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

From Wikisource
Jump to navigation Jump to search
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