whether this is a combination of four strokes, and so a true ideograph, can not be known. For six the Chinaman writes
Thus a series of signs may be accumulated.
In many cases the need for a series of number symbols arises when considerable progress has been made in the construction of an alphabet. The alphabet then furnishes a series of signs which follow each other in definite sequence, and as signs are fairly well understood and familiar. The result is that the letters of the alphabet are employed to designate the number ideas. This was done by the Hebrews, who make use of their twenty-two letters, and by the Greeks who had the twenty-four letters of their alphabet with three archaic signs interspersed.
As an example of this alphabetic designation the Greek system may be taken. The letters accented were the numerals: α', 1; β', 2; γ', 3; δ', 4; ε', 5; ς', 6; ζ', 7; η', 8; θ', 9; ι', 10; κ', 20; λ', 30; μ', 40; ν', 50; ξ', 60; ο', 70; π', 80; ρ', 90; ρ', 100; σ', 200; τ', 300; υ', 400 φ', 500; χ', 600; ψ', 700; ω', 800. The intervening numbers were expressed by combination; thus, γ' = 3 and ι' = 10, therefore ιγ' = 13; while the numbers for the thousands were expressed by sub-accenting the lower symbols; thus β' = 2, ͵β = 2000.
Here is a system comprehensive and excellent for the mere writing of numbers. It was, however, because of the numerous signs employed, cumbersome and complex. For example, in multiplication, where our nine numerals now in use require a knowledge of forty-five combinations—one times one, one times two, one times three, and so on—the Greek system with its twenty-seven characters required the memorizing of three hundred and seventy-eight—α' times α', α' times β', α times γ', and so forth. Other arithmetical processes were correspondingly difficult.
Another scheme, apparently much simpler, consists in using only a few letters or signs. As an example, the Roman system may be taken. For one a single stroke was employed, I; while groups of strokes were used for the numbers following, II, III, IIII. Five was designated by a symbol of its own, V, which was once thought to be a representation of the thumb and four fingers held up, but this theory has been abandoned. For ten, X was employed, the origin of which is not entirely clear. A study of the inscriptions, however, affords ground for the belief that the Romans in counting from one to ten used one, two, three, four, five, six, seven, eight, nine strokes; then, to avoid
