Bellwattle laid down her sock with the knob of wood inside it and she looked at both of us as though we were creatures from another world.
“And what in the name of goodness,” said she, “is an equi—whatever-you-call-it triangle?”
Cruikshank went on with his explanation quite cheerily. On this proposition he was so sure of himself that confidence was actually glowing in his face.
“Well,” said he, “you know what a triangle is, don’t you?”
“One of those things they sometimes play in bands.”
The look of confidence dropped heavily from Cruikshank’s face; but I seized the opportunity. She understood. At least she had grasped the shape of it. It mattered not at all that in her mind its functions were to play a tune. She appreciated the shape of it. That served its end.
“You’re quite right,” said I quickly. “They have it in an orchestra. It has three sides to it—hasn’t it?”
“Yes, and two little curly bits at the top where they tie the string on to hang it up by.”
But I acceded her the little curly bits. She had grasped the shape of a triangle.
“Well, try and forget the curly bits,” said I. “They have three sides—haven’t they?”
“Like this,” I went on hurriedly, and, dragging out my pencil again, I drew a triangle on a piece of paper.
“That’s it,” said she; “but they don’t meet at the top.”
“Some do,” I replied; “the ones that Euclid made did.”
“Well, go on,” she said, with greater interest. “What’s an equitriangle?”
“An equilateral triangle,” said Cruikshank, now stepping in when I had done all the hard work for him, “is a triangle which has all its sides of equal length. That side,”—he pointed to my drawing—“that side and that side all equal. Now Euclid’ll show you,” he continued, “how to construct an equilateral triangle on a given finite straight line. You needn’t measure anything. You only want a compass to make a couple of circles, and he’ll prove to your reason that all the lines of that triangle are one and the same length as this line you see on the paper now.”
I gave him the only one I had and he set to work to draw the most beautiful circles, though they had but little relation to A as their centre and B as their circumference, which were the letters he had written at each end of his given finite straight line.