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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CHAPTER VII--MEASUREMENT OF AREAS.
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(multiplier) as multiplied by two and (then) diminished by the value of the side (just arrived at) gives rise to the value of the top-side. And the (given) area divi led by the given (multiplier) gives rise to the value of the perpendicular (dropped from the ends of the top-side) in relation to this required quadrilateral figure with three equal sides.
An example in illustration thereof.
151. In the case of a certain quadrilateral figure with three equal sides, the accurate value of the area is 96. The given multiplier is 8. Give out the values of the base, of the sides, of the top-side and of the perpendicular.
The rule for arriving at the numerical measures of the topside, of the base, and of the other sides in relation to a quadrilateral figure having unequal sides, with the aid of 4 given divisors, when the accurate value of the area (of the required quadrilateral figare) is known :--
152. The square of the given area is divided (separately) by the four given divisors; (and the four resulting quotients are separately noted down). Half of the sum of (these) quotients is (noted down) in four positions, and is (in order) diminished (respectively) by those (quotients noted down above). The remainders (80 obtained) give rise to the numerical values of the sides of a quadrilateral figure (having unequal sides and consequently) named 'unequal.'
152. The area of a quadrilateral with unequal sides has already been men. tioned to be ♡ : (-a) (8-5) (8-0) (8-d), where :=balf the perimeter, and a, b, c, and d are the measures of the sides (ide note to stanza 50 in this chapter). The rule here given requires that the numerical value of the area should be squared and then divided separately by the four optionally chosen divisory. If (8-a) (8-b) (-c) (8-d) is divided by four suitably chosen divisors so as to give as quotients 8-a, 8-5, 8-c, and s-d, then on adding these quotients and halving their sum, the result is seen to be 8. If 8 is diminished in order by s-a, s-, 8-c, and s-d, the remainders represent respectively the values of the sides of the quadrilateral with onequal sides.
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