________________
ix
Fractions- Besides the fundamental arithmetical operations with fractions, knowledge of which has been assumed in the Dhavala, we find a number of interesting formulae relating to fractions, which are not found in any known mathematical work. Amongst these may be mentioned the following: -
[1]1
+
[2] Let a number m be divided by the divisors d and d', and let q and q' be the quotients (or the fractions). The following formula gives the result when. m is divided by d
d'
[3] If
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[4] I
and
n2 n(n/p)
[ 5 ] If
and
[6] If
m
d+ ď
or
8
b
&
b
= ¶
d (q-q) + m'
A
a
b+
b
8
b
a
b
8
b+c
q, then
n
b
n
-C
q' (979)±1
q
1 (9/9)
and
q,
1. Dhavala p. 46.
3. ibid p. 47, quoted verse 27. 4. ibid p. 46, quoted verse 24. 5. ibid p. 46, quoted verse 24. 6. ibid p. 46, quoted verse 25.
=
= q
=
=
9, and
. - q', then
=
= m.
then
9+
q
n
P1
q+
&
b'
q n+1
q n-1
b
C
=
q
+
q
b
;
;
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1
q+c, then
2. ibid p. 46.
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