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Fig.6.—This is what we wanted the Cards for.

I do not intend to trouble you much with Euclid in these lectures, but as many of my young friends have learned the sixth book, I will just refer to the well-known proposition, which tells us that the lengths of the corresponding sides of two similar triangles are proportional. We have here two similar triangles. There is the big one with the boy at one corner, the girl at the other, and the ball overhead. Here is the small triangle which we have just drawn. These triangles are similar because they have got the same angles, and it was to insure that they should have the same angles that we were so careful in shaping the cards. As these two triangles are similar, their sides must be proportional. We have agreed that the line A B, which is twelve inches long, is to represent the length of the table between the little boy and girl. Hence the distance, A C, must, on the same scale, be the interval between the ball and the boy at the end. This is twenty inches on the drawing, and therefore the actual distance from the end of the table to the ball is twenty feet.