पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४२६

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एतत् पृष्ठम् परिष्कृतम् अस्ति
230
GAṆITASĀRASAṄGRAHA.

sides of the equilateral triangle (if it be equilaterally triangular in shape)? Tell (me, O friend, the measures of the perpendicular side and the base, in (case the carpet happens to be) a longish quadrilateral figure (in shape).

The rule for arriving at an equilaterally quadrilateral figure or at a longish quadrilateral figure when the numerical value of the area of the figure is known:-

146. The square root of the accurate measure of the (given) area gives rise to the value of the side of the (required) equilateral quadrilateral figure. On dividing the (given) area with an optionally chosen quantity (other than the square root of the value of the given area, this) optionally chosen quantity and the resulting quotient constitute the values of the perpendicular-side and the base in relation to the (required) longish quadrilateral figure.

An example in illustration thereof.

147. What indeed is that equilateral quadrilateral figure, the area whereof is 64 ? The accurate value of the area of the longish (quadrilateral) figure is 60. What are the value of the perpendicular-side and the base here?

The rule for arriving at a quadrilateral figure with two equal sides having the given area of such a quadrilateral figure with two equal sides after getting at a derived longish quadrilateral figure with the aid of the given numerical bījas and also after utilizing a given number as the required multiplier, when the numerical value of the accurate measure of the area of the required quadrilateral figure with two equal sides is known:-

148. The square of the given (multiplier) is multiplied by the that (given) area. The (resulting) product is diminished by the value of the area (of the longish quadrilateral figure) derived (from the given bījas). The remainder, when divided by the base


148. The problem here is to construct a quadrilateral figure of given area and with two equal sides. For this purpose an optionally chosen number and a set of two bījas are given. The process described in the rule will become clear by applying it to the problem given in the next stanzna. The bījas mentioned therein are 2 and 3; and the given area is 7, the given optional number being 3.