A suitable illustration of the preceding exercise will be found in the Author's DIAGRAMS ILLUSTRATIVE OF FORM. No. I.

The DEFINITION of parallel lines will be found page 18.

The next lesson, or a continuation of the same lesson, may consist of a repetiton of PARALLEL LINES in various directions, as directed in Chapter VI.

For Illustrations, see DIAGRAMS, Nos. II, III, IV, V.

Useful QUESTIONS on this subject may be selected from Model Lessons for Infant Schools, Part II, pp. 186 to 190.

CHAPTER VIII.

To draw straight lines, forming ANGLES of various kinds.

The teacher will select such of the following exercises as he thinks most useful for his pupils. He will also determine upon how many times each exercise should be repeated; and he will be guided by the age and attainments of his pupils in introducing the DEFINITIONS.

EXAMPLE I. To draw two right

angles.

DIAGRAMS to illustrate the delineation of FORM, No. VI.

INSTRUCTION-1. Draw a horizontal line.

2. Draw a perpendicular, and make it stand upon, or touch, the horizontal.

The angle on each side of the perpendicular is a right angle.

DEFINITIONS. *

--

-1. "A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line."

2. "When a straight line standing on another straight line makes the adjacent angles equal to each other, each of these angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it."

QUESTION upon these definitions, if given.

*The definitions are taken from an excellent edition of Euclid, by R. Potts, M.A., published by W. Parker, West Strand, London.

EXAMPLE II. To draw four right

angles.

DIAGRAMS, No. VII.

+

INSTRUCTION.-1. Draw a horizontal line.

2. Draw a perpendicular through the middle of the horizontal;-making the length of the perpendicular below the horizontal equal to its height above it.

¶ Four right angles are described.

EXPLANATION. The point at which the perpendicular here cuts the horizontal, is called the point of bisection.

EXAMPLE III.-To describe va

rious angles.

DIAGRAMS, No. VIII.

INSTRUCTION.-1. Draw a horizontal line.

2. Draw a perpendicular standing upon the middle of the horizontal.

3. From a point which shall lie somewhere between the top of the perpendicular, and the left extre

mity of the horizontal, draw a line to touch the point where the perpendicular meets the horizontal.

4. On the right side of the perpendicular, draw a corresponding line.

¶ Various angles are described.

DEFINITION.- -“An obtuse angle is that which is greater than a right angle."

"An acute angle is that which is less than a right angle."

EXAMPLE IV. To draw various angles in opposite sides of a horizontal or perpendicular.

DIAGRAM, No. IX.

*

INSTRUCTION.-1. Draw a horizontal line.

2. Draw a perpendicular, cutting the horizontal. 3. Draw a straight line, slanting from left to right and passing through the point where the perpendicular cuts the horizontal.

4. Continue this line to some imaginary point below the horizontal.

5. Draw a corresponding line slanting from right to left.

¶ The various kinds of angles, acute, obtuse, and right angles, will be described on both sides of the horizontal and perpendicular.

EXERCISES.-1. Repetitions of the figure just

described.

2. After which, and to vary this EXERCISE, the pupils may be required to join the extremities of the lines;-as in the annexed diagram.

DEFINITION.-An angle divided by a right line into two equal parts is said to be bisected.

QUESTION on the various angles described in the above figures.

Useful questions on the subjects of this chapter will be found in Model Lessons for Infant Schools, Part II, pp. 166 to 170.

EXPLANATION.-Triangles are those rectilineal

figures which are contained by three straight lines.