Page:The Rhind Mathematical Papyrus, Volume I.pdf/192

176 "Die Zahlzeichen der Babyloner und Assyrer," pp. 18-29 (second edition. 22-32); "Die Zahlzeichen der Ägypter," pp. 29-38 (second edition, 14-21). Compare Pihan (1860).

, Die Mathematik im Altertum und im Mittelalter. (Die Kultur der Gegenwart, Part 3, section I.) Berlin and Leipzig, 1912. Pp.B9, 18B–B19,24B–26B, B29.

1914

, "A Byzantine table of fractions," Ancient Egypt, London. 1914. pp. 52–54.

The outer leaf of a set of writing tablets with two lists of fractions with denominators 15 and 16, and numerators 2 to 15, 16 respectively, expressed as the sums of fractions with numerators unity. For example $1/undefined$ of 11 is $1/undefined$ $1/undefined$ $1/undefined$ Headings of the columns indicate that this leaf is part of a series of tables giving the composition of various fractions. In Sethe (1916), p. 70, it is remarked that from the headings the fraction $1/undefined$ occurred on table 2 so that $2/3$ was probably on table 1. The leaf was bought in Egypt in 1913 and is now in University College, London.

1916

, "Mathematische Aufgaben auf Papyrus," Amtliche Berichte aus den königlichen Kunstsammlungen, Berlin, vol. 37, May, 1916, cols. 161-170.

This is a facsimile, transcription, and translation, with commentary, of one side of a Greek papyrus, P11529 (size 31.5 x 21 cm.) in the Berlin Museum. It is a document of the second century and is nearly related to the older (probably) Ayer papyrus; compare Goodspeed (1898). Some expressions used are the same as those of Heron of Alexandria in similar connections. The ﬁve problems are seemingly the work of a pupil, and in the ﬁrst three the areas of a rectangle, of a right-angled triangle, and of an isosceles triangle are reckoned in arurae, the old Egyptian unit for measuring ﬁelds. In the first of these the square root of 164 is found in the form 12 $2/3$ $1/undefined$ $1/undefined$ $1/undefined$. The fourth problem is to ﬁnd the volume of a stone in the shape of a rectangular parallelepiped, and the fifth problem suggests that the volume of a frustum of a cone [compare Grenfell (1903)] is being considered; but not all parts of the problem are clear. Schubart did not observe that the form of this problem is very similar to that of the ﬁrst of the fifty problems in Baillet (1892).

In the Berlin Museum are also undeciphered fragments of Greek ostraca of mathematical interest; they are numbered P11999, P12000, P12002, P12007, and P12008.

, ''Von Zahlen und Zahlworten bei den alten Ägyptern und was für andere Völker und Sprachen daraus zu lernen ist. Ein Beitrag ''