Page:Passages from the Life of a Philosopher.djvu/74

This page has been validated.
58
ADDITION.

execution, little beyond mechanical means of performing the arithmetical operation of Addition. Subtraction can, by the aid of a well-known artifice, be converted into Addition.

The process of Addition includes two distinct parts—1st. The first consists of the addition of any one digit to another digit; 2nd. The second consists in carrying the tens to the next digit above.

Let us take the case of the addition of the two following numbers, in which no carriages occur:—

6023

1970

——

7993

It will be observed that, in making this addition, the mind acts by successive steps. The person adding says to himself—

0 and 3 make three,

7 and 2 make nine,

9 and 0 make nine,

1 and 6 make seven.

In the following addition there are several carriages:—

2648

4564

——

7212

The person adding says to himself—

4 and 8 make 12 : put down 2 and carry one.
1 and 6 are 7 and 4 make 11 : put down 1 and carry one.
1 and 5 are 6 and 6 make 12 : put down 2 and carry one.
1 and 4 are 5 and 2 make 7 : put down 7.

Now, the length of time required for adding one number to another is mainly dependent upon the number of figures to