Prism

in geometry, is a body; or solid, whose two ends are any plain figures which are parallel, equal, and similar; and its sides connecting those ends, are parallelograms. Hence, every section parallel to the ends, is the same kind of equal and similar figure as the ends themselves are; and the prism may be considered as generated by the parallel motion of this plane figure. Prisms take their several particular names from the figure of their ends. Thus, when the end is a triangle, it is a triangular prism; when a square, a square prism; when a pentagon, a pentagonal prism; when a hexagon, a hexaconal prism; and so on. And hence the denomination prism comprises also the cube and pa- _ rallelopipedon, the former being a square prism, and the latter a rectangular one. And even a cylinder may be considered as a round prism, or one that has an infinite number of sides. Also a prism is said to be regular or irregular according as the figure of its end isa regular or an irregular polygon. The axis of a prism, is the line conceived to be drawn lengthways through the middle of it, connecting the centre of one end with that of the other end. _ Prisms, again, are either right or oblique. A tight.prism is that whose sides, and its axis, are perpendicular to its ends; like an up- ‘right tower. And ‘An oblique prism, is when the axis and sides _ are oblique to the ends; so that, when set upon one end, it inclines on one hand, like an in-. clined tower, The principal properties of prisms are, _ 1. That all prisms are to one another in the ratio. compounded of their bases and heights. 2, Similar prisms are to one another in the triplicate ratio of their like sides. 3. A prism is triple of a pyramid of equal base and height; and the solid content of @ prism is found by multiplying the base by the perpendicular height. ‘4, The upright surface of.a right prism ts equal to a rectangle of the same height, and its breadth equal to the perimeter of the base or end, And therefore such upright surface of a right prism is found by multiplying the perimeter of the base by the perpendicular height. Also the upright surface of an oblique prism is found by computing those of all its.parallelogram sides separately, and adding them together. And if to the upright surface be added the areas of the two ends, the sum will be the whole surface of the prism,