Page:The Rhind Mathematical Papyrus, Volume I.pdf/113

59] {|
 * ||1||7
 * ||$1/undefined$||3$1/undefined$
 * ||$1/undefined$||1$1/undefined$$1/undefined$
 * }
 * ||$1/undefined$||1$1/undefined$$1/undefined$
 * }
 * }
 * }
 * }

The seked is 5$1/undefined$ palms.

Problem 57

If the seked of a pyramid is 5 palms 1 finger per cubit and the side of its base 140 cubits, what is its altitude?

Divide 1 cubit by the seked doubled, which is 10$1/undefined$. Multiply 10$1/undefined$ so as to get 7, for this is a cubit: 7 is $2/3$ of 10$1/undefined$. Operate on 140, which is the side of the base: $2/3$ of 140 is 93$1/undefined$. This is the altitude.

{{smaller block|In this inverse problem and in 59B the author doubles the seked instead of taking $1/undefined$ of the side of the base, and instead of dividing the seized doubled by 7 and dividing the side of the base by the result, he divides 7 by the seked doubled and multiplies the side of the base by the result, which amounts to the same thing.

{{larger|Problem 56}}

If a pyramid is 93$1/undefined$ cubits high and the side of its base 140 cubits long, what is its seked?

Take $1/undefined$ of 140, which is 70. Multiply 93$1/undefined$ so as to get 70. $1/undefined$ is 46$2/3$, $1/undefined$ is 23$1/undefined$. Make thou $1/undefined$$1/undefined$ of a cubit. Multiply 7 by $1/undefined$$1/undefined$. $1/undefined$ of 7 is 3$1/undefined$, $1/undefined$ is 1$1/undefined$$1/undefined$. together 5 palms 1 finger. This is its seked.

The working out:

Make thou $1/undefined$$1/undefined$ of a cubit; a cubit is 7 palms.

This is its seked.

{{larger|Problem 59}}

If a pyramid is 8 cubits high and the side of its base 12 cubits long, what is its seked?

Multiply 8 so as to get 6, for this is $2/3$ of the side of the base. {{nop}}