Page:A history of Japanese mathematics (IA historyofjapanes00smitiala).pdf/37

Rh The number 38057, for example, would be represented thus:

The number 1267, represented by the sangi without the ruled board. Isboard, is [sic] shown in Fig. 7.

Fig. 7. The number 1297 represented by sangi.

From representing the numbers by the sangi on a ruled board came a much later method of transferring the lines to paper, and using a circle to represent the vacant square. This could only have occurred after the zero had reached China and had been passed on to Japan, but the date is only a matter of conjecture. By this method, instead of having 38057 represented as shown above, we should have it written thus:

In laying down the rods a red piece indicated a positive number and a black one a negative. In writing, however, a marked placed obliquely across a number indicated subtraction. Thus, meant  3, and  meant  6.

The use of sangi in the fundamental operations may be illustrated by the following example in which we are required