पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२७३

CHAPTER IV-MISCELLANEOUS PROBLEMS (ON FRACTIONS). 75 32 Of (the contents of) a treasury, one man obtained part; others obtained from in order to , in the end, of the successive remainders; and (at last) 12 pcs were seen by me (to remain) What is the (uumerical) measure of the puranas contained in the treasury)? Here end examples in the Sexe variety. The rule relating to the Mula variety of miscellaneous prob- lems on fractions) 33. Half of (the coefficient of) the square root of the unknown quantity) and (then) the known remainder should be (each) divided by one as diminished by the fractional (coefficient of the unknown) quantity The square root of the sum of the) known remainder (so treated), as combined with the square (of the coefficient) of the square root (of the unknown quantity dealt with as above), and (then) associated with (the similaily treated coefficient of) the square root (of the unknown quantity), and (thereafter) squared (as a whole), gives rise to the (required unknown) quantity in this mula variety (of miscellaneous problems on fractions) Examples in illustration thereof. 34. One-fourth of a herd of camels was seen in the forest, twice the square root (of that herd) had gone on to mountain- slopes; and 3 times 5 camels (were), however, (found) to remain on the bank of a river. What is the (numerical) measure of that herd of camels ? 35. After listening to the distinct sound caused-by the drum made up of the series of clouds in the rainy season, 7 and (of a collection) of peacocks, together with of the remainder and of 3 the remainder (thereafter), gladdened with joy, kept ou dancing on = 33 Algebraically expressed, this rule comes to (2)*}* 1-b 1-b + + this is easily obtained from the equation (bx+c√x+a)=0. This equation is the algebraical expression of probleins of this variety Here c stands for the coefficient of the square root of the unknown quantity to be found out.