Independent and dependent variables

The second variable, to which values may be assigned at pleasure within limits depending on the particular problem, is called the independent variable, or argument; and the first variable, whose value is determined as soon as the value of the independent variable is fixed, is called the dependent variable, or function.

Frequently, when we are considering two related variables, it is in our power to fix upon whichever we please as the independent variable; but having once made the choice, no change of independent variable is allowed without certain precautions and transformations.

One quantity (the dependent variable) may be a function of two or more other quantities (the independent variables, or arguments). For example, the cost of cloth is a function of both the quality and quantity; the area of a triangle is a function of the base and altitude; the volume of a rectangular parallelepiped is a function of its three dimensions.