EGYPTIAN AND BABYLONIAN NOTATION 29
was followed by similar columns appropriated, in order, to the
successive submultiples ~ s —&c., the number of sixtieths,
60 60 z
&c., being again denoted by the ordinary wedge-numbers.
Thus W « m ii represents 44.60 2 + 26.60 + 40 = 160,000 ;
«m «r <«in = 27.60 2 + 21.60 + 36 = 98,496. Simi
larly we find «< «< representing 30 +|§ and «< <«Im
representing 30 + •§£; the latter case also shows that the
Babylonians, on occasion, used the subtractive plan, for the 27
is here written 30 minus 3.
The sexagesimal system only required a definite symbol
for 0 (indicating the absence of a particular denomination),
and a fixed arrangement of columns, to become a complete
position-value system like the Indian. With a sexagesimal
system 0 would occur comparatively seldom, and the Tables of
Senkereh do not show a case; but from other sources it
appears that a gap often indicated a zero, or there was a sign
used for the purpose, namely i, called the ‘divider’. The
inconvenience of the system was that it required a multipli
cation table extending from 1 times 1 to 69 times 59. It had,
however, the advantage that it furnished an easy means of
expressing very large numbers. The researches of H. V.
Hilprecht show that 60 4 = 12,960,000 played a prominent
part in Babylonian arithmetic, and he found a table con
taining certain quotients of the number
= 60 8 + 10.60 7 , or 195,955,200,000,000. Since the number of
units of any denomination are expressed in the purely decimal
notation, it follows that the latter system preceded the sexa
gesimal. What circumstances led to the adoption of 60 as
the base can only be conjectured, but it may be presumed that
the authors of the system were fully alive to the convenience
of a base with so many divisors, combining as it does the
advantages of 12 and 10.
Greek numerical notation.
To return to the Greeks. We find, in Greek inscriptions of
all dates, instances of numbers and values written out in full;
but the inconvenience of this longhand, especially in such
things as accounts, would soon be felt, and efforts would be
made to devise a scheme for representing numbers more
