= When we wish to state that one quantity or number is equal to another quantity or number, the sign of equality = is employed. Thus 8 added to 2 = 6, or 8 added to 2 is equal to 6.

+ When the sum of two quantities or numbers is to be taken, the sign plus + is placed between them. Thus 8 + 2 = 6, that is, the sum of 3 and 2 is 5. This is the sign of Addition.

- When the difference of two numbers or quantities is to be taken, the sign minus - is used, and shows that the latter number or quantity is to be taken from the former. Thus 6 - 2 = 8. This is the sign of Subtraction.

X When the product of any two numbers or quantities is to be taken, the sign into x is placed between them. Thus 8 x 2 = 6. This is the sign of Multiplication.

/ When we are to take the quotient of two quantities, the sign by / is placed between them, and shows that the former is to be divided by the latter. Thus 6 / 2 = 8. This in the sign of Division. But in some cases in this work, the mode of division has been to place the dividend above a horizontal line, and the divisor below it, in the form of a vulgar fraction, thus:

Dividend 6

--- -------- = Quotient. - = 8.

Divisor 2

When the square of any number or quantity is to be taken, this is denoted by placing a small figure 2 above it to the right. Thus 61 shows that the square of 6 is to be taken, and therefore 62 = 6 X 6 = 36.

When we wish to show that the square root of any number or quantity is to be taken, this is denoted by placing the radical sign l √ before it. Thus √ 36 shows that the square root of 36 ought to be taken, hence √86 = 6.

The common marks of proportion are also used, viz, : :: : as 3: 6 :: 4: 8, being read 3 is to 6 as 4 is to 8.

The application of these signs to the expression of rules is exceedingly simple. Thus, connected with the circle we have the following rules:

1st. The circumference of a circle will be found by multiplying the diameter by 3.1416.

2d. The diameter of a circle may be found by dividing the circumference by 3.1416.

3d. The area of a circle may be found by multiplying the half of the diameter by the half of the circumference, or by multiplying together the diameter and circumference, and dividing the product by 4, or by squaring the diameter, and multiplying by •7854.

Now all these rules may be thus expressed: 1st. diameter X 3.1416 = circumference.

2d. circumference / 3.1416 = diameter.

3d diameter/2 x circumference /2 = area or, diameter X circumference / 4 = area.

or, diameter2 X .7854 = area.