Ganitasara Sangraha

Author(s): Mahaviracharya, M Rangacharya
Publisher: Government of Madras

Page 278

CHAPTER IV-MISCELLANEOUS PROBLEMS (ON FRACTIONS). 81
56. Four times the square root of the number of a collection of boars went to a forest wherein tigers were at play; 8 times the square root of its of the remainder (of the collection) went to a mountain; and 9 times the square root of į of the (further) remainder (left thereafter) went to the bank of a river; and boars equivalent in (numerical) measure to 56 were seen (ultimately) to remain (where they were) in the forest. Give out the (numerical) measure of (all) those (boars).
Thus ends the Amsamüla variety.
The rule relating to the Bhāgasamvarga variety (of miscellaneous problems on fractions) :
57. From the simplified) denominator of the specified compound fractional part of the unknown collective quantity), divided by its own (related) numerator (also simplified), subtract four times the given known part (of the quantity), then multiply this (resulting difference) by that same (simplified) denominator (dealt with as above). The square root of this product is to be added to as well as subtracted from that (same) denominator (so dealt with); (then) the half (of either) of these two quantities resulting as sum or difference is the unknown) collective quantity (required to be found out).
E.camples in illustration thereof. 58. A cultivator obtained (first) of a heap of paddy as multiplied by to (of that same heap); and (then) he had 24 vāhas (left in addition). Give out what the measure of the heap is.
59. One-sixteenth part of a collection of peacocks as multiplied by itself, (i.e., by the same to part of the collection), was found
56. The word sardūlarikrilita in this stanza means tigers at play,' and at the same time happens to be the name of the metre in which the stanza is coin posed.
57. Algebraically stated <==
and this value of x may
m
-u=0, where
and
are
easily be obtained from the equation <--xxx the fractions contemplates in the rule.
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