Logarithm of a number. The exponent of the power to which 10 must be raised in order to obtain the number.

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

Longitude of a point. The angle between two planes which are

supposed to pass through the centre of the earth and contain, the one the meridian of that point, and the other the standard meridian.

Loss. In business, the excess of the cost price above the selling price or net proceeds of sale.

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. The square of a mean proportional is equal to the product of the extremes.

Means. The terms of a proportion or of a series intervening between the extremes.

Meter. The unit of length in the metric system, equal to 39.37043 inches.

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 amount that remains of the money received for property after paying all expenses incurred in disposing of it. 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 number. A name used to designate the number of things in a group, as tens, hundreds, thousands, etc.

Oncometrics. The measurement of volumes.

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.

Permutation. The changing of the order of sequence in a given number of things.

Planet. A celestial body revolving about the sun.

Policy. The written contract of insurance.

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

Power. The product of two or more equal factors.

Premium. The sum paid for insurance computed at some rate per cent of the amount 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. The sum of 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 or net proceeds above cost.
Progression. A series.

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 compared.

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.

Roman notation. The system of expressing numbers adopted by
the Romans, which employs seven letters of the alphabet.
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 obligation.

Series. A set of terms any one of which can be derived from one or more of the terms that precede, according to some law.

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 together.

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.

Unit. A single thing. Also, an arbitrary length, adopted as a standard of measure, in terms of which all measurements are expressed. Verify. To establish, by experiment, the truth of any statement. Volume of a solid. The ratio of the solid to an assumed unit of measure; usually a cube of the linear unit.

ARITHMETIC.

CHAPTER I.

NUMBERS.

1. A FUNDAMENTAL IDEA, like that of number, cannot be defined. A number is the simple, direct answer to the question, How many?

2. A system of naming numbers is called numeration, and a system of representing numbers by symbols is called notation.

The first twelve numbers, formed by adding one thing at a time, are named:

One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.

These numbers are represented by Arabic figures, or digits, as follows:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

3. The digit 0, called naught, zero, or cipher, is used as a symbol of the words "none" or "nothing." A digit written in the second place to the left of another digit signifies tens. Thus, 10 is one ten and nothing; 11 is one ten and one; 12 is one ten and two; 23 is two tens and three; etc., etc.

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