J
>tlier hand
t + v = \Js.
the other,
tance, 849,
.Pllll, but
more self-
important
ir and says
istake and
ulty as the
d, Tannery,
r could only
r use until,
rchimedes’s
abetic nota-
y suspected
with Greek
to views are,
iurely we do
ut with the
for instance,
the figure 3
7 ; what we
ly the Greek
kou reacrapes
, this would
red and four
rerpaKocrLOL
or of 1000 or
ible, we say
ed by four =
or rpefy 67n
e that £ thirty
wo hundred
housand or a
(XKOVTCL yi’XiOi
K0LL Sl(T\l\iOl).
id Zeuthen), i,
COMPARISON OF THE TWO SYSTEMS 39
The truth is that in mental calculation (whether the opera
tion be addition, subtraction, multiplication, or division), we
reckon with the corresponding ivords, not with the symbols,
and it does not matter a jot to the calculation how we choose
to write the figures down. While therefore the alphabetical
numerals had the advantage over the ‘ Herodianic ’ of being
so concise, their only disadvantage,was that there were more
signs (twenty-seven) the meaning of which had to be com
mitted to memory : truly a very slight disadvantage. The
one real drawback to the alphabetic system was the absence
of a sign for 0 (zero) ; for the 0 for ovSegia or ovSer which
we find in Ptolemy was only used in the notation of sexa
gesimal fractions, and not as part of the numeral system. If
there had been a sign or signs to indicate the absence in
a number of a particular denomination, e. g. units or tens or
hundreds, the Greek symbols could have been made to serve
as a position-value system scarcely less effective than ours.
For, while the position-values are clear in such a number
as 7921 ko), it would only be necessary in the case of
such a number as 7021 to show a blank in the proper place
by writing, say, X~ koc. Then, following Diophantus's plan
of separating any number of myriads by a dot from the
thousands, &c., we could write £ ~^Ka . ^tttS for 79216384 or
X . - t - S for 70000304, while we could continually add
sets of four figures to the left, separating each set from the
next following by means of a dot,
(e) Notation for large numbers.
Here too the orthodox way of writing tens of thousands
was by means of the letter M with the number of myriads
/3 ¿pot-
above it, e.g. M = 20000, M ¿cooe = 71755875 (Aristarchus
Y
of Samos) ; another method was to write M or M for the
myriad and to put the number of myriads after it, separated
by a dot from the remaining thousands, &c., e. g."
Y
M pv-XNnS = 1507984
(Diophantus, IY. 28). ■ Yet another way of expressing myriads
was to use the symbol representing the number of myriads
with two dots over it; thus ¿¿^09/3 = 18592 (Heron, Geo
metrica, 17. 33). The word gvpidSe9 could, of course, be