History of Hindu Mathematics: A Source Book v2.c17.s8.100

v2.c17.s8.100

*Solution*. "Here the shadow is (taken to be) x. This being diminished by a third part of the hypotenuse becomes equal to fourteen fingers. Hence conversely, fourteen being subtracted from it, the remainder, a third of the hypotenuse, is x - 14. Thrice this, which is the hypotenuse, is 3x - 42. The square of it, 9x² - 252x + 1764, is equal to the square of the hypotenuse, x² + 144. On making equi-clearance, the two sides become $8x² - 252x + 0 = 0x² + 0x - 1620.$ Multiplying both these sides by 2 and adding the square of 63, the roots are $4x - 63 = ± (0x + 27).$ On forming an equation with these sides again, and (proceeding) as before, the values of x are 45/2, 9.