Mar.6] SOCIETYOF BIBLICAL AKCII.LOLOGY. [1S94.Addition,subtraction,halvingand doubling couldbe performed
with absolutesimplicity(so long as any fractionsinvolved in the
problemdid not require reduction to a greatest commonmeasure,*
andthe result did not contain anyfractionwith numeratorabove
unity; in these cases the fractions had of course to be altered,
involvingmorethan oneoperation). Multiplicationand division
by numbers otherthan 2 were complicatedoperations: excepting
with 10 and its half 5, the results of which wereobtainedby simple
inspectionand halving, thanksto the decimal systemof notation.
Strangeto say, the Egyptians couldtake—(=§) of any integer
by a single operation, andif J of a number wasrequired,theyin
variablyfoundit by halving its _ (§). Thisshowsthattheyhad
li
a table of —p values;—r, being the largest of the Egyptian fractions,
ij ij
tookthe lead, but I cannot see that it offered any advantages over£
as a starting point,f
Addition andsubtraction, doublingandhalving,multiplication
anddivisionby 10 —these are the prime weaponswith whichthe
Egyptian scribes attacked their mathematical problems. In the
secondrankcamemultiplication anddivisionby 5, and finding the
i£ value.
Thetablesof halves, doubles,and —j- values probablywerenot
J2
carried much beyond 10. J In the case of higher numbers,the
it has no real connection withthe calculations of the abacus. The game boards,
10x3 llu commonly found(Petrie, NebeshehandDefennch, p. 74, Kahun,
P- 3o), -.; 9 x 3, very ancient(Petrie,Seasonin Egypt, p. 15), and the "counting
stick,"rrn Illahun, p. 14, may be mentioned in this connection.* Compare Proceedings,XIII,p. 535.
f — values for the table wouldno doubt be obtained by the Egyptians thus:—
Supposing— of 5 were required; make 5 into 10 halves, thenI J (3 halves) must
l4
be repeated 3 times to make 10 halves, and I half will remain.
/,.,JLofS=3i=3i.
t I have not found any certain evidence,1-9 alonewouldbe necessary; these
shorttableswereperhapsneverwrittendown,but carried in the head.
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