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CHAPTER XII.

QUESTIONS AND ANSWERS CONCERNING THE

GEOMETRICAL FIGURES.

Useful knowledge can have no enemies, except the ignorant; it cherishes the mind of youth, and delights the aged, and who knows how many mathematicians in embryo, there may be in an Infant School.

AMONG the novel features of the Infant School system, that of geometrical lessons is the most peculiar. How it happened that a mode of instruction so evidently calculated for the infant mind was so long overlooked, I cannot imagine; and it is still more surprising that having been once thought upon, there should any be found incapable of perceiving its utility. Certain it is that the various form of bodies is one of the first items of natural education, and we cannot err when treading in the steps of Nature. It is undeniable that geometrical knowledge is of great service in many of the mechanic arts, and therefore proper to be taught those children who are likely to be employed in some one or other of those arts; but, independently of this, we cannot adopt a better method of exciting a spirit and strengthening their powers of observation. I have seen a thousand instances, moreover, in

the conduct of the children, which have assured me, that it is a very pleasing as well as useful branch of instruction. The children, being taught the first elements of form, and the terms used to express the various figures of bodies, find in its application to objects around them an inexhaustible source of amusement. Streets, houses, rooms, fields, ponds, plates, dishes, tables,-in short every thing they see, calls forth their observation as to its form, and afford an opportunity for the application of their little geometrical knowledge. Let it not, then, be said, that it is beyond their capacity-for it is the simplest and most comprehensible to them of all knowledge; - let it not be said that it is useless, since its application to the useful arts is great and indisputable; nor, lastly, let it be asserted that it is unpleasing to them, since it has been shewn to add much to their happiness.

It is essential in this, as in every other branch of education, to begin with the first principles, and proceed slowly to their application, and the complicated forms arising therefrom. The next thing is to promote that application of which we have before spoken to the various objects around them. It is this, and this alone, which forms the distinction between a school lesson and practical knowledge; and so far will the children be found from being averse to this exertion, that it makes the acquirement of knowledge a pleasure instead of a task. With these prefatory remarks I shall introduce a description of the method I have pursued, and a few examples of geometrical lessons.

We will suppose that the whole of the children are seated in the gallery, and that the teacher is

provided with a large board, having a paper pasted on it, on which are printed the geometrical figures. He first places the board in such a situation before the gallery, that every child may see it, and being provided with a pointer, points to a strait line, asking, What is this? A. A strait line. Q. Why did you not call it a crooked line? A. Because it is not crooked, but strait. Q. What are these? 4. Curved lines. Q. What do curved lines mean? A. When they are bent or crooked. Q. What are these? A. Parallel strait lines. Q. What does parallel mean? A. Parallel means when they are equally distant from each other in every part. Q. If any of you children were reading a book that gave an account of some town which had twelve streets, and it said the streets were parallel, would you understand what it meant? A. Yes; it would mean that the streets were all the same way, side by side, like the lines which we now see. Q. What are those? A. Diverging or converging strait lines. Q. What is the difference between diverging and converging lines and parallel lines? A. Diverging or converging lines are not at an equal distance from each other, in every part, but parallel lines are. Q. What does diverge mean? A. Diverge means when they go from each other, and they diverge at one end, and converge at the other. Q. What does converge mean? A. Converge means when they come towards each other. Q. Suppose the lines were longer, what would be the consequence? A. Please sir, if they were longer they would meet together at the end they converge. Q. What would they form by meeting together? A. By meeting together they would form an angle. Q. What kind of an angle?

A. An acute angle. Q. Would they form an angle at the other end? A. No, they would go further from each other. Q. What is this? 4. A. A perpendicular line. Q. What does perpendicular mean? A. A line up strait, like the stems of some trees. Q. If you look, you will see that one end of the line comes on the middle of another line; what does it form? A. The one which we now see forms two right angles. Q. I will make a strait line, and one end of it shall lean on another strait line, but instead of being upright like the perpendicular line, you see that it is sloping. What does it form? A. One side of it is an acute angle, and the other side is an obtuse angle. Q. Which side is the obtuse angle? A. That which is the most open. Q. And which is the acute angle? A. That which is the least open. Q. What does acute mean? A. When the angle is sharp. Q. What does obtuse mean? A. When the angle is less sharp than the right angle. Q. If I were to call any one of you an acute child, would you know what I meant? A. Yes, sir, one that looks out sharp and tries to think, and pays attention to what is said to him; then you would say he was an acute child.

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 triangle? 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. 4. 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 pointer is to be put to the other triangles, and the master must explain to the children the meaning of right-angled and obtuseangled.]

Scalene Triangle.

Q. What is this? A. An acute-angled scalene tri-angle. Q. Why is it called an acuteangled scalene tri-angle? 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 tri

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