THE HINDU-ARABIC NUMERALS 603 



Whether this is a combination of four strokes, and so a true ideograph, 

 can not be known. For six the Chinaman writes 



A* 



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 inter- 

 spersed. 



As an example of this alphabetic designation the Greek system may 

 be taken. The letters accented were the numerals : a, 1 ; ff, 2; y, 3 

 8', 4; c, 5; s', 6; £, 7; rf, 8; 0', 9; 1, 10; k, 20; A', 30; //, 40; v, 50 

 ?, 60; o, 70; «■', 80; <?', 90; p, 100; </, 200; t, 300; v, 400 

 <f>, 500; x, 600; \\i , 700; «/, 800. The intervening numbers were ex- 

 pressed by combination; thus, y'= 3 and 1= 10, therefore 17'= 13; 

 while the numbers for the thousands were expressed by sub-accenting 

 the lower symbols; thus (?= 2, J3 = 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 combina- 

 tions — one times one, one times two, one times three, and so on — the 

 Greek system with its twenty-seven characters required the memoriz- 

 ing of three hundred and seventy-eight — a times a, a times ft , a 

 times y, and so furth. Other arithmetical processes were correspond- 

 ingly difficult. 



Another scheme, apparently much simpler, consists in using only a 

 few letters or signs. As an example, the Eoman 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 s} T mbol of its own, V, which was once thought to be a representa- 

 tion 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 Eomans in counting from one to ten used one, 

 two, three, four, five, six, seven, eight, nine strokes; then, to avoid 



