पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४१८

220 GANITASĀRASANG RAHA. Subject of treatment known as Paisacika or devilishly difficult problems. Hereafter we shall expound the subject of treatment known as Parsācika The rule for arriving, in relation to the equilateral quadri- lateral or longish quadrilateral figures, at the numerical measure of the base and the perpendicular-side, when, out of the perpen- dicular side, the base, the diagonal, the area and the perimeter, any two are optionally taken to be equal, or when the area of the figure happens to be the product cbtained by multiplying respectively by optionally chosen multipliers any two desired quantities (out of the elements mentioned above) that is-(the rule for arriving at the numerical values of the base and the perpendicular-side in relation to an equilateral quadrilateral or a longish quadrilateral figure,) when the area of the figure is (numerically) equal to the measure of the perimeter (thereof); or when the area of the figure is numerically equal to the measure of the base (thereof); or, when the area of the figure is numerically equal to the measure of the diagonal (thereof); or, when the area of the figure is numerically equal to half the measure of the perimeter; or, when the area of the figure is numerically equal to one-third of the base; or, when the area of the figure is numerically equal to one-fourth of the measure of the diagonal; or, when the area of the figure is numerically equal to that doubled quantity which is obtained by doubling the quantity which is the result of adding together twice the diagonal, three times the base, four times the perpendicular- side and the perimeter and so on :- 112. The measure of the base (of an optionally chosen figure of the required type), on being divided by the (resulting) optional factor in relation thereto, (by multiplying with which the area 112. The rule will be clear from the following working of the first example given in stanza 113 Here the problem is to find out the measure of the side of an equilateral quadrilateral, the numerical value of the area where- of is equal to the numerical value of the perimeter. Taking an equilateral quadrilateral of any dimension, say, with 5 as the measure of its side, we have the perimeter equal to 20, and the area equal to 25. The factor with which