28 
GREEK NUMERICAL NOTATION 
EG 
parts, except f, which had a special sign <^> or < j : r > ; the 
submultiples were denoted by writing <zr> over the corre 
sponding whole number; thus 
mTni = -is > QQQ Hfl = xii 77 <2 nnn = TiVo • 
HU && nm 
Babylonian systems. 
(a) Decimal. (/3) Sexagesimal. 
The ancient Babylonians had two systems of numeration. 
The one was purely decimal based on the following signs. 
The simple wedge | represented the unit, which was repeated 
up to nine times: where there were more than three, they 
were placed in two or three rows, e.g. Xjft = 4, y|| = 7. 10 
was represented by 11 would therefore be . 100 had 
the compound sign and 1000 was expressed as 10 hun 
dreds, by the prefixed ^ (10) being here multiplicative. 
Similarly, the was regarded as one sign, and «1- de 
noted not 2000 but 10000, the prefixed ^ being again multi 
plicative. Multiples of 10000 seem to have been expressed 
as multiples of 1000; at least, 120000 seems to be attested 
in the form 100.1000 + 20.1000. The absence of any definite 
unit above 1000 (if it was really absent) must have rendered 
the system very inconvenient as a means of expressing large 
numbers. 
Much more interesting is the second Babylonian system, 
the sexagesimal. This is found in use on the Tables of 
Senkereh, discovered by W. K. Loftus in 1854, which may go 
back as far as the time between 2300 and 1600 b.c. In this 
system numbers above the units (which go from 1 to 59) are 
arranged according to powers of 60. 60 itself was called 
sussu ( = soss), 60 2 was called sar, and there was a name also 
(ner) for the intermediate number 10.60 = 600. The multi 
ples of the several powers of 60, 60 2 , 60 3 , &c., contained in the 
number to be written down were expressed by means of the 
same wedge-notation as served for the units, and the multi 
ples were placed in columns side by side, the columns being 
appropriated to the successive powers of 60. The unit-term 
was folic 
success! v 
&c., beh: 
Thus g 
«Rf < 
larly we 
represent 
Babylon! 
is here v 
The si 
for 0 (in 
and a fi: 
position-' 
system 0 
Senkerel 
appears i 
used for 
inconven 
cation ta 
however, 
expressin 
Hilprechi 
part in ' 
= 60 8 + ] 
units of 8 
notation, 
gesimal. 
the base < 
the authc 
of a base 
advantag 
To reti 
all dates, 
but the ; 
things as 
made to