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160 mind one of the paradoxes of Zeno who ﬂourished in the fifth century before Christ. It is also noted (p. 49) that about 1890 Prof. Adolf Erman had put together some small fragments of Middle Kingdom writing [2000—1800 B. C.] from Thebes making a calculation in which expressions resemble those in the Rhind papyrus. I have veriﬁed through Professor Erman that the fragments here referred to are papyrus 6619 in Berlin: see Schack-Schackenburg (1900).

Turning to another part of Petrie's Illahun, written by himself we find the following (p. 15): "A most curious article among the small objects (Pl. VIII, 17) is a counting stick. It is not intended for doing operations on like an abacus but apparently for teaching children. It is made from an old piece of furniture; the holes on the left hand being for fastening pegs. It begins with nefer [good, or beautiful], and then dots for 1 to 9; then 10, and dots for 11 to 19; then 20, 25, and 30 to 90; and lastly the sign for 100." This is not connected in any way with what are technically known as counting rods, which are somewhat related to the abacus. Such things were wholly unknown in Egypt (oral statement to me by Sir Flinders Petrie. July, 1926).

, "Zur Geschichte der Polyeder und der Zahlzeichen," Sitzungsberichte der mathemalisch-physikalischen Classe der königlichen bayerischen Akademie der Wissenschaften zu München, Jahrgang 1896, 1897, vol. 26, pp. 625-758 + 9 plates.

Signs for numbers in the papyrus discussed, directly or indirectly, on pages 664-670: 698-709

1898

, scribe, Facsimile of the Rhind Mathematical Papyrus, London, British Museum, Department of Oriental Antiquities, 1898. Large folio, 56 X 38 cm. 3 pp. + 21 plates.

British Museum Papyrus, nos. 10057-10058, with Introduction and Bibliography by E. A. T. W. Budge. Doctor Budge states: “The attention of Egyptologists was ﬁrst called to the existence of this unique mathematical document ["unique" no longer—compare Turaev (1917)] by the late Dr. Samuel Birch who published a brief but accurate account of it in the Zeitschift für Ägyptische Sprache. . . (Bd. VI, 1868);" the inaccuracy of the word "ﬁrst" in this statement will be noted on referring to the title given above for 1867. The same misstatement was made by Eisenlohr (1877), p. 2.

The titles given in the Bibliography, and references, are as follows: Birch (1868), Brugsch (1874 and 1891, 1), Cantor (1880), Ebers (1878), Eisenlohr (1875, 1876, 1877, and 1881), Erman (1891), Griffith (1891-1894), Rodet (1878 and 1881), Revillout (1881), Schack-Schackenburg (1882), Suter (1873), and Wiedemann (1884).

An inspection of this "facsimile" might readily suggest that the papyrus had been beautifully reproduced in natural colors, and so that even the texture of the papyrus is clear. Such an inference would be quite erroneous. On a fake background is given a reproduction of an imperfect hand copy of the