Indian Antiquary Vol 17

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

Page 43

FEBRUARY, 1888.]
THE BAKHSHALI MANUSCRIPT.
37
3rd century A. D., when the proper Sanskrit, how much is spent in one day P" Here it is hitherto the language of the Brahmanic schools, explained that the lower denomination (adhagradually came into general use also for secular ch-chheda) is 360 days, and the result (plula) compositions. The older literary language may
1807 : 2168400727 have lingered on some time longer among the Brent 240 * 727 800 360 Buddhists and Jains, but this would only have In connection with this question of the age been so in the case of religions, not of secular, of the Bakhshali work, I may note a circumcompositions. Its use, therefore, in the Bakh- stance which appears to point to a peculiar shali arithmetic points to a date not later than connection of it with the Brahma-Siddhanta the 3rd or 4th century A. D. for the composition of Brahmagupta. There is a curious resemof that work.
blance between the fiftieth sútra of the Bakh. In the third place, in several examples, the shali arithmetic, or rather with the algebraical two words dinára and dramma occur as deno- example occurring in that sútra, and the fortyminations of money. These words are the ninth sútra of the chapter on algebra in the Indian forms of the Latin denarius and the Brahma-Siddhánta. In that sitra, BrahmaGreek drakhme. The former, as current in gupta first quotes a rule in prose, and then adds India, was a gold coin, the latter a silver coin. another version of it in the aryú measure. Golden denarii were first coined at Rome in Unfortunately the rule is not preserved in the B. C. 207. The Indian gold pieces, corres- Bakhshali MS., but, as in the case of all other ponding in weight to the Roman gold denarius, rules, it would have been in the form of a were those coined by the Indo-Scythian kings, slöka and in the North-Western Prakrit (or whose line, beginning with Kadphises, about Gåthå dialect). Brahmagapta in quoting it, the middle of the 1st century B. C., probably would naturally put it in what he considered extended to abont the end of the 3rd century correct Sanskrit prose, and would then give A.D. Roman gold denarii themselves, as shown his own version of it in his favourite dryk by the numerous finds, were by no means measure. I believe it is generally admitted uncommon in India, in the earliest centuries that Iudian arithmetic and algebra, at least, of our era. The gold dináras most numerously
are of entirely native origin, While Siddhantafound are those of the Indo-Scythian kings
writers, like Brahmagupta and his predecessor Kanishka and Huvishka, and of the Roman
Aryabhaga, might have borrowed their astroemperors Trajan, Hadrian and Antoninus Pius,
nomical elements from the Groeks or from all of whom reigned in the 2nd century
books founded themselves on Greek science, A.D. The way in which the two terms are
they took their arithmetic from native Indian used in the Bakhshalt arithmetic seems to
sonroes. Of the Jains it is well known that indicate that the gold dinara and the silver
they possess astronomical books of a very dramma formed the ordinary currency of the
ancient type, showing no traces of western or day. This circumstance again points to some
Greek influence. In India arithmetic and time within the three first centuries of the
algebra are usually treated as portions of works Christian era as the date of its composition,
on astronomy. In any case it is impossible A fourth point, also indicative of antiquity,
that the Jains should not have possessed their which I have already adverted to, is the
own treatises on arithmetic, when they pos. peculiar use of the cross (+) as the sign of
sessed sucb on astronomy. The early Buddhists, the negative quantity.
too, are known to have been proficients in There is another point which may be worth
mathematics. The prevalence of Buddhism mentioning, though I do not know whether it
in North-Western India, in the early centuries may help in determining the probable date of
of our era, is a wellknown fact. That in the work. The year is reckoned in the Bakh
those early times there were also large Jain shali arithmetic as consisting of 360 days.
communities in those regions, is testified by Thus in one place the following calculation is
the remnants of Jain sculptare found near given :-“If in of a year, 2982 193 is spent, Mathura and elsewhere. From the fact of
• Seo poto 4 at the end of this article, also note 5.