27. It was remarked, in Art. 4, that the convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude; and in Art. 24, that the surface of a sphere is equal to its diameter into the circumference of a great circle: hence, the surface of a

QUEST.-25. What is the solidity of a sphere equal to? 26. If a semicircle and a rectangle revolve about the diameter of the semicircle, what will the semicircle describe? What will the rectangle describe? 27. How does the surface of a sphere compare with the convex surface of the circumscribing cylinder?

Of the Round Bodies.

sphere is equal to the convex surface of the circumscribing cylinder.

28. The solidity of a sphere is equal to two-thirds of the solidity of the circumscribing cylinder.

29. The cylinder, the cone, and the sphere are called the three round bodies.

QUEST.-28. What portion of the cylinder is the inscribed sphere? 29. What are the three round bodies?

8

PART II.

SECTION I.

PRACTICAL GEOMETRY.

1. Practical Geometry explains the methods of constructing or describing the Geometrical figures.

For these constructions, certain instruments are necessary. These we shall now describe.

DIVIDERS, OR COMPASSES.

a

2. The dividers is the most simple and useful of the instruments used for describing figures. It consists of two legs, ba and be, which may be easily turned around a joint at b.

QUEST.-1. What is Practical Geometry? 2. What are the dividers used for? Of how many parts are they composed? How are these parts moved?

Practical Geometry.-Instruments.

PROBLEM I.

On any line as CD, to lay off a distance equal to AB.

3. Take up the dividers with the thumb and second finger, and place the fore finger

on the joint at b. Then, set

4

B

one foot of the dividers at A,

ED

and extend the legs with the

thumb and fingers, until the other foot reaches to B. Then raising the dividers, place one foot at C, and mark with the other the distance CE, this will evidently be equal to AB.

PROBLEM II.

To describe from a given centre the circumference of a circle having a given radius.

C

B

4. Let C be the given centre, and CB the given radius. Place one foot of the dividers at C, and extend the other leg until it shall reach to B. Then turn the dividers around the leg at C, and the other leg will describe the required circumference.

QUEST-3. Explain the manner of laying off a given distance on a given line? 4. Explain the manner of describing from a fixed centre, the circumference of a circle that shall have a given radius ?