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

391
Second half of verse 21 and first half of verse 22.
H cos λ × H sin ω
───────────────── = H sin θ where θ is the Āyana Valana
H cos δ
The direction of this Valana is that of the hemisphere
north or south in which the Moon lies.
Comm. This is the formula we have already derived.
Regarding the direction of the Āyana Valana, the conven-
tion is that it is to be considered north, if the Moon be in
the northern hemisphere, otherwise south. The reason is
that at the time of a lunar eclipse, the Moon being in opposi-
tion, if he be north, the Sun will be south of the Equator,
and the line BA of fig. 80 representing the Ecliptic which
is roughly the join of the Sun and the Moon will be north
of the line JI which is parallel to the equator. Thus the
direction of the angle IMA gives the direction of the
Āyana Valana.
Latter half of verse 22 and verse 23. Sphuta Valana.
The Hsine of the sum or difference of the two Valanas
according as they are of the same or opposite directions,
multiplied by the sum of the angular radii of the Moon
and Rāhu, and divided by the radius gives the Hsine of
the Sphuta Valana. Those who said that the Valana is
proportional to the Hversine, do not know spherical
geometry properly.
Comm. The direction of the Akṣa Valana, was defined
in verse 20 that it is north if the hour angle is east, other-
wise south. The meaning of this convention is that the
diameter of the Moon's disc parallel to the Equator when
the hour angle is East, is north of the diameter which is
parallel to the prime-vertical. Thus combining the two
conventions regarding the directions of the Valanas, it is
clear that if both the Valanas are north, the line MI is
north of MG, and MA is north of MI (fig. 80) so that the