Page:A History Of Mathematical Notations Vol I (1928).djvu/35

½, ⅓, ⅔, ¼, each of which had its own symbol. Some of the numeral symbols in Ahmes deviate somewhat from the forms given in the two preceding tables; other symbols are not given in those tables. For the reading of the example in question we give here the following symbols:

Four	(symbol characters)	One-fourth	(symbol characters)
Five	(symbol characters)	Heap	(symbol characters)	See Fig. 7
Seven	(symbol characters)	The whole	(symbol characters)	See Fig. 7
One-half	(symbol characters)	It gives	(symbol characters)	See Fig. 7

Fig. 7.—An algebraic equation and its solution in the Ahmes papyrus, 1700 B.C., or, according to recent authorities, 1550 B.C. (Problem 34, Plate XIII in Eisenlohr; p. 70 in Peet; in chancellor Chace’s forthcoming edition, p. 76, as R. C. Archibald informs the writer.)

Translation (reading from right to left):

“10 gives it, whole its, ¼ its, ½ its, Heap No.34 ½ ¹⁄₂₈¼ ¼½1 1 ¹⁄₁₄½ ½3.. ¹⁄₁₄⅐½5 is heap the together 7 4 ¼ ⅐ Proof the of Beginning ¹⁄₁₄⅐½5 ¹⁄₂₈¹⁄₁₄¼½2 ½ ⅛¼ Remainder ⅛½9 together ¹⁄₅₆¹⁄₂₈⅛¼1 ¼ 14 gives ¼ ¹⁄₅₆¹⁄₂₈¹⁄₂₈¹⁄₁₄¹⁄₁₄⅐ 21 Together .7 gives ⅛ 1 2 2 4 4 8”