Mayi] PROCEEDINGS. [1894.
The dash S (in Eisenlohr's transcriptions replaced by an
a?terisk*)marksthe fractions whichare to be further utilised: in
this case the marked fractionsare to appear in the table as being the
valuesrequired.
Thetableof which the above are specimens occupies 8 columns:each column is headed with h (] ffl (or W alone I II r,|[). i
and I '=&» V\ ^ , but it was not necessaryto repeat these
wordsin the individual cases.
Theseshmtor "working out."—On glancingthroughthe table
(Conimentar,pp. 36-45), the reader will find that\ or — ( = | )
were the regular startingpointsfor the smt: even£ was obtained,
by halving \, and \ by halving |.
Fromthe starting pointof ^ or f the Egyptians proceededby
halvingonly,e.g.,in the calculation 2 ~- 13, i of 13 is required :—
£ is 6
•'• t » 3i
andin the calculation of 2 -f- 19, Jy of 19 is required :—
1 is I21- j. fi1
-. • 0 J-,, 00 li
. • 1 • A-a ,' ii J 3 1 1 -T-
Eachstepis. recordedin the papyrus wherethe problem requires
divisionof fractions, but not elsewhere; for instance, in the calcu
lationof 2 -4- 7, j'¥ °f 7 ls required :—
4 x 7 is 28.
Thuswithoutfurthertrouble\ is seen to be the answer.
In such cases, where the denominator of the fraction is a
multipleof the original divisor,the division is changed intoa multi
plicationsum. Thisis the process impliedin r\ = \ (of 5), above,
p. 204 in the calculation of 2 -f- 5.
Sometimesthe statement was rather inconsequent,e.g., in 2 -f 13,
^ and -j-^ of 13 are required.
/ 4TV i *'•'• 4 x 13 = 52 ••• <)V is i
/.8rn i 8 X 13 = 104 .'. yfr „ |.
andsometimestheywouldconfusedlywrite(in 2 -f- 31).
/ 4 124 i
/$ ittv">)t.
205