सामग्री पर जाएँ

पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२७१

विकिस्रोतः तः
एतत् पृष्ठम् परिष्कृतम् अस्ति
75
CHAPTER IV--MISCELLANEOUS PROBLEMS(ON FRACTIONS).

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 purāņas were seen by me (to remain). What is the (numerical) measure (of the purāņas contained in the treasury)?

Here end examples in the Śēșa variety.

The rule relating to the Mūla variety (of miscellaneous problems 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 similarly 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 mūla 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, and (of a collection) of peacocks, together with of the remainder and of the remainder (thereafter), gladdened with joy, kopt on dancing on

 

 

33. Algebraically expressed, this rule comes to ; this is easily obtained from the equation . This equation is the algebraical expression of problems of this variety. Here c stands for the coeffcient of the square rōt of the unknown quantity to be found out.