Pyramid and Cylinder. 14. The slant height of a right pyramid, is a line drawn from the vertex, perpendicular to one of the sides of the polygon which forms its base. Thus. SF is the slant height of the Pyramid S-ABCDE. B 15. If from the pyramid S-ABCDE the pyramid S-abcde be cut off by a plane parallel to the base, the remaining solid, below the plane, is called. the frustum of a pyramid. The altitude of a frustum is the perpendicular distance between the upper and lower planes. 16. A Cylinder is a solid, described by the revolution of a rectangle, AEFD, about a fixed side, EF. As the rectangle AEFD, turns around the side EF, like a door upon its hinges, the lines AE and FD describe circles, and the line AD describes the convex surface of the cylinder. The circle described by the line AE, is called the lower base of the cylinder, and the circle described by DF, is called Of the Cylinder. The immovable line EF is called the axis of the cylinder A cylinder, therefore, is a round body with circular ends 17. If a plane be passed through the axis of a cylinder, it will intersect the cylinder in a rectangle, PG, which is double the revolving rectangle DE. K 18. If a cylinder be cut by a plane parallel to the base, the section will be a circle equal to the base. For, while the side FC, of the rectangle MC, describes the lower base, the equal side MP, will describe the circle MLKN, equal to the F lower base. 19 If a polygon be inscribed in the lower base of a cylinder, and a corresponding polygon be inscribed in the upper base, and their vertices be joined by straight lines, the prism thus formed is said to be inscribed in the cylinder. Of the Cone. 20. A cone is a solid, described by the revolution of a right angled triangle, ABC, about one of its sides, CB. The circle described by the revolving side, AB, is called the base of the cone. The hypothenuse, AC, is called the slant height of the cone, and the surface described by it, is called the convex surface of the cone. A The side of the triangle, CB, which remains fixed, is called the axis, or altitude of the cone, and the point C, the vertex of the cone. 21. If a cone be cut by a plane parallel to the base, the section will be a circle. For, while in the revolution of the right angled triangle SAC, the line CA describes the base of the cone, its parallel FG will describe a circle FKHI, parallel to the base. If from the cone S-CDB, the cone S-FKH be taken away, the remaining part is called the frustum of the cone. 22. If a polygon be inscribed in the base of a cone, and straight lines be drawn from its vertices to the vertex of the cone, the pyramid thus formed is said to be inscribed in the cone. Thus, the pyramid S-ABCD is inscribed in the cone. F B A E Of the Sphere. 23. Two cylinders are similar, when the diameters of their bases are proportional to their altitudes. 24. Two cones are also similar, when the diameters of their bases are proportional to their altitudes. 25. A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a certain point within called the centre. |
