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

267 construing Rs / (H sin a) as the equinoctial shadow', means computing H sin ZT and there from ZT from the shadow gL of fig. 45. Then the process indicated by saying “Obtain H sin D = (H sin ZT × H sin δ) / (H sin φ) and therefrom D'' means computing ST. Then clearly ZS = ZT ± ST, ie. the required zenith- distance is got by what is technically called Samskāra between ZT and ST as is stipulated between φ and δ to obtain Z from the formula Z ± δ = φ (The word Samskāra was defined as meaning addition when the directions are the same and difference when they are opposite). Then the gnomonic shadow is got from this zenith-distance using the formula S = (12 H sin z) / (H cos z) . Thus the procedure adopted by Bhāskara was con- ceived by him first having Fig. 45 before him and then using figures 46 and 47. In this particular process, H sin a is given and H sin δ also, which means that it is sought to find the shadow on a given day in a given direction. Incidentally we shall find the locus of the extremity of the gnomonic shadow during the course of a day. Let in fig. 48 g represent the gnomon's foot, and S the shadow whose extremity is p. Required to find the locus of p. Take the gnomon to be of unit length so that the length of the shadow S = 12 tan z becomes tan z here. Take Eω and sn the east-west line and the north-south as the axes. Then we have x² + y² = tan² z (1). But we have from the triangle PZS sin δ = sin φ cos z + cos φ sin z sin a ie. sin δ / (cos φ cos z) = tan φ + tan z sin a = tan φ + y (2) ie. sec z / A = y + tan φ when A = cos φ / sin δ .