Vol. VIII, No. 9.] | The Bakhshali Manuscript. 359 
[N.S.] 
There are also three examples of the same kind of problem 
a ra.! erms these the Sesa variety 
miscellaneous problems on fractions, and in the Bakhshali 
manuse he abbreviation ge is used to denote the loss in 
such problems. This class of examples does wep occur in the 
works of cay as Brahmagupta and Sridhar 
Sit Having multiplied severally ths parts of gold 
with he a paatiis, let the total wastage be divided by the sums 
of the parts of gold. The results is the wastage of each part of 
gold. 
This means — if 4 A eam a, are different quantities 
of gold, and w, w,...... are the respective losses in weight, 
then aw, Sa= the average loss. 
Examples :—(1) Gold 1, 2, 3, 4 suvarnas, and losses 1, 2, 3, 4 
masakas. ‘Fhe average is 
1.142.2+3.3+4.4 | 
1+2+3+4+4 oe 
(3) Gold 5, 6, 7, 8, 9, 10 and ‘another metal 2, 3, 4. 
Losses 4, 5, 6, 7, 8, 9 and 1, 2, 3, respectively. 
Solution— 
5.4+6.5+7.6+8.7+9.8+10.94+2.1+3.2+43 
ia 5+6+7+8+9+10 


= 7%. 
Similar problems are a by Mahavira’ under the title 
Suvarna-kuttikara. Here 
There are 1 part of bd of 1 varna, 1 part of 2 varnas, 
1 part . 3 varnas, 2 parts of 4 varnas, 4 parts of 5 varnas, 7 parts 
of 14 varnas. Throwing these into the fire make them all into 
one, anal then say what the varna of the mixed gold is. This 
mixed gold is distributed among the owners of the foregoing 
et ? ; 
e also Bhaskara’s Lilavati.® Sridhara se _ similar 
rules,# while Brahmagupta gives no such problem 
Siitra 50. What number added to five is a square, that 
same number lessened by seven is a square. Which number is 
that? That is the question. 
This example, which may be expressed by 
x+5=m? | 
2—T=n* 
occurs in a more general form in Brabmagupta,° and el-Karchi 
elves several er of the same kind and it is dealt with 
p- 29-32. 2 138, 169-180. 
te Sec a a ofa B 38 810 5 Ch. xviii, § 84. 
