Mar.6] PROCEEDINGS.PROCEEDINGS. [1894.1 ua = l = IO°
n met =^10 =^101
e fe/(?)*= 100 = IO!
I kha - 1,000 =
103) zeba = 10,000=101
c^=, hefnu= 100,000 = io5
HighernumeralsSenaand heh existed, but were hardlyusedin
arithmetic: e.g., 10,000,000 is usually written'v^.
Eachmultipleof unity from 1 to 9 had a separate name,and
in hieratic each of the corresponding groups was formed into a
distinctsymbol. Thesamewas the case withthe tens from 1 to 90,
but the hundreds, etc., wereexpressedin Coptic as multiples of
100, etc. — "three hundred," "three thousand," "three ten-thou
sands," etc. and the Egyptian nomenclature was probably
much the same as the Coptic : for these againthe hieratic forms
ligatures,but they are less specialised thanthosefor the units and
tens. I will not now attempt to explain the forms and names of the
Egyptianintegralnumerals.
No mathematical expressionfor infinity has been found: for zero
•^^ auti (?) occurs in Ptolemaic texts. At an early periodt Tneferseems to stand for o in subtraction, etc., properlymeaning
"good,""level."
- Fractions. The only fractions that the Egyptians could
expresswerethe divisions of unity y4, \, \, \, \, etc., but there was
no limit to the divisor, e.g., -yJ^ occursin PI. XIII, No 33. For i
theypossesseda special sign / and a special name£s, in Coptic
<ToC,XOC. The sign in its early forme=£- is believed to repre
sentthe outline of one side of the human bodyup to the arm-pit,
and thence downthe inner sideof the arm. J The literal meaning
of ks is " side," thence" one side," " one half."
All the other fractionsare expressed in hieroglyphicsby meansof
a compound with<=>. Thus 1 1 1 is 3, but p=j^ ^, |=> ^
- Sethe in A.Z., XXXI,p. 112.
t See the balance sheetof the Bulak papyrusXVIII,the counting staffin
retrie'sJllahun,PI. VIII, fig. 17, both of about the XHIth dynasty;compare
alsoAfedum,PI. VIII, IVthdynasty.
t Piehl, Proceedings,XII,p. 115, wherethe true readingalso was given : as
wellas by Erman, Sprachedes Pap. Westcar,p. 77.
167