Page:Popular Science Monthly Volume 26.djvu/463

Rh plan of a quaternary arithmetic. Simon Stevin, of Bruges, had previously devised a system of duodecimal numeration like the one we use in computing time and the degrees of the circle. The almost unanimous choice of the number ten as the basis of numeration was probably suggested by the ten fingers.

Instead of increasing the height of our abacus by two squares to explain the duodecimal system, let us put in its place a rectangle two squares high and of any desired width. We shall then have the system of binary numeration, and be able to write all the numbers with only two figures, and 1. The numbers one, two, three, four, five,



and six, may be formed on this system as in Fig. 10. This system furnishes the explanation of the Chinese symbol "Je-Kim, or Book of Mutations," which is attributed to the venerable Emperor Fo-Hi. It is composed of sixty-four figures, each formed of six horizontal lines written one over the other, some of them whole, others broken in the middle. The whole lines represent units of different degrees, rising from the lowest, and the broken lines zeros.