ABSTRACT Mathematics

, otherwise called pure mathematics, is that which treats of the properties of magnitude, figure, or quantity, absolutely and generally confidered, without restriction to any species in particular: such as Arithmetic and Geometry. In this sense, abstract or pure mathematics, is opposed to mixed mathematics, in which simple and abstract properties, and the relations of quantities, primitively considered in pure mathematics, are applied to sensible objects; as in astronomy, hydrostatics, optics, &c.

Abstract Number, is a number, or collection of units, considered in itself, without being applied to denote a collection of any particular and determinate things. So, for example, 3 is an abstract number, so far as it is not applied to something: but when we say 3 feet, or 3 persons, the 3 is no longer an abstract, but a concrete number.