On May 31, 2025, I will present Practical Geometry and Carpenter Squares at the Early
American Trades Association (EAIA)* conference in Rochester, New York. I expect I will be introducing Practical Geometry and then explore how the use of a carpenter square began to change the visual character of our architecture. I hope to see tool collections and hear other members' thoughts.
What happened after 1820 when the carpenter square became a reliable drafting tool? When the compass, line, and scribe were joined by an L shaped piece of steel with a dependable, true 90* corner?
The squares shown here were made in southwestern Vermont c. 1830-50. They now live at the Bennington Museum, Bennington Vermont, and can be seen by appointment.
Here you can see the hand stamped numbers on the earliest squares as well as carefully drawn scales. Were the scales as important to the builder as the true 90*angle?
The square made design and layout accurate in fewer steps. Units (inches and feet) were uniform, corners were square, always 90*. A job could be drawn, measured, and laid out more quickly and accurately. However, loosing those steps also changed the proportions. I have written about how this can see seen in vernacular housing design.**** I wanted to learn how an architect might have used the carpenter square. Robert Shaw was a good choice because he wrote a book.
Robert Shaw's The Modern Architect was published in Boston in 1854.**
The pattern book's frontispiece shows the tools of the builder and the architect. The original drawing is an engraving which is quite dark. The color was added when the book was republished in 1995.
In the foreground is a large compass, probably used for stepping off. The architect holds a little one. The architect and builders are shown conferring, syncing the construction dimensions with the drawings .
Here is Plate 4, a 'Grecian Frontispiece'
Where did Shaw begin his design? Conceptually the design surrounds the door, giving it emphasis. So I began there.
Shaw himself stated that the door's height should be "...over twice the breadth of
its height as three and seven feet."***
I have added the scale below the door: 3 units for the door's width. Then a half unit for the columns on each side and a full unit for the width of the sidelights.
These proportions follow those recommended by James Gibbs in 1732. ****
Was Shaw using 'circle geometry' for his layout? I don't think so. The circles don't offer much information.
While the layout is 2 circles tall, the 12 points around the circumference of the circles give only the height, the width of the entry including the side lights, maybe the location of the transom. Note the arrows.
I think Shaw used a simple geometric pattern that is derived from the circle, but which doesn't need to start with a length - a radius - and compass. It starts with the square which is easily laid out by the carpenter square.
The width of the door and its sidelights was the dimension for a square. That shape was easy to lay out and make true with a carpenter square. Beginning with a length,
he set up the corners with the square, added the lines for the 4 sides, trued the box with diagonals. The diagonals used to find the
additional height comes directly from the square. Done. Note the arrows.
Was there a name for it? Not one I've found. It's basically a 'square and diagonal geometry'.
The door, its transom, sidelights, and columns are also a square.
Here the quarter circle arcs, based on the width, cross at the top of the door frame, just below the transom. This layout, creating a slightly smaller rectangle within the square, was often used in layout and design. **** I think here it is incidental.
I've extended the scale across the bottom and up the right side. It confirms the geometry.
The whole frontispiece is
8-1/2 units wide and 10-3/4 units tall. The door, the
pilasters and the sidelights are 6 units wide; the columns are
1-1/4 units each. The columns' capitals are a half unit tall. The entablature is 2
units; the pediment, 3/4 of a unit tall.
Each unit and its parts could be stepped off with a compass. In 1854 the length could also have been stepped off in 12 inches intervals as marked on the carpenter square. As shown in Shaw's frontispiece in his book, it seems the builders used both.
The geometry used for the door and its parts is also used for the overall size: the height of the frontispiece is equal to the diagonal of the square.
The lightly drawn dashed line is the arc of the width of the door, showing how it lays out the square. This geometric proportion is also used for the sidelight glass panes (see the image above), but not those in the transom.
When we architects, restoration trades people, and historians note from visual observation that a particular building is Greek Revival, not Late Georgian, we are seeing geometry. I think we are recognizing, even if subconsciously, that the rhythms, the proportions of Federal architecture are different from the Greek Revival proportions shown here.
* EAIA, Early American Trades Association https://www.eaia.us/
https://www.eaia.us/2025-rochester-ny
** Robert Shaw, The Modern Architect, Boston, 1854, originally published by Dayton and Wentworth, republished (unabridged) by Dover Publications in 1996.
*** Shaw, The Modern Architect, page 63.
**** For more information about James Gibbs' use of the door width as a unit of measure see: https://www.jgrarchitect.com/2025/01/james-gibbs-and-rockingham-meeting-house.html
For more information about the square and its rectangle see: https://www.jgrarchitect.com/2023/11/the-practical-geometry-of-parson_20.html
For information about buildings using the 3/4/5 triangle for layout:
https://www.jgrarchitect.com/2014/03/railroad-warehouse-frame-c-1850.html
https://www.jgrarchitect.com/2014/10/the-cobblers-house-c-1840.html
https://www.jgrarchitect.com/2013/10/1820s-farmhouse-north-of-boston.html