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190 the latter were the ﬁrst to be thought of, and indeed he speaks of it as first. Then he adopts Peet’s idea that the Egyptian began by separating 2 into two parts. He gives the same names to the two parts of 2 and gets the products of 1/n by them as the two parts of 2/n.

He suggests that the Egyptian might take for the principal part in the separation of 2 one of the "natural fractions," $1/undefined$,$1/undefined$,$1/undefined$,. . . $1/undefined$,$1/undefined$, . . ., and shows that $1/undefined$ 1/n will be a suitable principal part for 2/n if n is a multiple of 3, and $1/undefined$. 1/n if n is a multiple of 5, and that these and two or three other combinations of this kind explain all but ﬁfteen cases of the table. But in the case of any one of the fifteen "exception numbers," if not in most of the other cases, the Egyptian actually got first the completion-term, and so, after all, placed that first as it is in the papyrus.

The multiplication required to get the completion-term of $2/7$ is given in problem No. II of the Rhind papyrus, and so our author sees in problems 7, 9-15, the completion-table for $2/7$ Less clearly he associates problems 8, 16-20 with the completion-term of $2/9$. In this way he justifies the use of the word "completion" with No. 7, and supposes that the Egyptian may have had other completion-tables for the separation of 2/n in other cases.

Incidentally Neugebauer gives (pp. 14-15) a new explanation of problem 79 of the Rhind papyrus, which seems very natural and does away with speculation as to whether the Egyptians knew our algebraic formula for the sum of a number of terms of a geometric progression.

, "Über die Konstruktion von "Mal" im mathematischen Papyrus Rhind," Zeitschrift fūr Ägyptische Sprache vol. 62, 1926, pp. 61-62.

, "Das Zahlwort 'fünf',"Zeitschrift fūr Ägyptische Sprache. . ., vol. 62, 1926, pp. 60-61.

, Jak se počitalo a Měřilo na Usvitě Kultury [How one reckoned and measured at the dawn of culture], (Lidová Universita [people's university] series, vol. I 5), Prague, 1926, 141 pp.

After a number of paragraphs dealing with Babylonian reckoning and measuring, pages 63-138 are occupied with an account of such things among the ancient Egyptians.

, "Kannten die Ägypter den Begriff eines allgemeinen Bruches?", 'Mitteilungen zur Geschichte der Medizin und der Naturwissenschaften, vol. 25, 1926, pp. 1-4.

1927

, Egyptian Grammar, being an Introduction to the Study of Hieroglyphs, Oxford, 1927, 28 + 595 pp., quarto.

Monumental work entirely superseding earlier works of the kind. Numbers are