Elementary arithmetic, with brief notices of its history... by Robert Potts.

INTRODUCTION.

9

It seems obvious that had Archimedes and Apollonius proceeded
on the same principle for all numbers, their arithmetic would have
been greatly improved. And in expressing a number of significant
figures, it is strange that it was not perceived that no subscribed
marks would be necessary, as the position of the symbols alone would
be sufficient to indicate what orders of numbers the symbols were
intended to represent. The only difficulty that could arise would be
when all the different orders were not entirely filled up. This difficulty in the Indian method has been overcome by the introduction of
the character 0, whose numeral value is nothing by itself, but which
serves to keep every other symbol in the place of order it is intended
to occupy. It is extraordinary that this should have remained altogether undiscovered by so acute a people as the Greeks, when its necessity seems to arise so naturally from the case itself.
In an article by Mr. Whish in the first part of the Transactions of
the Literary Society of Madras,1 "On the Alphabetical System of the
Hindus," mention is made of a mathematical tract named after its
author Arya-Bhatta. This tract contains a very ancient system of
numerical notation by means of the letters of the Sanscrit alphabet.
Mr. Whish states that he has been unable to discover whether the
notation had been in use before the time of the author, or whether he
invented it himself, and adds that he is not aware of its use among
mathematicians, not having found it in their works. He remarks that
the Lilavati is composed from the second chapter of the tract.
Mr. Whish also notes another system which has from time immemorial prevailed among the learned in the southern part of India, and
from an astrological work shows that this system was in existence
nearly 2000 years ago. He concludes his article in these words:"Suffice it to say, that even though the decimal scale of arithmetic has
existed from time immemorial in India, it is still well ascertained that
an alphabetical notation has been in use 1600 years ago in Northern
India, the date of its origin cannot probably now be fixed; and that
a totally different system of notation by the letters of the same
alphabet, has been in use in the South of India, the period of whose
origin, though its existence is traced back for near two chiliads of
years, is also indeterminable." This subject engaged the attention of
the late Mr. Princep, who, by means of the inscriptions and the coins of
ancient Surashtra, informs his readers that he " has been fortunate
enough to light upon a clue to the ancient forms of the Sanscrit
numerals."2 He declares that the most ancient mode of denotilag
number in the Sanscrit language, was by the use of letters in alphabetical order, but is unable to state when this system was exchanged
for that of the decimal notation, and adds that the Nagari numerals
extant on numerous monuments of the ninth and tenth centuries do not
materially differ from those at present used in India.
From some grants recorded on plates of copper, and supposed to
be of the third century, AMr. Princep discovered that some letters
denote figures which express the dates of the grants, and ho considered
that he might venture to assign six of the nine digits.
1 " Transactions of the Literary Society of Madras." "On the Alphabetical
1Notation of the Hindus." London, 1827.
2 " Essays on Indian Antiquities," by J. Princep, F.R.S., edited with notes and
additional matter by E. Thomas, late of the Bengal Civil Service. 2 vols., Svo.
1858. "Essay on the ancient Sanscrit Numerals," art. xix., vol. iL