30 
GREEK NUMERICAL NOTATION 
concisely by means of conventional signs of some sort. The 
Greeks conceived the original idea of using the letters of the 
ordinary Greek alphabet for this purpose. 
(a) The £ Herodianic ’ signs. 
There were two main systems of numerical notation in use in 
classical times. The first, known as the Attic system and 
used for cardinal numbers exclusively, consists of the set of 
signs somewhat absurdly called £ Herodianic ’ because they are 
described in a fragment 1 attributed to Herodian, a gram 
marian of the latter half of the second century A.D. The 
authenticity of the fragment is questioned, but the writer 
says that he has seen the signs used in Solon’s laws, where 
the prescribed pecuniary fines were stated in this notation, 
and that they are also to be found in various ancient inscrip 
tions, decrees and laws. These signs cannot claim to be 
numerals in the proper sense; they are mere compendia or 
abbreviations; for, except in the case of the stroke I repre 
senting a unit, the signs are the first letters of the full words 
for the numbers, and all numbers up to 50000 were repre 
sented by combinations of these signs. I, representing the 
unit, may be repeated up to four times ; P (the first letter of 
nevre) stands for 5, A (the first letter of <5e/ca) for 10, H 
(representing eKarov) for 100, X (yfAlol) for 1000, and M 
(/wpLOL) for 10000. The half-way numbers 50, 500, 5000 
were expressed by combining P (five) with the other signs 
respectively; P, P, P, made up of P (5) and A (10), = 50; 
P, made up of P and H, = 500; F 3 = 5000 ; and = 50000. 
There are thus six simple and four compound symbols, and all 
other numbers intermediate between those so represented are 
made up by juxtaposition on an additive basis, so that each 
of the simple signs may be repeated not more than four times; 
the higher numbers come before the lower. For example, 
PI = 6, Aim = 14, HP = 105, XXXXPHHHHPAAAAPIIII 
= 4999. Instances of this system of notation are found in 
Attic inscriptions from 454 to about 95 b. c. Outside Attica 
the same system was in use, the precise form of the symbols 
varying with the form of the letters in the local alphabets. 
Thus in Boeotian inscriptions P or IT = 50, HI = 100, PHE =500, 
1 Printed in the Appendix to Stephanos's Thesaurus, vol. viii. 
V = 
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system 
other 
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50 
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system, 
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in app] 
happy 
written 
the Grei 
Yod foi 
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utilized 
Samech 
sibilants 
simple G 
spond to 
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place it 
The form 
1 Lar