# Dating directrix

### Dating directrix

The texts that survive do not reveal what, if any, special procedures the scribes used to assist in this.But for multiplication they introduced a method of successive doubling.

A remarkable result is the rule for the volume of the truncated pyramid (Golenishchev papyrus, problem 14).

One of the texts popular as a copy exercise in the schools of the New Kingdom (13th century ) was a satiric letter in which one scribe, Hori, taunts his rival, Amen-em-opet, for his incompetence as an adviser and manager. But the point of the humour is clear, as Hori challenges his rival with these hard, but typical, tasks.

“You are the clever scribe at the head of the troops,” Hori chides at one point, a ramp is to be built, 730 cubits long, 55 cubits wide, with 120 compartments—it is 60 cubits high, 30 cubits in the middle…and the generals and the scribes turn to you and say, “You are a clever scribe, your name is famous. What is known of Egyptian mathematics tallies well with the tests posed by the scribe Hori.

These problems reflect well the functions the scribes would perform, for they deal with how to distribute beer and bread as wages, for example, and how to measure the areas of fields as well as the volumes of pyramids and other solids.

The Egyptians, like the Romans after them, expressed numbers according to a decimal scheme, using separate symbols for 1, 10, 100, 1,000, and so on; each symbol appeared in the expression for a number as many times as the value it represented occurred in the number itself. This rather cumbersome notation was used within the hieroglyphic writing found in stone inscriptions and other formal texts, but in the papyrus documents the scribes employed a more convenient abbreviated script, called In such a system, addition and subtraction amount to counting how many symbols of each kind there are in the numerical expressions and then rewriting with the resulting number of symbols.

The process is then repeated, this time for the remainder (84) obtained by subtracting the entry at 8 (224) from the original number (308).

This, however, is already smaller than the entry at 4, which consequently is ignored, but it is greater than the entry at 2 (56), which is then checked off.

The scribe assumes the height to be 6, the base to be a square of side 4, and the top a square of side 2.

He multiplies one-third the height times 28, finding the volume to be 56; here 28 is computed from 2 × 2 2 × 4 4 × 4.

These elementary operations are all that one needs for solving the arithmetic problems in the papyri.

For example, “to divide 6 loaves among 10 men” (Rhind papyrus, problem 3), one merely divides to get the answer 1/2 1/10.

Since the entries 1, 2, 4, and 20 add up to 27, one has only to add up the corresponding multiples to find the answer.