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Shri Mahavir Jain Aradhana Kendra
www.kobatirth.org
Acharya Shri Kailassagarsuri Gyanmandir
CHAPTER VII--MEASUREMENT OF AREAS.
235
the optionally chosen quantity gives rise to the measure of the perpendicular.
An example in illustration thereof.
1571. In the case of an isosceles triangular figure, the accurate measurement of the area is 12. The optionally chosen quantity is 3. Give out quickly, O friend, the values of (its) sides, base, and perpendicular.
The rule for arriving, after knowing the exact numerical measure of a (given) area, at a triangular figure with unequal sides, having that same accurately measured area (as its own) =
1581. The giver area is multiplied by eight, and to the resulting product the square of the optionally chosen quantity is added. Then the square root (of the sum so resulting is obtained). The cube (of this square root) is (thereafter) divided by the optionally chosen number and (also) by the square root (obtained as above), Half of the optionally chosen number gives the measure of the base (of the required triangle). The quotient (obtained in the previous operation) is lessened (in value) by the (measure of this) base. (The resulting quantity) is to be used in carrying out the sankramana process in relation to the equare of the optionally chosen quantity as divided by two as well as the square root (mentioned above). (Thus) the values of the sides are arrived at.
158). If A represents the area of a triangle, and d is the optionally chosen number, then according to the role the required values are obtained thus :
2 == base ; (W 8A + da). + de
& N 8A + d2 2 2 788 + da and
-=sides.
2 When the area and the base of a triangle are given, the locus of the vertex is a line parallel to the base, and the sides oan have any set of values. In order to arrive at a specific set of values for the sides, it is evidently assumed here that the sum of the two sides is equal to the sum of the base and twice the altitude, i.e., equal to +24. With this assumption, the formula above
2" " " given for the measure of the sides can be derived from the general formula for the area of the triangle, Nils-a) (5-6) (8-c) given chapter.
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