Discount. Allowance made for the payment of money before it becomes due. Also, the difference between the market value and the face value when the market value is below the face value. Dividend. In division, the given number which is equal to the product of a given factor (called divisor) and required factor (called quotient). In business, the share of profits which belongs to each owner of stock, on his proportion of the capital. Division. The operation by which, when a product and one of its factors are given, the other factor is found.

Divisor. The number by which a given dividend is to be divided. Draft. A written order directing one person to pay a specified sum of money to another.

Drawee of a draft. The person to whose order the sum of money named in a draft is to be paid.

Drawer of a draft. The person who signs the draft.

Duties. Taxes required by the government to be paid on goods imported, exported, or put on the market for consumption. Equation. A statement that two expressions of number are equal. Equation of payments. The finding of an average time at which several payments may be justly made.

Exchange. A system of paying debts, due to persons living at a distance, by transmitting drafts instead of money.

Exponent. A small figure placed at the right of a number to show
how many times the number is taken as a factor.
Extremes. The first and last terms of a proportion.
Evolution. The process of finding the root of a number.

Factors. The factors of a number are a set of numbers whose product is the given number; they are assumed to be integral, except in the extraction of roots. In commerce, agents employed by merchants to transact business.

Figures. Symbols used to represent numbers in the common system

of notation. Also diagrams used to represent geometrical forms. Firm. The name under which a company transact business. Fractions. One or more of the equal parts into which the unit is divided.

Grace. An allowance of three days, after the date a note becomes due, within which to pay the note.

Gram. The unit of weight in the metric system.

Greatest common measure. The greatest number which is a common factor of two or more given numbers.

Improper fraction. A fraction whose numerator equals or exceeds the denominator.

Index. A figure written at the left and above the radical sign to show what root of the number under the radical sign is required. A fraction written at the right of a number, of which the numerator shows the required power of that number, and the denominator the required root of that power.

Instalment. A payment in part.

Insurance. A guarantee of a specified sum of money in the event of loss of property by fire, storm at sea, or other disaster; or of loss of life.

Integral number. A number which denotes whole things.
Interest. Money paid for the use of money.

Involution. The process of finding a power of a number.

Latitude of a point. The angle made by the vertical line at that point with the plane of the equator.

Least common multiple. The least number which is a common multiple of several given numbers.

Liability. A debt, or obligation to pay.

Line. Length without breadth or thickness. The path of a moving point.

Liter. The unit of capacity in the metric system equal in volume to a cube each edge of which is one-tenth of a meter.

Long division. The method of dividing in which the processes are written in full.

Longitude of a point. The angle between two planes supposed to
pass through the centre of the earth and to contain, the one the
meridian of that point, and the other the standard meridian.
Loss. The excess of the cost price above the selling price.
Maturity of a note. The date at which a note legally becomes due.
Mean proportional. A number which is both the second and third
terms of a proportion.

Means. The terms of a proportion between the extremes.
Meter. The unit of length in the metric system.

Minuend. The given number in subtraction which is equal to the sum of another given number called the subtrahend, and a required number called the difference or remainder.

Mixed number. A number that expresses both entire things and parts of things taken together.

Multiple of a number. The product obtained by taking the given number an integral number of times.

Multiplicand. The number to be multiplied by another.

Multiplication. The operation of finding a number bearing the same ratio to the multiplicand which the multiplier bears to unity. Multiplier. The number by which the multiplicand is multiplied. Net proceeds. The money that remains of the money received for property after all expenses and discounts are paid.

Notation. A system of expressing numbers by symbols.

Note. A written agreement to pay a specified sum of money at a specified time.

Number. The answer to the question, How many?

Numeration. A system of naming numbers.

Obligation. A debt, or liability to pay.

Order of units. A name used to designate the number of things in a group, as tens, hundreds, thousands, etc.

Partial payment. Part payment on a note.

Partnership. An association of two or more persons to carry on business.

Par value. Face or nominal value.

Pendulum. A body suspended by a straight line from a fixed point, and moving freely about that point as a centre.

Percentage. A part of any given number reckoned at some rate per cent.

Period. A group of three figures.

Policy. A written contract of insurance.

Poll tax. A tax levied by the head or poll.

Power. The product of two or more equal factors.

Premium. Money paid for insurance computed at some rate per cent of the value insured. Also the excess of market value above par value.

Present worth. The present value of a debt due at some future day. Prime number. A number which has no integral factors except

itself and one.

Principal. Money drawing interest.

Problem. A question to be solved.

Product. The result obtained by multiplying the multiplicand by the multiplier.

Profit. The excess of selling price above cost.

Proof. The evidence by which the accuracy of any result is established.

Proper fraction. A fraction, the numerator of which is less than the denominator.

Proportion. A statement that two ratios are equal.
Quantity. The answer to the question, How much?
Quotient. The number sought in division.

Rate per cent. Rate by the hundred.

Ratio. The relative magnitude of two numbers or of two quantities. Reciprocal of a number. One divided by that number.

Reduction. The process of changing the unit in which a quantity is expressed without changing the value of the quantity. Remainder. The number which, added to the subtrahend, gives a sum equal to the minuend.

Root of a number. One of the equal factors of the number.
Rule. The statement of a prescribed method.

Security. Property used to guarantee the payment of any debt. Share. One of a certain number of equal parts into which the capital of a company is divided.

Short division. The method of dividing in which the operations of multiplying and subtracting are performed mentally.

Solid. A magnitude which has length, breadth, and thickness. Solution. The process by which the answer to a question is obtained. Specific gravity of a substance. The ratio of the weight of a

given volume of it to that of an equal volume of water.

Square root. One of two equal factors.

Stock. Capital invested in business.

Subtraction. The process of finding a number which added to one of two given numbers will produce the other.

Sum. The number which results from combining two or more numbers by addition.

Surd. An indicated root the value of which cannot be exactly expressed in figures.

Surface. That which has only length and breadth.

Thermometer. An instrument for measuring heat.

Units. The standards by which we count separate objects or measure magnitudes.

Verify. To establish, by trial, the truth of any statement.

Volume of a solid. The volume of a solid is the number of units of volume it contains; the unit of volume being a cube whose edge is a unit of length.

A

GRAMMAR SCHOOL ARITHMETIC.

CHAPTER I.

PRELIMINARY DEFINITIONS.

1. Number. A fundamental idea, like that of number, cannot be defined. A simple, direct answer to the question "How many?" is a number.

2. A collection of several similar objects (as a collection of apples) gives the idea of number.

3. Units. In counting separate objects the standards by which we count are called units. Thus:

In counting the eggs in a nest, the unit is an egg.

In selling eggs by the dozen, the unit is a dozen eggs. In selling bricks by the thousand, the unit is a thousand bricks.

4. Measurement. Continuous magnitudes, such as length, surface, space, time, heat, cannot be counted; they are measured. Magnitudes, whether continuous or separate, are generally measured, and the standards by which they are measured are fixed by law, or by common consent.

5. Units of Measure. The standards by which we measure magnitudes are called units of measure. Thus : An inch, a foot, a yard, a rod, a mile, are units of length. A square inch, a square foot, are units of surface. A cubic inch, a cubic foot, are units of volume.