Mayi] PROCEEDINGS. [1854.
THE RHIND MATHEMATICAL PAPYRUS.By F. L. Griffith.PartII.( Contintied from page173.)PartI. —Tables and Rule to facilitate the employment
of Fractions.Section 1. — Table of expressions in simple fractions
(stamm-briiche)for the ratios of 2 to the oddnumbers
from 3 to 99. (Eisenlohr,PL I-VIII; Commentar,pp. 30-
48).Sincethe Egyptians possessedno expressions for fractions with
a numerator above unity, they were compelled to exercise their
ingenuity in order to make the root-fractions (stamm-bruche in
German)servethe same end. They werenot satisfied withsuch
clumsyexpressionsas TV + Vr + t? + tV + tV + tV + tV for tV :
consideringthe notion of T7, as the division of 7 by 1 5, they could
havereckoned 5 -f- 1 5 = J, 2 remaining; to be divided by 1 5 : this
latterwouldthenbe found to be equivalent to -jV + A, so that the
notion-fa could be expressed as \ + ^ + 3V.
Nowit has been pointedout by Professor Cantorthat any simple
fraction can be resolved into stamm-bruche by subdivision into
stamm-bruche(i-fractions)and 2-fractions(giventhatA = i + o's'
t"t = tV + t't + A = t't + 1 + A = i + tV + Vj). and that the
Egyptiansbecameawareof this.
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