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.