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2. He then draws the lines; joining the dots himself, as an example to the pupils.

NOTE. The horizontal line, ba, is to be drawn before the slanting line, c a.

EXERCISES.-1. The teacher marks the dots, and the pupils draw the lines.

2. The pupils mark the dots, and draw the lines.

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line a b is drawn before c a—and that in no case an upstroke is made.

EXPLANATION.-Two straight lines cannot in

close a space.

This may be illustrated by means of

two long pencils or pen-holders.

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

* Properly speaking, we should say, "a plane rectilineal angle;" but this part of the definition may be deferred for the present, if the teacher think proper.

EXAMPLE II.

OBSERVE-1. The number of lines drawn to the point of the angle are here increased.

2. The points of commencement should be dotted by the teacher.

EXERCISES.-1. The childr en

join the dots by lines, as before.

2. The children make the dots and connect them.

EXAMPLE III.

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INSTRUCTION. The teacher makes dots for straight lines to cross one another.

EXERCISES.-1. The children

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*The dots between these lines are not to be made until the next exercise.

EXPLANATION.-The straight line in the last Example, which crosses the horizontal, is called a vertical line.

EXAMPLE IV.

INSTRUCTION.-The teacher draws the cross lines as in the preceding exercise, and puts dots between them.-See note, page 17.

EXERCISES.-1. The children join these dots; drawing the lines which connect them through the point at which the horizontal and vertical lines cross. 2. The children make the dots as well as join the lines.

CHAPTER VI.

To draw STRAIGHT LINES of various lengths. (The children at the teacher's desk, as before.)

To draw HORIZONTAL parallel lines of various lengths.

EXAMPLE I.

DEFINITION.- "Parallel straight lines are such as (are in the same plane, and which*) being produced ever so far both ways do not meet."

*This part of the definition may be omitted for the present.

INSTRUCTION.-1. Draw a horizontal line from left to right, not exceeding one inch in length.

2. About half an inch below this line, draw another of equal length, and keep it parallel to the first.

3. In the same direction, continue this line, adding a piece of the same length as the first.

¶ In the middle of this line there will be a small break, caused by taking off the pencil at the first rest; but the whole line will be double the length of the first.

4. About half an inch below the line just drawn, draw another line in a similar manner, making it three times the length of the first.

5. Draw another line in a similar manner, making it four times the length of the first.

EXERCISE.-Repetition of the above, at the teach

er's discretion.

QUESTIONS may be asked upon parallels; and upon the comparative lengths of the lines.

To draw VERTICAL parallel lines of various lengths.

EXAMPLE II.

EXPLANATION.-Lines are said to be vertical when they are upright; this is, when they are parallel to the straight sides of a slate.

INSTRUCTION.-Draw the lines in parts of equal lengths, as in the last exercise; but in the present instance let the lines be drawn in a downward direction, instead of from left to right.

EXERCISES.-1. The lines just described.

2. Repetition of the preceding exercise.

QUESTIONS may be asked on parallel, horizontal, and vertical lines; and on the comparative lengths of such lines.

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