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