Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

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GANITASARASANGRAHA.
reference). The quotients (80 obtained) are multiplied respectively by the perpendicular-side and the base of the smaller (oblong of reference. The resulting) products give rise to the measures of the perpendiculars (in relation to the required quadrilateral). To these two perpendiculars), the above values of the two sides (other than the base and the top-side) are (separately) added, (the larger side being added to the larger perpendicular and the smaller side to the smaller perpendicular). The differences between these perpendiculars and sides are also obtained (in the same order). The sums (above noted) are multiplied (respectively) by (these) differences. The square roots (of the products so obtained) give rise to the values of the segments of the base in relation to the required quadrilateral). Half of the product of the diagonals (of the required quadrilateral) gives the value of (its) area.
The rule for arriving at an isosceles triangle with the aid of a single derived oblong (of reference).
1081. The two diagonals (of the oblong of reference constructed with the aid of the given bijas) become the two (equal) sides of the (required) isosceles triangle. The base (of the oblong of reference), multiplied by two, becomes the base of the required triangle). The perpendicular-side (of the oblong of reference) is the perpendicular (of the required triangle from the apex to the base thereof). The area (of the required triangle) is the area (of the oblong of reference).
108. The rationale of the rule may be made out thus :- Let ABCD be an oblong and let AD be produced to E so that AD=DE. Join EC. It will be Seen that ACE is an isosceles triangle whose equal sides are equal to the diagonals of the oblong and whose area is equal to that of the ublong.