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Formation of combined angles, or of Trilateral, Quadilateral, and Multilateral figures or Polygons.

The mother draws a threesided or trilateral figure, saying, this is a triangle. She draws, after this, several triangles, &c.

She draws quadilateral figures. A square.

An oblong.

A rhomb.

A rhomboid.

Five-sided Figures, or Penta-
gons, &c.


and makes him count the number of each sort of figures.

After this she tells him to find out similar figures on surrounding objects, either in the house, the garden, or the fields.

In this the child must be well exercised, as, while affording him amusement, it will greatly strengthen his faculties; but the mother will recollect that the object, at present, simply is, Intuition and Denomination; and she will avoid every attempt at definition.


Points, united and separate.

The mother makes two points, joining one another, but so as to be distinguished as two; then two more, separate from each other; saying, these two points are in contact; these two are separate.

Try to make two points, which join each other or are in contact; three which are separate: make a number of each sort, and tell me how many you have made of each.


Straight lines, and rectilinear figures, considered as united and separate.

Mother draws two, three, four separate straight lines, &c. She draws two, three, four straight lines in contact. Two lines in contact, and a third not joining the former.


The mother draws a number of lines which are in contact, and a number which are separate, and asks, How many are in contact, and how many separate?

She then draws a number of triangles, Squares, and polygons, both separate and in

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Mother. Can you show me in this room, two lines, two angles, triangles; and two foursided figures in contact? &c.

Can you point out any lines or figures of the same sort, separate from each other? &c.

SECTION VIII. Elements of form, considered with respect to

The mother makes two points of equal size or magnitude, and two of unequal size, saying? These two are equal, and those two unequal points. Try to do the same. How many points of equal magnitude do you see here? She now draws two lines, equally long, and says, Two lines of equal length. She makes two, three, six, eight, &cc. lines of equal length. Two lines of unequal length, three, four, five, &c.

This exercise should be long continued, as it is of great importance to the child to judge accurately of lines of equal and unequal length.

The mother may occasionally measure with a compass or rule, to show him whether she has been correct, or how far she has failed.


Mother. Can you point out two lines of equal length? How many equal lines are there in this table?


Magnitude and position of lines and forms combined.

The mother makes two, three, four points of equal magnitude, so as to be in contact,

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