ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

GNOMON USED FOR FINDING THE DIRECTIONS 357
declination gets changed. It follows. therefore, that the East-
West line in the above determination is not the true position
of the actual East-West line. Brahmagupta (628 A. D.) was
the first Hindu astronomer who prescribed the determination of
the East-West line with proper allowance for the change in the
Sun's declination. (Shukla) The details of the method intended
by him have been supplied by his commentator Pṛthūdaka
Svāmī (860 A. D.).
Bhāskara and Brahmagupta both give another
method of determining directions : (BrSpSi. III. 2 ;
MBh. III. 3) : With the three points (at the ends of the three
shadows of the gnomon) corresponding to (any three) different
times (in the day), draw two fish-figures (each with two of the
three points) in accordance with the usual method. From the
point of intersection of the lines passing through the mouth and
tail (of the two fish-figures), determine the north and south
directions. (MBh. III. 3).
Brahmagupta in his rule is more precise :
The point where the lines passing through the two
fish-figures, which are drawn by means of three shadow
ends (of the gnomon), intersect each other is for places
in the northern hemisphere, the south direction, (if
the midday shadow falls to the north of the foot of the
gnomon). If the midday shadow falls towards the
south of the foot of the gnomon, it is the north
direction. (BrSpSi. III. 2).
This rule is obviously based on the assumption that the
the locus of the end of the shadow of the gnomon is a circle.
In tact the locus for places whose latitude is less than (90°—the
obliquity of the ecliptic), this locus is a hyperbola.
Brahmagupta has made numerous uses of gnomon. He
and Bhāskara, for example, both give the rules for finding the
latitude and colatiude and the zenith distance and altitude of
the Sun by finding out the length of the shadow and the length
of the gnomon (BrSpSi. III. 10 ; MBh. III. 5) ; also rule for
the determination of the latitude with the help of the Sun's
meridian zenith distance and declination (BrSpSi. III. 13 ; MBh.