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4. Make a six sided polygon of unequal sides. (fig.4.) The word polygon means many-angled. To make a polygon, the best method is, first to place dots at the angles, and then draw right lines from dot to dot.

5. Make a five sided polygon of unequal sides. (fig.5.) 6. Make two polygons of unequal but parallel sides, (figs. 5 and 6.)

7. Make a six sided polygon of equal sides.

8. Make a five sided polygon of equal sides.

A polygon of equal sides is called a regular polygon. 9. From one point of a polygon draw diagonals, and then draw a parallel polygon. (fig. 7.)

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After drawing a polygon, from either of the points carry right lines to all the rest, thus making several triangles. These lines are called diagonals. Then you have only to draw parallels to the several sides from diagonal to diagonal.

To vary the exercise, let the pupil draw a polygon outside of that first drawn. He will then only have to lengthen the diagonals.

10. Draw a polygon, and from a central point draw diagonals, then draw a parallel polygon within and outside of the first drawn. (fig. 8.)

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11. Make a triangular pyramid. (fig. 9.) First draw the triangle which forms the base, then place a dot for the point or apex, and draw right lines from the point to each angle of the base.

12. Draw a quadrangular (or four angled) pyramid, (fig. 10,) then cut it by a plane parallel to its base.

The process is the same as in the preceding figure. The plane, or parallel to the base, must be the last thing done. The height of a pyramid is a perpendicular dropped from the apex or summit to the base. The pupil must be careful to distinguish the front lines from the back lines of the figure.

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13. Make a six sided pyramid. (fig. 11.)

14. Make a five sided pyramid. (fig. 12.)

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15. Make a five sided pyramid, and cut it by a plane parallel to the base. (fig. 12.)

Note. When the base of the pyramid is a regular polygon, and the height falls in the centre of it, the pyramid is upright and regular; such are figures 10, 11 and 12.

16. On two polygons of parallel sides, raise a pyramid. (fig. 12.)

This is merely another way of performing the last figure, by drawing both polygons before you draw the trunk of the pyramid.

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17. Make an upright triangular prism. (fig. 13.) A prism is a body formed from two equal and parallel polygons, whose corresponding points are joined by lines, all parallel and equal to each other; such are figures 13 to 20 inclusive.

The height of a prism is a perpendicular to the two bases. The prism is said to be upright when its sides are perpendicular, and oblique when its sides lean or are inclined.

18. Make an oblique triangular prism. (fig. 14.)

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19. Make an upright five sided prism. (fig. 15.)

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20. Make an upright parallelopiped. (fig. 16.)

When the bases of the prism are parallelograms, the body is called a parallelopiped. All the six faces are then parallelograms, and the two opposite faces are equal.

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21. Make an oblique parallelopiped. (fig. 17.) 22. Make a Cube. (fig. 18.)

The cube is a parallelopiped, all of whose faces are equal squares, and each placed at right angles with the contiguous or next squares.

A cube is a solid square, but it will be perceived, that in consequence of perspective, only the front and back face appear square. These two faces should be traced first, and the rest will easily be added. Dice are cubes.

23. Draw an oblique cube. (fig. 17. making the sides equal.)

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24. Cut a prism by a plane parallel to its bases. (fig. 19.)

A plane is a level. Place one die upon another, and together they make a prism, cut by a plane where the separation between the dice is.

25. Make a six sided prism, and double it by lengthening it. (fig. 19.)

When one die is put upon another, the first die is doubled in length.

26. Make a five sided prism, and cut it by three planes parallel to its base.

A long prism may be drawn and cut as in Prop. 24, or a short prism be first made and lengthened as many times as you please.

27. Draw a five sided prism in a horizontal position. (fig. 20.) Cut it by a plane parallel to its base.

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THIRD CLASS.

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1. Describe a circle and mark its centre. (fig. 1.) By constant practice the pupil will be able to draw a circle, and mark its centre with great exactness. The monitor with a pair of dividers will prove it. The pupils in the Monitorial School have various methods of making circles, without the aid of dividers, the most