पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४१५

217 105-107. 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 perpendicular-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 reference, each) multiplied successively by the two dia- gonals (one of each of the oblongs of reference), give rise to the measures (respectively) of the two (lateral) sides (of the required quadrilateral). The difference between the base and the perpen- dicular-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 perpendicular-side of the smaller (oblong of reference) with the perpendicular-side of the larger (oblong of reference) The two sums (so obtained), when multiplied by the diagonal of the smaller (oblong of refer- euce), give rise to the values of the two diagonals (of the required quadrilateral). The diagonals (of the required quadrilateral) are (separ..tely) divided by the diagonal of the smaller (oblong of CHAPTER VII-MEASUREMENT OF AREAS. 106-107. The same values as are mentioned in the footrote to stanza 103 above are given here for the measures of the sides, etc, only they are stated in a slightly different way Adopting the same symbols as in the note to stanza 103, we have -- Diagonals-- [ {2cd-(c²-d²) ] 2«b+ {2ab +(a²_b²)} c²−d²,] × (a² +6²), na[ { 20 {2cd-(2²−2²) } (a² −6²) + { 2ab + (a² − b² -6²)]} (c²-α²) ] × (a² +6²). Perpendiculais = [{2cd-(0²-²)} and x 2ab + {200+ (1 b²) } (c² — d²) ]<a² + b²) 2ab + (a²-b²) (a² + b²; [{₂ { 2cd−(cª — d²) } (a² − b² + ) { 2ab + (a² — 1², } (c²—d) ]a³ + b³²). (a² +1²) -(a²-6²), x 2 ab. The above four expressions can be reduced to the form in which the measures of the diagonals and the porpendiculars are given in stanza No 103). The measures of the segments of the b'se are here derived by extracting the square root of the difference between the squares of the side and of the perpendi- cular corresponding to the segment. 28