P. HISTORY OF ' AATHEMATICAL - School of Mathematics

OLD NUMERAL SYMBOLS 23
M M M F T T T . . . . ; i.e., "Total
hva[A&a~os~] air hi T[~s] dpxijs
of expenditures during our office three hundred and fifty-three
talents. . . . .
7 7
36. The exact reason for the displacement of the Herodianic symbols
by others is not known. It has been suggested that the commercial
intercourse of Greeks with the Phoenicians, Syrians, and
Hebrews brought about the change. The Phoenicians made one important
contribution to civilization by their invention of the alphabet.
The Babylonians and Egyptians had used their symbols to
represent whole syllables or words. The Phoenicians borrowed hieratic
FIG. l2.-The computing table of Salamis
signs from Egypt and assigned them a more primitive function as
letters. But the Phoenicians did not use their alphabet for numerical
purposes. As previously seen, they represented numbers by vertical
and horizontal bars. The earliest use of an entire alphabet for designating
numbers has been attributed to the Hebrews. As previ6uslp
noted, the Syrians had an alphabet representing numbers. The
Greeks are supposed by some to have copied the idea from the Hebrews.
But Moritz Cantor1 argues that the Greek use is the older and
that the invention of alphabetic numerals must be ascribed to the
Greeks. They used the twenty-four letters of their alphabet, together
with three strange and antique letters, < (old van), (koppa), '3
(sampi), and the symbol M. This change was decidedly for the worse,
for the old Attic numerals were less burdensome on the memory inas-
1 Vorlesungen t7ber Geschichte der Mathemalik, Vol. I (3d ed., 1907), p. 25.