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CHAPTER VII-MBASUREMENT OF AREAS.
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137. The squares (of the ratio-values) of the perimeters (of the required isosceles triangles) are multiplied by the ratio-values of) the areas (of those triangles) in alternation. (Of the two produots so obtained), (the larger one is) divided by the smaller ; and (the resulting quotient) is multiplied by six and is also separately multiplied) by two. The smaller (of the two products so obtained) is diminished by one. The larger product and the diminished smaller product constitute the two bijine in relation to the longish quardrilateral figure) from which one (of the required triangles) is to be obtained. The differonoe hetween those (two bijas above noted) and twico the analler ono (of those bijax) constitute the tijas (in relation to the longish quadrilateral tigure) from which the other (required triangle) is to be obtainod. (From the two longish quadrilateral figures forined with tho aid of their respective bijas), tho sides and the other things (rolating to the required triangles) are to be arrivod at as (explainod) before.
187. When a : b in the ratio of the perimeters of the two inosoelos triunglon, and c: d the ratio of their arean, thon, according to tho rule, and 10 1
48 C and a à + 1 and a de
- 2 ure the two sets of bijas, with the help of which the values of the various required elements of the two isosoolen trianglou may be arrived at. The measures of the sides and the altitudin, calculated from those
ljen nooording to stanea 108 in this chapter, when multiplied ronpootively by a and b. (the quantities occurring in the ratio of iho periunetors), kive the required measures of the sides and the ultitude of the two iDonooles triangles. They are a follow :
Equal sido = a* {(VI) + ( 2 )"} Bmw = x 2 x 2 x - ?) Altitudo = ax { ) - -)} 11 Equal oido = 6 * { leta 1) -)"}
Antado =bx { lett +1)-(
-2)}
Now it may be easily proved from these values that the ratio of the perime. tors is a: 6, and that of the areas inc: d, as taken for granted at the beginning.
