Elementary arithmetic, with brief notices of its history... by Robert Potts.

9

And as tell units of any order are eclual to one unit of the next
superior order, it follows that the sum of two or more numbers of any
order is found by the same operation as if they were of the first order,
and all additions are reduced to the simple process of finding the sum
of two or more single figures.
As an error is always possible in the performance of the process of;addition, not much confidence can be placed in the so-called proofs of
the process of addition. In the addition of numbers, if the sum be
obtained by commencing with the last line of figures and adding
upwards, in case any error be made, it may probably be detected by
repeating the process, beginning with the first line of figures and
adding downwards; and if the two results are the same, it is probable
the addition is correct.
Besides the characters or symbols of numbers there are other
assumed symbols which denote arithmetical operations.
The symbol + placed between two numbers indicates that the
latter number is to be added to the former. Thus 3 +- 5 means that 5
is to be added to 3, and is read 3 plus 5.
The symbol = is used to indicate the equality or equivalence of
two numbers; and is read " is equal to." Thus 3 + 5 _ 8, means that
5 added to 3 is equal to 8.
By the help of these two symbols of operation, any number can
be expressed as the sum of the several orders of numbers of which it
is composed; as, for example: -Thirty-five thousands, seven hundreds,
forty and nine, can be thus expressed35749 = 30000 + 5000 + 700 + 40 + 9.
4. PBOB.-To find th7e difference of two numbers, eackh consisting of one,or two figures.
The difference of two small numbers will be found by subtracting
from the greater number in succession as many units as are contained
in the less.
Let it be required to find the difference between the two numbers
8 and 3.
3 is composed of three units, 1, 1, 1.
less trouble in practice, also the probability of error is considerably lessened by the
use of small numbers only.
Instead of adding all the figures in each column at once, the sum of each column
may be found as follows:
Add together the first two or more figures which produce a number between 10
and 19; place a mark for the 10, and add the units over to the next figures of the.column, and mark the 10 as before, and add the units over to the next figures, and so
on, marking all the tens until all the figures of the column have been added. Wrrite
the units over after the last addition under the column of units, and add to the:second column of tens as many units as are equal to the number of marked tens in
the first column. Proceed in the same way with the third and other columns.