THE ORDINARY ALPHABETIC NUMERALS 33
([0]aXaT?7?;
d from some
ce from the
dng through
tury form \
century the
e San which
r e form of 7r).
nician V au (F)
pa = Qoph (9)
;t ended with
m apparently
etters <h, X, 9
numerals are
j nine denote
die tens, from
m 100 to 900.
= 100
= 200
= 300
= 400
= 500
= 600
= 700
= 800
)] = 900
, form of the
ghth centuries
a its similarity
numerals was
it from the
for numerical
i. The earliest
ipears to be in
after 450 B.c.
solemn built at
ed to the time
ath the letters
TNA = 754 and ZpP = 293. A list of priests of Poseidon
at Halicarnassus, attributable to a date at least as early as the
fourth century, is preserved in a copy of the second or first
century, and this copy, in which the numbers were no doubt
reproduced from the original list, has the terms of office of the
several priests stated on the alphabetical system. Again, a
stone inscription found at Athens and perhaps belonging to
the middle of the fourth century b.c. has, in five fragments
of columns, numbers in tens and units expressed on the same
system, the tens on the right and the units on the left.
There is a difference of opinion as to the approximate date
of the actual formulation of the alphabetical system of
numerals. According to one view, that of Larfeld, it must
have been introduced much earlier than the date (450 b.c. or
’a little later) of the Halicarnassus inscription, in fact as early
as the end of the eighth century, the place of its origin being
Miletus. The argument is briefly this. At the time of the
invention of the system all the letters from A to fi, including
F and 9 in their proper places, were still in use, while
Ssade (T, the double ss) had dropped out; this is why the
last-named sign (afterwards ~^) was put at the end. If
C (= 6) and 9 (= 90) had been no longer in use as letters,
they too would have been put, like Ssade, at the end. The
place of origin of the numeral system must have been one in
which the current alphabet corresponded to the content and
order of the alphabetic numerals. The order of the signs
9, X, T shows that it was one of the Eastern group of
alphabets. These conditions are satisfied by one alphabet,
and one only, that of Miletus, at a stage which still recognized
the Vau (f) as well as the Koppa (9). The 9 is found along
with the so-called complementary letters including il, the
latest of all, in the oldest inscriptions of the Milesian colony
Naucratis (about 650 b.c.); and, although there are no
extant Milesian inscriptions containing the F, there is at all
events one very early example of F in Ionic, namely Aya-
(n\eFo (Ayaa-iXijFov) on a vase in the Boston (U.S.) Museum
of Fine Arts belonging to the end of the eighth or (at latest)
the middle of the seventh century. Now, as D. is fully
established at the date of the earliest inscriptions at Miletus
(about 700 b.c.) and Naucratis (about 650 b.c.), the earlier
1523 X)
