thickness, it is said to have no dimension. It

has position only.

A point is therefore not a magnitude.

5. Name the number of points that are made by the intersection of the twelve lines of a cube. We cannot with a pencil make a point on paper-we represent a point.

When any two straight lines meet together from any other two directions than those which are perfectly opposite, they are said to make an angle.

And the point where they meet is called the angular point.

Thus two lines that meet each other on a cube make an angle.

6. Represent on paper a rectilineal angle.

7. Can two lines meet together without being in the same plane?

8. Point out two lines on a cube that exist on the same surface, and yet do not make an angle.

9. Name the number of plane angles on

the six surfaces of a cube, and the number of angular points, and say why the angular points are fewer than the plane angles.

The meeting of two plane surfaces in a line --for example, the meeting of the wall of a room with the floor, or the meeting of two of the surfaces of a cube-is called a dihedral angle.'

has.

10. Say how many dihedral angles a cube

The corner made by the meeting of three or more plane surfaces is called a solid angle. 11. Say how many solid angles there are in a cube.

When a surface is such that a line, when resting upon it in any direction, will be touched by it toward the middle of the line only, and not at both ends, such surface is called a convex surface.

12. Give an example of a convex surface.

When a surface is such that a line while rest

ing upon it, in any direction, will be touched by

1 Dihedral means two-surfaced.

it at the ends, and not toward the middle of the line, such surface is called a concave surface.

13. Give an example of a concave surface.

A simple curve is such, that on being turned on its extremities, every point along it will change its place in space; so that, in a simple curve, no three points are in a straight line.

14. Give an example of a simple curve.

Lines or curves grouped together by way of illustration, or for ornament, without regard to magnitude or surface, take the name of diagrams.

15. Give an example of a diagram.

When a surface' is spoken of with regard to its form and size, it takes the name of figure.

If the boundaries of a surface are straight lines, the figure is called a rectilinear figure, and each boundary is called a side.

Thus we have rectilinear figures of four sides, of five sides, of six sides, etc.

16. Make a few rectilinear figures.

In the definitions and questions of this work, when the word surface is used, a plane surface is meant.

When a surface is inclosed by one curve, it is called a curvilinear figure, and the boundary is called its circumference.

17. Make a curvilinear figure with one curve for its boundary, and in it write its name, and around it the name of its boundary.

18. Make a curvilinear figure with more than one curve for its boundaries.

A figure bounded by a line and a curve, or by more lines and more curves than one, is called a mixed figure.

19. Make a mixed figure, having for its boundaries a line and a curve.

20. Make a mixed figure, having for its boundaries one line and two curves.

21. Make a mixed figure, having for its boundaries one curve and two lines.

When a figure has a boundary of such a form that all lines drawn from a certain point within it to that boundary are equal to one another, such figure is called a circle, and such point is called the centre of that circle; and

the boundary is called the circumference of the circle, and the equal lines drawn from the centre to the circumference are called the radii of the circle.

22. Make four circles. On the first write its name. Around the outside of the second, write the name of the boundary. In the third, write against the centre its name. And between the centre and the circumference of the fourth circle, draw a few radii and write on each its name.

23. Can you place two circles to touch each other at a particular point?

21. Can you place three circles in a row, and let each circle touch the one next to it?

A part of the circumference of a circle is called an arc.

When the circumference of a circle is divided into two equal arcs, each arc is called a semi-circumference.

All arcs of circles which extend beyond & semi-circumference are called greater arcs.