पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४८३

CHAPTER IX.-CALCULATIONS RELATING TO SHADOWS. 285 O you who have gone to the other shore of the ocean of calculation, say what (the measure of) the intervening horizontal distance is between the style and the lamp. The rule for arriving at the numerical measure of the height of the lamp (above the floor).- 45. The measure of the (horizontal) distance between the lamp and the style is divided by the shadow of the style (Then) one is added (to the resulting quotient) The quantity so obtained, on being multiplied by the measure of the height of the style, gives rise to the measure of the height of the lamp (above the floor). An example in illustration thereof. 46-17. The (length of the) shadow of the style is exactly twice (its hight). The measure of the intervening (horizontal) distance between the style and the lamp is 200 angulas. What is the measure of the height of the lamp (above the floor) in this case? Here and also in the foregoing example, the measure of the height of the style has to be understood as consisting of 12 angulas, and then the way in which the meaning of the rule works out is to be learnt well. The rule for arriving at the numerical measure of the height of a tree, when the measure (of the length) of the shadow of a man in terms of (his) foot and the measure of the length of the shadow of the tree in terms of the measure of that same foot are known; as also for arriving at the numerical measure (of the length) of the shadow of the tree in terms of that same foot-measure, when the numerical measure of the height of the tree and the numerical measure (of the length) of the shadow of a man in terms of (his) foot are known :- 48. The measure (of the length) of the shadow of the tree chosen by a person is divided by (the foot-measure of the length 45. Similarly, b = (²+ 8 + 1) a. 48. This deals with a converse case of the rule given in the latter half of stanza 12 above. The relation between the height of a man and his foot-measure is utilized in the statement of the rule as given here.