Page:Indian mathematics, Kaye (1915).djvu/75

 39. A snake's hole is at the foot of a pillar 9 hastas high and a peacock is perched on the summit. Seeing a snake, at a distance of thrice the pillar, gliding towards his hole, he pounces obliquely on him. Say quickly at how many hastas from the snake's hole do they meet, both proceeding an equal distance? Answer—12. 40. From a tree a hundred hastas high, a monkey descended and went to a pond two hundred hastas distant, while another monkey, jumping a certain height off the tree, proceeded quickly diagonally to the same spot. If the space travelled by them be equal, tell me quickly, learned man, the height of the leap, if thou hast diligently studied calculation? Answer—50. 41. The man who travels to the east moves at the rate of 2 yojanas, and the other man who travels northward moves at the rate of 3 yojanas. The latter having journeyed for 5 days turns to move along the hypotenuse. In how many days will he meet the other man? Answer—13. 42. The shadow of a gnomon 12 añgulas high is in one place 15 añgulas. The gnomon being moved 22 añgulas further its shadow is 18. The difference between the tips of the shadows is 25 and the difference between the lengths of the shadows is 3. Find the height of the light? Answer—100. 43. The shadow of a gnomon 12 añgulas high being lessened by a third part of the hypotenuse became 14 añgulas. Tell, quickly, mathematician, that shadow? Answer—$$\scriptstyle{22\frac{1}{2}}$$. L=the Līlāvatī, V=Vīja Gaņita, both by Bhāskara, M=Mahāvīra, S=SrīdharaŚrīdhara [sic], C=Chaturveda.