y; but when
any arithmetical operations are to be performed with them, it is best
to preserve the established arrangement.

One cube and one other, are called two.

Two what?

Two cubes.

One glass, and one glass, are called two glasses. One raisin, and one
raisin, are called two raisins, &c. One cube, and one glass, are
called what? _Two things_ or two.

By a process of this sort, the meaning of the abstract term _two_ may
be taught. A child will perceive the word _two_, means the same as the
words _one and one_; and when we say one and one are called two,
unless he is prejudiced by something else that is said to him, he will
understand nothing more than that there are two names for the same
thing.

"One, and one, and one, are called three," is the same as saying "that
three is the name for one, and one, and one." "Two and one are three,"
is also the same as saying "that three is the name of _two and one_."
Three is also the name of one and two; the word three has, therefore,
three meanings; it means one, and one, and one; _also_, two and one;
also, one and two. He will see that any two of the cubes may be put
together, as it were, in one parcel, and that this parcel may be
called _two_; and he will also see that this parcel, when joined to
another single cube, will _make_ three, and that the sum will be the
same, whether the single cube, or the two cubes, be named first.

In a similar manner, the combinations which form _four_, may be
considered. One, and one, and one, and one, are four.

One and three are four.

Two and two are four.

Three and one are four.

All these assertions mean the same thing, and the term _four_ is
equally applicable to each of them; when, therefore, we say that two
and two are four, the child may be easily led to perceive, and indeed
to _see_, that it means the same thing as saying one _two_, and one
_two_, which is the same thing as saying two _two's_, or saying the
word _two_ two times. Our pupil should be suffered to rest here, and
we should not, at present, attempt to lead him further towards that
compendious method of addition which we call multiplication; but the
foundation is laid by giving him this view of the relation between two
and two in forming four.

There is an enumeration in the note[16] of the different combinations
which compose the rest of the Arabic notation, which consists only of
nine characters.

Before we proceed to the number ten, or to the new ser