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.