The large compass has the big advantage of allowing you to stand up while using them. And most of all to me they are of great historical interest.

The method described is how it is thought they built churches and cathedrals, among other things, in the Middle Ages. The documentary evidence certainly suggests it, as does the mensural evidence. The system works, and works quite well. It gives the architect the means of scaling up his plans to create the building. This is important because it makes so that he knows his drawing will meet the specifications of the job.

What would have been done is that the person ordering a building would specify one specific measurement for a certain dimension of the building, in the case of a church or cathedral this usually meant that some important measurement such as the length of the nave was equal to 153 feet, 153 feet being the number of fish in Peter's net. The architect could then set that measurement on his drawing to something proportionately equal to that somewhere in the neighborhood of 1/150th or maybe 1/180th the size. This measurement would then be used as the basis for the geometry of the rest of the structure.

The most important thing is that this system allowed buildings to be built by people who were usually totally illiterate, and very innumerate by today's standards -possessing only the most basic skills of mathematics. It made it possible for the master to lay out plans and instructions for people who could not read, barely even add, and may not even have spoken the same language as him.

This would be of use for me today, because the systems of geometry I have developed work the same way. When I make a geometric design, I pick 1 measurement and use it as the basis of my entire geometry. I use some mathematics so that I can scale up my drawing with a measuring tape, but I would like to be able to take that out of the picture as well.

I doubt proportional dividers would work very well for making measurements on the order of several feet, perhaps 10 feet or more at times. I despise using trammel points on the ground, it's very disagreeable to my knees and back.

The large compass becomes very attractive when there is the prospect of swinging a lot of arcs...

I am interested in this tool as a building site tool that will allow me to leave my measuring tape at home...

To illustrate what I am talking about, I will use a real example.

For a building I have designed for myself using pure geometry I have come up with a measurement for the ceiling height that would be somewhat too short if using a perfect inches to foot system from drawing to real world. There are two solutions to this problem. The first is to measure out my master dimension when I go to make the full size plan by using a foot that is actually 13 inches long instead of 12. The second is to use the factorial 2 compass system, but just change my factor a little bit to make the building slightly larger. The current factor is 1:24, but I could just as easily make it 1:26 (which would yield the same dimensions as if I were to use a 13 inch foot)

If I would use the first solution, that means I would have to redo all of my geometry at full scale. If I would use the second system then I could take a lot of shortcuts when making the full plan.

Just for a quick example, as designed 3 inches on the plan equals 6 feet. Right now my ceiling height comes out to about 7 feet, which would be 6.5 feet with the frame taken into consideration. If I make it a proportion of 1:26 then the ceiling height becomes about 7.58 feet, which would be about 7 foot ceiling after framing (a little less). I am considering using a factor 27 system (9x3) which would make the floor plan of my building 13 1/2 by 27, instead of the current 12 by 24. I wouldn't mind those extra 76 1/2 square feet...

You may ask the question, why didn't I just make the walls higher to begin with? The reason is I did not like the way the proportions came out when I did, the building looked too high compared to its width. So I decided I would rather just scale up the width a little bit. the 12 foot width was the master dimension I used for my geometry, but it was just a guideline. I wasn't married to it so I didn't mind changing it to make things come out right. I had a couple feet to fudge with