34
GREEK NUMERICAL NOTATION
extension of the alphabet by the letters $ X t must have
taken place not later than 750 b.c. Lastly, the presence in
the alphabet of the Van indicates a time which can hardly
be put later than 700 B.c. The conclusion is that it was
about this time, if not earlier, that the numerical alphabet
was invented.
The other view is that of Keil, who holds that it originated
in Dorian Caria, perhaps at Halicarnassus itself, about
550-425 B.c., and that it was artificially put together by
some one who had the necessary knowledge to enable him
to fill up his own alphabet, then consisting of twenty-four
letters only, by taking over F and 9 from other alphabets and
putting them in their proper places, while he completed the
numeral series by adding T at the end. 1 Keil urges, as
against Larfeld, that it is improbable that F and 41 ever
existed together in the Milesian alphabet. Larfeld’s answer 2
is that, although F had disappeared from ordinary language
at Miletus towards the end of the eighth century, we cannot
say exactly when it disappeared, and even if it was practically
gone at the time of the formulation of the numerical alphabet,
it would be in the interest of instruction in schools, where
Homer was read, to keep the letter as long as possible in the
official alphabet. On the other hand, Keifs argument is open
to the objection that, if the Carian inventor could put the
F and 9 into their proper places in the series, he would hardly
have failed to put the Ssade T in its proper place also, instead
of at the end, seeing that T is found in Caria itself, namely
in a Halicarnassus (Lygdamis) inscription of about 453 B.C.,
and also in Ionic Teos about 476 h.c. 8 (see pp. 31-2 above).
It was a long time before the alphabetic numerals found
general acceptance. They were not officially used until the
time of the Ptolemies, when it had become the practice to write,
in inscriptions and on coins, the year of the reign of the ruler
for the time being. The conciseness of the signs made them
‘particularly suitable for use on coins, where space was limited.
When coins went about the world, it was desirable that the
notation should be uniform, instead of depending on local
alphabets, and it only needed the support of some paramount
1 Hermes, 29, 1894, p. 265 sq. 2 Larfeld, op. cit., i, p. 421.
3 lb., i, p. 358.
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