पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४२०

222 GANITASARASANGRAHA. 117. In the case of a longish quadrilateral figure, (the numeri- cal measures of) twice the diagonal, three times the base and four times the perpendicular-side heing taken, the measure of the perimeter is added to them. Twice (this sum) is the (numerical) measure of the area. (Find out the measure of the base.) 118. In the case of a longish quadrilateral figure, the (numerical) measure of the perimeter is 1. Tell me quickly, after calculating. what the measure of its perpendicular side is, and what that of the base. 119. In the case of a longish quadrilateral figure, the (nume- rical measures of twice the diagonal, three times the base, and four times the perpendicular, on being added to the (numerical) measure of the perimeter, become equal 1. (Find out the measure of the base.) Another rule regarding the process of arriving at the number representing the bijas in relation to the derived longish quadri- lateral figure:- 120. The operation to arrive at the generating (bijas) in re- lation to a longish quadrilateral figure consists in getting at the square roots of the two quantities represented by (1) half of the diagonal as diminished by the perpendicular-side and (2) the difference between this quantity and the diagonal. An example in illustration thereof. 121. In the case of a long: quadrilateral figure, the per- pendicular-side is 55, the base is 48, and then the diagonal is 73. What are the bajas here? 120 The rule in stanza 951 of this chapter relates to the method of arriv- ing at the bijas from the base or the perpendicular cr the diagonal of a longish quadrilateral. But the rule in this stanza gives a method for finding out the bigas from the perpendicular and the diagonal of a longish quadrilateral. The process described is based on the following identities:- a²+ b²(a²-32) b; and a²+b_ a² + b² - (a²-6²) 2 =a₂ 2 where a² +62 is the measure of the diagonal, and a²-62 is the measure of the perpendicular-side of a longish quadrilateral, a and b being the required bējas.