Page:The Rhind Mathematical Papyrus, Volume I.pdf/39

Rh 5, which we have already in the first table. But it seems strange that he should omit the proof for 3 and put in those for 1 and 2. All that remains of the second proof in the Rhind papyrus would fit 2 or 3 equally well, and Eisenlohr assumes that it is for 3, but the New York fragments show that really it is for 2.

It is not difficult to show how the Egyptians would derive the expressions in this table. Take, for example, the case of 3. To divide 3 by 10 we have to multiply 10 so as to get 3. We have:

or, taking 7,

In order to make these problems seem practical the author supposes that we have a certain number of loaves of bread to divide among 10 men.

Problems 7-20 are problems in multiplication that consist of two groups. In the first the multiplier is 1 $1/undefined$ $1/undefined$ and in the second, 1 $1/undefined$ $1/undefined$. Problems 7 and 9–15 belong to the first group and problems 8 and 16–20 to the second. One problem of each group is given and then the rest of those of the first followed by the rest of those of the Second. In Problem 7, $2/3$ $2/3$ is multiplied by 1 $1/undefined$ $1/undefined$ and in each of the problems of this group