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

381
Natāṁśa (defined before) and H sin z may be taken to be
roughly equal to 90h / (D/2) (as depicted before).
In the East the Ākṣa Valana is north, for, in fig. 80
ĜMI which gives the East of the Equator with respect to the
the East of the prime vertical, is north; whereas in the
West ĤMJ is south. (The definition of the direction of
the Valana is given as a directive to add the two kinds of
Valanas if they be of the same direction otherwise to take
the difference; in the fig. 80, the Āyana Valana ie. ÎMA
is also north, so that adding ĜMI + ÎMA = ĜMA is the
Sphuta Valana or the actual Valana). Hence Sphuta
Valana measured by GMA is had by the sum or difference
of the two angles ĜMI and ÎMA which define respectively
the Āyana and the Ākṣa Valanas.
Similarly, at the point of intersection of the Ecliptic
and the prime-vertical, the Sphuta Valana is a maximum
which is the sum or difference of the Valanas as the case
may be. At points removed 90° on either side, from the
point of intersection of the Ecliptic and the prime vertical,
in as much as the north-south directions with respect to
the Ecliptic and the prime-vertical coincide, the Sphuta
Valana is zero.
If (as Lallāchārya said) the Valana varies as the
Hversine at those points which are removed by 90° from
the points of intersection of the Ecliptic and the prime-
vertical, the Sphuta Valana will not be zero (which is
against common sense). Hence the Valanajya varies as
Hsine and not as Hversine.
We shall look at the subject from another point of
view for the sake of clarity.........Fix a circle on the sphere
with the celestial pole as centre and ω as the angular