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178 1917

, "Algebraical developments among the Egyptians and the Babylonians," American Mathematical Monthly, vol. 24, 1917, pp.257–265. "Algebraical ideas in Egypt," pp. 258-263.

, "The volume of the truncated pyramid in Egyptian mathematics," Ancient Egypt, London, 1917, pp. 100–102.

This paper exhibits one of "nineteen" problems (four of which are geometrical) occurring in a hieratic mathematical papyrus, written about 1800 B.C., which was probably also the date of the original of the Rhind mathematical papyrus, the copy we possess having been written one or two hundred years later. This papyrus,formerly the property of Golenishchev, compare Cantor 1894 [1880], now professor of Egyptian philology at the Egyptian University, Cairo, was acquired about 1916 by the Museum of Fine Arts in Moscow. It appears to indicate a familiarity with the formula for the volume of the frustum of a square pyramid, $$V = (h/3)(a_1^2+a_2^2+a_1 a_2)$$, where h is the altitude of the frustum, the sides of whose bases are a$1$ and a$2$.

This extraordinary result, and the facts here revealed by the late Professor Turaev, would suggest that accounts of Egyptian mathematics may have to be rewritten so soon as all of the contents of this Mosoow papyrus are generally known. But Professor Peet who had access to a photograph of the papyrus has written, Feet (1923, 2), p. 6: "though the papyrus is of the highest interest owing to its early date and admirable state of preservation (in part at least) it contains nothing, with the exception of the problem of the truncated pyramid, which will greatly modify the conception of Egyptian mathematics given to us by the already published papyri and fragments.