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

ADDITION AND SUBTRWCTION.
ART. 1 The simplest elementary operations which follow the notation and numeration of numbers are named Addition and Subtraction.
By Addition is meant the process or operation by which two or
more numbers are combined into one number, called their sum.
Subtraction is the reverse operation, by which a less number is
taken from a greater, and the remainder, or difference, is found.
It is obvious that the operations of Addition and Subtraction are
related, so that if 4 be added to 3, the sum is 7; and if 3 be subtracted
from 7, the remainder is 4. Also, if 7 be taken from 7, the remainder'
is 0; and any number greater than 7, as 9, cannot be subtracted
from 7.
It may also be remarked that Addition and Subtraction are the
two fundamental operations in arithmetic, into which all others may be
resolved; for whatever operation is to be performed, the change made
in any given number must either be an increase or diminution of it.
The nature of the processes of numerical addition and subtraction
imply that the abstract units employed are always the same.
2. PnOB. To find the sum of aGey two numbers consisting of single figures.
This process will be effected by simply taking each unit of one of
the numbers and successively adding it to the other. Thus the sumof the numbers 3 and 5 may be found by considering 3 as composed.
of three units, 1, 1, 1, and adding each in succession to the number 5.
The sum of 5 and 1 is 6,,, 6and 1 is 7,,, 7 and 1 is 8,
that is, the sum of 3 and 5 is 8.
In a similar way the sum of 5 and 3 may be shown to be 8, by
considering 5 as composed of five units, 1, 1, 1, 1 1, and adding each.
in succession to the number 3.
Hence the sum of 5 and 3 is the same as the sum of 3 and 5;
or the sum of two numbers is the same in whatever way they may be
added together.
The sums of every two numbers consisting of single figures may be'
found in this manner, and the results exhibited as follows:
The sun of 1 and 1 is 2 The sum of 2 and 1 is 3 The sum of 3 and 1 is 4,, 2,, 3,, 2,, 4,, 2,, 5,, 3,, 4,, 3,, 5,, 3,,,, 4,, 5,, 4,, 6,, 4,, 7,, 5,, 6,, 5,, 7,, 5,, &,, 6,, 7,, 6,, 8,, 6,, 9
7,, 8,, 7,, 9,, 7,, 1,, 8,, 9 8,, 10,, 8,, 11,, 9,10 9,, 9,, 12;