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

12

INTRODUCTION.

"It is said that the composing the Lilavati was occasioned by the
following circumstance. Lilavati was the name of the daughter of
the author, Bhascara, concerning whom it appeared, from the qualities
of the ascendant at her birth, that she was destined to pass her life
unmarried, and to remain without children. The father ascertained
a lucky hour for contracting her in marriage, that she might be firmly
connected, and have children. It is said that when that hour
approached he brought his daughter and his intended son near him.
He left the hour-cup on the vessel of water, and kept in attendance a
time-knowing astrologer, in order that when the cup should subside in
the water, those two precious jewels should be united. But, as the
intended arrangement was not according to destiny, it happened that
the girl, from a curiosity natural to children, looked into the cup, to
observe the water coming in at the hole, when by chance a pearl
separated from her bridal dress, fell into the cup, and, rolling down
to the hole, stopped the influx of the water. So the astrologer waited
in expectation of the promised hour. When the operation of the cup
had thus been delayed beyond all moderate time, the father was in
consternation, and examining, he found that a small pearl had stopped
the course of the water, and that the long-expected hour was past.
In short, the father, thus disappointed, said to his unfortunate daughter,
I will write a book of your name, which shall remain to the latest
times: for a good name is a second life, and the groundwork of
eternal existence."
There are several commentaries in Sanscrit extant on this work.
The oldest on the Lilavati was composed about A.D. 1420. Another
bears a date corresponding to A.D. 1545, and exhibits a copious
exposition of the text of the Lilavati, with demonstrations of the
rules. Frequent references in one of the commentaries on the Lilavati
are made to Arya-Bhatta, who was regarded as the most ancient of
their uninspired writers. He flourished not later than the fifth
century, but probably as early as the third or fourth century of the
Christian era.
It is highly probable he was the chief of those who improved and
advanced the science of arithmetic to that state of perfection at which
it has been nearly stationary in Hindustan for ages. The Hindus
themselves can give no account of the origin or discovery of the
science of arithmetic, nor even of the decimal notation, one of the
most simple, and at the same time the most perfect of inventions.
One of their commentators writes, that "the invention of nine figures
with device of place to make them suffice for all numbers, is ascribed
to the beneficent Creator of the universe." This opinion at least
points to a period of great antiquity, probably antecedent to the
existence of any written account of the invention.
La Place, in his great work, has expressed the following opinion
of the Indian notation:-" The idea of expressing all quantities by
nine figures whereby is imparted to them both an absolute value and
one by position, is so simple, that this very simplicity is the reason for
our not being sufficiently aware how much admiration it deserves. But
it is this simplicity, and the facility which calculations acquire by
it, that raises the arithmetical system of the Indians to the rank of
the most useful inventions. How difficult it was to discover such
a method may be inferred from the circumstance that it escaped
the talents of Archimedes and Apollonius of Perga, two men of the
most profound genius of antiquity."