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.

- A practical and theoretical system of arithmetic…also a treatise on mensuration, and a brief practical system of book-keeping. by George WilsonCall Number: QA101 .W74Published/Created: Canandaigua, NY: C. Morse, 1836

- Addition
- 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:
- The
**Dividend**, or number to be divided. - The
**Divisor**, or number by which it is divided. - The
**Quotient**, or result of the division, showing how many times the divisor is contained in the dividend. P. 19.

- The
- 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.

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