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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?

24. 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 are is called a semi-circumference.

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

All arcs of circles that are not so great as a semi-circumference are called less arcs.

A line that joins the extremities of an arc is called the chord of that arc.

When two radii connect together any two points in the circumference of a circle which are on exactly the opposite sides of the centre, they make a chord, which is called the diameter of the circle, and such diameter divides the circle into two equal segments,' which take the name of semicircles.

25. Make a circle, and in it draw two radii in such a position as to divide it into two equal parts, and write on each part its specific name.

All segments of a circle which occupy more than a semi-circle are called greater segments.

26. Make a greater segment, and on it write its name.

27. Make a greater segment, and on the outside of each of its boundaries write its name.

1 The word segment means a piece cut off: thus we have segments of a line and segments of a sphere, as well as segments of a circle.

All segments of a circle that do not contain so much as a semi-circle are called less segments.

28. Make a less segment, and in it write its

name.

29. Make a less segment, and on the outside of each of its boundaries write its name.

30. Can

you

cut from a circle more than one

greater segment?

31. Can you cut from a circle more than one less segment?

32. Place two circles so that the circumference of each may rest upon the centre of the other, and show that the curved figure common to both circles consists of two segments, and may be called a double segment.

33. In how many ways can you divide a double segment into two equal and similar parts?

34. In how many ways can you divide a double segment into four equal and similar parts?

35. Can you make two angles with two lines?

When two lines are so placed as to make two angles, one of the lines is said to stand upon the other, and the angles they thus make are called adjacent angles.

36. Make two unequal adjacent angles with two lines.

When one line stands upon another line, in such a direction as to make the adjacent angles equal to one another, then each of these angles is called a right angle.

37. Make two equal adjacent angles, and in each angle write its proper name.

Either of the sides of a right angle is said to be perpendicular to the other; and the one to which the other is said to be perpendicular is called the base.

38. Make a right angle, and against the sides of the right angle write their respective names.

39. Can you make three angles with two lines?

40. Can you make four angles with two lines? 41. Can you make more than four angles with two lines?

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