Page:The Rhind Mathematical Papyrus, Volume I.pdf/204

188 the volume of the frustum of a square pyramid. Tsinserling professes to give Turaev's transcription, and a translation of ﬁve problems, only four of which are geometrical. Since the ﬁfth problem has nothing whatever to do with geometry it is not clear why it was included in this paper. On the other hand, as already noted, a geometrical problem for ﬁnding the area of a triangle occurs on one of the fragments. The transcription is incorrect, incomplete, and probably misprinted; obviously a piece of unfinished work on the part of Turaev.

The ﬁrst of the geometrical problems, which is number 1 in the Golenishchev papyrus, is as follows: Given that the area of a rectangle is 12 arurae and the ratio of the lengths of the sides 1 : $1/undefined$ $1/undefined$, ﬁnd the sides. It will be noted that the solution of this problem leads to the equations xy = 12, x : y = 1 : $3/4$ which are identical with those occurring in a problem of the Kahun papyri; compare Griffith (1897).

The second and fourth problems (second and twelfth of the Golenishchev papyrus) are really the same as the First; but the areas are here right triangles. In the First of them the ratio of the "length" to the "breadth" is $2 1/2$ : 1, in the second $1/undefined$ $1/undefined$ $1/undefined$ : 1. In each case the area is given as 20. These three problems seem to prove that the Egyptians of 1850 B.C. were familiar with the following results: The area of a rectangle is the product of the lengths of a pair of adiacent sides; the area of a right triangle is one half the area of the rectangle with one right angle the same as that of the triangle and with a diagonal coincident with the hypotenuse of the triangle.

The third of the problems given by Tsinserling (ninth in the Golenishchev papyrus) is that one which we have already discussed under Turaev (I917).

, Histéria das Matemdticas na Antiguidade, Paris and Lisbon, 1925.

Egyptian mathematics, pp. 59-89. Refers to Eisenlohr (1877), Revillouts (1881). Baillet (1892), Milhaud (1911), Cantor (1880), and Vasconcellos (1923).