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

10

INTRODUCT ION.

On some Surashltra coins, besides a legend in corrupted Greek
characters, he observed a few strange marks, which he found to be
numerals of the same form and equal variety as those on the copperplate grants. He also remarks that there are varieties in some of the
forms of the nine numerals; and besides that, in many of the ancient
systems, separate symbols were used to denote 10, 20, &c., in combination with the nine units severally.
Mr. Princep further states in his essay, that he was in hopes of
tracing the ancient Sanscrit symbols of number by a comparison of
them with the numeral systems of those Indian alphabets which have
most resemblance to the forms of the earliest centuries. In a plate he
exhibits the forms of the numeral letters of several alphabets, and
remarks: "Upon regarding attentively the forms of many of the
numerals, one cannot but be led to suppose that the initial letters of
the written names were, many of them, adopted as their numerical
symbols." This similarity may clearly be seen in the forms of some
of the Sanscrit numerals, and his editor observes: "It is possible that
the new data, which has lately become available, may contribute
materially to solve the general problem of the system under which the
ancient Indian scheme was primarily conceived."
The oldest treatise known to be extant on decimal arithmetic forms
the twelfth chapter of a System of Astronomy written by Brahmegupta in India. Mr. Colebrooke has determined with great probability that this writer flourished in the sixth or at the beginning
of the seventh century of the Christian era, and antecedent therefore
to the cultivation of those sciences by the Mohammedans. It is
written in Sanscrit verse, and comprises twenty-one chapters. The
twelfth treats of arithmetic, and is divided into ten sections: Algorithm, Mixture, Progression, Plane Figure, Excavations, Stacks, Saw,
Mounds of Grain, Measure of Shadow, Supplement.
There is also a perpetual commentary on the whole work. Each
verse of the text is quoted at length, and interpreted with elucidations
and remarks. It is moreover certain that this treatise on arithmetic
was not the first written in Hindustan. It is impossible to doubt of
the knowledge of these sciences, and of their wide extension long
before they assumed the form in which they are found in writing.
The fact of a treatise on arithmetic being found in the midst of a
system of astronomy, and the employment of the principles of one
science used to aid in the development of another, afford a very strong.presumption in favour of their existence in a previous age, and of
their having passed through many stages of addition and improvement.
This treatise, though the most ancient known, is not so complete
or extensive as the Lilavati,1 another treatise on arithmetic, which
1 The oldest treatise on arithmetic possessed by the Hindus, the Lilavati,
remounts no higher than the eleventh century of our era. This famous composition,
to which the vanity and ignorance of that people claim a divine original, is but a
very poor performance, containing merely a few scanty precepts couched in obscure
memorial verses. The examples annexed to these rules, often written probably by
later hands in the margin, are generally trifling and ill-chosen. Indeed, the
Lilavati exhibits nothing that deserves the slightest notice, except the additions
made by its Persian commentators. The Hindus had not the sagacity to perceive
the various advantages to be derived from the denary notation. They remained.
entirely ignorant of decimal fractions, with which their acute neighlbours, the
Chinese, have been familiarly acquainted from the remotest ages. Their nume-: