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1910] be given to H. K. Brugsch,Grammaire Démotique, contenant les Principe: généraux de la Langue et de l'Écriture Populaires des anciens Égyptiens, Berlin, 1855; chapter 5, pages 58-70, is entitled: "Des véritables signes idéographiques des chiffres." From these two sources plate I of Sethe (1916) was made up. More recent is W. Spiegelberg, Demotische Grammatik, Heidelberg, 1925, "Zahlwörter," pp. 47-51; but these pages were largely based on Sethe (1916).

, ''Hieratische Paläiographie. Die aegyptische Buchschrift in ihrer Entwicklung von der fiinften Dynaste bis zur römischen Kaiser-zeit'', Leipzig, 3 vols., 1909, I909, 1912.

This is the fundamental work of reference in the subject and was constantly employed by Chancellor Chace in preparing plates for the second volume of his edition of the Rhind papyrus. The origin of the hieratic forms of number signs from the original hieroglyphic pictures can here be readily seen. Numerals, Numerals in dates (days of the month), Fractions, and Measures, are dealt with in volumes 1-3, nos. 614-719; most of nos. 56-60 of the Rhind papyrus, in two colors, is on plate VII in volume 1. Moreover we have in volume 1 descriptions (pp. 13-18) of the Rhind and Bulak I8 papyri, and a catalogue of signs occuring in them; similarly for the Rollin papyri in volume 2.

, Geschichte der Mathematik im Altertum in Verbindung mit antiker Kulturgeschichte, Berlin, 1909, pp. 24-53.

Popular review of contents of the Rhind papyrus, and of the varied interpretations of difficult points.

,"“Sulla quadratura del circolo secondo l'egiziano Ahmes," Bollettino di Bibliograﬁa e Storia delle Scienze Matematiche, Turin, Ju1y—September, 1908, vol. 11, pp. 65-67.

Gives a ﬁgure by means of which the value (16/9)$2$ for π, as given in the Rhind papyrus is found; also other values which may be derived in a similar manner. The article is dated: "Firenze, Gennaio 1909."

Compare a ﬁfteenth century anonymous paper "De inquisicione capacitatis figurarum" edited with notes by M. Curtze, Abhandlungen zur Gerchichte der Mathematik, Heft 8, 1898, pp. 45-46, 63; this Heft appeared also as a supplement to Zeitschrift für Mathematik und Physik, vol. 42.

1910

, "Algebra-History," Encyclopedia Britannica, eleventh edition, Cambridge, vol. 1, 1910, p. 616.

Not important for our inquiry.

, "Egypt-mathematics," Encyclopaedia Britannica, eleventh edition, Cambridge, vol. 9, 1910, pp. 46-47.