________________
CHAPTER VIIMEASUREMENT OF ARFAS.
238
(multiplier) as multiplied by two and (thon) diminished by the value of the side (just arrived at) givos riso to the value of the top-side. And the (given) area divi led by the given (multiplier) gives rise to the value of the perpendicular (dropprd from the ends of the top-side) in relation to this required quadrilateral figure with three equal sides.
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 sideg, of the top-side and of the perpendicular.
The rule for arriving at the numerical measures of the topside, of the base, and of the other) sites in relation to a quadrilateral figure having unequal sides, with the aid of 4 given divisors, when the accurate value of the area (of the required quadrilateral figare) 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 (those) quotients is (noted down) in four positions, and is (in order) diminished (respectively) by those (quotients noted down abovo). The remainders (80 obtained) give rise to the numerical values of the sides of a quadrilateral figure (having unequal wides and 00180quently) named uneqnal.'
162. The area of a quadrilateral with unequal side. bas already been men. Hobed to be -a) (-ba-o le-d), whero e = ball tho perimetor, and a, b, c, and d are the measures of the siden (tide potato tante 30 in this chapter). The rule here given requires that the numerical valoe of the area should be squared and then divided separately by the four optioually chosen divlegru. 11 (-a) (1-0)(1-c) (-d) in divided by four suitably choron divinors so an to give u quotient -9,-6, .-C, and Id, then on adding these quotionta and halving their sam, the result is seen to be .. 11 , is diminiebed in order by i-,.-,.-C, and ,-d, the remaindera refinent respectively the valdes of the sides of the quadrilateral with unequal sidou.
80
