Page:The Rhind Mathematical Papyrus, Volume I.pdf/193

zur Geschichte van Rechenkunst und Sprache, (Schrifen der wissenschaftlichen Gesellschaft in Slrassburg, Heft 25). Strasbourg, 1916, 8 + 147 pp. and 3 plates.

A work of prime importance in the field indicated by its title. There are definite references to the Rhind mathematical papyrus as edited by Eisenlohr, on pages 50, 6o, 73, 85. 87, 99, 1oo, 119,-at least. Compare Crum (19o2),and Sethe, Gottingische Gelehrte Anzeigen, 1916, pp.476–490; review of his own book.

Reviewed by B. Gunn, Journal of Egyptian Archaeology, vol. 3. 1916, pp. 279–286; critical and valuable.

Ungnad, A., "Zur babylonischen Mathematik," Orientalistische Literaturzeitung, vol. 19, December, 1916, cols. 363-368.

Reference is made in Weidner (1916)and Zimmern (1916), as well as here, to two tablets 85194, 85210, transcribed in Cuneiform Texts from Babylonian Tablets, &c., in the British Museum, London, part IX, 1900, plates 8-15. The first of these contains about 35 problems and the second 12, but no one has yet been able to interpret the mathematics. Ungnad here includes a translation of the first problem of 85194 but he had to confess: "Auf eine Lösung der mathematischen Probleme, die hier vorliegen, muss ich leider verzichten." The problem is one regarding the volume of earth in a ramp^[1] (inclined plane for entering, say, a vessel) and the amount of work one man could do as compared with a larger number. The fourth problem discusses circular canals.

Weidner, E. F., "Die Berechnung rechtwinkliger Dreiecke bei den Akkadem um 2000 v. Chr.," Orientalistische Literaturzeitung, vol. 19, September, 1916, cols. 257-263.

Interesting contribution to our knowledge of Babylonian geometry. It is the text of a table giving two methods for the calculation of the diagonal of a rectangle with sides 40 and 10 units. The first leads in numbers to the approximation $c=a+{\frac {2ab^{2}}{3600}}$ , if a is the greater side, 17 the lesser, and c the diagonal.^[2] The second, to $c=a+b^{2}/2a$ which is what one arrives at in calculation of ${\sqrt {a^{2}+b^{2}}}$, if terms after the second are neglected. Compare W. Lietzmann, Zeitschrift fur mathematischen und natunoissenschaftlichen Unterricht, vol. 49, 1918, pp. 148-149.

Zimmern, H., "Zu den altakkadischen geometrischen Berechnungsaufgaben," Orientalistische Literaturzeitung, vol. 19, November, 1916, cols. 321-325.

1. For this word in translation, unknown to Ungnad, I am indebted to Mr. Sidney Smith of the British Museum.
2. The impossibility of such a non-homogeneous relation is obvious.