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

519
Verses 17 to 21. Ancient astronomers happened to
give a list of polar longitudes and polar latitudes at a time
when there were no Ayanāṁsas ie. when the zero-point of
the ecliptic as taken by the Hindu Astronomers namely
Aświnī coincided with the modern zero-point namely r.
In fact these polar longitudes and latitudes do change
if there be Ayanāṁsas. Here in this case from the polar
latitudes the celestial latitudes are to be computed in a
reverse process; with the half of these celestial latitudes,
the Āyana-Dṛk-Karma is to be effected in the reverse
process to obtain the celestial longitudes. After having
obtained the correct celestial longitudes and celestial
latitudes, now, bringing the Ayanāṁsas into the picture,
compute the correct Dṛk-Karma and also rectify the
celestial longitudes, to obtain the correct polar longitudes
and polar latitudes to compute the moment of polar
latitudinal conjunction. This case may be taken when the
Ayanāṁsas are large, otherwise, a small difference there
will be, (which does not matter).
Comm. Bhāskara·gives the process in the course of
the commentary. We have the formula
Asphuṭa Vikṣepa × Yaṣṭi
Sphuṭa Vikṣepa = ———————————————————————
Radius
Here we know Sphuṭa Vikṣepa. At once, we could not
Sphuṭa Vikṣepa × Radius
say Asphuṭa Vikṣepa = ———————————————————————
Yaṣṭi
computing Yaṣṭi from the modern Ayanāṁsas. Yaṣṭi is
a function of declination too, because the Āyanavalana is
a function of declination. We know, the declinations
change in the wake of precession of the equinoxes. So,
there is no point in taking the value of the present Yaṣṭi.
We should compute it for the Āyanaśūnyakāla or for the
time when Aświnī coincided with r. Then the formula
could be applied. Then with this celestial latitude obtained,
Āyana-Dṛk-Karma is to be effected to obtain the present