Page:The Rhind Mathematical Papyrus, Volume I.pdf/130

114 c

d

e

This problem is interesting since it gives a very full table of fractional parts of a hekat in terms of "Horus eye" fractions and in terms of the hînu. There are a few errors in the papyrus and in some places it is difficult to determine just what the author intended to write. In the translation given above I have made the corrections that seem most probable.

Except for the ﬁrst section, which is a repetition of Problem 80, the table is in three columns. The first column gives an expression in "Horus eye" fractions. the second column in terms of the hînu and the third (in red in the papyrus) as a simple part of a hekat. In section a this third column was placed before the other two and written in black. Peet has suggested (page 124) that the scribe, writing the black portions ﬁrst, forgot to leave room for this ﬁrst red section in its proper place.

In the fourth and ﬁfth lines of section a the quantities expressed are$1/undefined$$2/3$ and $1/undefined$$1/undefined$ hekat. equal to 5 and 3 times 56 hekat. In the third column (placed in the papyrus before the other two) the author wrote 51; and 3. If $1/undefined$ were a mistake for 5, a superfluous dot being inserted. we might suppose that he thought of $1/undefined$ hekat as a kind of unit of which he takes 5 and 3. respectively. The expressions in these two lines are given correctly as lines 1 and 2 of section d.

The sixth line of section 'a, as written in the papyrus, is the most confusing. The best explanation seems to be that the author intended to write $1/undefined$ of a hekat getting this line by halving the quantities in the third line, although he says $1/undefined$. In the him; column he wrote for 3$1/undefined$,3$1/undefined$$1/undefined$$1/undefined$. and in the third line for 6$1/undefined$, 6$1/undefined$$1/undefined$. In a large part of the table the fractions of a hînu happen to be fractions whose denominators are powers of 2 like the "Horus eye" fractions and it may be that he attempted to write the fractions in the third and sixth lines in this way. In lines 3 and 4 of section d he gives correctly