Indian Antiquary Vol 17

Author(s): John Faithfull Fleet, Richard Carnac Temple
Publisher: Swati Publications

Page 41

FEBRUARY, 1888.]
THE BAKHSHALI MANUSCRIPT.
35
bhd 32
8
+
8
+
8
+
might perhaps be explained by the fact that, in its transfer to the Saradå alphabet, the
phalam 108 letter ka has snffered less change of form than many others of the old Aśôka characters.
means * X 32 = 108, and may be thus erHowever, for the present, the question must plained, "a certain number is found by dividbe left an open one.
ing with and multiplying with 32; that A whole number, when it occurs in an arithmetical operation, as may be seen from the
number is 108." above given examples, is indicated by placing
The dot is also used for another purpose, the number ander it. This, however, is a
namely as one of the ten fundamental figures practice which is still occasionally observed
of the decimal system of notation, or the
sero (0 1 2 3 4 5 6 7 8 9). It is still so used in in India. It may be worth noting that the number 1 is always designated by the word
India for both purposes, to indicate the un
known quantity as well as the naught. With rúpa ; thus sarúpa or rúpadhika 'adding one,' rúpõna deducting one. The only other in
us the dot, or rather its substitate the circle stance of the use of a symbolic numeral word
(O), has only retained the latter of its two is the word rasa for six,' which occurs once
intents, being simply the zero figure, or the in an example in the fifty-third sútra.
mark of position' in the decimal system. The following statement, from the first
The Indian usage, however, seems to show example of the twenty-fifth stra, affords a
how the zero arose, and that it arose in India. good example of the system of notation em
The Indian dot, unlike our modern zero, is not ployed in the Bakhshali arithmetic :
properly a numerical figure at all. It is simply
a sign to indicate an empty place or a hiatus. i bhá 32 phalan 108 This is clearly shown by its name súnya 8 + 9 + 3+
"empty.' The empty place in an arithmetical
statement might or might not be capable of Here the initial dot is used very much in the
being filled up, according to circumstances. same way as we use the letter to denote the
Occurring in a row of figures arranged deciunknown quantity the value of which is sought.
mally or according to the value of position, The number 1 under the dot is the sign of the
the empty place could not be filled up, and the whole (in this case, unknown) number. A
dot therefore signified naught,' or stood in the fraction is denoted by placing one number
place of the zero. Thus the two figures 3 and under the other without any line of separation;
7, placed in juxtaposition (37) mean thirtythus, is , i. e. one-third. A mixed number is
seven,' but with an empty space' interposed shown by placing the three numbers under
between them (
3 7), they mean 'three hundred one another ; thus is 1 + for 1}, i. e. one and seven.' To prevent misunderstanding
the presence of the empty space' was indiand one-third. Hence i means 1-$ (i. e. f). cated by a dot (
37); or by what is now the Multiplication is usually indicated by placing
zero (307). On the other hand, occurring in the numbers side by side ; thus
the statement of a problem, the empty place i phalani 20,
could be filled up, and here the det which
marked its presence, signified a something means X 32 = 20. Similarly in
which was to be discovered and to be put in means x x or ()', i.e. Bhd is an
the empty place. In the course of time, and
ont of India, the latter signification of the abbreviation of bhiga, part,' and means that
dot was discarded ; and the dot thus becamo the number preceding it is to be treated as
simply the sign for 'nanght' or the zeru, and a denominator. Hence thú means assumed the value of a proper figure of the
decimal system of notation, being the mark 1: or. The whole statement, therefore of position.' In its double signification, which
3
+
+
3+
• This word was at first read by me tipa. The rending ripa was suggested to me by Professor A. Weber
of Berlin, and it is. I have now no doubt, the correct one