A curve or a plane figure is symmetrical with respect to a given line, and a line, surface, or solid with respect to a plane, when for each point on one side of the line or plane there is a corresponding point on the other side, so situated that the line joining the two corresponding points is perpendicular to the line or plane and is bisectad by it. Two solids are symmetrical when they are so situate dwith the respect to an intervening plane that the several points of their surfaces thus correspond to each other in position and distance. In analysis, an expression is symmetrical with respect to several letters when any two of them may change places without affecting the expression; as, the expression a^2b + ab^2 + a^2c + ac^2 + b^2c + bc^2, is symmetrical with respect to the letters a, b, c. Symmet"rically, Symmet"ricalness.
Origin: Cf. F. Symetrique. See Symmetry.
(01 Mar 1998)
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