The acquisition of a scale for which we had no other means of expression than that just described would be a matter of the extremest difficulty, and could never, save in the most exceptional circumstances, progress beyond the attainment of a limit of a few hundred.
If the various numbers in question were designated by words instead of by symbols, the difficulty of the task would be still further increased.
Hence, the establishment of some number as a base is not only a matter of the very highest convenience, but of absolute necessity, if any save the first few numbers are ever to be used.
In the selection of a base,--of a number from which he makes a fresh start, and to which he refers the next steps in his count,--the savage simply follows nature when he chooses 10, or perhaps 5 or 20.

But it is a matter of the greatest interest to find that other numbers have, in exceptional cases, been used for this purpose.

Two centuries ago the distinguished philosopher and mathematician, Leibnitz, proposed a binary system of numeration.

The only symbols needed in such a system would be 0 and 1.

The number which is now symbolized by the figure 2 would be represented by 10; while 3, 4, 5, 6, 7, 8, etc., would appear in the binary notation as 11, 100, 101, 110, 111, 1000, etc.