233 (multiplier) as multiplied by two and (then) diminished by the value of the side (just arrived at) gives rise to the value of the top-side. And the (given) arca divibed by the given (multiplier) gives rise to the value of the perpendicular (dropped from the ends of the top-side) in relation to this required quadrilateral figure with three equal sides. CHAPTER VII-MEASUREMENT OF ARFAS. An example in illustration thereof. 151 In the case of a certain quadrilateral figure with three equal sides, the accurate value of the area is 96. The given multiplier is 8. Give out the values of the base, of the sides, of the top-side and of the perpendicular. The rule for arriving at the numerical measures of the top- side, of the base, and of the (other) sides in relation to a quadrila- teral figure havmg unequal sides, with the aid of 4 given divisors, when the accurate value of the area (of the required quadrilateral figure) is known :-- 152 The square of the given area is divided (separately) by the four given divisors; (and the four resulting quotients are separately noted down). Half of the sum of (these) quotients is (noted down) in four positions, and is (in order) diminished (respectively) by those (quotients noted down above) The remainders (so obtained) give rise to the numerical values of the sides of a quadrilateral figure (having unequal sides and conse- quently) named ' unequal.' 152. The area of a quadrilateral with unequal sides has already been men- tioned to be √ (s-a) (s-b) (s-c) (s-d), where s half the perimeter, and a, b, c, and d are the measures of the sides (de note to stanza 50 in this chapter). The rule here given requies that the numerical value of the area should be squared and then divided separately by the four optionally chosen divisors. If (s-a) (s-b) (8-c) (s-d) is divided by four suitably chosen divisois so as to give as quotients 8-a, 8-b, s-c, and s-d, then on adding these quotients and halving their sum, the result is seen to be s. If s is diminished in order by s-a, s-b, s-c, and s-d, the remainders represent respectively the values of the sides of the quadrilateral with unequal sides 30
