P. HISTORY OF ' AATHEMATICAL - School of Mathematics

OLD NUMERAL SYMBOLS 17
Proof.-5 + 3 -,I4- is multiplied by (1 + a) and the partial products
are added. In the first line of the proof we have 5 + 3 ilp, in the second
line half of it, in the third line one-fourth of it. Adding at first only
the integers of the three partial products and the simpler fractions
3, 4, a, a, +, the partial sum is 9 + &. This is a & short of 10. In the
fourth line of the proof (1.9) the scribe writes the remaining fractions
and, reducing them to the common denominator 56, he writes (in
&
- &
HI~~O~LIPIIIQUFS.
crcux cL plain.
C111lli~ connnun
11cv diz;~illes :
fn Ot1
n
SlChES
III~~ATIQUES,
nvec lnrianles.
xXb
% X
X X
+A
17
LETTRES
mu~inr~nr
cul'les.
-
1
-
K
-
2,
-
-
II
-
z
-
0
U S
3%
/
N(14
80
VALECR
der
s'onus.
--
10
3~
30
bo
50
(io
50
I
Db 'ONung EII
clialecle tl~i.bsiin.
tnetrl.
djOu61.
innab.
hme.
laiorc.
re.
chfe.
inetbe.
FIG. 8.-Hieroglyphic, hieratic, and Coptic numerals. (Taken from A. P.
Pihan, Ezposi des signes de numtalion [Paris, 18601, p. 26, 27.)
red color) in the last line the numerators 8,4,4, 2, 2, 1 of the reduced
fractions. Their sum is 21. But 21 --=- 14+7 --- I I which is the exact
56 56 4 8'
amount needed to make the total product 10.
A pair of legs symbolizing addition and subtraction, as found in
impaired form in the Ahmes papyrus, are explained in 5 200.
25. The Egyptian Coptic numerals are shown in Figure 8. They
are of comparatively recent date. The hieroglyphic and hieratic are