As far as _twelve_ we make use of simple unrelated terms.

Thenceforward we apply derivatives and compounds, formed from these in their regular order, till we arrive at a _hundred_.

This one new word, _hundred_, introduced to prevent confusion, has nine hundred and ninety-nine distinct repetitions in connexion with the preceding terms, and thus brings us to a _thousand_.

Here the computation begins anew, runs through all the former combinations, and then extends forward, till the word _thousand_ has been used nine hundred and ninety-nine thousand times; and then, for ten hundred thousand, we introduce the new word _million_.
With this name we begin again as before, and proceed till we have used it a million of times, each combination denoting a number clearly distinguished from every other; and then, in like manner, we begin and proceed, with _billions, trillions, quadrillions, quintillions, etc._, to any extent we please.
20.

Now can any one suppose that words are not here, in some true sense, the instruments of thought, or of the intellectual process thus carried on?
Were all these different numbers to be distinguished directly by the mind itself, and denominated by terms destitute of this artificial connexion, it may well be doubted whether the greatest genius in the world would ever be able to do what any child may now effect by this orderly arrangement of words; that is, to distinguish exactly the several stages of this long progression, and see at a glance how far it is from the beginning of the series.