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the Jaina school of Indian mathemtics brings out the general and formal statements of these laws but to the particular base.
In modern time, John Napier (1550-1617) and Jobst Bürgy (1552-1632) have discovered logarithms, but through an entirely different line of approach. The former's approach was geometric as the latter's was algebric.
[3.1] ARDHACHHEDA
Nemicandra defines 'ardhachheda' as follows - दलवारा होंति अद्धछिदी ।
(TLS, v.76, the last quarter, p.69)
The number of times that (a particular rasi) is successively halved (to get the number reduced to unity) is the addhachidi (ardhachheda in Sanskrit) of the number.
That is to say that if
R = 2'
then, r is called the ardhachheda of R. Denoting the ardhachheda by the abbreviation AC, we can write the above as
AC(R) = r.
For instance,
AC(16) = 4.
H.R. Kapadia (p. XXV) is the first scholar to have brought to our mind the fact that
AC(R) = log2R.
A.N. Singh (p.7) followed by L.C. Jain (1958, p.22), A.K. Bag (p.55), H.B. Jain (p.83), Navjyoti Singh (pp. 218-219, 26 and 31-32) and so forth is the first mathematician who have recognized the above fact.
The term 'ardhachheda' is derived from the two words 'ardha' (half) and 'chheda' (division into parts). Sometimes the word 'ardha' is deleted and we have simply the term 'chheda': vide TLS, v.8, p.12 and v.105, p.101. Here it may be interestingly noted that the term 'logarithm' is derived from the two Greek words 'Logos' (ratio) and 'arithmos' (number) (Cf. Smith, p.513).
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The concept of the 'ardhachheda' may be traced back to the period of the AS. In it (v.423, p.349), the total number of developable human souls is stated as a number which can be divided (by two) ninety six times. The term by name occurs first in the TP (v.1.131, p.30) and thereafter in the
Arhat Vacana, 15 (4), 2003
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