पृष्ठम्:महाभास्करीयम्.djvu/१७६

LOCUS OF THE SHADOW-END 91 the values of the upright and the base (corresponding to the hypotenuse equal to the shadow of the gnomon). Now take straight bamboo scales of breadth equal to the diameter of the gnomon and of lengths equal to the base and the upright (obtain- ed above) (and one equal to the shadow); and with their help construct an accurate framework instrument in the form of a rectangle or a (right-angled) triangle having the shadow (of the gnomon) for the hypotenuse. At the corner (where the base and the hypotenuse meet) fix a gnomon. Then put the instru- ment (on level ground) and rotate it (about the gnomon) until the shadow (of the gnomon) falls along the hypotenuse. Then having determined the directions (north and south, east and west) as indicated by the base and the upright, mark two points at the end of the shadow-hypotenuse (one towards the east and the other towards the west). At the end of the midday shadow, take the third point. The above stanzas give the method for finding the points A, B, and C (see Fig. 10), when the lines EW and NS are not known. The method. is as follows: Construct a triangular frame of bamboo scales having its sides equal to those of the triangle AXO or a rectangular frame having its sides equal to those of the rectangle OXAY, and let a gnomon (having its diameter equal to the breadth of the bamboo scales) be fitted at O vertically to the frame. Place the frame on level ground with the point O at the centre of a circle drawn on the ground and with the hypotenuse OA in coincidence with the shadow of the gnomon. Then OX is directed south to north and AX west to east. Draw the lines OX and AX on the ground and produce them bothways. With centre O and radius equal to OA, the shadow of the gnomon, draw an arc of a circle cutting the line AX at two points. These are the points A and B. The point C is obtained as before. Construction of the locus of the end of the shadow of a gnomon: 52. Through all the three points (thus obtained) a circle is (then) drawn with the help of two fish-figures. The shadow (of the