ARITHMETIC. SECTION I. 1. Definitions. 1. QUANTITY is a term applied to whatever may be increased, diminished, or measured. 2. A CONCRETE UNIT is any quantity which may be considered by itself, and made the measure of other similar quantities. (a.) It may be a single thing, as an apple, a book, a pound, a foot, a dollar; or it may be a collection of single things, as a dozen of apples, a score of sheep. 3. An ABSTRACT UNIT is the idea or conception of one, or of unity, without reference to any particular thing or quantity. Any number of abstract units, considered as forming a single collection or whole, may also be regarded as an abstract unit; as, one ten, one hundred, one thousand, &c. (a.) The term unit, when used without any limitation, always refers to a single thing or quantity, or to the abstraction, one. 4. A CONCRETE NUMBER expresses a single thing or quantity, considered as a unit of measure; or it expresses how many such units there are in any given quantity; as, one yard, three shillings, eight barrels, ten birds. 5. An ABSTRACT NUMBER expresses how many times a unit is taken or repeated, without any reference to the nature of the unit; as, one, eight, twelve. 6. The unit which any number expresses is called the UNIT OF MEASURE, or the UNIT OF COMPARISON. (a.) In an abstract number it is the abstract unit, and in a concrete |