Regulating Lines - at least 3 geometries

This fall and winter I read David Leviatin's articles in Timber Framing, The Journal of the Timber Framers Guild. He beautifully describes a 'regulating line technique' he has documented in England in East Anglia. I got out my atlas to be sure of the location of East Anglia where Leviatin worked with the line technique. No more than 100 miles away across the North Sea are the Netherlands. Did the men who used these lines share their knowledge with the joiners in Holland and vice versa? Did those ideas influence the men who built the Van Alen house in 1737 in Kinderhook, NY?

Today I know of 3 regulating systems:

1) The Daisy Wheel, circle geometry researched by Laurie Smith in Wales and England.

2) The use of the Golden Section as used in New England pre-1850 and later advocated by Jay Hamlin and Le Corbusier

3) The 'regulating line technique' described by David Leviatin in Timber Framing.

However, here is Asher Benjamin in his 1797 pattern book, The Country Builder's Assistant, containing A Collection of New Designs of Carpentry and Architecture Which Will Be Particularly Useful to Country Workmen in General. (his spelling and punctuation)

"To proportion Architraves to doors, Windows, &c. divide the width of your Door or Window, into seven or eight parts, and give one to the width of the Architrave : Divide that into the same number of parts, as are contained in the Architrave you make use of, if a Frieze or Cornice to the Door, give the Frieze equal to the width of the Architrave ; or it may be one forth or one third wider, the Cornice four fifths or five sixths of the Architrave."

An architrave is the header above the door supported by the posts on each side. It supports the frieze. The frieze is underneath the cornice. My post: "Regulating Lines, Asher Benjamin" includes a picture of Benjamin's Plate XVIII. It shows a fireplace with the architrave and cornice and the division into parts.

I find that the systems we know of were fluid, changing not only by new challenges and inventive master craftsmen, but by cross fertilization of ideas that came inevitably as people all over Europe met each other and worked together.

David Leviatin, "The Lordship Barn and Regulating Line Technique", Timber Framing, The Journal of the Timber Framers Guild, p. 4-7, Number 101, September 2011, and

"Topics, Scribe Rule, Square Rule, Democracy and CNC", p. 2-7, Number 102, December 2011.