठ 184, कुल 573 में से
संदर्भ में पढ़ें164
From III & IV cos ξ / cos θ = (r cos ϕ − R) / (R cos ϕ − r) V
Equating cos ξ / cos θ from II and V
− u / v = (r cos ϕ − R) / (R cos ϕ − r) so that (ru + Rv) / (rv + Ru) = cos ϕ
If m be the Śīghra anomaly m = 180 − ϕ
so that cos m = − (ru + Rv) / (rv + Ru) VI
Now we shall show that Bhāskara's formula accords with
this Spaṣṭagati = Śīghragati − (H cos E δm) / K . As per
Bhāskara
Spaṣṭagati = 0 if Śīghragati = (H cos E δm) / K VII
ie. Jupiter appears stationary as seen from Earth, if Śīghra-
gati = (H cos E δm) / K
The angular velocities of Earth and Jupiter are respect-
ively u / r and v / R so that the Sun's apparent velocity is also
u / r and δm = Kēndra gati = Sun's apparent velocity
minus Jupiter's heliocentric velocity = u / r − v / R
∴ Substituting in VII
Śīghragati = u / r = (H cos E / K) (u / r − v / R)
∴ u / r ( (H cos E / K) − 1 ) = (H cos E / K) × v / R
ie. u / r ( (H cos E − K) / K ) = (H cos E / K) × v / R