1911 Encyclopædia Britannica/Dimension

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DIMENSION (from Lat. dimensio, a measuring), in geometry, a magnitude measured in a specified direction, i.e. length, breadth and thickness; thus a line has only length and is said to be of one dimension, a surface has length and breadth, and has two dimensions, a solid has length, breadth and thickness, and has three dimensions. This concept is extended to algebra: since a line, surface and solid are represented by linear, quadratic and cubic equations, and are of one, two and three dimensions; a biquadratic equation has its highest terms of four dimensions, and, in general, an equation in any number of variables which has the greatest sum of the indices of any term equal to n is said to have n dimensions. The “fourth dimension” is a type of non-Euclidean geometry, in which it is conceived that a “solid” has one dimension more than the solids of experience. For the dimensions of units see Units, Dimensions of.