by Bob Rozaieski
The very first lesson any woodworker learns is that precise work requires square corners. We ensure that stock is square before cutting any joinery. We check to make sure that casework is square during assembly. Almost everything we do is dependent upon things being square. That is, until we need an angle other than square.
Throw in an angle other than 90° and panic sets in quickly. How do we cut, fit or adjust a joint that can’t be confirmed with our try square? The secret is, of course, another tool. We can purchase the necessary tools. But making our own is a good lesson in simple techniques, and a low-risk way of stepping outside the square box.
Geometry to the Rescue
Many period woodworking books include a section on geometry. Having an understanding of geometry allowed our forebears to work faster and more precisely. This was important, considering that their rulers were typically graduated down to only 1⁄8″ increments, and often not very accurately so.
As Peter Nicholson stated in his book “The Mechanic’s Companion,” “The use of Geometry is not confined only to speculative truths in Mathematics, but the operations of mechanical arts owe their perfection to it; drawing and setting out every description of work are entirely dependent upon it.