[Footnote b: Mr. Chambers has been good enough to call the instrument referred to, a gonograph; to that name I have no objection.]
[Footnote B: Desire the children to hold up two fingers, keeping them apart, and they will perceive they diverge at top and converge at bottom.]
Equi-lateral Triangle.
Q. What is this? A. An equi-lateral triangle. Q. Why is it called equi-lateral? A. Because its sides are all equal. Q. How many sides has it? A. Three sides. Q. How many angles has it? A. Three angles. Q. What do you mean by angles? A. The space between two right lines, drawn gradually nearer to each other, till they meet in a point. Q. And what do you call the point where the two lines meet? A. The angular point. Q. Tell me why you call it a tri-angle. A. We call it a tri-angle because it has three angles. Q. What do you mean by equal? A. When the three sides are of the same length. Q. Have you any thing else to observe upon this? A. Yes, all its angles are acute.
Isoceles Triangle.
Q. What is this? A. An acute-angled isoceles triangle. Q. What does acute mean? A. When the angles are sharp. Q. Why is it called an isoceles triangle? A. Because only two of its sides are equal. Q. How many sides has it? A. Three, the same as the other. Q. Are there any other kind of isoceles triangles? A. Yes, there are right-angled and obtuse-angled.
[Here the other triangles are to be shewn, and the master must explain to the children the meaning of right-angled and obtuse-angled.]
Scalene Triangle.
Q. What is this? A. An acute-angled scalene triangle. Q. Why is it called an acute-angled scalene triangle? A. Because all its angles are acute, and its sides are not equal. Q. Why is it called scalene? A. Because it has all its sides unequal. Q. Are there any other kind of scalene triangles? A. Yes, there is a right-angled scalene triangle, which has one right angle. Q. What else? A. An obtuse-angled scalene triangle, which has one obtuse angle. Q. Can an acute triangle be an equi-lateral triangle? A. Yes, it may be equilateral, isoceles, or scalene. Q. Can a right-angled triangle, or an obtuse-angled triangle, be an equilateral? A. No; it must be either an isoceles or a scalene triangle.
Square.