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not parallel circular lines. Two parallel ones. Show me a concave angle. (The point of a knife generally forms such an angle.) Show me a convex angle. Try whether you can find, in the field or in the garden, leaves which have convex, concave, or mixed angles. Search today for leaves which form only concave angles. Try to find some of an oval form. The flower or the tree, of which the child has taken the leaves, may be named to him.

Look to-day for leaves of a triangular form; for such as form convex-angled triangles, &c.

Look for four, five, and six-angled figures. The mother now and then takes a plant, and asks the child how many, and what sort of angles its leaves have, &c.

Drawing Exercises in curve Lines, and Forms composed of them.

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Produce a symmetrical form, by a combination of parallel and not parallel curve lines.

Draw one composed of curve-lined angles.

Another, by a combination of separate curvelined concave angles.

Produce one or two drawings of convex twoangled figures. Another of mixed two-angled figures, &c.

Invent a figure, by combining convex-angled triangles. Another, by curve-lined parallel trapeziums.

Produce some pretty forms of curve-lined pentagons, hexagons, &c.

Another, by a combination of ovals. Draw a combination of spiral and of waved or serpentine lines.




Make a form of two-angled figures, being in contact with each other.

Produce figures composed of triangles, of squares, or of ovals, in contact with each other.

Draw figures of any sort of curve lines you fancy. Copy this leaf: any curve-lined ornament on a piece of furniture. (Should some of these ornaments be too complicated, the child limits himself to the principal forms only, by omitting all minutiae.)


Curve Lines and Circular Figures, considered with respect to Magnitude.

Mother. Draws two, three, four, five circles of equal magnitude. Draw two-arched lines of equal magnitude. Draw two circles of unequal magnitude. Draw two, three, four, &c. concave angles, of equal magnitude in regard to their sides. Draw convex angles of equal magnitude. Draw two, three, four, five, six-angled figures of equal magnitude. Concave and convexangled figures of equal magnitude. Draw

ovals, waved or serpentine lines, spiral lines of equal magnitude: make ovals of unequal magnitude.


Mother. Find out two curve lines of equal magnitude. Look out, to-day, for concave twoangled figures and triangles. Four and fiveangled figures of equal magnitude. Can you find any object on which the spiral line is visible? (The shell of a snail, &c.)

Relations of Mensuration.

Whatever has been done with the straight

lines relative to mensuration, may also be

done with circular, curve, and arched lines.

For instance; the moot.

ther draws the four

lines, a, b, c, d, and

says: the second curve

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line, by is twice as long as the first, a. The fourth, d, is four times as long as the third, c, &c.

Mother. Draw two curve lines, of which the second is five, six, or nine times as long as the first.

This two-angled figure, in its greatest length, is twice as long as it is broad.

Draw a two-angled figure which is a little longer than it is broad. Draw one which is four times as long as it is broad: twice as long, &c.

In the same manner can the three and fourangled figures be treated.


Mother. How many times is this oval table as long as it is broad? or how many times is its breadth contained in its length? How many times is this two-angled leaf longer than it is broad? How many times this three, four, five, six-angled leaf, &c.

Combination of straight and curve Lines.

The mother draws a straight and a curve line, and says, these two lines are not parallel.

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