Asher Benjamin's first book, published in 1797, gives proportions on every plate except those of buildings: Plates 25, 26, 27; and Plate 23 which shows how to place newel posts on a stair.
The photograph is of Plate 18, a fireplace mantle. He notes: "B, Cornice, half size; C, Architrave, half size; A, Moulding round tablet full size for practice." All the numbers on the drawing refer to parts. B, the shelf of the mantle - drawn in the fireplace opening - states "17 parts" on the left side, and the divisions are ticked off on the right side. Across the mantle base are tick marks to scale the mantle itself, and then the note on the right: "8 parts". A is that little piece of moulding beside the mantle in the upper left corner.
The next photograph is of Plate 29. The top figure is how to size a arched ceiling over a room. The lower figures show roof frames - the bottom one is intended for a meeting house. The proportions to use are shown marked off and in notation: Figure D is 7 parts long and 2 parts high.
Here too the compass arc is shown. The 2 intertwined circles on the right of the top figure determine the arch for the ceiling. Note that the circles themselves are based on the size of the room. In the roof frames the arc of the circle - with its center at the center of the lower chord - determines the placement of the trusses.
So, was the use of the compass and geometric design so common that Asher Benjamin simply needs to allude to it? If so, why didn't that knowledge get passed on?
"Why didn't this information get passed on?" I think some of it has, but not to architects -- you will find some of this information resides in the world of carpentry - both large scale and furniture.
I have a number of thoughts about why we lost much of this - I will try to write some posts that outline what I think the issues are. Thanks for asking. Jane
I have a couple of blogs you might be interest in.
Ad Quadratum - Seed of Life - Ad Triangulum Router Templates
A lesson in Applied Geometry and Euclidean Geometry
More questions arise than answers, but at least I now know, according to Vitruvius, that towers should be either round or polygonal, never square. And that the distance between each tower should not exceed an arrow's flight.
Sim: Thanks for telling me of your blogs. I have been tending to deadlines and family so I have not had time to really look at your work, but I do like knowing I am not alone thinking about regulating lines.
i too am glad to find i am not alone in thinking about regulating lines. it is my mission to understand how building were designed, and yours is the only site i have found that seems to think this worth studying.
Thank you for posting here.
Asher Benjamin in his pattern books called regulating lines 'Practical Geometry'. He and the other writers of the time assumed we knew the basics.
I have been teaching Practical Geometry in hands-on sessions for PTN - the Preservation Trades Network. My classes are well attended, the participants enthusiastic. So a bunch of us do think this is worth studying.
Laurie Smith in England is working on these ideas as they apply to medieval construction. His website is http://www.thegeometricaldesignworks.com/
When he comes to the States I make sure I get to work with him.
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