Chapter II.

Conventional Rule for Square Root.

(For explanation of principle on which the rule is founded see chapter beginning on page 72.)

Separate the given number into periods, by pointing every second figure, beginning with the unit's place.

Find the greatest square in the left hand period and place its root on the right; subtract the square of this root from the first period and to the remainder bring down the next period for a dividend.

Divide this dividend, omitting the last figure, by double the root already found, and annex the result to the root and also to the divisor, multiply the divisor as it now stands, by the figure of the root last obtained, and subtract the product from the dividend.

If there are more periods to be brought down, continue the operation in the same manner as before.

Example:

What is the square root of 144?

144(12
1

22

44
44

The greatest square in the left hand period or 1, is 1. Subtracting leaves nothing and bringing down the next period gives 44 for the new dividend. Doubling the root already found gives 2 for a trial divisor and trying this in the first figure of the new dividend gives 2 for the next root figure. Annexing this to the trial divisor gives 22 for the true divisor and multiplying by 2 gives 44, coming out even in this case.

are necessary.

Sometimes several trials

Chapter III.

Conventional Rule for Cube Root.

(For explanation of principle on which the rule is founded, see chapter beginning on page 85).

Separate the given numbers into periods, by pointing every third figure, beginning with the unit's place.

Find the greatest cube in the left hand period and place its root on the right; subtract the cube of this root from the left hand period and to the remainder bring down the next period for a dividend.

Divide this dividend, omitting the last two figures, by three times the square of the root already found; annex the quotient to the root.

Add together the trial divisor, with two ciphers annexed, three times the product of the last root figure by the rest of the root, with one cipher annexed; and the square of the last root figure.

Multiply the divisor, as it now stands,

by the figure of the root last obtained, and subtract the product from the dividend. If there are more periods to be brought down, continue the operation in the same manner as before.

By following the rules closely in the manner illustrated in the square root example, there will be no difficulty in understanding the operation.

Chapter IV.

Formulas.

As it is well to become familiar with the tools we are to use, the following signs are given, with their meanings, before we proceed to use them.

π called "pi"=3.1416, which is the circumference of a circle whose diameter is 1. This can be 1 inch, 1 foot or 1 mile, and the circumference will be 3.1416 inches, feet or miles as the case may be.

d2=d squared or multiplied by itself. d3=d cubed or multiplied by itself twice, d4d fourth, etc.

The small figures at top are called exponents.

√=square root and denotes that the square root is to be extracted from the number following it; when bar extends over other figures, it applies to all beneath it, thus √2+7=3 (square root of sum.) This can also be represented by √(2+7)=3 as before, the brackets showing that all