Mar.6J SOCIETY OF BIBLICAL ARCHEOLOGY. [1894.
2, 3, etc., andour popular terms" fractions," " two-thirds," etc.,are
all founded on this idea; but it is just as easy to conceive of £ as
the ratio or comparison between 1 and 2, % between 1 and 3,
^ between 1 and 4, etc.
I am inclined to see in the word ^-pra, the meaning "com
parison,"thence "ratio," and in the expressions re-homt,re-aftu,
" the ratio of three," " the ratio of four," thatis the ratios of (unity
to) three and to four. It is very temptingto speak of Egyptian
"ratios" instead of "fractions," but I would rather obtain the
verdictof my colleagues on this matter beforechangingthe name ;
it is a great advantageto treat Egyptian mattersfroman Egyptian
point of view, and the point of view expressed by ratio is entirely
differentfromthatexpressedby fraction ; yet, for practical purposes,
the latter name even if essentially incorrect will not mislead in
questionsof simple mathematics.
What other explanationcan be suggested? could, for instance,
f=^=>tmean" that portion(of one thing)whichbelongsto (each of)
3 (part-owners) "?
Perhapsparallelsfromotherlanguageswill settle the question.
For
ra ua £s, but "^n5*whichhas equal authority,placesthe half before
the whole : ra ks ua is hardly possible,for the larger amountalways
precedesthe smaller in enumeration ; ra ks hr ua might be used,
"the ratioof (unity to) \ added to 2"; but this is clumsy: the
fraction—- is of high importancein Egyptian arithmetic,and probably
had a more convenientname.tLimits of the fractionalexpressions.
As the <r> system did not express a numerator, it was not
adaptedfor fractions havinga numerator greaterthanunity. -J, J, \,* From " comparison" we might obtainin reference to numbers either
"difference"or " ratio": the latter is the most naturalidea; 1 when compared
to 3 appears as J of 3, rather thanas 3 minus 2.
t II occursonceas a playful monogramfor rs I -czr> I I in a very late
text ; ste Brugsch, Wlb.Sitppl.,p. 736.
170