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