ORDINARY ALPHABETIC NOTATION 
37 
dp]tabetic 
ber to be 
say, units 
ir numbers 
inerally the 
die inscrip- 
,'st, i. e. the 
111 may be 
ngement is 
/he numbers 
led in later 
ing Roman 
3 to express 
to 9000} the 
k; this was 
: ,A = 1000, 
:e might be 
a 'A = 1000, 
{¡XVpLOL) was 
Is would be 
•s from the 
es are used: 
r :, or separ- 
In Imperial 
stroke above 
S)v X, other 
familiar the 
ndrine scholars 
lomer with the 
led 24, doubled 
For example, 
mong these are 
, &c., and again 
numbering by 
enoting the full 
24+17 = 41. 
orthodox way of distinguishing numerals was by a horizontal 
stroke above each sign or collection of signs; the following 
was therefore the scheme (with ^ substituted 'for F repre 
senting 6, and with = 900 at the end) : 
units (1 to 9) a, &_y, 8, ?,j, fj, в; 
tens (10 to 90) I, к, A, ¡1, v, £, o, if, 9j_ 
hundreds (100 to 900) p, a, f, v, 0, x, \jr, w, ^ ; 
thousands (1000 to 9000) p, Д / y, Д f, /, f], ,0 \ 
(for convenience of printing, the horizontal stroke above the 
sign will hereafter, as a rule, be omitted). 
(S) Comparison of the two systems of numerical notation. 
The relative merits of the two systems of numerical 
notation used by the Greeks have been differently judged. 
It will be observed that the '¿miiaZ-numerals correspond 
closely to the Roman numerals, except that there is no 
formation of numbers by subtraction as IX, XL, XC ; thus 
ХХХХГ н ННННРАДАДП11М = MMMMDCCCCLXXXX VI i 11 
as compared with MMMMCMXCIX = 4999. The absolute 
inconvenience of the Roman system will be readily appreci 
ated by any one who has tried to read Boetius (Boetius 
would write the last-mentioned number as IV.DCCCCXCVIIII). 
Yet Cantor 1 draws a comparison between the two systems 
much to the disadvantage of the alphabetic numerals. 
‘ Instead he says, ‘ of an advance we have here to do with 
a decidedly retrograde step, especially so far as its suitability 
for the further development of the numeral system is con 
cerned. If we compare the older “Herodianic” numerals 
with the later signs which we have called alphabetic numerals, 
we observe in the latter two drawbacks which do not attach 
to the former. There now had to be more signs, with values 
to be learnt by heart; and to reckon with them required 
a much greater effort of memory. The addition 
AAA + ДАДД = РАД (30 + 40 = 70) 
could be coordinated in one act of memory with that of 
HHH + HHHH = ffHH (300 + 400 = 700) 
in so far as the sum of 3 and 4 units of the same kind added 
1 Cantor, Gesch. d. Math. I 3 , p. 129.