पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४७७

CHAPTER IX-CALCULATIONS RELATING TO SHADOWS. 279 The rule for arriving at the measure of the shadow correspond- ing to a time (of day) given in ghatis. 18. The measure of the style is divided by twice the measure of the (given) portion of the day; (from the resulting quotient) the measure of the style is subtracted, and (to it) the (equinoctial) noon-shadow is added. This gives rise to the measure of the shadow at the required time of day. An example in illustration thereof. 19 If, in the case of a style of 12 ungulas, the (equinoctial) shadow is 2 angulus, what is the measure of the shodow (of the style) at a time when 10 ghatis have clapsed or have to elapse, the duration of the day-time being 30 ghatis? The definition of the measure of a man's foot in relation to measurements carried out by means of the foot-measure as involved. in the shadow. 20. One seventh of the height of a person happens to be the length of that person's foot. If this be so, that person shall be fortunate. (Thus) the measure of the shadow in terms of the foot- measure is obvious. The rule for arriving at the numerical measure of the shadow which has ascended up (a perpendicular wall). 21. (The height of) the style is multiplied by the measure of the human shadow (in terms of the man's height). The resulting) 18 Algebraically 3= --a + e, where is the measure of the time of 2 g This formula may be seen to follow fica that given in the the day m ghutes. note to stanza 15 above 21. Algebraically, h= C axb-C, where a is the altitude of the shadow- b casting style, h the height of the shadow on the wall, b the measure of the human shadow in terms of the man's height, and a the distanee be- tween the pillar and the wall. The diagram here given eluci- dates the rule It has to be noted here that the distance between the pallar and the wall has to he measured along the line of the shadlow which is cast in sunlight.