286 GANITABARASANGRAHA. of) his own shadow, and then it is multiplied by seven: this gives rise to the height of the tree. This (height of the tree) divided by seven and multiplied by the foot-measure of his shadow surely gives rise to the measure (of the length) of the shadow of the tree exactly. An exampie in illustration thereof. 49 The foot-measure (of the length) of one's own shadow is t. The (length of the) shadow of a tree is 100 in terms of the (same) foot-measure. Say what the height of that tree is in terms of the measure of one's own foot. An example for arriving at the numerical measure of the shadow of a tree. 50. The measure (of the length) of one's own shadow (at the time) is 4 times the measure of (one's own) foot. The height of a tree is 175 (in terms of such a foot-measure). What is the measure of the shadow of the tree then? 51-52. After going over (a distance of) 8 yojanas (to the east) of a city, there is a hill of 10 yöjunas in height. In the city also there is a hill of 10 yöjenas in height. After going over (a distance of) 80 yojanas (from the) eastern hill to the west, there is another hill. Lights on the top of this (last mentioned hill) are seen at nights by the inhabitants of the city. The shadow of the hill lying at the centre of the city touches the base of the eastern hill. Give out quickly, O mathematician, what the height of this (western) hill is. Thus ends the eighth subject of treatment, known as Calculations relating to shadows, in Sãrasangraha, which is a work on arithmetic by Mahavirācārya. SO ENDS THIS SARASANGRAHA. 51-52. This example is intended to illustrate the rule given in stanza 45 above.
