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

INTRODUCTION.

11

constitutes the first part of Mr. Colebrooke's work. The Lilavati
stands as one of the preliminary portions of a course of astronomy,
by Bhascara. He informs his readers that his work is compiled and
abridged from more diffuse works, and was completed at a period
corresponding to A.D. 1150.
The Lilavati appears to have gained in past times great authority,
and to have superseded the preceding treatises, and formed the subject
of study in countries and places so remote from each other as the
north and west of Hindustan and the southern peninsula. There
is a Persian version of the Lilavati, which was undertaken by
Faizi at the command of the Emperor Acbar, and was completed
A.D. 1587.1
The occasion of writing the Lilavati, given by Faizi in the preface
to his Persian translation, was rendered into English by Mr. Strachey,
and printed in the introduction to Dr. Taylor's translation of the
Lilavati. The account2 thus proceeds:rical operations are unnecessarily complicated, following closely the procedure
which the application of an alphabet had obliged the Greeks to employ.-Leslie's
Philosophy of Arithmetic, p. 225.
There is another Eastern people [the Chinese] remarkable at once for the great
antiquity and unchangeable character of their existing institutions, who possess a
numerical language of great extent, connected with a very perfect system of
numeration.
As the Chinese are not in the possession of the method of arithmetical notation
by nine figures and zero, they clearly can have no proper claim to its invention,
however nearly in some respects they may have approximated to it; for it is next to
impossible that a system of numeration, so much more perfect and commodious than
their own, if once generally known or practised, could ever have been lost or
abandoned. —Dean Peacock's History of Arithmetic in the Encyclocedia Metropolitana,
vol. i., pp. 375, 376.
1 The following works on the Indian Arithmetic and Algebra have been translated into the English language:"Bija Ganita. or the Algebra of the Hindus," by Edward Strachey, of the East
India Company's Bengal Civil Service. London, 1813.
"Lilawati; or, a Treatise on Arithmetic and Geometry," by Bhascara Acharya
translated from the original Sanscrit by John Taylor, M.D., of the Hon. East India
Company's Bombay Medical Establishment. Bombay, 1816.
"Algebra, with Arithmetic and Mensuration," from the Sanscrit of Brahmegupta
and Bhascara; translated by Henry Thomas Colebrooke, F.R.S. London, 1817.
2 This account is not found in the Sanscrit copies of the Lilavati, nor in any
of the commentaries on that work. The language of the following questions which
appear in pages 5, 6, 21, 24, 31, of Mr. Colebrooke's translation from the Sanscrit,
supplies some internal evidence for the truth of the story:" Dear, intelligent Lilavati, if thou be skilled in addition and subtraction, tell
me the sum of 2, 5, 32, 193, 18, 10, and 100 added together; and the remainder,
when their sum is subtracted from 10,000."
" Beautiful and dear Lilavati, whose eyes are like a fawn's, tell me what are the
numbers resulting from 135 taken into 12."
"If thou be skilled in multiplication by whole or by parts, whether by subdivision
of form or separation of digits; tell me, auspicious woman, what is the quotient of
the product divided by the same multiplier."
" Pretty girl, with tremulous eyes, if thou know the correct method of inversion,
tell me what is the number, which, multiplied by three, and added to three-quarters
of the quotient, and divided by seven, and reduced by subtraction of a third part of
the quotient, and then multiplied into itself, and having fifty-two subtracted from
the product, and the square root of the product extracted, and eight added, and the
sum divided by ten, yields two?"
" Out of a swarm of bees, one-fifth part settled on a blossom of Cadamba, and
one-third on a flower of Silind'hri; three times the difference of these numbers flew
to the bloom of a Cutaja; one bee, which remained, hovered and flew about in the
air, allured at the same moment by the pleasing fragrance of a, Jasmin and Pandanus.
Tell me, charming woman, the number of bees."