Page:A history of Japanese mathematics (IA historyofjapanes00smitiala).pdf/16

4 down to us concerning the very early mathematics of Japan, and this relates to the number system. Tradition tells us that in the reign of Izanagi-no-Mikoto, the ancestor of the Mikados, long before the unbroken dynasty was founded by Jimmu (660 B. C.), a system of numeration was known that extended to very high powers of ten, and that embodied essentially the exponential law used by Archimedes in his Sand Reckoner that aa=a. In this system the number names were not those of the present, but the system may have been the same, although modern Japanese anthropologists have serious doubts upon this matter. The following table has been given as representing the ancient system, and it is inserted as a possibility, but the whole matter is in need of further investigation: