Page:The Rhind Mathematical Papyrus, Volume I.pdf/53

Rh 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.

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 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 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.