Page:The Rhind Mathematical Papyrus, Volume I.pdf/92

76 Problem 34 A quantity, its $1/undefined$, and its $1/undefined$, ''added together, become 10. What is the quantity?''

Multiply 1$1/undefined$$1/undefined$ so as to get 10.

The total is the quantity required, 5$1/undefined$$1/undefined$$1/undefined$.

Proof. The whole numbers and simpler fractions (powers of $1/undefined$) make a total of 9$1/undefined$$1/undefined$, the remainder is $1/undefined$$1/undefined$. The remaining fractions, namely,

$1/undefined$$1/undefined$$1/undefined$$1/undefined$

applied to 56, are equal to

844221,

making a total of 21, while $1/undefined$ and $1/undefined$ make 14 and 7, and so also a total of 21. Therefore the result obtained is correct.

SECTION VII

In these problems in the papyrus the questions are put in a curious way: "I have gone a certain number of times into the hekat-measure, certain parts have been added to me, and I return ﬁlled. What is it that says this?" It is stated as if the vessel represented as speaking had gone