GENERALITY

A French territorial division under the government prior to the Revolution. The generalities amounted in all to 34. This division was principally with reference to the collection of taxes. GENERALIZATION, in Logic, has been defined as the act of comprehending under a common name several objects agreeing in some point which we abstract from each of them, and which that common term serves to indicate. ( Whateley's Logic, p. 388.) GENERATION, or GENESIS, in Geometry, denotes the formation or production of a geometrical figure or quantity. A line is said to be generated by the motion of a point, a surface by the motion of a line, and a solid by that of a surface. A sphere or spheroid is generated by the revolution of a semicircle, or semi-ellipse, about its diameter; and a circle by the revolution of its radius about one of its extremities. The figure thus produced, or generated, is called the generant; and it is a general property of every such figure that its area or content is equal to the product which arises from multiplying the generating quantity; into the length of the path described by its centre of gravity. All quantities may be considered as generated by motion; and hence arose the terms fluxion a.n^ fluent in the infinitesimal analysis. GENESIS, [s. 502]