पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

INTRODUCTION xxxiii
and at the other place, we have
कस्मात् कारणा । तयोर्योगवियोगस्यावियोगस·······
(BM, 35 recto)
Although the quotation occurs in a mutilated form in both
the places, but there is no doubt about the line quoted.
The occurrence of the above hemistich in the Bakhshālî
Manuscript as well as in the present commentary seems to
suggest that the work from which it has been taken was quite
popular in the north-west region of India.
Amongst the notable features of the commentary may
be mentioned (1) the use of the symbol + for the minus sign,
and (2) the use of a dot as well as a small circle for the zero.
The symbol + is generally used after the number affected, but
sometimes it is also found to be used before the number
affected. Thus, - 2 is written as 2+ , and sometimes as +2.
The symbols + and the dot are known to have been used in
the same sense in the Bakhshālî Manuscript also. Their occur-
rence in the Bakhshālî Manuscript and the present commen-
tary seems to suggest that they were in general use in the
north-west division of India.
The dot as a symbol for the zero is believed to be more
ancient than the small circle. The use of both these symbols
in the present commentary shows that the mathematicians in
the north-west region of India had not totally given up the use
of a dot and were using it as an alternative symbol for the zero.
In other parts of India the use of the dot was totally given up
and do we not find it used in any other work written after the
seventh century A.D. Absence of the use of a small circle as
a symbol for the zero in the Bakhshālî Manuscript shows that
this work is much older than the present commentary.
There are five places in the present commentary where
the scribe of the manuscript has made certain interpolations
by way of filling up the apparent gaps in the commentary.
In all these places, however, he has clearly stated what inter-
polations he has made.