पृष्ठम्:महाभास्करीयम्.djvu/१७५

90 DIRECTION, PLACE AND TIME respectively. the foot of the gnomon as centre and any arbitrary radius. Let EW and NS be the east-west and north-south lines Then the construction stated in the text is as follows: From O, along ON, measure a distance d and mark there a point, say X. Through X stretch a thread (or draw a line) parallel to EW. Let this be LM. Now from centre O and radius equal to the shadow of the gnomon draw an arc of a circle cutting LM at the points A and B. Then OA and OB are the positions of the threads, equal in length to the shadow of the gnomon, laid off obli- quely from the centre. The two points thus obtained are A and B. If OC be the midday shadow of the gnomon, then the thirdp oint is C. The three points thus determined are A, B, and C. E Fig. 10 A rule for determining the same three points when the directions are not known: S W M A L N 46-51. For one who does not know the directions with regard to the centre but wants to determine the directions and the locus of (the end of) the shadow (of the gnomon), I state the method such that (the end of) the shadow (cf the gnomon) may not leave the periphery of the large circle distinctly drawn amidst the directions (representing the path of the shadow-end). Calculate the Rsine of the Sun's zenith distance, the Rsine of the Sun's altitude, and the sankvagra corresponding to the desired shadow; then take the difference or sum of the two agras (i.e., of the sankvagra and the agra) (according as they are of unlike or like directions). This (difference or sum) is the base, the Rsine of the Sun's zenith distance is the hypotenuse, and the square root of the difference between their squares is called the upright corresponding to the hypotenuse equal to the Rsine of the Sun's zenith distance. On multiplying these, upright and base, (severally) by the (length of the) shadow and dividing by the Rsine the Sun's zenith distance are obtained