Full text: From Thales to Euclid (Volume 1)

THE ORDINARY ALPHABETIC NUMERALS 35 
must have 
presence in 
can hardly 
that it was 
;al alphabet 
it originated 
tself, about 
together by 
enable him 
twenty-four 
Iphabets and 
mipleted the 
eil urges, as 
and H ever’ 
ski’s answer 2 
ary language 
y, we cannot 
as practically 
■ical alphabet, 
chools, where 
ossible in the 
ument is open 
sould put the 
would hardly 
:e also, instead 
itself, namely 
ibout 453 B. C., 
1-2 above), 
umerals found 
used until the 
actice to write, 
a-n of the ruler 
>-ns made them 
,ce was limited, 
irable that the 
nding on local 
ome paramount 
p. dt., i, p. 421. 
political authority to secure the final triumph of the alphabetic 
system. The alphabetic numerals are found at Alexandria 
on coins of Ptolemy II, Philadelphus, assigned to 266 B.c. 
A coin with the inscription ’AXegdvSpov KA (twenty-fourth 
year after Alexander’s death) belongs, according to Keil, to 
the end of the third century. 1 A very' old Graeco-Egyptian 
papyrus (now at Leyden, No. 397), ascribed to 257 B.C., 
contains the number kO = 29. While in Boeotia the Attic 
system was in use in the middle of the third century, along 
with the corresponding local system, it had to give way about 
200 b.c. to the alphabetic system, as is shown by an inventory 
from the temple of Amphiaraus at Oropus 2 3 ; we have here 
the first official use of the alphabetic system in Greece proper. 
From this time Athens stood alone in retaining the archaic 
system, and had sooner or later to come into line with other 
states. The last certainly attested use of the Attic notation 
in Athens was about 95 b. C.; the alphabetic numerals were 
introduced there some time before 50 B.C., the first example 
belonging to the time of Augustus, and by a.d. 50 they were 
in official use. 
The two systems are found side by side in a number of 
papyrus-rolls found at Herculaneum (including the treatise 
of Philodemus De pietate, so that the rolls cannot be older than 
40 or 50 b. c.); these state on the title page, after the name of 
the author, the number of books in alphabetic numerals, and 
the number of lines in the Attic notation, e.g. EH I KOVROV i 
HERI | 0YZEHZ | IE dpiQ . . XXXHH (where IE = 15 and 
XXXHH = 3200), just as we commonly use Roman figures 
to denote Books and Arabic figures for sections or lines? 
1 Hermes, 29, 1894, p. 276 n. 
2 Keil in Hermes, 25, 1890, pp, 614-15. 
3 Reference should be made, in passing, to another, gwasi-numerical, 
use of the letters of the ordinary alphabet, as current at the time, for 
numbering particular things. As early as the fifth century we find in 
a Locrian bronze-inscription the letters A to 0 (including f then and 
there current) used to distinguish the nine paragraphs of the text. At 
the same period the Athenians, instead of following the old plan of 
writing out ordinal numbers in full, adopted the more convenient device 
of denoting them by the letters of the alphabet. In the oldest known 
example opos K indicated ‘boundary stone No. 10’ ; and in the fourth 
century the tickets of the ten panels of jurymen were marked with the 
letters A to K. In like manner the Books in certain works of Aristotle 
(the Ethics, Metaphysics, Politics, and Topics) were at some time
	        
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