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1897], A History of Elementary Mathematics, New York, 1897. Revised and enlarged edition, New York, 1917.

Pages 19-26, and other references in the index under "Ahmes" and "Egyptians." Descriptive sketch referring to writings of Baillet, Cantor, Eisenlohr, Loria, Matthiessen, and Sylvester. In one place Cajori gives in hieroglyphics what purports to be a quotation from the Rhind papyrus; this is, of course, the usual manner of quoting the hieratic of the original.

, ''The Petrie Papyri. Hieratic Papyri from Kahun and Gurob (principally of the Middle Kingdom''), edited by F. L. Grifith, 2 vols. London, 1898. Vol. 1, pp. 15-18, 101, 107; vol. 2, plate VIII. In March, 1897, part 1, "containing Plates I to VIII and the text pertaining to them, were issued to subscribers" (Preface).

In this volume six bits of hieratic mathematical papyri, dating from about 1800 B. C. are reproduced in facsimile, translated, and discussed; they were found by Petrie at Kahun in 1889, and are now in University College, London. On these papyri are found: (a) a table for expressing fractions 2/n, n = 3, 5, 7,. ., 21 in terms of the sum of fractions with numerators unity; the results are identical with those given in the Rhind papyrus in this same connection. (b) $1/undefined$ + $1/undefined$ is multiplied by 9 giving 3 + ⅔ + $1/undefined$; in the next line the number 110 having apparently been divided by 8 gives 13 + ⅔ + $1/undefined$ which is 10 in excess of the above product; $10/12$ is subtracted 9 times from 13 + ⅔ + $1/undefined$, and its successive remainders, giving once more a series of numbers in arithmetic progression as in the Rhind papyrus, nos. 40 and 64. (c) It seems that the problem is to find the contents of a right circular cylindrical granary whose diameter is 12 and height is 8 cubits, the result being given in terms of the unit khar (two-thirds of a cubic cubit). Schack-Schackenburg (1899) was the first to explain this problem and the corresponding very difficult no. 43 in the Rhind papyrus; (d) shows the hieratic form of eight very large numbers. (e) Problem ½x-¼x = 5, what is x? (f) a vague arithmetic problem apparently requiring the base dimensions of a rectangular parallelopipedal container given the area of the base and the ratio of its sides. (The following misprint in Griffith's commentary may cause trouble for a moment: "¾ = 1×1⅓). Griffith found a new word for square root in this problem. Schack-Schackenburg (1900) observed that we here have the equivalent of the solution of a two-term quadratic equation, or of two simultaneous equations x :y = 1 :¾4, xy = 12, one of these equation being identical with what is called for in Berlin papyrus 6619, while both equations arise in the first problem of the Golenishchev papyrus. (g) Accounts of a poultry-yard.

Griffith does not here make any reference to another Kahun fragment which he described as follows on page 48 of W. M. F. Petrie, Illahun, Kahun, and Gurob, 1889-90, London, 1891: "one [fragment] I fear is beyond hope: it was beautifully written in columns, and still contains the most tantalising phrase 'multiply by ½ to inﬁnity.' Was it the famous problem that 'took in' Hercules?" Griffith probably made a slip in referring to Hercules when he had in