Page:The Rhind Mathematical Papyrus, Volume I.pdf/112

96 Proof.

Thus you ﬁnd that the area is 3 setat.

These two problems are simple division problems—10 is multiplied so as to get 7, and 5 so as to get 3—and they have been translated both by Eiscnlohr and by Peet, "Divide . . . into . . . fields." But the preposition sometimes means from and does not mean into, and the verb at the beginning, which is used several times in the papyrus, elsewhere always means take away or subtract. Gunn (page 133) has suggested that these words can be used here with their ordinary meanings in the sense of taking away an equal part from each field.

In each of these problems a product and multiplier are given to ﬁnd the multiplicand. Problem 54 is, How large a ﬁeld taken 10 times (once from each of the given 10 fields) will make 7 setat, and Problem 55, How large a ﬁeld taken 5 times will make 3 setat? As the Egyptian cannot solve these problems directly, he forms new ones in which the multipliers in these become multiplicands and the answers are obtained ﬁrst as multipliers (see Introduction. page 6). In writing down the multiplications of these new problems he writes all of his numbers as mere numbers, but in Problem 55 he writes ﬁrst the statement of his new problem as a problem in setat. The answer to this new problem is $1/undefined$$1/undefined$, and if it is taken as a problem in setat, the argument for the answer to the given problem will be, $1/undefined$$1/undefined$ times 5 setat makes 3 setat, therefore 5 times $1/undefined$$1/undefined$ of a setat (or. as he has to write it, $1/undefined$ setat 10 cubit-strips) will be 3 setat, and so the answer to the given problem is $1/undefined$ setat 10 cubit-strips.

SECTION IV

Problem 56

If a pyramid is 250 cubits high and the side of its base 360 cubits long, what is its seked?

Take $1/undefined$ of 360; it makes 180. Multiply 250 so as to get 180; it makes $1/undefined$$1/undefined$$1/undefined$ of a cubit. A cubit is 7 palms. Multiply 7 by $1/undefined$$1/undefined$$1/undefined$