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CHAPTER VII-MEASUREMENT OP ARRAN.
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onlar (to the base) as also of the segments (of the baso caused thereby)?
53. In the case of a soalene triangle one of the sides is 13 (in moagure), the opposite side is 15, and the base is 14. What indeod is the caloulated measure of the area of this figure), and what of the perpendicular (to the base) and of the basal segments
Hereafter (wo give the rule for arriving at the valuo of the Jiagonal of the five varieties of quadrilateral figures.
54. The two quantities obtained by multiplying the basal sido by the larger and the smaller of the right and the loft) sides are (respectively) combined with the two (other) quantitics obtained by multiplying the top side by the smaller and the larger of the right and the left sides. T'ho (rosulting) two suns constitute tbe multiplier and the divisor as also the divisor and the multiplier in relation to the sum of the products of the opposite sides. The square roots of the quantities so obtained) give thoroquired measures of the diagonals.
Examples in illustration thereof. 55. In the case of a cqnilateral quadrilateral which has all around a sido measure of 5, tell me quickly, () friend who know the secret of caloulation, the value of the diagonal and also the acourate value of the rea.
64. Algebraically representod the meaRDM of the diagonal of quadrilateral figure as given here ik --
lac+bd) (ab + cd) /(ac + bd) (ad + bc) N ad + bc of N
abi od These formula alan are oorrect only for oyclic quadrilaterals. Bhankara. cirys is aware of the futility of attempting to give the monsure of the wes of 4 quadrilateral without previously knowing the values of the perpendicular or of the diagonal.. Vide the following stanza from his Lild vati :
लम्बयोः कर्णयोर्वेकमनिर्दिश्यापरान् कथम् । पृच्छत्यनियतत्वेऽपि नियतं चापि तत्फलम् !! स पृच्छकः पिशाचो वा वक्ता वा नितरां ततः । यो न वेति चतुर्बाहुक्षेत्रस्यानियतां स्थितिम् ।।
