Monday, November 20, 2023

The Practical Geometry of the Parson Barnard House: the Bents


This is the second part of my study of the use of geometry in the layout and design of the Parson Barnard House, in North Andover, Massachusetts.

Here's the house. The left section, the 'front', was built in 1715; the saltbox added in 1720. The rear extension to the right came in the 1950's. 


For my first post on the Parson Barnard House please see the link at the bottom of this page.*




The first floor plan shows the 2 back wings. The middle section, labeled kitchen, back hall, and study is the 1720 saltbox addition. The laundry and entry spaces were added 230 years later.



The geometry of the first and second floor plans match. The posts and beams of the second floor match those of the first floor.

The plan shows a step down into the saltbox addition.




The side elevation also shows this step down. The dashed lines locates the floors and the step down.



The layout Lines locate the inside edge of the posts and the inside width between the posts on either corner of the house. Together they outline 3 sides of a rectangle, the layout for the bents of the frame.  The radii of the arcs is the width of the frame. They cross at the placement for the lower side of the beam which supports the attic floor joists. It is the upper beam of the bents that frame the house.  

This use of geometry matches the way the parlor width was determined. The thin black Line marks the rectangle which is the inside of the bent.






The rectangle from that layout crossed with its diagonals. Where the Lines cross is the height of the beam which carries the second floor joists. 

*See note below for more information.

For reference here is the geometry of the first floor plan with the Hall on the right, a square; the Parlor on the left, a rectangle whose width is laid out by the arcs. This geometry is laid out from the inside edges of the posts. 




When the same geometry is used to lay out the bent using the width from the outside of one post to the other as the dimension, the crossing of the arcs is at the upper side of the attic beam.

**Look back at the elevation of the house with the rectangle derived from the interior dimensions. Note that the second floor and attic windows - which appear to be original - are centered on the space. Using the outer dimensions the windows are no longer centered.





Here is the design for the 6 bents for the Parson Barnard House (without the braces). This simple layout requires only basic knowledge of Practical Geometry. 

The bottom red line is the sill.



Do the layout differences I've shown here - between the use of the inside and the outside widths - provide evidence that the interior widths were used? Or do they simply mean the drawing is too small, my lines too thick or not perfectly placed, that the attic framing might yield other information for an accurate assessment?



Tuesday, November 7, 2023

The Practical Geometry of the Parson Barnard House

The Parson Barnard House, North Andover, Massachusetts, built in 1715. This picture was taken in 2022.

The original house is the front (left) section: 2 rooms up and down, each with a fireplace. The chimney in the middle served all the fireplaces and acted as a radiator.

The saltbox extension was added c.1720. The rear wing dates to the 1950's.






John Abbott measured and drew the floor plans and elevations of the house for HABS in 1934. At that time it was thought that Simon Bradstreet had lived here. Now we know the families of the Reverend Thomas Barnard and his son, the Reverend John Barnard, were the first residents from 1715  to 1757.


Here are the tools a  Massachusetts Bay Colony carpenter had in 1715 for planning and laying out buildings*. He used a compass, a square, horizontal and vertical levels, a straight edge marked in regular increments (which might or might not be inches) and a line with a spool on one end and a plumb bob on the other. The builder also had an awl, chalk, charcoal, and an 8 or 10 ft. rod.

His square was small and might not have a true 90* corner. His inch, foot, rod, varied from those of other carpenters. He would have learned his skills as an apprentice to a master carpenter, become a journeyman, then a full-fledged carpenter. His training would have included practical geometry. Tape measures had not been invented, paper was precious. He drew plans on framing floors, on sheathing, on dirt. He did not need to be literate.

Using a compass, a straight edge and a scribe a carpenter could layout the plan on a board, then step off the plan on the site with his rod or his compass, set his lines, and true them. This is the same order in which we layout buildings today; we simply use more modern tools.

This is the floor plan of the original house.
Noted in black are the sills, the posts and beams for the first floor frame . 

 The carpenter knew the first floor would have a Hall - on the right labeled 'living room', and a Parlor - on the left called the 'dining room'. 


Between them, in the center of the house would be the chimney stack with a separate flue for each of 4 fireplaces.

Here is the chimney above the roof with articulated flues.  

These spaces add up to a house about 18 ft. wide by 42 ft. long.



The width and length of the house were stepped off with a compass or marked on a length of twine. The exterior of the house would have been staked.  3 foot units could have been stepped off 6 times for the width and 7 times for the length. Layout with a rod marked in feet would probably have been faster. A chalk line might have been snapped. Lines could have been tied to stakes for the men digging the foundation. Diagonals would have trued the foundation. All of this is similar to how we layout buildings today.

Stone foundations of  pre-1900 houses tend to be vertical on the inside of the wall, the basement side, battened into the soil on the exterior. 2 lines would be required to accurately set the top of the foundation - where the sill would sit, where the outside wall of the house would stand.   

The length of the beams of the frame, approximately 18 ft., probably determined the house width.  

The Hall, the biggest room, was a multi- purpose room, used for cooking, chores, gathering. Often set in the southeast corner of the house, it had sunshine from early morning to late afternoon.  Here the room is square with a beam to support the 2nd floor across its center. The arc of the 18' width locates the posts.

Note that the dimensions appear to begin at the inner side of the right hand posts, indicating that while the exterior of the foundation was laid 18 ft. x 42 ft., the layout for the timber frame appears to have been set from the sill and those first posts. 

Laying out the geometry from the inside of the frame would have been a practical choice. The sills would not cover the line, but located beside it. Truing a rectangle by checking its diagonals to the outside corner of a post would be tricky, especially after the posts were in place. The framing timbers also needed to set to the line. And, the outside of a stone foundation could be irregular - as field stones are - without compromising the bearing of the frame on the foundation. 

This length, this inside dimension, would also have been the one the framers used to lay out the mortise and tenon joints on the beams.

Next to the Hall is the chimney stack. In plan it is a 3/4/5 rectangle often used by masons to keep the bricks plumb and level during construction. The fireplaces fit within, their fires creating a massive heat sink.  

The entry and staircase fit into the leftover space in front of the stack.



The Parlor, the room to the left, was used for business and formal occasions, to welcome and entertain visitors. Sometimes it was also the master bedroom.

It was smaller than the Hall and also had a centered beam.  The arcs cross at the outside edge of the wall, setting the width of the room. 

The length of that width could easily be measured from the layout of the Hall. Here the arcs cross, giving 2 points for drawing a line which, extended, is the width of the Parlor. Note the black line with arrows.

Yes, if the line which measured the width of the square of the Hall  had been folded in half and marked, it also would have given the point needed to determine the width of the parlor. In either instance the framer needed to understand the geometry. Geometry was a tool. It was practical. It is also why the proportions of these buildings are graceful; why they speak to us.



The Parson Barnard House, seem from its front garden in 2022.

 Note that the geometry of the house is so strong that the front door of the house seems to be in the middle of the facade. Actually the right side is wider than the left side. The windows on the left  are closer together than those on the right and the wall spaces between the door and the windows on either side are not equal. 

The geometry of the frame and the elevations will be another post.  

* the image is the frontispiece  for  Giancomo Barozzi Da Vignola, *Canon of the Five Orders  of Architecture, translated by John Leeke, published by William Sherwin, 1669. 

** A square can be laid out by a compass. Square corners can be determined and proved by a daisy wheel. Here is the visual explanation: the width A-B as the radius of the circle and locates the 6 points of the circumference A, B, C, D, E, F, G. Then: Lines A-F and B-E are perpendicular to A-B. Line G-C locates the end (west) wall  of the Parlor.

For more information and a tutorial see:

Tuesday, October 3, 2023

Teaching Practical Geometry

 Several educators, curious about Practical Geometry, have asked me how I would share this geometry in the classroom. This post is an introduction to how I would begin.

In September, 2023, I presented 3  workshops at IPTW, the International Preservation Trades Workshops.* The last day was open to the public. About 10 people, aged 10-70+, came to learn about Practical Geometry. Some had never held a compass.  

Here is what we did:

We drew circles with compasses. Then we divided the circumferences into 6 equal parts and connected the points to make rectangles and squares. We used no numbers. 


We  explored the  design and layout tools a carpenter would have had before the Industrial Revolution: the compass, a line and a scribe. We talked about how those tools were used and are still used. We compared cubits (the length from your elbow to your longest finger).  We set carpenter's dividers for a day's work by the radius or the diameter of a daisy wheel. One of the participants taught the others how to snap a chalk line.

I brought my daisy wheel with me. It was scribed into a 9 ft tall board which was once sheathing on Vermont barn, c.1780. The barn was deconstructed about 10 years ago. The deconstruction contractor gave me the board.



I showed them the floor plan of one of the early Virginia folk houses recorded by Henry Glassie,** which used the geometry we had drawn. 




I shared a few pictures including this house whose plan we had just laid out.  



That image introduced the class to the chimney wing. Its plan would have used the 3/4/5 rectangle to make sure the wing was parallel to the house so that all the roof framing could be cut the same length.  




I showed the group a Menagery, a retreat intended for an English gentleman's estate, designed by James Gibb's ***, c. 1720.  



 The wings are laid out in the same way, using the 3/4/5 rectangle. Here it is because the rough laid stone on the exterior would have made an accurate layout and construction difficult.


Then the class learned about the 'star', the Lines, in the center of the Menagery. Those are also the lines on our cellphones which help us edit images, known by artists as the Rule of Thirds.  

Here is the geometry: the diagonal of the square and the Lines from the ends of one side (the corners) to the middle of the opposite side. The  pattern is turned 4 times.



Where the lines cross are points. 2 points connected are a line. That line is always straight.

Here, the points divide the large square into 9 small squares - the diagram used on cellphones - or 3 equal rectangles.

There are also 4 squares within the large square. If their diagonals are drawn, the large square can be divided into 16 small squares or 4 equal rectangles.


The Lines on the elevation for this brick house tell the mason where the sides of the door and window openings are. On the plan the Lines show the fireplace edges and the placement of the interior walls. 

The drawing is Plate 56 in Owen Biddle's pattern book, The  Young Carpenter’s Assistant,  published in 1805, by Benjamin Johnson, Philadelphia.





 I ended with these Lines in Sebastiano Serlio's Book I, c. 1540. It explains where to place a door in a castle wall. He ends Book I: On Geometry, " However, honest reader, although the things resulting from the various intersections of lines is infinite, to avoid being long-winded I shall come to an end."


This was more than enough for one 75 minute session. 

Several shorter lessons would have been easier for everyone. There was very little time for questions, more examples, or in-depth understanding.  


For more information: In 2020,  I wrote 7 posts entitled 'Lessons' for students of all ages. .

*The 25th International Preservation Workshops were held this year in Frederick, MD, at the Hargett Farm which will become the Historic Preservation Trade Center for the National Park Service.          See the Preservation Trades Network website,, for more information.

** Henry Glassie,. Folk Housing in Middle Virginia, U of Tennessee Press: Knoxville, 1979

*** James Gibbs,  Book on Architecture, London, 1728, Dover reprint

**** Sebastiano Serlio . On Architecture, Lyon, France 1530, translated in1611,  on-line and translated by Vaughan Hart and Peter Hicks, 1996, Yale University Press, New Haven

To read more about this diagram see 


Wednesday, August 23, 2023

Stratford Hall, Part IV: Placing the Windows

Updated 8/26/2023

In the previous post* I wrote about all the construction details of Stratford Hall which William Walker, the Master Builder, had to work out before the masons could begin laying the walls.

They are all visible in this photograph: the brick pattern (Flemish Bond) and its variations, the brick headers over the windows in the ground floor and the main floor, the corner brick pattern and that around the windows, the cap at the shoulder, where the walls become thinner by one brick.

The Hall needed big windows on the main (family) floor above, smaller ones on the ground (service) floor below. As William Walker placed and sized the windows he would have considered all these constraints.

I wondered:

Was he drawing on paper, a board, a plaster wall, a framing floor? 

Drawings about framing can still be seen on cathedral walls and floors. So perhaps Walker did his layouts on the floor of the Hall.

He could have used the ground floor as a framing floor as soon as the foundation was set. The floor itself, his sketches and calculations, would become covered with pavers when the Hall was finished and ready for use.

It would also have been easier to lay out his ideas, check his dimensions for both floors from the inside, rather than working on scaffolding outside or in a shed nearby.

Walker used 5 equally sized squares to lay out Stratford Hall's floor plan. Perhaps he used a similar simplicity for the elevations. I drew squares.  

The red boxes show the interior of the wing. My tentative pencil marks are barely visible.


Simple squares (using the room height as the length) lay out the window locations for the Hall. Here is the main floor wall with 2 squares. They mark the edges of the center window for the main floor and the ground floor below.



They also locate the center of the window. The window frame is 2 squares tall - as noted by the diagonal line.

The size of the main floor windows and the width of the ground floor windows is set.

Squares of the same proportions, moved to the sides of the window, locate the outer edges of the windows on the left and right. Note: Square A-A and Square B-B.  

Those windows will be the same size as the center windows. There is plenty of room for the flat arches above the windows; the edging brick patterns are not crowded.


The only unknown is the vertical height of the ground floor windows and how far above the floor they will sit. Space must be given for the rowlock arches over the windows.

The Lines which located and sized the main floor windows extend to the ground floor. I've labeled them A-B, B-A, A-B to match what I drew earlier. 

Using the window width as a radius, and the floor of the lower level as the base, (the Line below 3) the center of the circle can be found, the circle and its daisy wheel drawn. It marks the brick arch over the window. It also intersects the Lines of the window widths  locating the height of the ground floor windows. 

The windows are 3/4/5 rectangles.

Walker trained as a joiner in Scotland at the time when James Gibbs, also a Scotsman, was there, and when Gibb's book, 'On Architecture', was published. Gibbs' book included plans for 2 'menageries'.** One was laid out with similar crossed squares, the other used the inside for its geometry as the exterior wall - shown here - was irregular, as is the exterior surface at Stratford Hall. Gibbs also used the 3/4/5 rectangle for layouts.

Copies of James Gibbs' book came to the Colonies. It is possible both William Walker and the Lee family had read the book in Virginia.

* Previous posts:

** My posts on Gibbs' geometry:

*  See previous posts: 

**Personal note: I have been asked at workshops how I use practical geometry. Here is an example of how I would approach a design today. The geometry would tell me what size the windows would be and their spacing.

Monday, August 21, 2023

Stratford Hall - Part III: Designing with Brick


I had just published 2 posts on the practical geometry used to frame/construct Stratford Hall.*

The thinking, drawing, and writing about the overall structure of the Hall was done. 

I began exploring the drawings. 

The window layout was rhythmic, straight forward: all the windows on each floor were the same size. The space between them as well as the spaces between them and the corners were equal.  


As an architect I have used this pattern on new wings for old houses. I would size the windows to compliment the existing; then divide the remaining space evenly. Or perhaps I would give a little more width to the outside walls, depending on room layout requirements.**

Here, I thought, is a similar layout. 

However,  I was wrong.

As I thought about the proportions I was laying out a wood frame:  locating posts, beams, center lines of windows, heights indicated for headers, a window schedule. I was building the structure. The character of the exterior and interior would come later with the addition of sheathing, siding, and plaster finished with trim and moldings. 

The interior and the exterior of a brick frame are the structure, they are not added later. Stratford Hall was built of brick. Its character comes from the manipulation of the brick.

So, from the beginning the masons who worked for William Walker, the Master Builder, needed to know:  


Where to lay Flemish Bond using brick of just one color? Where use the whiter bricks as headers?

Where to leave window openings? How wide, how tall? 




What brick pattern to use at the window openings? How many bricks? At the corners of the wings too?

Where to use a flat arch as a header? Where a rowlock arch? 

Where to place the brick cap and make the brick wall thinner?

That question was easy to answer: where the wall diminishes just above the joist pockets which hold the main floor joists.



In this image you can see how much information William Walker had to give the masons as they began. 

How many rows at grade before the  
the corner brick pattern begins, as well as the use of lighter headers?

What is the height of the ground floor windows, and their width?  

The brick details at the sides windows and at the corner which needed careful calculations are visible here.             

The black line at the corner is an electrical cord.


When I knew the issues I could ask the question:  

How did William Walker, Master Builder, lay out the elevations?


I will propose some answers in the next post.

*  See previous posts: 

** I knew about the use of proportion and rhythm in architecture and applied it for many years before I 'discovered' Practical Geometry. I studied the illustration in pattern books without understanding the numbers engraved along the sides of those drawings nor pausing to read the texts. I did not 'discover' the practical use of geometry: I finally read the text in the books and studied the scales.