CHAPTER VII-MEASUREMENT OF AREAS. reference is further constructed) with the aid of the measurements of the base and the perpendicular-side (of the inmediately derived quadrilateral, above referred to, used as bajas. Then, with the aid of these two last derived secondlary quadrilaterals, all the required) quantities appertaining to the quadrilateral with three equal sides are (to be obtained) as in the case of the quadrilateral with two equal sides. An example in illustration thereof. 102. In relation to a quadrilateral with three equal sides and having 2 and 3 as its bijas, give out the measures of the top-side, of the base, of (any one of) the (equal) sides, of the perpendicular (from the top to the base), of the diagonal, of the (lesser) segment (of the base) and of the area. The rule for arriving at the measures of the top-side, of the base, of the (lateral) sides, of the perpendiculars (from the ends of the top-side to the base), of the diagonals, of the segments (of the base) and of the area, in relation to a quadrilateral the sides of which are (all) unequal :- 103. With the longer and the shorter diagonals (of the two derived rectangular quadrilateral figures related to the two sets 103 The rule will be clear from the following algebraical representation. Let a, b, and c, d, be two sets of given bias Then the various required elements are as follow- Lateral sides 2ab (c² + d²)(a + b²) and (a²-b²) (c + d²)(a + b²) Base 2cà (a + b)(a+b) 215 Top-side (c²d²)(a +b²) (a² + b²). Diagonals = {(a²-6²) x 2 ²) × 2cd + (c² — d²)²ab } × (a² + 6²), and {(a²-b²) (c²-a²) + 4abcd } × (a² + b²) Perpendiculars = {(a²-b²) x 2cd + (c²-d²) 2ab } x 2ab, and {{a² − b ) (c² −dª) + ¹abcd} × (a²-6²) Segments= { (a² −6²) × 2cd + (c² −d²) × 2ab } (a −6²), and {(a²-8ª) (c²—6²) + kabed] x 2ab.
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