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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1052—1073. The square of the diagonal of the smaller (of the two derived oblongs of reference), as multiplied (separately) by the base and also by the perpendicular-side of the larger (oblong of reference, gives rise to the measures (respectively) of the base and of the top-side of the required quadrilateral having unequal sides). The base and the perpendicular-side of the smaller (oblong of reference, each) multiplied successively by the two diagonals (one of each of the oblongs of reference), give rise to the measures (respeotively) of the two (lateral) sides (of the required quadrilateral). The difference between the base and the perpendicular-side of the larger (oblong of reference) is in two positions (separately) multiplied by the base and by the perpendicular-side of the smaller (oblong of reference). The two (resulting) products (of this operation) are added (separately) to the product obtained by multiplying the sum of the base and the perpendicular-side of the smaller (oblong of reference) with the perpendicular-side of the larger (oblong of reference). The two sums (80 obtained), when multiplied by the diagonal of the smaller (oblong of reference), give rise to the values of the two diagonals (of the required quadrilateral). The diagonals (of the required quadrilateral) are (separately) divided by the diagonal of the smaller (oblong of
105-107}. The same values an are mentioned in the footnote to stanza 1031 above are given here for the measures of the sides, etc.; only they are stated in a slightly different way. Adopting the same symbols as in the note to stanza 103}, we hare:
Diagonals- [{2cd=(^ — de) } 2ab + {2ab +(02–00)} --- 4*)] *<a* +o*); und[ { 2cd=60° –)}(22 –69)+ {2ab +(2° 6°)}(co-a)] x (a® +69). [{2cd= (07- do)} x 2ab + { 2ab +(a? –b") } co – d”)](a? +6?)
[{2cd=((2 – do)}(* – b2+){2ab +(22–6)?(6-d) ?a* +62).
Perpendiculars =
(a-6%);
(a2 +62)
and
--x 2 ab. (a? + 5%) The above four expressions can be reduced to the form in which the measures of the diagonale and the perpendiculars are given in stanza No. 103. The measures of the gegments of the base are here derived by extracting the square root of the difference between the sqnares of the side and of the perpendi. cular corresponding to the segment.
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