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

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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 .