________________
(1) log ( a/b) = log a - log b . . (2) log (a,b) = log a + log b (3) log 2c = C, where base is 2, (4) log (aa)2 = 2 a log a (5) log log (aa)2 = log a + 1 + log log a (6) log (aa joa = aa log aa .
Further, if we donote the
Ist vargita-samvargita of x= x* =
x
1
1
,
2nd vargita-samvargita of x = x1 = x12
3rd vargita-samvargita of x = x)2 * = 18 Virasena shows log2 log2 x | <{x}}}2 loga x3 = 512 log2 x/2 and so on.
It may be noted that the theory of logarithms was discovered by Baron Napier (+ 1550 to + 1617) and J. Burgi (+ 1552 to 1632). Sanford remarks, "The discovery of logarithms, on the other hand, has long been thought to have been independent of contemporary work, and it has been characterized as standing isolated, breaking in upon human thought abruptly without borrowing from the work of other intellects or following known lines of mathematical thought.”69
(d) Fraction-manipulation :
The examples used by Virasena show the relics of an age when division was considered in terms of set-theoretic approach, because the dealings were in terms of rāśis : 70
a 2
а
a (/)
= a I 741
(2)
If q and r are the quotients when a is divided by b and c, then
69. A Short History of Mathematics, p. 193. 70. Cf. Mathematics of Dhavalā, op. cit.
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