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CHAPTER VIIMEASUREMENT OY AREAS.
819
'An example in illustration thereof. 1097. O mathematician, calculate and tell me quickly the measures of the two (equal) sides, of the base and of the perpendicular in relation to an isoroeles triangle derived with the aid of 3 and 5 as bijas.
The rule regarding the manner of constructing a trilateral figure of unequat sides :
1101. Half of the base of the (oblong of reference) derived (with the aid of the given bijas) is divided by an optionally chosen factor. With the aid of the divisor and the quotiont (in this operation as bijas), another (oblong of reference) is derived. The sum of the perpendicnlar-sides belonging to these two (oblongs of reference) gives the moasure of the buso of the (roquired) trilateral figure having unequal sides. The two diagonals (related to the two oblongs of reference) give the two sides (of the required triangle). The base (of eithor of the two oblonge of reference) gives the measure of the perpendicular (in the case of the l'equirod triangle).
An eaample in illustration thereof. 1113. After constructing a second (derived oblong of reference) with the aid of half the base of the original) figure (i.e, oblong of reference) derived with the aid of 2 and 3 as lījas, you tell (me) by means of this (operation) the values of the sides, of the base and of the perpendicular in a trilateral figure of unequal sides.
Thus ends the subject of treatment known ng the Janya operation,
1104. The rule will be clear from the following construction :-Lot ABCD and EFGH be the two BK derived oblongi, such that the base AD = the base EL. Produce BA to K 10 that AK= EF. It can be sually shown that DK = A
DE EG and that the triangle BDK has its base BK = BA + Er, called the perpendiculars of the oblongn, and has its sides equal to the diagonals of the same oblongu. .
