DEFINITIONS OF SOLIDS, AND THEM PnorEwriEs.
A prism is a solid, the ends of which are similar and equal parallel plane figures, and the sides parallelo grams ; and if the ends of the prism are perpendicular to the sides, the prism is called a right prism, but if otherwise, it is termed oblique : If the sides and ends are equal squares, the prism is called a cube ; and if the base or ends are parallelograms, the prism is called a parallelopiped : If all the planes of the parallelopiped are at right angles to each other, then the prism is called a rectangular prism : It CI: ends of the prism are circles, the prism is carted a cylinder ; but if they are ellipses, it is called a cylindroid.
All the sections of a cylinder, or cylindroid, arc either circles, ellipses, or parallelograms, excepting when partly through the sides, and partly through the ends, and then they are portions of circles or ellipses.
All parallel sections of a prism are equal and similar polygons.
All sections whatever, except partly through the base, and partly through the sides of a parallelopiped, arc parallelograms.
All sections of a cylinder, or cylindroid, through the curved surface, are either ellipses or circles ; and as sections parallel to the axis are parallelograms.
A solid having any plane figure for its base. and its
sides triangles, meeting in a common point. is called a pyramid ; and this point is called the vertex of the pyramid. A pyramid is denominated triangular, square, pentagonal, hexagonal, &c. If the base be a circle. the pyramid is called a cone.
The axis of a cone is a straight line, extending frem the centre of the base to the vertex.
Properties.
All parallel sections of a pyramid arc similar figures, except they be parallel to a plane within the pyramid, passing through the vertex.
All sections through the vertex within the pyramid are triangles.
All sections of a cone parallel to the plane, passing through the vertex without the cone, but not parallel to the base, are ellipses.
All sections of a cone parallel to the base are circles. All sections of a cone parallel to a plane touching the curved surface arc parabolas.
All sections of a cone parallel to a plane within the cone, passing through the vertex, are hyperbolas.
The frustum of a pyramid, or cone, is that which is left by cutting away the part which contains the vertex by a plane parallel to the base.
An ungula of a pyramid, or cone, is that which is left by cutting away the part which has the vertex, by a plane not parallel to the base.