complete triangle has 6 for base and 60 for meret. This word in other connections means bank or wharf, which would indicate a side and not the altitude. It does not seem probable that the author had much conception of different kinds of triangles. We may suppose that he has in mind a piece of land, of a certain width at one end and coming to a point, or at least narrower, at the other end. Thus to get the area he thinks of a rectangle with the average width of the piece of land.[1]
Pyramids. The Relation of the Lengths of Two Sides of a Triangle
The relation of the lengths of two sides of a right triangle is illustrated in Problems 56-60, which deal with the distinguishing lines of a pyramid. In these problems the scribe uses certain special terms. In 56-59 he uses the words ukha-thebet and per-em-us for two lines, and “pyramid” for the structure. In Problem 60 he calls the structure iwn[2] and the two lines sentet and kay-en-heru, and the height is much greater in proportion to the base. In both cases he uses the word seked[3] for the relation of the lengths of the two lines, but he thinks of the seked, not as a ratio, but as so many palms per cubit.
The diagrams themselves do not show definitely what these lines are, and there are two opinions respecting them. Eisenlohr in his translation takes the ukha-thebet as the diagonal of the base and the per-em-us as the lateral edge, while he takes sentet and kay-en-heru as the side of the base and the altitude. Borchardt (1893) contends that ukha-thebet and sentet both mean the side of the base, and that per-em-us and kay-en-heru both mean altitude.[4]
- ↑ Sethe in his review of Peet (see Bibliography under Peet, 1923, 2) regards meret as “clearly” meaning height, because the 7 in 53 is written at the vertex of the triangle (but in 51 the 10 is written along the middle of the side), and because mention is made of only one meret. Peet suggests, “half doubtfully” as Sethe says, that meret probably means height, but his reasoning is rather inconclusive and not very clear.
Gunn suggests (page 133) that meret is a pair of lines forming a right angle with each other, one of them perpendicular to the base at one end, and the other passing through the vertex, or, with a truncated triangle, lying on the line opposite the base. This idea was suggested to him by a (vertical) cross-section of a wharf and the sloping bank under it, although he himself says that to the Egyptian mind triangles mostly lie flat on the ground. To me a bank or wharf suggests the dividing line between the water and the land and would be applied to the side of a triangle of land as separating the ground within from the ground outside. The idea of a cross-section of a wharf is one of four arguments that Gunn ofiers. The other three are not so definite and can be modified, if necessary, so as to apply equally well to the interpretation of meret as the side of the triangle.
- ↑ yûn, a word generally meaning “pillar.”
- ↑ Peet translates this batter.
- ↑ This interpretation had been suggested by E. and V. Revillout (1881).
