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We do not find such idea of logarithms in no school other than the Jaina scchool of Indian mathematis not only in India but also in the rest of the world.It was an exclusive invention of the Jaina school of Indian mathematics and was used only in its canonical texts such as the TP, DVL, JDPS, TLS, GJK etc. but not in its exclusive texts (on mathematics) such as the GPV, PG and TSK of Sridhara (c.799 A.D.), GSS etc.
Therefore, it is recommended that the above idea of logarithms should be known as Jaina logarithms as 10 is known as Jaina value for л (= the ratio between the circumference and diameter of a circle).
[4] THE THEORIES LIE IN THE DOUBLE SERIES
[4.1] Michael Stifel (or Stifelus) (1486?-1567) was the greatest German algebraist of the sixteenthy century. He was born in Esslingen and died in Jena. In 1544 A.D., he published, in Latin, a book titled 'Arithmatic Integra'. The book is divided into three parts dealing respectively with rational numbers, irrational numbers and algebra.
Most writers refer him as the first mathematician who sets forth the laws of indices. At first, he uses the series in which the first one is an arithmetic progression (abbreviated as A.P.) and seond one is a geometric progression (abbreviated as G.P.).
0
1
distinctly calling the upper numbers exponents.
In an expressive manner, he lays down four laws, namely, [a] that addition in A.P. corresponds to multiplication in G.P.,
[b] that subtraction corresonds to division,
[c] multiplication to the finding of powers and
[d] division to the extracting of roots. (Cf. Smith, p.521)
Now a days, we have only to write the series
2o 21 22 23 24 25
1
2 3 4 5
2 4 8 16 32
to see at glance the connection between A.P. and G.P., but in 1600 A.D. this symbolism had yet to be developed. (Cf. Hooper, p.193)
(cf. Smith, p.521) 64
Furthermore, he also saw the great importance of considering the negative exponents of the base which he selected, using the series
-3
-1
0 1
2
1 2
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