yp = 
Vol. IV, No. 3.] Notes on Indian Mathematics. 133 
[N.S.] 
rahmagupta has (XII., ii, 15) the following rule: “The 
product of the time and principal divided by the further time is 
twice set down. From the product of the one by the mixt amount, 
added to the square of half the other, extract the square root ; that 
root less half the second, is the interest of the principal.” In symbols 
/ M'Pt'/t+ (Pe’/2t)*— Pt /2t= Prt’. This can be obtained direct 
from Aryabhata’s equation by multiplying both sides by ¢’ and 
putting M’ for M?t’'/t. It would, however, appear more natural to 
sede Aryabhata’s rule from that of Brahmagupta by putting 

Bik rahmagupta’s commentator, Chaturvéda, ae the follow- 
ing example: ‘‘ Five hundred drammas were at rate of 
was lent to another person at the same rate; and it accumulated 
in ten months to seventy- -eight. Tell the rate of interest on the 
principal. Answer 60.” 
Chaturvéda’s working may be set down as follows: Let y be 
the interest on 500 drammas for 4 months; then y*/200 is the 
interest on y for the 10 months, and 2 1/200 + y=78, whence y =60. 
The actual rate, 3°/, per mensem, is not ae oned. 
onsiderable acquaintance with the rules that govern interest 
problems must have obtained in these times and at least the 
rudiments of compound interest were understood. 
26. In the rule of three the Ed Lene by the ‘demand’ 
and divided by the ‘measure’ gives the ‘ fruit of the demand.’ 
he first term is the ‘measure’ ; the second is — ‘fruit’; and 
the third is the ‘ demand’ or question. Thus in a: b:: ¢: 2, the 
measure’ is a; the ‘ “ad >is 6; the demand’ is c and the ‘fruit 
of the demand’ is bc/a= 
Brahmagupta (XU, i; i., 10) and Bhaskara (Il. 70f.) use the 
same nomenclature and deal with “ Three or more uneven terms, 
up to eleven.’ 
27. (a) The denominators are multiplied by one another in 
multipliction and in division. (5) Multiply separately by the opposite 
denominator to get the same kind 
Cf. Brahmagupta (XII, i., 2f). 
28. Multiplication becomes division and division multiplica- 
tion ; profit becomes loss and loss profit in the inverse. 
Cf. Bhaskara (Lil. 47-48). 
29. If the sum of several numbers joined together be diminished 
by each in turn and divided by the number of terms less one such tt is 
exactly. 
If there be three terms the rule means that 
(m+n+p)/2=a+b+e 
