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

4

INTRODUCTION.

are too numerous, both in the numerals and in other fragments of
elementary names, to be regarded as merely accidental. And considering the remote period alluded to, being above four thousand years,
the mind is naturally led to the conclusion that the fragments of these
primeval names are derived by each language from one of its
cognates, or by all from one common source.
Little is known respecting the origin and the early history of
arithmetic of the ancient Hebrews or Syrians.1 It has been conjectured that they were indebted to the Phoenicians, their neighbours,
for what they knew of the art of numbering. The most ancient
books-the writings of Moses-afford no evidence of the use of any
numerical system of notation. In the text of the writings of Moses
all numbers are expressed in words atlength, and the counting is
made by tens, hundreds, &c.
It is clear from the second chapter of the Second Book of the
Chronicles that the Hebrews had commercial intercourse with the
Phoenicians above a thousand years before the times of the Messiah.
And the ancient tradition of the Greeks also tends to favour the
opinion that Cadmus [Tip], a man from the East, was the first who
introduced the use of letters into Greece from the Phoenicians. And
it may be added that Proclus, in his Commentary on the First Book
of Euclid's Elements, states that the Phoenicians, by reason of their
traffic and commerce, were accounted the first inventors of arithmetic.
The ancient Hebrew and Samaritan alphabets consisted of twentytwo letters, and were employed to denote the nine digits, the nine
tens, and the first four of the nine hundreds. The remaining five
hundreds were represented by combining the symbols of the first four
hundreds. In later times the final caph, mern, num, pe, tsadi were
added to make up the nine simple characters for the hundreds. All
other numbers were expressed by placing together the simple characters denoting the component numbers required to make up their
amount, with some few exceptions. The number 15 is denoted
by t0, or 9 and 6, and not by i,, 10 and 5; because rn, Jah, being
one of the names of God, it was imagined that such a use of the
name would infringe the third commandment. For the same reason,
perhaps, the number 1030 was not expressed by the characters L,
which form another of the names of the Deity.
The following are the characters of the Hebrew and Greek Alphabets, as they are applied to denote numbers:1 2 3 4 5 6 7 8 9
Units 3;1 I n t, Hebrew.
aoq~ 7 e, 0, Greek.
Tens P 3 b 3 D 7 5, Hebrew.
es K A o r i, Greek.
Hundreds P I) C D T ) V, Hebrew.
p r T v p X 4 w - ),Greek.
1 In the third volume of the new series of the Journal of Sacred Literature, Dr.
WV. Wright, the Professor of Arabic at Cambridge, has explained in his notice
(pp. 128-130) of the Aneicdota Syriaca of Dr. Land, a system of arithmetical notation employed in many of the oldest Syrian manuscripts not later than the ninth
century. There are simple characters to denote 1, 2, 5, 6, 10, 20, 100; and those
appear to have been combined to express other numbers, in some respects like the
liomian notation.