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

Page 416

CHAPTER VII- MEASUREMENT OF AREAS.
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An example in illustration thereof. 1091. O mathematician, calculate and tell me quickly the measures of the two (equal) sides, of the base and of the perpendicular in relation to an isosceles triangle derived with the aid of 3 and 5 as bējas.
The rule regarding the manner of constructing a trilateral figure of unequal sides
1101. Half of the base of the (oblong of reference) derived (with the aid of the given bājas) is divided by an optionally chosen factor. With the aid of the divisor and the quotient (in this operation as bijas), another (oblong of reference) is derived. The sum of the perpendicular-sides belonging to these two (oblongs of reference) gives the measure of the base of the required) trilateral figure having unequal sides. The two diagonals (related to the two oblongs of reference) give the two sides (of the required triangle). The base (of either of the two oblongs of reference) gives the measure of the perpendicular (in the case of the required triangle).
An eaample in illustration thereof. 1111. After constructing a second (derived oblong of reference) with the aid of half the base of the (original) figure (i.e. oblong of reference) derived with the aid of 2 and 3 as būjas, you tell (me) by means of this (operation) the values of the sides, of the base and of the perpendicular in a trilateral figure of unequal sides.
Thus ends the subject of treatment known as the Janya operation.
1104. The role will be clear from the following construction :-Let ABCD and EFGH be the two B
OF derived oblongs, such that the base AD = the base EH. Produce BA to Ko that Ak=EF. It can be easily shown that DK = A
DE EG and that the triangle BDK has its base BK= BA + EF, called the perpendiculars of the oblongs, and has its sides equal to the diagonals of the same oblongs,