Page:The Rhind Mathematical Papyrus, Volume I.pdf/180

164 First sentence: "Die von Borchardt (ÄZ 1897, S. 150) auf die Berechnung einer Halbkugel bedeutete Stelle des mathematischen Papyrus von Kahun scheint mir eine andere Erkléirung zu fordern." Most important interpretation which led to the ﬁnal understanding of the difﬁcult no. 43 of the Rhind mathematical papyrus. Compare Griffith (1897).

1900

, Vorlesungen über Geschichte der Trigonometrie, Leipzig, Erster Teil, 1900, pp. 1-3.

Unimportant in this connection.

, Hierakonopolis, Part I (Egyptian Research Account), London, 1900.

Plate XXVIB represents a great mace of the time of King Nar-mer, who flourished before the ﬁrst dynasty, about 3500 B. C. There is here "a register of captive animals, 'oxen 400,000, goats 1,422,000,' showing that the system of numeration was as fully developed before the 1st dynasty as it was in any later time" (p. 9). There is also a reference to "captives 120,000."

, "Der Berliner Papyrus 6619," Zeitschrift für Ägyptische Sprache. . . ,vol. 38, 1900, pp. 135-140 + plate.

First sentence: "Aus Taf. 8 der Kahuner Papyri hat Grifffith [Griffith (I897)] zum ersten Male eine ägyptische Rechnung verbﬁentlicht, die unseren rein quadratischen Gleichungen entspricht; dem gütigen Entgegenkommen der Berliner Museum Verwaltung verdanke ich die Möglichkeit, ein zweites Beispiel aus dem Berliner Papyrus 6619 vorlegen zu können." The problem here referred to may be stated thus: Distribute 100 square ells between two squares whose sides are in the ratio 1 to ¾; whence the equations x$2$ + y$2$ = 100, x : y= 1 : ¾, corresponding to those given in Griffith (1897). The equations are solved by the method of false position and the solution of two term quadratic equations. On the back of this fragment of the papyrus is another problem somewhat similar to no. 69 of the Rhind papyrus. A translation of both sides of this fragment is given in A. Erman and F. Krebs, Aus den Papyrus der königlichen Museen, Berlin, 1899, pp. 81-82, "Aus einem Rechenbuch;" but the authors acknowledged their inability to give an explanation. The papyrus became the property of the Museum in 1887.

The method of false position or "false hypothesis" was a favorite one of Diophantus of Alexandria (about 250 A. D.); compare Heath (1910), pp. 175, 195; also Heath (1921), vol. 2, pp. 441, 488, 489. The following are examples of equations solved by false position in connection with problems of the Rhind papyrus: $1/undefined$x + x =19 (no. 24); x + ⅔x — ⅓ (x + ⅔ x) = 10 (no. 28); ⅔ x + ½ x + $1/undefined$x +x = 33 (no. 33).

See also under 1902.