________________
nor
logarithm (of sin ) increases (from zero) as the number (0) itself decreases
(from 90°). Moreover, he took log sin 90o = 0 or log 10% = 0. [b] The notion of a 'base' is inapplicable to his system of logarithms. [c] With his system
log ab is not log a + logb
log (a - b) is loga - logb. (cf. Cajori, p. 150 and Bose, p.28) [4.3] Jobst Bürgi (1552 - 1632) was a Swiss watchmaker and instrument - maker. He independently invented logarithms. His approach was entirely different from Napier's. It was algebraic and was definitely based on the structure of a G.P. (Cf. Hooper, p.192)
He published his work under the title 'Arthmetische and Geometrische Progress Tabulen' at Prague in 1620 A.D. He neglected to have it published until Napier's logarithms were known and admired throughout Europe. (Cf Cajori, p.152)
5. DISCUSSION
[5.1] Simon Jacob (1565 A.D.) followed closely Stifel and recognized the latter's four laws. He, in turn, influenced Bürgi. (Cf. Smith, pp 520 and 522)
On the basis of this information, we may draw a line of study as follows: ........ Stifel (1486 ? - 1567) - Jacob (1565) →Bürgi (1552-1632) ........
The present author thinks that in Europe through this line {a! it may have been possible to understand the fact that an index (or exponent)
is simply a (natural) logarithm and a ground may have been prepared to transform the laws of indices into the laws of (natural) logarithms.
On the other hand, the same business had been worked out in India definitely in the time of the DVL (rather the Satkhandagama) and formally in the time of the TLS as we have seen in the gone pages.
From the above discussion, we may easily infer that the laws of indices had been transformed into the laws of logarithms in India at least six centuries earlier than that in abroad. (5.2) Theory of logarithms to the base 2, 3 and 4 was an exclusive invention of the aia shoot Indian mathematics. It was not sared by any non- Jaina het leverin like Anyjabliua-I (bom 4700) Thumte (c. 028 DI Som Tis 629 AD) Arubhaici! 950
1039
Afidi Vilia,
2003
67
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