Dimension

Dimension. In Geometry, a point, since it has merely position, is said to have no, or to be of zero, dimensions; a line, straight or curved, is of one dimension—viz. length; a plane surface has two—length and breadth; while a solid is said to be of three dimensions—length, breadth, and thickness. Thus it will be seen that by the term dimension is meant a direction in which extension may be reckoned or measured. The three last-named dimensions are found sufficient to determine all known forms of extension. Hence space is tridimensional. The possibility of space of higher dimensions existing has been much discussed. Since points, lines, and surfaces in general generate by their motion lines, surfaces, and solids respectively, so it is held that some analogous generation of a fourth dimensional figure by one of three dimensions is conceivable. The subject, although interesting, is wholly speculative.—In Algebra, the term dimension is employed in much the same sense as degree, to express the sum of the indices of those letters with reference to which the term containing them is considered—e.g. $xy$, $x^2$, are both of two dimensions, or of second degree; $x^2y$, $x^3$, are of three dimensions, or third degree, &c.