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

291
Comm. Under verse 58, we had to form Hvers h; a
doubt might arise as to what this Hvers h would be if
h > 90. Hence Bhāskara defines it and the definition is
clear from fig. 57. The Unmandala S'anku has the
formula R sin δ sin φ so that either when δ is negative or
when φ is negative, it will be negative which means it will
be in the opposite direction ie. vertically downwards.
Since negative latitudes are not considered by the Hindu
astronomers, the other case alone is considered. Even
from a figure it is evident that when the Sun is in the
south of the Equator, the Unmandala S'anku is vertically
downwards. In proportions like I given under verse 62,
we can use the magnitude of this Unmandala S'anku also
and it does not vitiate the results, when we take its
numerical value.
Verse 65. The Sun crosses the prime-vertical when
his northern declination falls short of the latitude. Then
alone there is sense in giving the magnitude of his shadow
at that moment. When the Sun does not cross the prime-
vertical at all, the Sama S'anku which could be computed
out of its formulation, though it does not exist, under the
Sun, yet, it could be used in proportions (like I under
verse 62) and no blunder is committed.
Comm. This is a beautiful example cited by Bhāskara
where he intuitively uses the so-called principle of
geometrical continuity. We have formulated Sama
S'anku as (R sin δ) / (sin φ) ie. H cos z = (R sin δ) / (sin φ) . We have a real
value of z when δ > φ, for, then only H cos z < R. When
φ > δ, then H cos z > R which is impossible, for, no
Hindu sine or Hindu cosine could be greater than R just
as no modern sine or cosine could be greater than unity.