es that six cannot be
subtracted (taken) from four: more especially a child who is
familiarly acquainted with the component parts of the names six and
four: he sees that the sum 46 is less than the sum 94, and he knows
that the lesser sum may be subtracted from the greater; but he does
not perceive the means of separating them figure by figure. Tell him,
that though six cannot be deducted from four, yet it can from
fourteen, and that if one of the tens which are contained in the (9)
ninety in the uppermost row of the second column, be supposed to be
taken away, or borrowed, from the ninety, and added to the four, the
nine will be reduced to 8 (eighty), and the four will become fourteen.
_Our_ pupil will comprehend this most readily; he will see that 6,
which could not be subtracted from 4, may be subtracted from fourteen,
and he will remember that the 9 in the next column is to be considered
as only (8). To avoid confusion, he may draw a stroke across the (9)
and write 8 over[18] it [8 over (9)] and proceed to the remainder of
the operation. This method for beginners is certainly very distinct,
and may for some time, be employed with advantage; and after its
rationale has become familiar, we may explain the common method which
depends upon this consideration.

"If one number is to be deducted from another, the remainder will be
the same, whether we add any given number to the smaller number, or
take away the same given number from the larger." For instance:

Let the larger number be 9
And the smaller 4
If you deduct 3 from the larger it will be 6
From this subtract the smaller 4
--
The remainder will be 2
--

Or if you add 3 to the smaller number, it
will be 7
--
Subtract this from the larger number 9
7
--
The remainder will be 2

Now in the common method of subtraction, the _one_ which is borrowed
is taken from the uppermost figure in the adjoining column, and
instead of altering that figure to _one