Page:The Rhind Mathematical Papyrus, Volume I.pdf/124

108 That is, one of the loaves contains 25$1/undefined$ro, or $1/undefined$$1/undefined$ hekat $1/undefined$ ro.

Proof.

This problem is similar to the preceding. The reduction of the given number of hekat to ro is omitted in the papyrus, but the result, 2520, is given, and given as if it were the result of the multiplication used to prove the first part of the solution. Evidently, in copying this solution, the scribe let his eye drop from one "Total" to the next, and so left out the result of one multiplication and all the partial products of the next (Feet, page 116). See note to Problem 28.

There are some interesting steps in the first multiplication and in the first proof.We may notice also that in the first multiplication, as also in Problem 69, we have the "Horus eye" fractions given in the statement of the problem written as ordinary fractions. See Introduction, page 31, footnote 3.

Problem 71

From 1 des-measure of beer $1/undefined$ ''has heen poured of, and then the measure has been filled up with water. What is the pefsu of the diluted beer''?

Reckon the amount of besha in 1 des of beer; it is $1/undefined$ hekat. Take away $1/undefined$ of it, namely $1/undefined$ hekat; the remainder is $1/undefined$$1/undefined$ hekat. Multiply $1/undefined$$1/undefined$ hekat so as to get 1 hekat; the result is 2$1/undefined$, and this is the pefsu.

Problem 72

''Example of exchanging loaves for other loaves. Suppose it is said to thee, 100 loaves of pefsu 10 are to be exchanged for a number ofloaves of''pefsu 45. How many of these will there he?