and the compass without resorting to the protractor; only then will they know geometry.
“Through the eyes and the hand to the brain” this is the true principle of economy of time in teaching. I remember, as if it were yesterday, how geometry suddenly acquired for me a new meaning, and how this new meaning, facilitated all ulterior studies. It was as we were mastering at school a Montgolfier balloon, and I remarked that the angles at the summits of each of the twenty strips of paper out of which we were going to make the balloon must cover less than the fifth part of a right angle each. I remember, next, how the sinuses and the tangents ceased to be mere cabalistic signs when they permitted us to calculate the length of a stick in a working profile of a fortification; and how geometry in space became plain when we began to make on a small scale a bastion with embrasures and barbettes — an occupation which obviously was soon prohibited on account of the state into which We brought our clothes. “ You look like navvies,” was the reproach addressed to us by our intelligent educators, while we were proud precisely of being navvies, and of discovering the use of geometry.