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एतत् पृष्ठम् परिष्कृतम् अस्ति
214
GAṆITASĀRASAṄGRAHA.

101. The difference between the (given) bījas is multiplied by the square root of the base (of the quadrilateral immediately derived with the aid of those bījas). The area of (this immediately) derived (primary) quadrilateral is divided (by the product so obtained). Then, with the aid of the resulting quotient and the divisor (in the operation utilized as bījas, a second derived quadrilateral of reference is constructed. A third quadrilateral of


101. If a and b represent the given bījas, the measures of the sides of the immediately derived quadrilateral are :-

Perpendicular-side
Base
Diagonal
Area

As in the case of the construction of the quadrilateral with two equal sides (vide stanza 99 ante), this rule proceeds to construct the required quadrilateral with three equal sides with the aid of two derived rectangles. The bījas in relation to the first of these rectangles are :-

Applying the rule given in stanza 90 above, we have for the first rectangle :

Perpendicular-side
Base
Diagonal

The bījas in the case of the second rectangle are:

The various elements of this rectangle are :

Perpendicular-side
Base
Diagonal

With the help of these two rectangles, the measures of the sides, diagonals, etc., of the required quadrilateral are ascertained as in the rule given in stanza 99 above. They are :

Base =sum of the perpendicular-sides
Top-side = greater perpendicular-side minus smaller perpendicular-side
Either of the lateral sides = smaller diagonal
Lesser segment of the base = smaller perpendicular-side
Perpendicular = base of either rectangle
Diagonal = the greater of the two diagonals
Area = area of the larger rectangle

It may be noted here that the measure of either of the two lateral sides is equal to the measure of the top-side. Thus is obtained the required quadrilateral with three equal sides.