पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२७८

80 GANI ASARASANGRAHA. multiplied by the (given proportional) fraction; then that result which is arrived at by means of the operation of finding out (the unknown quantity) in the Sesamüle variety (of miscellaneous problems ou fractions), when divided by the (given proportional) fraction, becomes the required quantity in the imamilu variety (of miscellaneous problems on fractions! Another rule relating to the samūla variety 52 The known quantity given as the (ultimate) remainder is divided by the (given proportional) fraction and multiplied by four, to this the square (of the coefficient) of the square root (of the given fraction of the unknown collective quantity) is added; then the square root (of this sum), combined with (the above mentioned coefficient of) the square root (of the fractional unknown quantity), and (then) halved, aud (then) squared, and (then) multiplied by the (given proportional) fraction, becomes the required result Examples in illustration thereof 53. Eight times the square root of part of the stalk of a lotus is within water, and 16 angulas (thereof are) in the air (above water); give out the height of the water (above the bed) as well as of the stalk (of the lotus). 54-55. (Out of a herd of elephants), nine times the square root of part of their number, and six times the square root of of the remainder (left thereafter), and (finally) 24 (remaining) elephants with their broad temples wetted with the stream of the exuding chor, were seen by me in a forest. How many are (all) the elephants" under stanza 17, x-bx becomes here also. After substituting as desired, and dividing the result by b, we get = This value of + + N (cb) ² e may be easily arrived at from the equation x-c6²-a=0 52. Algebraically stated, 2 the equation given in the note under the previous stanza. + ab 4a 2 ८+ c² + 3 b s x b. This is obvious from