THE DECIMAL SYSTEM 
27 
23-911 a 4. 
1 Boetius, De Inst. Ar., &c., p. 395. 6-9, Friedlein. 
AKITH- 
ollowed the 
ready been 
There are, 
in terms of 
w (to ‘ five ’) 
es was pro 
as ; five was 
and the use 
ate category 
i was found 
)olism estab- 
arithraetical 
at to such a 
was in use 
a vigesimal 
Bnch quatre- 
?, three-score 
hmal system, 
ations, is to 
/e practice of 
then of both 
tion (making 
t was mooted 
eks, count up 
,s 2, 3, 4, or 5, 
s-five (for 6), 
two-p/us-five (for 7), as they say one-p£ws-ten (evSeKa, for 11), 
two-pius-ten (ScoStKa, for 12), while on the other hand they 
do not go beyond ten for the first halting-place from which to 
start again repeating the units'? For of course any number 
is the next before it plus 1, or the next before that plus 2, 
and so with those preceding numbers ; yet men fixed definitely 
on ten as the number to count up to. It cannot have been 
chance; for chance will not account for the same thing being 
done always: what is always and universally done is not due 
to chance but to some natural cause.’ 
Then, after some fanciful suggestions (e.g, that 10 is a 
‘ perfect number ’), the author proceeds: 
‘ Or is it because men were born with ten fingers and so, 
because they possess the equivalent of pebbles to the number 
of their own fingers, come to use this number for counting 
everything else as well ? ’ 
Evidence for the truth of this latter view is forthcoming in 
the number of cases where the word for 5 is either the same 
as, or connected with, the word for ‘ hand Both the Greek 
\eip and the Latin manus are used to denote ‘ a number ’ (of 
men). The author of the so-called geometry of Boetius says, 
moreover, that the ancients called all the numbers below ten 
by the name digits (‘ fingers ’J. 1 
Before entering on a description of the Greek numeral signs 
it is proper to refer briefly to the systems of notation used 
by their forerunners in civilization, the Egyptians and 
Babylonians. 
Egyptian numerical notation. 
The Egyptians had a purely decimal system, with the signs 
I for the unit, n for 10, @ for 100, ^ for 1,000, 'j for 10,000, 
for 100,000. The number of each denomination was 
expressed by repeating the sign that number of times; when 
the number was more than 4 or 5, lateral space was saved by 
arranging them in two or three rows, one above the other. 
The greater denomination came before the smaller. Numbers 
could be written from left to right or from right to left; in 
the latter case the above signs were turned the opposite way. 
The fractions in use were all submultiples or single aliquot