thanks for coming on board, I am sure everyone is enjoying this discussion.
I would ask what everyone thinks of this in relation to pitches of roofs:
This is a method to lay out a roof to a 1\3rd pitch, related in a 100 yr old text,
(remember this is to make it exactly a 1\3rd pitch)
a) draw AB AND BC at right angles b) describe an arc from A c) divide the arc in 3 equal parts as indicated by E and E1 d) draw lines from E and E1 connecting them to A e) place a square with the blade on 12 on A and the tongue so that it disects the arc f) Placing the square as shown we find that a third pitch (or hexagon mitre) is 7 inches to the foot instead of 8 as most workmen suppose
Using the same method we find:
The quarter pitch (or octagon mitre) is 5 inches to the foot,
The half pitch or (square mitre) is 12 inches to the foot