________________
DVL, JDPS (vv.12.66-67, p.230 and 12.77-78, p.231), TLS, GJK (v.215, p.129 etc.) and so forth.
Here, it should be noted that with the Neo-Pythagoreans the 'even-times even' number is that which has its halves even, the halves of the halves even, and so on till unity is reached; in short, it is a number of the form 2" (Cf. Heath, Part-1, p.72).
[3.2] A.N: Singh (p.7) followed by L.C. Jain (1982, pp.29 and 51) opines
that
[a] the consideration of the ardhachheda was certainly inspired by mediation. and
[b] mediation must have been current in India before the advent of the place value numerals.
Here we should turn our mind to the fact that the operation of mediation was considered important when the place value numerals were unknown. It was considered to be important by Egyptians and Greeks and was recognized as such in their works on Arithmetic.7
By the way, in India the Jaina school traces this operation through the AS (v.423, p.349) wherein the total nu,ber of developable human souls is stated as a number which can be divided (by two) ninety six times.
[3.3] VARGASALĀKĀ
Nemicandra defines this term as follows:
वग्गिदवारा वग्गसलागा रासिस्स अद्धछेदस्स ।
The number of times that (2 is successively) squared (until a particular number is obtained) is the vaggasalāgā (vargasalākā in Sanskrit) of the number (rasi, rasi in Sanskrit).
That is to say that if
For instance,
R = 22,
then is called the vargasalaka of R. Denoting the vargasalākā by the abbreviation VS, we can write the above as
VS(R) = r.
(TLS, v.76, the first two quarters, p.69)
Arhat Vacana, 15 (4), 2003
Jain Education International
VS(65536) = 4. अध्दिदवारा वा खलु
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