# Useful Definitions

All definitions on this page are from a contemporaneous text used in an English language textbook on arithmetic. This work contains instruction and problem solving exercises used in business arithmetic.

Putting together several smaller numbers to find their amount, or sum total: thus, 4 dollars and 8 dollars in one sum, are 12 dollars. P. 8.
Annuity
A sum paid annually; or, at equal stated periods. P. 167.
Arithmetic
Arithmetic treats of the properties, relations, and combination of numbers. Its principal branches are, notation or numeration, addition, subtraction, multiplication, and division. P. 5.
Arithmetical Progression
A series of numbers increasing or decreasing by a common difference, constitutes an arithmetical progression.
Compound Numbers
are such as express quantities consisting of different denominations, but of the same generic kind; as Tons, Hundreds, Quarters,&c.; Bushels, Pecks, Quarts, Pints. P.33
Decimal Fraction
A fraction whose denominator is 10, 100, 1000 &c. p.66.
Division
The operation by which we find how many times one number is contained in another and is a concise way of performing several subtractions. Three principal parts are to be noticed:
1. The Dividend, or number to be divided.
2. The Divisor, or number by which it is divided.
3. The Quotient, or result of the division, showing how many times the divisor is contained in the dividend. P. 19.
Duodecimals
These are fractional parts of a foot resulting from the division of it into 12 equal parts, and of each of those parts into twelfths, and so on. P. 81.
Evolution
Evolution is the reverse of involution. It is the operation by which, having a power given us, we find the root which, by multiplication, produced the power. P. 141.
Fraction
A broken number. P. 50.
Geometrical Progression
When a series of numbers increases by a common multiplier, or decreases by a common divisor, it constitutes a geometrical progression. P. 164.
Interest
A premium paid for the use of money. It is computed at a certain percent, per annum. Per cent means by the hundred; and interest is so many dollars on a hundred. The sum on which it is paid is called the Principal, and the percent, the Rate. The principal and interest added together are called Amount. P. 117.
Involution
The raising of powers from any given number as a root. P. 141.
Multiplication
Increasing or repeating the greater of two numbers given, as often as there are units in the less or multiplying number: hence it performs the work of many additions in the most compendious manner. P. 14.
Power
A power is the product of a number, multiplied into itself any number of times. P. 140.
Proportion/ratio
From the comparison of numbers we derive their ratio. Ratio is the mutual relation of two numbers in respect to quantity. P. 91.
Reduction
Bringing or changing numbers from one denomination to another without altering their value. Thus, 1 yard, reduced to the next inferior denomination, is 3 feet; and these reduced again, are 36 inches. P. 39.
Square Root
The name Square Root Is derived from a particular application of the rule, in finding the side of a square from its area or superficial contents. P. 142.
Subtraction
Taking a less number from a greater, in order to find the difference or remainder: thus, 4 dollars taken from 6 dollars, the remainder or differences is 2 dollars. P. 11.
Vulgar Fractions
A Fraction, or broken number, is an expression of some part or parts, of any thing or number considered as a whole. Fractions are either Vulgar or Decimal. A vulgar fraction is denoted by two numbers placed one below the other, with a line between them. The number below the line is called the denominator; and that above, the numerator. P. 50.