By Florian Cajori

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A (a 2d)] 3d) 4- (a 4cZ), whence d the difference d is 5-J- times the last term. term = 1, he gets his first progression. The should be 100; hence multiply by If, for We have here a method of solution which appears again later among the Hindus, Arabs, and modern the method of false position. It will be ex Europeans plained more fully elsewhere. Still more curious is the following in Ahmes. of a ladder consisting of the numbers 7, 49, He speaks 343, 2401, 16807. Adjacent to these powers of 7 are the words picture, cat, mouse, barley, measure.

56 Gow, p. 50 ; FRIEDLEIN, p. 76 ; my History of Mathematics, 1895, p. 65. d. or Volker, p. 393 ; ; GBEECE 27 = yf 2-. Other fractions were usually indicated by once with an accent and the denomina numerator the writing tor twice with a double accent. Thus, i J. As Thus, pt/3" WW = with the Egyptians; unit-fractions in juxtaposition are to be added. Like the Eastern nations, the Egyptians and Greeks employ two aids is not to computation, the abacus known what and finger symbolism. If the signs used in the latter were, but by the study of ancient statuary, bas-reliefs, and paintings this secret may yet be unravelled.

Into Greece done thus The length of the shadow of the pyramid is to the shadow of a vertical staff, as the unknown height of the pyra mid is to the known length of the staff. But according to : Diogenes Laertius the measurement was different The height pyramid was taken equal to the length of its shadow at : of the the its moment when the shadow own length, 1 of a vertical staff was equal to The first method implies a knowledge of the proportionality of the sides of equiangular triangles, which some critics are unwilling to grant Thales.