पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४१२

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216
GAṆITASĀRASAṄGRAHA.

of given bījas), the base and the perpendicular-side (of the smaller and the larger derived figures of reference) are respectively multiplied. The products (so obtained) are (separately) multiplied (again) by the shorter diagonal. The resulting products give the measures of the two (unequal) sides, of the base and of the top-side (in relation to the required quadrilateral). The perpendicular-sides (of the derived figures of reference) are multiplied by each other's bases; and the two products (so obtained) are added together. Then to the product of the (two) perpendicular-sides (relating to the two figures of reference), the product of the bases (of those same figures of reference) is added. The (two) sums (so obtained), when multiplied by the shorter of the two) diagonals (of the two figures of reference), give rise to the measures of the (required) diagonals. (Those same) bums, when multiplied by the base and the perpendicular-side (respectively) of the smaller figure (of reference), give rise to the measures of the perpendiculars (dropped from the ends of the diagonals); and when multiplied (respectively) by the perpendicular-side and the base (of the same figure of reference), give rise to the measures of the segments of the base (caused by the perpendiculars). The measures of these segments, when subtracted from the measure of the base, give the values of the (other) segments (thereof). Half of the product of the diagonals (of the required figure arrived at as above) gives the measure of the area (of the required figure).


An example in illustration thereof.

104. After forming two derived figures (of reference) with 1 and 2, and 2 and 3 as the requisite bījas give out, in relation to a quadrilateral figure the sides whereof are all unequal, the values of the top-side, of the base, of the (lateral) sides, of the perpendiculars, of the diagonals, of the segments (of the base), and of the area.

Again another rule for arriving at (the measures of the sides, etc., in relation to) a quadrilateral, the sides of which are all unequal :-