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Another by combining equal obtuse angles:

Another by equilateral triangles, of equal magnitude, joining each other:

Another of equilateral pentagons.

SECTION XXI.

Relations of Mensuration.

The mother tells the

child to draw two lines,

of which the second is

twice as long as the first; and two others, of which the latter is

three times as long as

the former. Two lines, , .—.

one of them four times as long as the other, &c.

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Make two angles, one of which has its sides twice as long as the other.

The exercise with angles may be extended, as in separate lines.

Form a triangle which has one of its sides four times as long as one of the two others. The mother makes a triangle, and tells the child to compare its sides; for instance, How many times is this line longer than that, &c.

Make four triangles, of different magnitude, and compare their sides one to another.

Make two equilateral triangles, of which the first has its sides twice as long as the sides of the second.

Draw two scaleHe triangles, where the base of the second is twice as long as the base of the first.

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Draw an oblong which is two,three, four times as long as

it is broad, | j |

five, six, se-
ven times, &c.

Make a rhomboid three ^- v

times as long as it is broad. \ A

Make three rhomboids twice v y as long as they are broad, &c. ^

SECTION XXII.

Application of the above Exercise to external Objects.

a. TO OBJECTS IN THE ROOM.

Mother. Can you show me in the room two lines, of which one is twice as long as the other? How many times do you think this table is as long as it is broad? or how many times is the broad side of this table contained in its long side? Is this room much longer than it is broad?

The mother, pointing to the floor of the room, and to the ceiling, says, this is the height of the room. Is the height of this room equal to its breadth, or does the breadth exceed its height? Is it much longer than high? Is this table higher than it is broad?

b. TO OBJECTS IN THE FIELDS.

Mother. Look at this tree: how many times do you think it is as high as I am?

Measure, by your eye, the space between this spot and that tree: how many times do you suppose it is contained in the space between this spot and that house? Measure it. He may afterwards measure it by paces or with a stick. Try how far you can throw this piece of wood. Try whether you can throw it further to-day, than yesterday. How many times in a minute can you jump from hence to yonder tree? How many times is this field longer than it is broad? , .

Will you count how many paces this piece of ground measures in length and breadth?

These, and similar exercises, will greatly tend to strengthen the mental and bodily powers of children, and will afford them much pleasure *.

SECTION XXIII.

Exercises in drawing Objects from Nature.

The mother finds out any object on which lines of different length are perceptible, which the child may try to represent on a slate. In these exercises also, it is necessary to proceed step by step, and to direct the child's attention at first only to the proportions of length, in order to prevent confusion: as soon as he is firm in them, she may gradually proceed to more complicated relations, directing his attention towards the difference between the symbol and the object. Copy with exactness the outline of this table; of this floor; of this ceiling; of this wall; of this door; of this window; of this mirror; of the front of the house; of the roof; of this field, &c.

In this manner the child may learn to copy the outlines of all objects.

* " Tout ce qui donne du mouvement au corps, sans le contraindre, est toujours facile a obtenir des enfans. Il-y-a mille moyens de les interesser a mesurer, a conn6itre, a estimer les distances."

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