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CHAPTER VII-XEASUREMENT OF ARBAS.
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1051–1077. The square of the diagonal of the smaller (of the two derived oblongs of reference), as multiplied (separately) by the base and also by the perpendioular-side of the larger (oblong of reference, gives rise to the measures (respectively) of the base and of the top-side (of the required quadrilateral having unequal sides). The base and the perpendicular-side of the smaller (oblong of referenoe, each) multiplied successively by the two diagonals (one of each of the oblongs of referenco), give rise to the measures (res peotively) of the two (lateral) sides (of the required quadrilateral). The difference between the bago and the perpendioular-side of the larger (oblong of reference) is in two positions (separately) multiplied by the base and by the perpendicular-side of the smaller (oblong of reference). The two (resulting) products (of this operation) are added (separately) to the product obtained by multiplying the sum of the base and the porpondioular-side of the smaller (oblong of reference) with the perpendiculør-side of the larger (oblong of referenco). The two sums (80 obtained), when multiplied by the diagonal of the smaller (oblong of reference), give rise to the values of the two diagonale (of the roquired quadrilateral). The diagonals (of the required qualrilatoral) are (separutely) divided by tho diagonal of the smaller (oblong of
106-107). The name values as are mentioned in the footroto to mtanza 103 above are given here for the measure of the wides, etc.; only they are stated in a slightly different way. Adopting the same symbols as in the bote to stanza 103}, we hayo:
Diagonals- [ { 2cd – (c–d") } 21b + {2a1 +(24–40)] co-)] *(* +"); pa[ {2cd=(0) –d")}(20–0°)+ {2ab + (a1 +00)}(co-4"}]x (2"+W). [{2cd=(09–")} * 2ab + { 2ab +(29–60, } (c– d") ]ca+61) .
[{2cd=(co-d") }(2° -6° +) 2ab +(a2-1", }(– ) Top+b).
Perpendiculars =
*2 ab. 'The above four expressions can bo reduced to the form in which tho mbasures of the diagonalo and the perpendicalors are given in stanza No. 108). The mesures of the segments of the balle are here derived by extracting the square root of the difference betweon the squares of the side and of the perpend oular corresponding to the segment.
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