Of the Regular Solids.

2. The Hexaedron or cube, is a solid, bounded by six

equal squares.

3. The Octaedron, is a solid, bounded by eight equal triangles.

4. The Dodecaedron, is a solid, bounded by twelve equal pentagons.

QUEST.-2. What is the regular Hexaedron, or cube? 3. What is an Octaedron? 4. What is a Dodecaedron ?

Of the Regular Solids.

5. The Icosaedron, is a solid, bounded by twenty equal triangles.

6. The regular solids may easily be made of pasteboard.

Draw the figures of the regular solids accurately on pasteboard, and then cut through the bounding lines: this will give figures of pasteboard similar to the diagrams. Then, cut the other lines half through the pasteboard, after which, turn up the parts, and glue them together, and you will form the bodies which have been described.

QUEST.-5. What is the Icosaedron? 6. Describe the manner of making the regular solids with pasteboard.

Of the Round Bodies.

SECTION XII.

OF THE THREE ROUND BODIES.

1. 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 the upper base.

The immoveable line EF, is called the axis of the cylinder.

A cylinder, therefore, is a round body with circular ends.

QUEST.-1. How is a cylinder described? Point out the line which describes the convex surface of the cylinder. Point out the line which describes the lower base of the cylinder. Also the one which describes the upper base. What is the immoveable line called? What is a cylinder?

Of the Round Bodies.

2. If a plane be passed through the axis of a cylinder, it will intersect it in a rectangle PG, which is double the revolving rectangle EB.

E

3. If a cylinder be cut by a plane parallel to the base, the section will be da a circle equal to the base. Thus, MLKN, is a circle equal to the base FGC.

4. The convex surface of a cylinder D is equal to the circumference of the base, multiplied by the altitude. Thus, the convex surface of the cylinder AC is equal to

circumference of base × AD.

G

QUEST.-2. If a plane be passed through the axis of a cylinder, in what figure will it intersect the cylinder? How does this rectangle compare with the revolving rectangle? 3. If a cylinder be cut by a plane, parallel to the base, what will the section be? 4. What is the convex surface of a cylinder equal to ?

Of the Round Bodies.

5. The solidity of a cylinder is equal to the area of the base, multiplied by the altitude. Thus, the solidity of the cylinder AC, is equal to

area of base x FE.

6. A cone, is a solid, described by the revolution of a right angled triangle ABC, about one of its sides СВ.

The circle described by the revolving side AB, is called the base of the

cone.

B

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.

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.

QUEST.-5. What is the solidity of a cylinder equal to? 6. How is a cone described? Point out the line which describes the base of the cone. What is the hypothenuse of the revolving triangle called? What does it describe? What is the side of the triangle which remains fixed called? What is the vertex of the triangle called?