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 275

78
GANITASĀRASANG RAHA.
at last 12 ascetics were seen (to remain without being included among those mentioned before). O (you) excellent ascetic, of what numerical value was (this) collection of ascetics?
46. Five and one-fourth times the square root (of a herd) of elephants are sporting on a mountain slope ; of the remainder sport on the top of the mountain ; five times the square root of the remainder (after deducting this) sport in a forest of lotuses; and there are 6 elephants then (left) on the bank of a river. How many are (all) the elephants here?
Here ends the Sésamūla variety (of miscellaneous problems on fractions).
The rule relating to the Sesamūla variety involving two known (quantities constituting the remainders :
47. The (coefficient of the) square root (of the unknown collective quantity), and the (final) quantity known (to remain), should (both) be divided by the product of the fractional (proportional) quantities, as subtracted from one (in each case) ; then the first known quantity should be added to the other) known quantity (treated as above). Thereafter the operation relating to the Sesamūla variety (of miscellaneous problems on fractions is to be adopted).
47. Algebraically, this rule enables us to arrive at the expressions
... + an, which are required to (1-6) (1-0) x &c. (1---) (1.-) * &o. be substitnted for c and a respectively in the formola for sesamüla, which is
2
+
+ a
.
In applying this formula tho valac of
becomes zero, as the mūla or square root involved in the dvirajra-mumúla is that of the total collective quantity and not of a fractional part of that quantity. Substitating as desired, we get *=12 (1--10) xde +
с
2
.
W (21 – 6,) (1 – ba) * &c.) + (1 – 63) (1-bg) * &c. + uns. may easily be obtained from the equation x -- a, -- bz (-)-- bas --- --
-.... -CN- ag=0, where bi, b, &c., are, the various fractional parts of the successive remainders; and a, and an are the first known quantity and the final known quantity respectively.