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 407

210
GANITASĀRASANGRAHA.
the squares of that (sum and the difference of the bājas) gives rise (respectively) to the measures of the other) side and of the hypotenuse. This also is a process in the operation of (constructing a geometrical) figure to be derived (from given lījas).
An example in illustration thereof. 941. O friend, who know the secret of calculation, construct a derived figure with the aid of 3 and 5 as bājas, and then think out and mention quickly the numbers measuring the perpendicular-side, the other side and the hypotenuse (thereof).
The role for arriving at the bīja numbers relating to a given figure capable of being derived (from bējas).
954. The operation of sankramana between (an optionally chosen exact) divisor of the measure of the perpendicular-side and the resulting quotient gives rise to the (required) bējas. (An optionally chosen exact) divisor of half the measure of the (other) side and the resulting quotient (also) form the bījas (required). Those (bijas) are, (respectively), the square roots of half the sum and of half the difference of the measure of the hypotenuse and the square of a (suitably) chosen optional number.
An example in illustrution thereof. 964. In relation to a certain geometrical figure, the perpendigular is 16 : what are the bījas? Or the other side is 30 : what are the būjas? The hypotenuse is 34 : what are they (the bējas)?
The rule for arriving at the numerical measures of the other side and of the hypotenuse, when the numerical measure of the perpendicular-side is known; for arriving at the numerical measures of the perpendicular-side and of the hypotenuse, when the numerical measure of the other side is known; and for arriving
934. In the rule given bere, a -, 2 ab, and a + b2 are represented as
(a + b)? - (a - b), (a + b)* + (a - b) la + b)(a - b),
2 953. The processes mentioned in this rule may be seen to be converse to the operations mentioned in stanza 90).